diff --git a/.github/pull_request_template.md b/.github/pull_request_template.md new file mode 100644 index 00000000..a872ee84 --- /dev/null +++ b/.github/pull_request_template.md @@ -0,0 +1,37 @@ +# Pull Request Template + +## Description +Please include a summary of the change and which issue is addressed. Please also include relevant motivation and context. + +## Type of Change +- [ ] Bug fix +- [ ] New feature +- [ ] New model +- [ ] Code improvement +- [ ] README update + +## Code Changes +### Summary of Changes +- Describe the changes made in the codebase. +- Link to any relevant issues or discussions. + +### Unit Testing +- Provide a list of unit tests added or updated. +- Ensure all tests pass before submitting the PR. + +## Supporting Analysis +- Provide description of analysis and relevant output + +## Example Job +### Subheader Describing any Comparisons / Analysis +- Provide a description of how to execute the new feature/model. +- Compare to benchmark results if applicable. +- Include any relevant logs, graphs, or data files. + +## Checklist +- [ ] Code is commented +- [ ] I have made corresponding changes to the documentation +- [ ] Unit tests are present and working + +## Additional Notes +- Add any other context about the pull request here. diff --git a/.github/workflows/FormatCheck.yml b/.github/workflows/FormatCheck.yml new file mode 100644 index 00000000..6be5fea6 --- /dev/null +++ b/.github/workflows/FormatCheck.yml @@ -0,0 +1,37 @@ +name: format-check + +on: + push: + branches: + - 'main' + pull_request: + branches: + - dev* + - staging + - main + +jobs: + format_check: + runs-on: ubuntu-latest + steps: + - name: Checkout Repository + uses: actions/checkout@v4 + + - name: Set up Python + uses: actions/setup-python@v4 + with: + python-version: '3.12' + + - name: Create and activate virtual environment + run: | + python -m venv venv + source venv/bin/activate + + - name: Install black in virtual environment + run: | + venv/bin/pip install black + + - name: Check Python Code Formatting + run: | + venv/bin/black --check --diff ./cellmodeller/ + venv/bin/black --check --diff ./scripts/ diff --git a/.github/workflows/SpellCheck.yml b/.github/workflows/SpellCheck.yml new file mode 100644 index 00000000..ed4fe177 --- /dev/null +++ b/.github/workflows/SpellCheck.yml @@ -0,0 +1,13 @@ +name: Spell Check + +on: [pull_request] + +jobs: + typos-check: + name: Spell Check with Typos + runs-on: ubuntu-latest + steps: + - name: Checkout Actions Repository + uses: actions/checkout@v4 + - name: Check spelling + uses: crate-ci/typos@v1.18.0 diff --git a/.github/workflows/validate-branch-targets.yml b/.github/workflows/validate-branch-targets.yml new file mode 100644 index 00000000..182f9dd2 --- /dev/null +++ b/.github/workflows/validate-branch-targets.yml @@ -0,0 +1,58 @@ +name: Validate PR Branch Targets + +on: + pull_request: + branches: + - dev* + - staging + - main + +jobs: + validate: + runs-on: ubuntu-latest + steps: + - name: Check branch naming and targets + run: | + HEAD="${{ github.head_ref }}" + BASE="${{ github.base_ref }}" + + echo "Head branch: $HEAD" + echo "Base branch: $BASE" + + # + # === ALLOWED HEAD BRANCH PATTERNS === + # + if [[ ! "$HEAD" =~ ^(feature|bug|hotfix)/ && ! "$HEAD" =~ ^dev.*$ && "$HEAD" != "staging" ]]; then + echo "❌ Branch name must start with 'feature/', 'bug/', 'hotfix/', 'dev*', or be 'staging'." + exit 1 + fi + + # + # === MERGE RULES === + # + + # 1. feature/bug/hotfix/dev* may NOT merge directly into main + if [[ ( "$HEAD" =~ ^(feature|bug|hotfix)/ || "$HEAD" =~ ^dev.*$ ) && "$BASE" == "main" ]]; then + echo "❌ '$HEAD' cannot merge into 'main'. Merge into 'staging' instead." + exit 1 + fi + + # 2. feature/bug/hotfix branches may only merge into dev* or staging + if [[ "$HEAD" =~ ^(feature|bug|hotfix)/ && ! "$BASE" =~ ^(dev.*|staging)$ ]]; then + echo "❌ Feature/bug/hotfix branches may only merge into 'dev*' or 'staging'." + exit 1 + fi + + # 3. dev* branches may only merge into staging or other dev* branches + if [[ "$HEAD" =~ ^dev.*$ && ! "$BASE" =~ ^(staging|dev.*)$ ]]; then + echo "❌ Dev* branches may only merge into 'staging' or another dev* branch." + exit 1 + fi + + # 4. staging may only merge into main + if [[ "$HEAD" == "staging" && "$BASE" != "main" ]]; then + echo "❌ 'staging' may only merge into 'main'." + exit 1 + fi + + echo "✅ PR branch name and target are valid." diff --git a/.gitignore b/.gitignore new file mode 100644 index 00000000..fd658f9a --- /dev/null +++ b/.gitignore @@ -0,0 +1,11 @@ +__pycache__/ +*.py[cod] +*.egg-info/ +build/ +dist/ +.eggs/ +.ipynb_checkpoints/ +.vscode/ +.idea/ +.DS_Store +data/ diff --git a/CellModeller/Biophysics/BacterialModels/CLBacterium.cl b/CellModeller/Biophysics/BacterialModels/CLBacterium.cl deleted file mode 100644 index b121da0d..00000000 --- a/CellModeller/Biophysics/BacterialModels/CLBacterium.cl +++ /dev/null @@ -1,1045 +0,0 @@ -#define EPSILON 0.1f -#define MARGIN 0.01f -#define RHS_FRAC 1.f -#define ANG_LIMIT ((float)(5.f*3.14159f/180.f)) -#define ISQRT2 ((float)(1.f/sqrt(2.f))) -#define POINT 0.01f - -// multiply a matrix and a vector -// m -- 4x4 matrix -// v -- 4-vector -float4 matmul(float4 m[], float4 v) { - return m[0]*v.s0 + m[1]*v.s1 + m[2]*v.s2 + m[3]*v.s3; -} - - -// transpose a matrix -// m -- matrix to transpose (vector of columns) -// t -- result -void transpose(float4 m[], float4 t[]) { - t[0].s0 = m[0].s0; - t[0].s1 = m[1].s0; - t[0].s2 = m[2].s0; - t[0].s3 = m[3].s0; - t[1].s0 = m[0].s1; - t[1].s1 = m[1].s1; - t[1].s2 = m[2].s1; - t[1].s3 = m[3].s1; - t[2].s0 = m[0].s2; - t[2].s1 = m[1].s2; - t[2].s2 = m[2].s2; - t[2].s3 = m[3].s2; - t[3].s0 = m[0].s3; - t[3].s1 = m[1].s3; - t[3].s2 = m[2].s3; - t[3].s3 = m[3].s3; -} - - -// multiply two 4x4 matrices -// a -- left matrix -// b -- right matrix -// r -- result -// this is the naive way -void matmulmat(float4 a[], float4 b[], float4 r[]) { - r[0].s0 = a[0].s0 * b[0].s0 + a[1].s0 * b[0].s1 + a[2].s0 * b[0].s2 + a[3].s0 * b[0].s3; - r[1].s0 = a[0].s0 * b[1].s0 + a[1].s0 * b[1].s1 + a[2].s0 * b[1].s2 + a[3].s0 * b[1].s3; - r[2].s0 = a[0].s0 * b[2].s0 + a[1].s0 * b[2].s1 + a[2].s0 * b[2].s2 + a[3].s0 * b[2].s3; - r[3].s0 = a[0].s0 * b[3].s0 + a[1].s0 * b[3].s1 + a[2].s0 * b[3].s2 + a[3].s0 * b[3].s3; - r[0].s1 = a[0].s1 * b[0].s0 + a[1].s1 * b[0].s1 + a[2].s1 * b[0].s2 + a[3].s1 * b[0].s3; - r[1].s1 = a[0].s1 * b[1].s0 + a[1].s1 * b[1].s1 + a[2].s1 * b[1].s2 + a[3].s1 * b[1].s3; - r[2].s1 = a[0].s1 * b[2].s0 + a[1].s1 * b[2].s1 + a[2].s1 * b[2].s2 + a[3].s1 * b[2].s3; - r[3].s1 = a[0].s1 * b[3].s0 + a[1].s1 * b[3].s1 + a[2].s1 * b[3].s2 + a[3].s1 * b[3].s3; - r[0].s2 = a[0].s2 * b[0].s0 + a[1].s2 * b[0].s1 + a[2].s2 * b[0].s2 + a[3].s2 * b[0].s3; - r[1].s2 = a[0].s2 * b[1].s0 + a[1].s2 * b[1].s1 + a[2].s2 * b[1].s2 + a[3].s2 * b[1].s3; - r[2].s2 = a[0].s2 * b[2].s0 + a[1].s2 * b[2].s1 + a[2].s2 * b[2].s2 + a[3].s2 * b[2].s3; - r[3].s2 = a[0].s2 * b[3].s0 + a[1].s2 * b[3].s1 + a[2].s2 * b[3].s2 + a[3].s2 * b[3].s3; - r[0].s3 = a[0].s3 * b[0].s0 + a[1].s3 * b[0].s1 + a[2].s3 * b[0].s2 + a[3].s3 * b[0].s3; - r[1].s3 = a[0].s3 * b[1].s0 + a[1].s3 * b[1].s1 + a[2].s3 * b[1].s2 + a[3].s3 * b[1].s3; - r[2].s3 = a[0].s3 * b[2].s0 + a[1].s3 * b[2].s1 + a[2].s3 * b[2].s2 + a[3].s3 * b[2].s3; - r[3].s3 = a[0].s3 * b[3].s0 + a[1].s3 * b[3].s1 + a[2].s3 * b[3].s2 + a[3].s3 * b[3].s3; -} - - -// return the inverse of a quaternion -// q -- a quaternion -float4 quat_inv(float4 q) { - float l2 = dot(q, q); - if (l2==0.f) - return(q); - float4 inv = {-q.x/l2, -q.y/l2, -q.z/l2, q.w/l2}; - return inv; -} - - -// multiply two quaternions -// a -- a quaternion -// b -- a quaternion -float4 quat_prod(float4 a, float4 b) { - float4 res; - res.x = a.x*b.w + a.y*b.z - a.z*b.y + a.w*b.x; - res.y = -a.x*b.z + a.y*b.w + a.z*b.x + a.w*b.y; - res.z = a.x*b.y - a.y*b.x + a.z*b.w + a.w*b.z; - res.w = -a.x*b.x - a.y*b.y - a.z*b.z + a.w*b.w; - return res; -} - - -// rotate a vector using a quaternion -// q -- quaternion -// v -- vector, w ('real') component is ignored -float4 quat_rot(float4 q, float4 v) { - v.w = 0.f; - float4 qi = quat_inv(q); - float4 v_prime = quat_prod(q, quat_prod(v, qi)); - v_prime.w = 0.f; - return v_prime; -} - - -// rotate a vector -// axis -- axis about which to rotate -// angle -- amount to rotate (radians) -// v -- the vector to rotate -float4 rot(float4 axis, float angle, float4 v) { - float4 q = axis*sin(angle/2.f); - q.w = cos(angle/2.f); - return quat_rot(q, v); -} - - -void print_matrix(float4* m) { - /* - printf("\ - % 3.3f % 3.3f % 3.3f (% 3.3f)\n\ - % 3.3f % 3.3f % 3.3f (% 3.3f)\n\ - % 3.3f % 3.3f % 3.3f (% 3.3f)\n\ -(% 3.3f)(% 3.3f)(% 3.3f)(% 3.3f)\n\n", - m[0].x, m[1].x, m[2].x, m[3].x, - m[0].y, m[1].y, m[2].y, m[3].y, - m[0].z, m[1].z, m[2].z, m[3].z, - m[0].w, m[1].w, m[2].w, m[3].w); - */ -} - -void cyl_inertia_tensor(float muA, float l, float4 axis, float4 res[]) { - // first find the inv inertia tensor for a capsule along the x axis - float diag = (muA*l*l*l) / 12.f; - - // now find the matrix that transforms from the x-axis to the axis - float4 x_axis = {1.f, 0.f, 0.f, 0.f}; - float4 y_axis = {0.f, 1.f, 0.f, 0.f}; - float4 z_axis = {0.f, 0.f, 1.f, 0.f}; - float rot_ang = acos(dot(x_axis, axis)); - - float4 empty = {0.f, 0.f, 0.f, 0.f}; - - float4 y_prime = y_axis; - float4 z_prime = z_axis; - - if (rot_ang > EPSILON) { - y_prime = rot(z_prime, rot_ang, y_axis); - z_prime = normalize(cross(x_axis, axis)); - } - - float4 M[4]; - M[0] = axis; - M[1] = y_prime; - M[2] = z_prime; - M[3] = empty; - - float4 MT[4]; - transpose(M, MT); - - float4 I[4]; - I[0] = empty; - I[1] = empty; - I[2] = empty; - I[3] = empty; - I[0].s0 = 0.f; - I[1].s1 = diag; - I[2].s2 = diag; - I[3].s3 = 0.f; - - // M^T(I)M - float4 IM[4]; - matmulmat(I, M, IM); - matmulmat(MT, IM, res); -} - -void cyl_inv_inertia_tensor(float muA, float l, float4 axis, float4 res[]) { - // first find the inv inertia tensor for a capsule along the x axis - float diag = 12.f/(muA*l*l*l); - - // now find the matrix that transforms from the x-axis to the axis - float4 x_axis = {1.f, 0.f, 0.f, 0.f}; - float4 y_axis = {0.f, 1.f, 0.f, 0.f}; - float4 z_axis = {0.f, 0.f, 1.f, 0.f}; - float rot_ang = acos(dot(x_axis, axis)); - - float4 y_prime = y_axis; - float4 z_prime = z_axis; - - if (rot_ang > EPSILON) { - y_prime = rot(z_prime, rot_ang, y_axis); - z_prime = normalize(cross(x_axis, axis)); - } - - float4 M[4]; - M[0] = axis; - M[1] = y_prime; - M[2] = z_prime; - M[3] = 0.f; - - float4 MD[4]; - MD[0] = 0.f; - MD[1] = M[1]*diag; - MD[2] = M[2]*diag; - MD[3] = 0.f; - - float4 MDT[4]; - transpose(MD, MDT); - - // I in the world is = M(I_D)M^T - matmulmat(M, MDT, res); -} - - - -// Set the sq of each cell based on its position. -__kernel void bin_cells(const int grid_x_min, - const int grid_x_max, - const int grid_y_min, - const int grid_y_max, - const float grid_spacing, - __global const float4* centers, - __global int* sqs) -{ - int i = get_global_id(0); - int x = (int)floor(centers[i].x / grid_spacing) - grid_x_min; - int y = (int)floor(centers[i].y / grid_spacing) - grid_y_min; - sqs[i] = y*(grid_x_max-grid_x_min) + x; -} - - -// find the closest points on two line segments -void closest_points_on_segments(const float4 r_a, // center of first segment - const float4 r_b, // center of second segment - const float4 a, // direction of first segment (unit) - const float4 b, // direction of second segment (unit) - const float len_a, // length of first segment - const float len_b, // length of second segment - float4* p_a, // (return) point on first segment - float4* p_b, // (return) point on second segment - float4* p_a2, // (return) 2nd point on first segment - float4* p_b2, // (return) 2nd point on second segment - int* two_pts) // (return) were two points picked? -{ - float hlen_a = len_a / 2.f; - float hlen_b = len_b / 2.f; - float4 r = r_b - r_a; - float a_dot_r = dot(a, r); - float b_dot_r = dot(b, r); - float a_dot_b = dot(a, b); - float denom = 1.f - a_dot_b * a_dot_b; - - float t_a = 0.f; - float t_b = 0.f; - - *two_pts = 0; - float t_a2 = 0.f; - float t_b2 = 0.f; - - if (sqrt(denom) > EPSILON) { - // non-parallel lines - - // closest points on the same lines if they were infinitely long - float t_a0 = (a_dot_r - b_dot_r * a_dot_b) / denom; - float t_b0 = (a_dot_r * a_dot_b - b_dot_r) / denom; - - // there are a few different cases we have to handle... - bool on_a = fabs(t_a0) < hlen_a; - bool on_b = fabs(t_b0) < hlen_b; - if (!on_a && !on_b) { - // the corner - float c_a = copysign(hlen_a, t_a0); - float c_b = copysign(hlen_b, t_b0); - - // signs of partials at the corner - float dd_dt_a = 2.f*(c_a - a_dot_b*c_b - a_dot_r); - float dd_dt_b = 2.f*(c_b - a_dot_b*c_a + b_dot_r); - - if (sign(dd_dt_a) == sign(c_a)) { - // on the other edge - t_b = c_b; - t_a = clamp(t_b*a_dot_b + a_dot_r, -hlen_a, hlen_a); - } else { - t_a = c_a; - t_b = clamp(t_a*a_dot_b - b_dot_r, -hlen_b, hlen_b); - } - } else if (on_a && !on_b) { - t_b = copysign(hlen_b, t_b0); // +/- end of b? - t_a = clamp(t_b*a_dot_b + a_dot_r, -hlen_a, hlen_a); - } else if (!on_a && on_b) { - t_a = copysign(hlen_a, t_a0); // +/- end of a? - t_b = clamp(t_a*a_dot_b - b_dot_r, -hlen_b, hlen_b); - } else { - t_a = t_a0; - t_b = t_b0; - } - } else { - // lines are roughly parallel, this case is degenerate - // start off assuming the lines are in the same direction - // project a onto b - - // use the same _dot_r for each for consistency - float x_dot_r = copysign(min(a_dot_r, b_dot_r), a_dot_r); - - // project the ends of a into b coordinates - float a_l = -x_dot_r - hlen_a; - float a_r = -x_dot_r + hlen_a; - - // find the intersection of the two on b - float i_l = max(a_l, -hlen_b); - float i_r = min(a_r, hlen_b); - - if (i_l > i_r) { - // they don't intersect - if (a_l < -hlen_b) { - t_a = hlen_a; - t_b = -hlen_b; - } else { - t_a = -hlen_a; - t_b = hlen_b; - } - } else { - // the segments intersect, pick two points - *two_pts = 1; - t_b = i_l; - t_a = t_b + x_dot_r; - t_b2 = i_r; - t_a2 = t_b2 + x_dot_r; - } - - // if they weren't in the same direction, negate - if (a_dot_b < 0.f) { - t_b = -t_b; - t_b2 = -t_b2; - } - } - *p_a = r_a + t_a*a; - *p_b = r_b + t_b*b; - if (two_pts) { - *p_a2 = r_a + t_a2*a; - *p_b2 = r_b + t_b2*b; - } -} - - -// intest distance from a point p to a plane passing through point v -// with unit normal n -float pt_to_plane_dist(float4 v, float4 n, float4 p) -{ - return dot((p-v), n); -} - -// intest distance from a point p to a sphere at point v -// with radius r -float pt_to_sphere_dist(float4 v, float rad, float4 p) -{ - return length(p - v) - rad; -} - -__kernel void find_sphere_contacts(const int max_cells, - const int max_contacts, - const int n_spheres, - __global const float4* sphere_pts, - __global const float* sphere_coeffs, - __global const float* sphere_rads, - __global const float* sphere_norms, - __global const float4* centers, - __global const float4* dirs, - __global const float* lens, - __global const float* rads, - __global int* n_cts, - __global int* frs, - __global int* tos, - __global float* dists, - __global float4* pts, - __global float4* norms, - __global float* reldists, - __global float* stiff) -{ - int i = get_global_id(0); - - // collision count - int k = n_cts[i]; //keep existing contacts - - float4 end1 = centers[i] - 0.5f*lens[i]*dirs[i]; // 'left' end of the cell - float4 end2 = centers[i] + 0.5f*lens[i]*dirs[i]; // 'right' end of the cell - - for (int n = 0; n < n_spheres; n++) { // loop through all spheres - int to1 = -2*n - 1; // 'to' if left end has contact with sphere n - int to2 = to1 - 1; // 'to' if right end has contact with sphere n - - float dist1 = sphere_norms[n] * pt_to_sphere_dist(sphere_pts[n], sphere_rads[n], end1)-rads[i]; - float dist2 = sphere_norms[n] * pt_to_sphere_dist(sphere_pts[n], sphere_rads[n], end2)-rads[i]; - - // check for old contacts with this sphere - int cti1 = -1; - int cti2 = -1; - for (int m = i*max_contacts; m < i*max_contacts+n_cts[i]; m++) { - if (tos[m] == to1) cti1 = m; - else if (tos[m] == to2) cti2 = m; - } - - bool two_pts = ((cti1 >= 0) || (dist1<0.f) ) && ( (cti2 >= 0) || (dist2<0.f) ); - float stiffness = two_pts*ISQRT2 + (!two_pts)*1.0; - - // if we're in contact, or we were in contact, recompute - if ((cti1 >= 0) || (dist1<0.f) ){ - // need to make a new contact - if (cti1 < 0) { - cti1 = i*max_contacts+k; - k++; - } - - frs[cti1] = i; - tos[cti1] = to1; - dists[cti1] = dist1; - pts[cti1] = end1; // FIXME: not really the right point - norms[cti1] = sphere_norms[n] * normalize(-end1 + sphere_pts[n]); - reldists[cti1] = stiffness*sphere_coeffs[n]*dist1; - stiff[cti1] = stiffness*sphere_coeffs[n]; - } - - if ( (cti2 >= 0) || (dist2<0.f) ){ - if (cti2 < 0) { - cti2 = i*max_contacts+k; - k++; - } - - frs[cti2] = i; - tos[cti2] = to2; - dists[cti2] = dist2; - pts[cti2] = end2; - norms[cti2] = sphere_norms[n] * normalize(-end2 + sphere_pts[n]); - reldists[cti2] = stiffness*sphere_coeffs[n]*dist2; - stiff[cti2] = stiffness*sphere_coeffs[n]; - } - } - n_cts[i] = k; -} - - -__kernel void find_plane_contacts(const int max_cells, - const int max_contacts, - const int n_planes, - __global const float4* plane_pts, - __global const float4* plane_norms, - __global const float* plane_coeffs, - __global const float4* centers, - __global const float4* dirs, - __global const float* lens, - __global const float* rads, - __global int* n_cts, - __global int* frs, - __global int* tos, - __global float* dists, - __global float4* pts, - __global float4* norms, - __global float* reldists, - __global float* stiff) -{ - int i = get_global_id(0); - - // collision count - int k = n_cts[i]; //keep existing contacts - - float4 end1 = centers[i] - 0.5f*lens[i]*dirs[i]; // 'left' end of the cell - float4 end2 = centers[i] + 0.5f*lens[i]*dirs[i]; // 'right' end of the cell - - for (int n = 0; n < n_planes; n++) { // loop through all planes - int to1 = -2*n - 1; // 'to' if left end has contact with plane n - int to2 = to1 - 1; // 'to' if right end has contact with plane n - - float dist1 = pt_to_plane_dist(plane_pts[n], plane_norms[n], end1)-rads[i]; - float dist2 = pt_to_plane_dist(plane_pts[n], plane_norms[n], end2)-rads[i]; - - // check for old contacts with this plane - int cti1 = -1; - int cti2 = -1; - for (int m = i*max_contacts; m < i*max_contacts+n_cts[i]; m++) { - if (tos[m] == to1) cti1 = m; - else if (tos[m] == to2) cti2 = m; - } - - // common to both ends - float4 norm = -plane_norms[n]; - - bool two_pts = ((cti1 >= 0) || (dist1<0.f) ) && ( (cti2 >= 0) || (dist2<0.f) ); - float stiffness = two_pts*ISQRT2 + (!two_pts)*1.0; - - // if we're in contact, or we were in contact, recompute - if ((cti1 >= 0) || (dist1<0.f) ){ - // need to make a new contact - if (cti1 < 0) { - cti1 = i*max_contacts+k; - k++; - } - - frs[cti1] = i; - tos[cti1] = to1; - dists[cti1] = dist1; - pts[cti1] = end1; // FIXME: not really the right point - norms[cti1] = norm; - reldists[cti1] = stiffness*plane_coeffs[n]*dist1; - stiff[cti1] = stiffness*plane_coeffs[n]; - } - - if ( (cti2 >= 0) || (dist2<0.f) ){ - if (cti2 < 0) { - cti2 = i*max_contacts+k; - k++; - } - - frs[cti2] = i; - tos[cti2] = to2; - dists[cti2] = dist2; - pts[cti2] = end2; - norms[cti2] = norm; - reldists[cti2] = stiffness*plane_coeffs[n]*dist2; - stiff[cti2] = stiffness*plane_coeffs[n]; - } - } - n_cts[i] = k; -} - - -// -__kernel void find_contacts(const int max_cells, - const int n_cells, - const int grid_x_min, - const int grid_x_max, - const int grid_y_min, - const int grid_y_max, - const int n_sqs, - const int max_contacts, - __global const float4* centers, - __global const float4* dirs, - __global const float* lens, - __global const float* rads, - __global const int* sqs, - __global const int* sorted_ids, - __global const int* sq_inds, - __global int* n_cts, - __global int* frs, - __global int* tos, - __global float* dists, - __global float4* pts, - __global float4* norms, - __global float* reldists, - __global float* stiff, - __global float* overlap) -{ - // our id - int i = get_global_id(0); - - // collision count - int k = n_cts[i]; //keep existing contacts - - // what square are we in? - int grid_x_range = grid_x_max-grid_x_min; - int grid_y_range = grid_y_max-grid_y_min; - int sq_row = sqs[i] / grid_x_range; // square row - int sq_col = sqs[i] % grid_x_range; // square col - - // loop through our square and the eight squares surrounding it - // (fewer squares if we're on an edge) - for (int row = max(0, sq_row-1); row < min((int)(sq_row+2), grid_y_range); row++) { - for (int col = max(0, sq_col-1); col < min((int)(sq_col+2), grid_x_range); col++) { - - // what square is this? - int sq = row*grid_x_range + col; - - // loop through all the cell ids in the current square (but - // don't go past the end of the list) - for (int n = sq_inds[sq]; n < (sq < n_sqs-1 ? sq_inds[sq+1] : n_cells); n++) { - - int j = sorted_ids[n]; // the neighboring cell - - if (j<=i) continue; // we can't collide with ourself, only find low -> hi contacts - - // Look for any existing contacts, count them, and store idx's - int n_existing_cts=0; - int existing_cts_idx[2]; - for (int m=i*max_contacts; m 0.5*(lens[i]+lens[j])+rads[i]+rads[j]+MARGIN && n_existing_cts==0) - { - // if not... - continue; - } - - // if so, find closest points - float4 pi, pj; // pi is point on our line seg, pj point on other - float4 pi2, pj2; // optional second points - int two_pts = 0; // are there two contacts? - closest_points_on_segments(centers[i], centers[j], - dirs[i], dirs[j], - lens[i], lens[j], - &pi, &pj, &pi2, &pj2, &two_pts); - - float4 v_ij = pj-pi; // vector between closest points - float dist = length(v_ij) - (rads[i]+rads[j]); - float4 norm = normalize(v_ij); // normal on our cell at the contact - float4 pt = pi + rads[i]*norm; // point on the capsule surface - - int ct_i; - ct_i = i*max_contacts+k; // index of this contact - - float stiffness = two_pts*ISQRT2 + (!two_pts)*1.0; - - float overlap_length = two_pts*fabs(dot(pi-pi2,dirs[i]))/(2*POINT) + (!two_pts)*1.0; - - if (dist < MARGIN) - { - if (n_existing_cts==0) - { - // make new contact and compute distance etc. - k++; // next contact - frs[ct_i] = i; - tos[ct_i] = j; - dists[ct_i] = dist; - pts[ct_i] = pt; - norms[ct_i] = norm; - reldists[ct_i] = stiffness*RHS_FRAC*dist; - stiff[ct_i] = stiffness; - overlap[ct_i] = overlap_length; - } - } - if(n_existing_cts>0){ - // recompute dist etc. for existing contact - int idx = existing_cts_idx[0]; - dists[idx] = dist; - pts[idx] = pt; - norms[idx] = norm; - reldists[idx] = stiffness*RHS_FRAC*dist; - stiff[idx] = stiffness; - overlap[idx]=overlap_length; - } - - - if (!two_pts){ - if(n_existing_cts>1){ - // Not parallel, but were before - how to deal with this? - // Set stiffness and rhs (reldists) to zero so that this row has no effect - int idx = existing_cts_idx[1]; - /*dists[idx] = 0.0; - pts[idx] = pt; - norms[idx] = norm;*/ - reldists[idx] = 0.0; - stiff[idx] = 0.0; - overlap[idx]=overlap_length; - } - continue; - } - - // if we had two contacts, add the second point - v_ij = pj2-pi2; - dist = length(v_ij) - (rads[i]+rads[j]); - norm = normalize(v_ij); - pt = pi2 + rads[i]*norm; - - // Are cells moving together or penetrating? - if (dist < MARGIN) - { - if (n_existing_cts<2) - { - ct_i = i*max_contacts+k; - k++; - frs[ct_i] = i; - tos[ct_i] = j; - dists[ct_i] = dist; - pts[ct_i] = pt; - norms[ct_i] = norm; - reldists[ct_i] = stiffness*RHS_FRAC*dist; - stiff[ct_i] = stiffness; - overlap[ct_i]=overlap_length; - } - } - if(n_existing_cts>1){ - // recompute dist etc. for existing contact - int idx = existing_cts_idx[1]; - dists[idx] = dist; - pts[idx] = pt; - norms[idx] = norm; - reldists[idx] = stiffness*RHS_FRAC*dist; - stiff[idx] = stiffness; - overlap[idx]=overlap_length; - } - - } - } - } - n_cts[i] = k; - - // zero out unused contacts - // this IS necessary for calculate_Mx to work - for (int u = k; u < max_contacts; u++) { - frs[i*max_contacts+u] = 0; - tos[i*max_contacts+u] = 0; - } -} - - - -__kernel void collect_tos(const int max_cells, - const int n_cells, - const int grid_x_min, - const int grid_x_max, - const int grid_y_min, - const int grid_y_max, - const int n_sqs, - const int max_contacts, - __global const int* sqs, - __global const int* sorted_ids, - __global const int* sq_inds, - __global const int* n_cts, - __global const int* frs, - __global const int* tos, - __global int* cell_tos, - __global int* n_cell_tos) -{ - // our id - int i = get_global_id(0); - - // what square are we in? - int grid_x_range = grid_x_max-grid_x_min; - int grid_y_range = grid_y_max-grid_y_min; - int sq_row = sqs[i] / grid_x_range; // square row - int sq_col = sqs[i] % grid_x_range; // square col - - int k = 0; // how many cts are we the 'to' of? - - // loop through our square and the eight squares surrounding it - // (fewer squares if we're on an edge) - for (int row = max(0, sq_row-1); row < min((int)(sq_row+2), grid_y_range); row++) { - for (int col = max(0, sq_col-1); col < min((int)(sq_col+2), grid_x_range); col++) { - - // what square is this? - int sq = row*grid_x_range + col; - - // loop through all the cell ids in the current square (but - // don't go past the end of the list) - for (int n = sq_inds[sq]; n < (sq < n_sqs-1 ? sq_inds[sq+1] : n_cells); n++) { - - int j = sorted_ids[n]; // the neighboring cell - - if (j>=i || j<0) continue; // only looking at cells with lower ids - - // look through all the other cell's contacts - for (int m = 0; m < n_cts[j]; m++) { - int ct_i = (int)(j)*(int)(max_contacts)+m; - if (tos[ct_i] == i) { - // if one of them is us, collect it - cell_tos[i*max_contacts+k] = ct_i; - k++; - } - } - } - } - } - n_cell_tos[i] = k; - - // zero out unused tos - // this probably isn't necessary - for (int u = k; u < max_contacts; u++) { - cell_tos[i*max_contacts+u] = 0; - } - -} - - -__kernel void build_matrix(const int max_contacts, - __global const float4* centers, - __global const float4* dirs, - __global const float* lens, - __global const float* rads, - __global const int* n_cts, - __global const int* frs, - __global const int* tos, - __global const float4* pts, - __global const float4* norms, - __global float8* fr_ents, - __global float8* to_ents, - __global float* stiff) -{ - int id = get_global_id(0); - int ct = get_global_id(1); - - if (ct >= n_cts[id]) return; - - int i = id*max_contacts + ct; - - int a = frs[i]; - float4 r_a = pts[i]-centers[a]; - float8 fr_ent = 0.f; - - float4 nxr_a = 0.f; - nxr_a = cross(norms[i], r_a); - - fr_ent.s012 = norms[i].s012; - fr_ent.s345 = -nxr_a.s012; - //fr_ent.s3 = -dot(nxr_a, Ia[0]); - //fr_ent.s4 = -dot(nxr_a, Ia[1]); - //fr_ent.s5 = -dot(nxr_a, Ia[2]); - fr_ent.s6 = dot(dirs[a], r_a) * dot(dirs[a], norms[i])/(lens[a]+2.f*rads[a]); - fr_ents[i] = fr_ent * stiff[i]; - - int b = tos[i]; - - // plane and sphere contacts have no to_ent, and have negative indices - if (b < 0) { - to_ents[i] = 0.f; - return; - } - - float4 r_b = pts[i]-centers[b]; - float8 to_ent = 0.f; - - float4 nxr_b = 0.f; - nxr_b = cross(norms[i], r_b); - - to_ent.s012 = norms[i].s012; - to_ent.s345 = -nxr_b.s012; - //to_ent.s3 = -dot(nxr_b, Ib[0]); - //to_ent.s4 = -dot(nxr_b, Ib[1]); - //to_ent.s5 = -dot(nxr_b, Ib[2]); - to_ent.s6 = dot(dirs[b], r_b) * dot(dirs[b], norms[i])/(lens[b]+2.f*rads[b]); - to_ents[i] = to_ent * stiff[i]; -} - -__kernel void calculate_Bx(const int max_contacts, - __global const int* frs, - __global const int* tos, - __global const float8* fr_ents, - __global const float8* to_ents, - __global const float8* deltap, - __global float* Bx) -{ - int id = get_global_id(0); - int ct = get_global_id(1); - int i = id*max_contacts + ct; - int a = frs[i]; - int b = tos[i]; - if (a == 0 && b == 0) return; // not a contact - float8 to_ents_i = b < 0 ? 0.f : to_ents[i]; - //my machine can't dot float8s... - float res0123 = dot(fr_ents[i].s0123, deltap[a].s0123) - dot(to_ents_i.s0123, deltap[b].s0123); - float res4567 = dot(fr_ents[i].s4567, deltap[a].s4567) - dot(to_ents_i.s4567, deltap[b].s4567); - Bx[i] = res0123 + res4567; -} - - -__kernel void calculate_BTBx(const int max_contacts, - __global const int* n_cts, - __global const int* n_cell_tos, - __global const int* cell_tos, - __global const float8* fr_ents, - __global const float8* to_ents, - __global const float* Bx, - __global float8* BTBx) -{ - int i = get_global_id(0); - int base = i*max_contacts; - float8 res = 0.f; - for (int k = base; k < base+n_cts[i]; k++) { - float8 oldres = res; - res += fr_ents[k]*Bx[k]; - } - for (int k = base; k < base+n_cell_tos[i]; k++) { - int n = cell_tos[k]; - if (n < 0) continue; - res -= to_ents[n]*Bx[n]; - } - BTBx[i] = res; -} - -__kernel void calculate_Mx(const float muA, - const float gamma, - __global const float4* dirs, - __global const float* lens, - __global const float* rads, - __global const float8* x, - __global float8* Mx) -{ - int i = get_global_id(0); - float l = lens[i] + 2.f * rads[i]; - - float8 xi = x[i]; - float8 v = 0.f; - v.s012 = xi.s012 * muA * l; - - float4 I[4]; - cyl_inertia_tensor(muA, l, dirs[i], I); - float4 L = 0.f; - L.s012 = xi.s345; - float4 w = matmul(I, L); - v.s345 = w.s012; - - //float4 w = 0.f; - //w.s012 = xi.s345; - //float4 a = dirs[i]; - //float4 vv = (w - a*dot(a,w)) * muA * l*l*l / 12.f; - //v.s345 = vv.s012; - - v.s6 = xi.s6 * gamma; - - Mx[i] = v; -} - - -__kernel void calculate_Minv_x(const float muA, - const float gamma, - __global const float4* dirs, - __global const float* lens, - __global const float* rads, - __global const float8* x, - __global float8* Minvx) -{ - int i = get_global_id(0); - - float8 xi = x[i]; - float8 v = 0.f; - v.s012 = xi.s012/(muA*(lens[i]+2.f*rads[i])); - - float4 Iinv[4]; - cyl_inv_inertia_tensor(muA, lens[i]+2.f*rads[i], dirs[i], Iinv); - float4 L = 0.f; - L.s012 = xi.s345; - float4 w = matmul(Iinv, L); - v.s345 = w.s012; - - v.s6 = xi.s6/gamma; - - Minvx[i] = v; -} - - -__kernel void predict(__global const float4* centers, - __global const float4* dirs, - __global const float* lens, - __global const float4* dcenters, - __global const float4* dangs, - __global const float* dlens, - __global float4* pred_centers, - __global float4* pred_dirs, - __global float* pred_lens) -{ - int i = get_global_id(0); - float4 center_i = centers[i]; - float4 dir_i = dirs[i]; - float len_i = lens[i]; - float4 dcenter_i = dcenters[i]; - float4 dang_i = dangs[i]; - float dlen_i = dlens[i]; - - pred_centers[i] = center_i + dcenter_i; - - if (length(dang_i)>1e-12) - { - float4 rot_axis = normalize(dang_i); - float rot_angle = length(dang_i); - pred_dirs[i] = normalize(rot(rot_axis, rot_angle, dir_i)); - } else { - pred_dirs[i] = dir_i; - } - - pred_lens[i] = len_i + dlen_i; - -} - -__kernel void integrate(__global float4* centers, - __global float4* dirs, - __global float* lens, - __global float4* dcenters, - __global float4* dangs, - __global float* dlens) -{ - int i = get_global_id(0); - float4 center_i = centers[i]; - float4 dir_i = dirs[i]; - float len_i = lens[i]; - float4 dcenter_i = dcenters[i]; - float4 dang_i = dangs[i]; - float dlen_i = dlens[i]; - - centers[i] = center_i + dcenter_i; - - if (length(dang_i)>1e-12) - { - float4 rot_axis = normalize(dang_i); - float rot_angle = length(dang_i); - dirs[i] = normalize(rot(rot_axis, rot_angle, dir_i)); - } - - lens[i] = len_i + dlen_i; - - // fully damped - dcenters[i] = 0.f; - dangs[i] = 0.f; - dlens[i] = 0.f; -} - -__kernel void add_impulse(const float muA, - const float gamma, - __global const float8* deltap, - __global const float4* dirs, - __global const float* lens, - __global const float* rads, - __global float4* dcenters, - __global float4* dangs, - __global const float* target_dlens, - __global float* dlens) -{ - int i = get_global_id(0); - - float4 dir_i = dirs[i]; - float len_i = lens[i]; - float rad_i = rads[i]; - float8 deltap_i = deltap[i]; - - float4 dplin = 0.f; - dplin.s012 = deltap_i.s012; - dcenters[i] += dplin; - - // FIXME: should probably store these so we don't recompute them - //float4 Iinv[4]; - //cyl_inv_inertia_tensor(muA, len_i+2.f*rad_i, dir_i, Iinv); - //float4 dL = 0.f; - //dL.s012 = deltap_i.s345; - //float4 dpang = matmul(Iinv, dL); - - float4 dpang = 0.f; - dpang.s012 = deltap_i.s345; - float dpangmag = length(dpang); - if (dpangmag>ANG_LIMIT) - { - dpang *= ANG_LIMIT/dpangmag; - } - dangs[i] += dpang; - - float dplen = deltap_i.s6; - //dlens[i] += max(0.f, target_dlens[i] + dplen); - dlens[i] = max(0.f, dlens[i]+dplen); -} - - diff --git a/CellModeller/Biophysics/BacterialModels/CLBacterium.py b/CellModeller/Biophysics/BacterialModels/CLBacterium.py deleted file mode 100644 index 85d8180d..00000000 --- a/CellModeller/Biophysics/BacterialModels/CLBacterium.py +++ /dev/null @@ -1,1254 +0,0 @@ -import sys -import math -import numpy -import pyopencl as cl -import pyopencl.array as cl_array -from pyopencl.array import vec -from pyopencl.array import max as device_max -from pyopencl.elementwise import ElementwiseKernel -from pyopencl.reduction import ReductionKernel -import random -import time - - -ct_map = {} - -class CLBacterium: - """A rigid body model of bacterial growth implemented using - OpenCL. - """ - - def __init__(self, simulator, - max_substeps=8, - max_cells=10000, - max_contacts=24, - max_planes=1, - max_spheres=1, - max_sqs=192**2, - grid_spacing=5.0, - muA=1.0, - gamma=10.0, - dt=None, - cgs_tol=5e-3, - jitter_z=True, - alternate_divisions=False, - printing=True, - compNeighbours=False): - - # Should we compute neighbours? (bit slow) - self.computeNeighbours = compNeighbours - - self.frame_no = 0 - self.simulator = simulator - self.regulator = None - - self.time_begin = time.time() - self.seconds_elapsed = 0 - self.minutes_elapsed = 0 - self.hours_elapsed = 0 - - self.max_cells = max_cells - self.max_contacts = max_contacts - self.max_planes = max_planes - self.max_spheres = max_spheres - self.max_sqs = max_sqs - self.grid_spacing = grid_spacing - self.muA = muA - self.gamma = gamma - self.dt = dt - self.cgs_tol = cgs_tol - - self.max_substeps = max_substeps - - self.n_cells = 0 - self.n_cts = 0 - self.n_planes = 0 - self.n_spheres = 0 - - self.next_id = 0 - - self.grid_x_min = 0 - self.grid_x_max = 0 - self.grid_y_min = 0 - self.grid_y_max = 0 - self.n_sqs = 0 - - self.init_cl() - #self.init_kernels() - self.init_data() - - self.parents = {} - - self.jitter_z = jitter_z - self.alternate_divisions = alternate_divisions - self.printing = printing - self.progress_initialised = False - self.sub_tick_initialised = False - - # Biophysical Model interface - def reset(self): - self.n_cells=0 - self.n_cts=0 - self.n_planes=0 - self.n_spheres=0 - - def setRegulator(self, regulator): - self.regulator = regulator - self.init_kernels() - - - def addCell(self, cellState, pos=(0,0,0), dir=(1,0,0), rad=0.5, **kwargs): - i = cellState.idx - self.n_cells += 1 - cid = cellState.id - self.cell_centers[i] = tuple(pos+(0,)) - self.cell_dirs[i] = tuple(dir+(0,)) - self.cell_lens[i] = cellState.length - self.cell_rads[i] = rad - self.initCellState(cellState) - self.set_cells() - self.calc_cell_geom() # cell needs a volume - - #--- - # Some functions to modify existing cells (e.g. from GUI) - # Eventually prob better to have a generic editCell() that deals with this stuff - # - def moveCell(self, cellState, delta_pos): - print("cell idx = %d"%cellState.idx) - i = cellState.idx - cid = cellState.id - print("cell center = ") - print(self.cell_centers[i]) - print("delta_pos") - print(delta_pos) - pos = numpy.array(tuple(self.cell_centers[i])) - pos[0:3] += numpy.array(tuple(delta_pos)) - self.cell_centers[i] = pos - self.simulator.cellStates[cid].pos = [self.cell_centers[i][j] for j in range(3)] - self.set_cells() - self.updateCellState(cellState) - - def addPlane(self, pt, norm, coeff): - pidx = self.n_planes - self.n_planes += 1 - self.plane_pts[pidx] = tuple(pt)+(0,) - self.plane_norms[pidx] = tuple(norm) + (0,) - self.plane_coeffs[pidx] = coeff - self.set_planes() - - def addSphere(self, pt, rad, coeff, norm): - sidx = self.n_spheres - self.n_spheres += 1 - self.sphere_pts[sidx] = tuple(pt)+(0,) - self.sphere_rads[sidx] = rad - self.sphere_coeffs[sidx] = coeff - self.sphere_norms[sidx] = norm - self.set_spheres() - - def hasNeighbours(self): - return False - - def divide(self, parentState, daughter1State, daughter2State, *args, **kwargs): - self.divide_cell(parentState.idx, daughter1State.idx, daughter2State.idx) - # Initialise cellState data - self.initCellState(daughter1State) - self.initCellState(daughter2State) - - def init_cl(self): - if self.simulator: - (self.context, self.queue) = self.simulator.getOpenCL() - - def init_kernels(self): - """Set up the OpenCL kernels.""" - from pkg_resources import resource_string - kernel_src = resource_string(__name__, 'CLBacterium.cl').decode() - - self.program = cl.Program(self.context, kernel_src).build(cache_dir=False) - # Some kernels that seem like they should be built into pyopencl... - self.vclearf = ElementwiseKernel(self.context, "float8 *v", "v[i]=0.0", "vecclearf") - self.vcleari = ElementwiseKernel(self.context, "int *v", "v[i]=0", "veccleari") - self.vadd = ElementwiseKernel(self.context, "float8 *res, const float8 *in1, const float8 *in2", - "res[i] = in1[i] + in2[i]", "vecadd") - self.vsub = ElementwiseKernel(self.context, "float8 *res, const float8 *in1, const float8 *in2", - "res[i] = in1[i] - in2[i]", "vecsub") - self.vaddkx = ElementwiseKernel(self.context, - "float8 *res, const float k, const float8 *in1, const float8 *in2", - "res[i] = in1[i] + k*in2[i]", "vecaddkx") - self.vsubkx = ElementwiseKernel(self.context, - "float8 *res, const float k, const float8 *in1, const float8 *in2", - "res[i] = in1[i] - k*in2[i]", "vecsubkx") - self.vmulk = ElementwiseKernel(self.context, - "float8 *res, const float k, const float8 *in1", - "res[i] = k*in1[i]", "vecmulk") - self.vnorm = ElementwiseKernel(self.context, - "float8 *res, const float8 *in1", - "res[i] = dot(in1[i], in1[i]", "vecnorm") - - - # cell geometry kernels - self.calc_cell_area = ElementwiseKernel(self.context, "float* res, float* r, float* l", - "res[i] = 2.f*3.1415927f*r[i]*(2.f*r[i]+l[i])", "cell_area_kern") - self.calc_cell_vol = ElementwiseKernel(self.context, "float* res, float* r, float* l", - "res[i] = 3.1415927f*r[i]*r[i]*(2.f*r[i]+l[i])", "cell_vol_kern") - - # A dot product as sum of float4 dot products - - # i.e. like flattening vectors of float8s into big float vectors - # then computing dot - # NB. Some openCLs seem not to implement dot(float8,float8) so split - # into float4's - self.vdot = ReductionKernel(self.context, numpy.float32, neutral="0", - reduce_expr="a+b", map_expr="dot(x[i].s0123,y[i].s0123)+dot(x[i].s4567,y[i].s4567)", - arguments="__global float8 *x, __global float8 *y") - - - def init_data(self): - """Set up the data OpenCL will store on the device.""" - # cell data - cell_geom = (self.max_cells,) - self.cell_centers = numpy.zeros(cell_geom, vec.float4) - self.cell_centers_dev = cl_array.zeros(self.queue, cell_geom, vec.float4) - self.cell_dirs = numpy.zeros(cell_geom, vec.float4) - self.cell_dirs_dev = cl_array.zeros(self.queue, cell_geom, vec.float4) - self.cell_lens = numpy.zeros(cell_geom, numpy.float32) - self.cell_lens_dev = cl_array.zeros(self.queue, cell_geom, numpy.float32) - self.pred_cell_centers = numpy.zeros(cell_geom, vec.float4) - self.pred_cell_centers_dev = cl_array.zeros(self.queue, cell_geom, vec.float4) - self.pred_cell_dirs = numpy.zeros(cell_geom, vec.float4) - self.pred_cell_dirs_dev = cl_array.zeros(self.queue, cell_geom, vec.float4) - self.pred_cell_lens = numpy.zeros(cell_geom, numpy.float32) - self.pred_cell_lens_dev = cl_array.zeros(self.queue, cell_geom, numpy.float32) - self.cell_rads = numpy.zeros(cell_geom, numpy.float32) - self.cell_rads_dev = cl_array.zeros(self.queue, cell_geom, numpy.float32) - self.cell_sqs = numpy.zeros(cell_geom, numpy.int32) - self.cell_sqs_dev = cl_array.zeros(self.queue, cell_geom, numpy.int32) - self.cell_n_cts = numpy.zeros(cell_geom, numpy.int32) - self.cell_n_cts_dev = cl_array.zeros(self.queue, cell_geom, numpy.int32) - self.cell_dcenters = numpy.zeros(cell_geom, vec.float4) - self.cell_dcenters_dev = cl_array.zeros(self.queue, cell_geom, vec.float4) - self.cell_dangs = numpy.zeros(cell_geom, vec.float4) - self.cell_dangs_dev = cl_array.zeros(self.queue, cell_geom, vec.float4) - self.cell_dlens = numpy.zeros(cell_geom, numpy.float32) - self.cell_dlens_dev = cl_array.zeros(self.queue, cell_geom, numpy.float32) - self.cell_target_dlens_dev = cl_array.zeros(self.queue, cell_geom, numpy.float32) - self.cell_growth_rates = numpy.zeros(cell_geom, numpy.float32) - - # cell geometry calculated from l and r - self.cell_areas_dev = cl_array.zeros(self.queue, cell_geom, numpy.float32) - self.cell_vols_dev = cl_array.zeros(self.queue, cell_geom, numpy.float32) - self.cell_old_vols_dev = cl_array.zeros(self.queue, cell_geom, numpy.float32) - - # gridding - self.sq_inds = numpy.zeros((self.max_sqs,), numpy.int32) - self.sq_inds_dev = cl_array.zeros(self.queue, (self.max_sqs,), numpy.int32) - self.sorted_ids = numpy.zeros(cell_geom, numpy.int32) - self.sorted_ids_dev = cl_array.zeros(self.queue, cell_geom, numpy.int32) - - # constraint planes - plane_geom = (self.max_planes,) - self.plane_pts = numpy.zeros(plane_geom, vec.float4) - self.plane_pts_dev = cl_array.zeros(self.queue, plane_geom, vec.float4) - self.plane_norms = numpy.zeros(plane_geom, vec.float4) - self.plane_norms_dev = cl_array.zeros(self.queue, plane_geom, vec.float4) - self.plane_coeffs = numpy.zeros(plane_geom, numpy.float32) - self.plane_coeffs_dev = cl_array.zeros(self.queue, plane_geom, numpy.float32) - - # constraint spheres - sphere_geom = (self.max_spheres,) - self.sphere_pts = numpy.zeros(sphere_geom, vec.float4) - self.sphere_pts_dev = cl_array.zeros(self.queue, sphere_geom, vec.float4) - self.sphere_rads = numpy.zeros(sphere_geom, numpy.float32) - self.sphere_rads_dev = cl_array.zeros(self.queue, sphere_geom, numpy.float32) - self.sphere_coeffs = numpy.zeros(sphere_geom, numpy.float32) - self.sphere_coeffs_dev = cl_array.zeros(self.queue, sphere_geom, numpy.float32) - self.sphere_norms = numpy.zeros(sphere_geom, numpy.float32) - self.sphere_norms_dev = cl_array.zeros(self.queue, sphere_geom, numpy.float32) - - # contact data - ct_geom = (self.max_cells, self.max_contacts) - self.ct_frs = numpy.zeros(ct_geom, numpy.int32) - self.ct_frs_dev = cl_array.zeros(self.queue, ct_geom, numpy.int32) - self.ct_tos = numpy.zeros(ct_geom, numpy.int32) - self.ct_tos_dev = cl_array.zeros(self.queue, ct_geom, numpy.int32) - self.ct_dists = numpy.zeros(ct_geom, numpy.float32) - self.ct_dists_dev = cl_array.zeros(self.queue, ct_geom, numpy.float32) - self.ct_pts = numpy.zeros(ct_geom, vec.float4) - self.ct_pts_dev = cl_array.zeros(self.queue, ct_geom, vec.float4) - self.ct_norms = numpy.zeros(ct_geom, vec.float4) - self.ct_norms_dev = cl_array.zeros(self.queue, ct_geom, vec.float4) - self.ct_stiff_dev = cl_array.zeros(self.queue, ct_geom, numpy.float32) - self.ct_overlap_dev = cl_array.zeros(self.queue, ct_geom, numpy.float32) - self.neighbours = numpy.zeros(ct_geom, numpy.int32) - self.cell_cts = numpy.zeros(self.max_cells, numpy.int32) - - # where the contacts pointing to this cell are collected - self.cell_tos = numpy.zeros(ct_geom, numpy.int32) - self.cell_tos_dev = cl_array.zeros(self.queue, ct_geom, numpy.int32) - self.n_cell_tos = numpy.zeros(cell_geom, numpy.int32) - self.n_cell_tos_dev = cl_array.zeros(self.queue, cell_geom, numpy.int32) - - - # the constructed 'matrix' - mat_geom = (self.max_cells*self.max_contacts,) - self.ct_inds = numpy.zeros(mat_geom, numpy.int32) - self.ct_inds_dev = cl_array.zeros(self.queue, mat_geom, numpy.int32) - self.ct_reldists = numpy.zeros(mat_geom, numpy.float32) - self.ct_reldists_dev = cl_array.zeros(self.queue, mat_geom, numpy.float32) - - self.fr_ents = numpy.zeros(mat_geom, vec.float8) - self.fr_ents_dev = cl_array.zeros(self.queue, mat_geom, vec.float8) - self.to_ents = numpy.zeros(mat_geom, vec.float8) - self.to_ents_dev = cl_array.zeros(self.queue, mat_geom, vec.float8) - - - # vectors and intermediates - self.deltap = numpy.zeros(cell_geom, vec.float8) - self.deltap_dev = cl_array.zeros(self.queue, cell_geom, vec.float8) - self.Mx = numpy.zeros(mat_geom, numpy.float32) - self.Mx_dev = cl_array.zeros(self.queue, mat_geom, numpy.float32) - self.BTBx = numpy.zeros(cell_geom, vec.float8) - self.BTBx_dev = cl_array.zeros(self.queue, cell_geom, vec.float8) - self.Minvx_dev = cl_array.zeros(self.queue, cell_geom, vec.float8) - - # CGS intermediates - self.p_dev = cl_array.zeros(self.queue, cell_geom, vec.float8) - self.Ap_dev = cl_array.zeros(self.queue, cell_geom, vec.float8) - self.res_dev = cl_array.zeros(self.queue, cell_geom, vec.float8) - self.rhs_dev = cl_array.zeros(self.queue, cell_geom, vec.float8) - - - def load_from_cellstates(self, cell_states): - for (cid,cs) in list(cell_states.items()): - i = cs.idx - self.cell_centers[i] = tuple(cs.pos)+(0,) - self.cell_dirs[i] = tuple(cs.dir)+(0,) - self.cell_rads[i] = cs.radius - self.cell_lens[i] = cs.length - - self.n_cells = len(cell_states) - self.set_cells() - self.calc_cell_area(self.cell_areas_dev, self.cell_rads_dev, self.cell_lens_dev) - self.calc_cell_vol(self.cell_vols_dev, self.cell_rads_dev, self.cell_lens_dev) - - def load_test_data(self): - import CellModeller.Biophysics.BacterialModels.CLData as data - self.cell_centers.put(list(range(len(data.pos))), data.pos) - self.cell_dirs.put(list(range(len(data.dirs))), data.dirs) - self.cell_lens.put(list(range(len(data.lens))), data.lens) - self.cell_rads.put(list(range(len(data.rads))), data.rads) - self.n_cells = data.n_cells - self.set_cells() - - def load_1_cell(self): - self.cell_centers.put([0], [(0,0,0,0)]) - self.cell_dirs.put([0], [(1,0,0,0)]) - self.cell_lens.put([0], [2.0]) - self.cell_rads.put([0], [0.5]) - self.n_cells = 1 - self.set_cells() - - - def load_2_cells(self): - root2 = numpy.sqrt(2.0) - self.cell_centers.put([0,1], [(-root2-0.5, 0, 0, 0), (root2+0.5, 0, 0, 0)]) - self.cell_dirs.put([0,1], [(root2/2.0, root2/2.0, 0, 0), (-root2/2.0, root2/2.0, 0, 0)]) - self.cell_lens.put([0,1], [4.0, 4.0]) - self.cell_rads.put([0,1], [0.5, 0.5]) - self.n_cells = 2 - self.set_cells() - - - def load_3_cells(self): - root2 = numpy.sqrt(2.0) - self.cell_centers.put([0,1,2], [(-root2-0.5, 0, 0, 0), (root2+0.5, 0, 0, 0), (root2+0.5+3.3, 0, 0, 0)]) - self.cell_dirs.put([0,1,2], [(root2/2.0, root2/2.0, 0, 0), (-root2/2.0, root2/2.0, 0, 0), (1, 0, 0, 0)]) - self.cell_lens.put([0,1,2], [3.0, 3.0, 3.0]) - self.cell_rads.put([0,1,2], [0.5, 0.5, 0.5]) - self.n_cells = 3 - self.set_cells() - - - def load_3_cells_1_plane(self): - root2 = numpy.sqrt(2.0) - self.cell_centers.put([0,1,2], [(-root2-0.5, 0, 0, 0), (root2+0.5, 0, 0, 0), (root2+0.5+3.3, 0, 0, 0)]) - self.cell_dirs.put([0,1,2], [(root2/2.0, root2/2.0, 0, 0), (-root2/2.0, root2/2.0, 0, 0), (1, 0, 0, 0)]) - self.cell_lens.put([0,1,2], [3.0, 3.0, 3.0]) - self.cell_rads.put([0,1,2], [0.5, 0.5, 0.5]) - self.n_cells = 3 - self.set_cells() - - self.n_planes = 1 - self.plane_pts.put([0], [(0, 0, -0.5, 0)]) - self.plane_norms.put([0], [(0, 0, 1, 0)]) - self.plane_coeffs.put([0], [0.5]) - self.set_planes() - - def load_3_cells_2_planes(self): - root2 = numpy.sqrt(2.0) - self.cell_centers.put([0,1,2], [(-root2-0.5, 0, 0, 0), (root2+0.5, 0, 0, 0), (root2+0.5+3.3, 0, 0, 0)]) - self.cell_dirs.put([0,1,2], [(root2/2.0, root2/2.0, 0, 0), (-root2/2.0, root2/2.0, 0, 0), (1, 0, 0, 0)]) - self.cell_lens.put([0,1,2], [3.0, 3.0, 3.0]) - self.cell_rads.put([0,1,2], [0.5, 0.5, 0.5]) - self.n_cells = 3 - self.set_cells() - - self.n_planes = 2 - self.plane_pts.put([0,1], [(0, 0, -0.5, 0), (0, 0, 0.5, 0)]) - self.plane_norms.put([0,1], [(0, 0, 1, 0), (0, 0, -1, 0)]) - self.plane_coeffs.put([0,1], [0.5, 0.1]) - self.set_planes() - - - def load_1_cell_1_plane(self): - self.cell_centers.put([0], [(0,0,0,0)]) - self.cell_dirs.put([0], [(1,0,0,0)]) - self.cell_lens.put([0], [3.0]) - self.cell_rads.put([0], [0.5]) - self.n_cells = 1 - self.set_cells() - - self.plane_pts.put([0], [(4, 0, 0, 0)]) - self.plane_norms.put([0], [(-1, 0, 0, 0)]) - self.plane_coeffs.put([0], [0.5]) - self.n_planes = 1 - self.set_planes() - - - def load_1024_cells(self): - d = 32 - for i in range(-d/2,d/2): - for j in range(-d/2,d/2): - n = (i+d/2)*d + (j+d/2) - x = i*3.5 + random.uniform(-0.05,0.05) - y = j*2.0 + random.uniform(-0.05,0.05) - th = random.uniform(-0.15, 0.15) - dir_x = math.cos(th) - dir_y = math.sin(th) - self.cell_centers.put([n], [(x, y, 0, 0)]) - self.cell_dirs.put([n], [(dir_x, dir_y, 0, 0)]) - self.cell_lens.put([n], [2]) - self.cell_rads.put([n], 0.5) - self.n_cells = d*d - self.set_cells() - - def get_cells(self): - """Copy cell centers, dirs, lens, and rads from the device.""" - self.cell_centers[0:self.n_cells] = self.cell_centers_dev[0:self.n_cells].get() - self.cell_dirs[0:self.n_cells] = self.cell_dirs_dev[0:self.n_cells].get() - self.cell_lens[0:self.n_cells] = self.cell_lens_dev[0:self.n_cells].get() - self.cell_rads[0:self.n_cells] = self.cell_rads_dev[0:self.n_cells].get() - self.cell_dlens[0:self.n_cells] = self.cell_dlens_dev[0:self.n_cells].get() - self.cell_dcenters[0:self.n_cells] = self.cell_dcenters_dev[0:self.n_cells].get() - self.cell_dangs[0:self.n_cells] = self.cell_dangs_dev[0:self.n_cells].get() - - def set_cells(self): - """Copy cell centers, dirs, lens, and rads to the device from local.""" - self.cell_centers_dev[0:self.n_cells].set(self.cell_centers[0:self.n_cells]) - self.cell_dirs_dev[0:self.n_cells].set(self.cell_dirs[0:self.n_cells]) - self.cell_lens_dev[0:self.n_cells].set(self.cell_lens[0:self.n_cells]) - self.cell_rads_dev[0:self.n_cells].set(self.cell_rads[0:self.n_cells]) - self.cell_dlens_dev[0:self.n_cells].set(self.cell_dlens[0:self.n_cells]) - self.cell_dcenters_dev[0:self.n_cells].set(self.cell_dcenters[0:self.n_cells]) - self.cell_dangs_dev[0:self.n_cells].set(self.cell_dangs[0:self.n_cells]) - - def set_planes(self): - """Copy plane pts, norms, and coeffs to the device from local.""" - self.plane_pts_dev[0:self.n_planes].set(self.plane_pts[0:self.n_planes]) - self.plane_norms_dev[0:self.n_planes].set(self.plane_norms[0:self.n_planes]) - self.plane_coeffs_dev[0:self.n_planes].set(self.plane_coeffs[0:self.n_planes]) - - - def set_spheres(self): - """Copy sphere pts and coeffs to the device from local.""" - self.sphere_pts_dev[0:self.n_spheres].set(self.sphere_pts[0:self.n_spheres]) - self.sphere_rads_dev[0:self.n_spheres].set(self.sphere_rads[0:self.n_spheres]) - self.sphere_coeffs_dev[0:self.n_spheres].set(self.sphere_coeffs[0:self.n_spheres]) - self.sphere_norms_dev[0:self.n_spheres].set(self.sphere_norms[0:self.n_spheres]) - - - def get_cts(self): - """Copy contact froms, tos, dists, pts, and norms from the device.""" - self.ct_frs[0:self.n_cts] = self.ct_frs_dev[0:self.n_cts].get() - self.ct_tos[0:self.n_cts] = self.ct_tos_dev[0:self.n_cts].get() - self.ct_dists[0:self.n_cts] = self.ct_dists_dev[0:self.n_cts].get() - self.ct_pts[0:self.n_cts] = self.ct_pts_dev[0:self.n_cts].get() - self.ct_norms[0:self.n_cts] = self.ct_norms_dev[0:self.n_cts].get() - self.cell_n_cts[0:self.n_cells] = self.cell_n_cts_dev[0:self.n_cells].get() - - def matrixTest(self): - x_dev = cl_array.zeros(self.queue, (self.n_cells,), vec.float8) - Ax_dev = cl_array.zeros(self.queue, (self.n_cells,), vec.float8) - opstring = '' - for i in range(self.n_cells): - x = numpy.zeros((self.n_cells,), vec.float8) - for j in range(7): - if j>0: - x[i][j-1]=0.0 - x[i][j]=1.0 - x_dev.set(x) - self.calculate_Ax(Ax_dev, x_dev) - Ax = Ax_dev.get() - for ii in range(self.n_cells): - for jj in range(7): - opstring += str(Ax[ii][jj]) - if ii!=self.n_cells-1 or jj!=6: - opstring = opstring + '\t' - opstring = opstring + '\n' - print("MTM") - print(opstring) - open('CellModeller/Biophysics/BacterialModels/matrix.mat', 'w').write(opstring) - - - def dump_cell_data(self, n): - import pickle - filename = 'data/data-%04i.pickle'%n - outfile = open(filename, 'wb') - data = (self.n_cells, - self.cell_centers_dev.get(), - self.cell_dirs_dev.get(), - self.cell_lens_dev.get(), - self.cell_rads_dev.get(), - self.parents), - pickle.dump(data, outfile, protocol=-1) - - def dydt(self): - self.set_cells() - - def finish(self): - # pull cells from the device and update simulator - if self.simulator: - self.get_cells() - for state in list(self.simulator.cellStates.values()): - self.updateCellState(state) - - def progress_init(self, dt): - self.set_cells() - # NOTE: by default self.dt=None, and time step == simulator time step (dt) - if self.dt: - self.n_ticks = int(math.ceil(dt/self.dt)) - else: - self.n_ticks = 1 - # print("n_ticks = %d"%(self.n_ticks)) - self.actual_dt = dt / float(self.n_ticks) - self.progress_initialised = True - - def progress(self): - if self.n_ticks: - if self.tick(self.actual_dt): - self.n_ticks -= 1 - return False - else: - return True - - def progress_finalise(self): - self.frame_no += 1 - self.progress_initialised = False - self.seconds_elapsed = numpy.float32(time.time() - self.time_begin) - self.minutes_elapsed = (numpy.float32(self.seconds_elapsed) / 60.0) - self.hours_elapsed = (numpy.float32(self.minutes_elapsed) / 60.0) - if self.frame_no % 10 == 0: - print('% 8i % 8i cells % 8i contacts %f hour(s) or %f minute(s) or %f second(s)' % (self.frame_no, self.n_cells, self.n_cts, self.hours_elapsed, self.minutes_elapsed, self.seconds_elapsed)) - # pull cells from the device and update simulator - if self.simulator: - self.get_cells() - # TJR: added incremental construction of this dict to same places as idToIdx - not fully tested - #idxToId = {idx: id for id, idx in self.simulator.idToIdx.iteritems()} - # TJR: add flag for this cos a bit time consuming - if self.computeNeighbours: - self.updateCellNeighbours(self.simulator.idxToId) - for state in list(self.simulator.cellStates.values()): - self.updateCellState(state) - - def step(self, dt): - """Step forward dt units of time. - - Assumes that: - cell_centers is up to date when it starts. - """ - if not self.progress_initialised: - self.progress_init(dt) - if self.progress(): - self.progress_finalise() - return True - else: - return False - - def sub_tick_init(self, dt): - # set target dlens (taken from growth rates set by updateCellStates) - #self.cell_target_dlens_dev.set(dt*self.cell_growth_rates) - #self.cell_dlens_dev.set(dt*self.cell_dlens) - self.cell_dlens_dev[0:self.n_cells].set(dt*self.cell_growth_rates[0:self.n_cells]) - - # redefine gridding based on the range of cell positions - self.cell_centers[0:self.n_cells] = self.cell_centers_dev[0:self.n_cells].get() - self.update_grid() # we assume local cell_centers is current - - # get each cell into the correct sq and retrieve from the device - self.bin_cells() - - # sort cells and find sq index starts in the list - self.cell_sqs = self.cell_sqs_dev[0:self.n_cells].get() # get updated cell sqs - self.sort_cells() - self.sorted_ids_dev.set(self.sorted_ids) # push changes to the device - self.sq_inds_dev.set(self.sq_inds) - - self.n_cts = 0 - self.vcleari(self.cell_n_cts_dev) # clear the accumulated contact count - self.sub_tick_i=0 - self.sub_tick_initialised=True - - def tick(self, dt): - if not self.sub_tick_initialised: - self.sub_tick_init(dt) - if self.sub_tick(dt): - self.sub_tick_finalise() - return True - else: - return False - - def sub_tick(self, dt): - old_n_cts = self.n_cts - self.predict() - # find all contacts - self.find_contacts() - # place 'backward' contacts in cells - self.collect_tos() - - self.sub_tick_i += 1 - alpha = 10**(self.sub_tick_i) - new_cts = self.n_cts - old_n_cts - if (new_cts>0 or self.sub_tick_i==0) and self.sub_tick_i0:#not a plane contact - self.neighbours[i, cell_cts[i]] = idx2Id[ct_tos[i,j]] - cell_cts[i] += 1 - self.neighbours[ct_tos[i,j], cell_cts[ct_tos[i,j]]] = idx2Id[i] - cell_cts[ct_tos[i,j]] += 1 - self.cell_cts = cell_cts - - def updateCellState(self, state): - cid = state.id - i = state.idx - - state.vel = [self.cell_centers[i][j]-state.pos[j] for j in range(3)] - state.pos = [self.cell_centers[i][j] for j in range(3)] - state.dir = [self.cell_dirs[i][j] for j in range(3)] - state.radius = self.cell_rads[i] - state.length = self.cell_lens[i] - state.strainRate = (state.length - state.oldLen)/state.oldLen - - #currently the effective growth rate is calculated over the entire history of the cell - state.effGrowth = state.effGrowth * state.cellAge + state.strainRate * state.oldLen - state.cellAge += 1 - state.effGrowth = state.effGrowth / state.cellAge - state.oldLen = state.length - - state.neighbours = [] #clear contacts - if self.computeNeighbours: #populate cellstate.neighbours - for n in range(self.cell_cts[i]): - if self.neighbours[i,n] not in state.neighbours: - state.neighbours.append(self.neighbours[i,n]) #ids of all cells in physical contact - state.cts = len(state.neighbours) - - state.volume = state.length # TO DO: do something better here - pa = numpy.array(state.pos) - da = numpy.array(state.dir) - state.ends = (pa-da*state.length*0.5, pa+da*state.length*0.5) - # Length vel is linearisation of exponential growth - self.cell_growth_rates[i] = state.growthRate*state.length - - - def update_grid(self): - """Update our grid_(x,y)_min, grid_(x,y)_max, and n_sqs. - - Assumes that our copy of cell_centers is current. - """ - coords = self.cell_centers.view(numpy.float32).reshape((self.max_cells, 4)) - - x_coords = coords[:,0] - min_x_coord = x_coords.min() - max_x_coord = x_coords.max() - self.grid_x_min = int(math.floor(min_x_coord / self.grid_spacing)) - self.grid_x_max = int(math.ceil(max_x_coord / self.grid_spacing)) - if self.grid_x_min == self.grid_x_max: - self.grid_x_max += 1 - - y_coords = coords[:,1] - min_y_coord = y_coords.min() - max_y_coord = y_coords.max() - self.grid_y_min = int(math.floor(min_y_coord / self.grid_spacing)) - self.grid_y_max = int(math.ceil(max_y_coord / self.grid_spacing)) - if self.grid_y_min == self.grid_y_max: - self.grid_y_max += 1 - - self.n_sqs = (self.grid_x_max-self.grid_x_min)*(self.grid_y_max-self.grid_y_min) - - - def bin_cells(self): - """Call the bin_cells kernel. - - Assumes cell_centers is current on the device. - - Calculates cell_sqs. - """ - self.program.bin_cells(self.queue, - (self.n_cells,), - None, - numpy.int32(self.grid_x_min), - numpy.int32(self.grid_x_max), - numpy.int32(self.grid_y_min), - numpy.int32(self.grid_y_max), - numpy.float32(self.grid_spacing), - self.cell_centers_dev.data, - self.cell_sqs_dev.data).wait() - - - def sort_cells(self): - """Sort the cells by grid square and find the start of each - grid square's cells in that list. - - Assumes that the local copy of cell_sqs is current. - - Calculates local sorted_ids and sq_inds. - """ - self.sorted_ids.put(numpy.arange(self.n_cells), numpy.argsort(self.cell_sqs[:self.n_cells])) - self.sorted_ids_dev[0:self.n_cells].set(self.sorted_ids[0:self.n_cells]) - - # find the start of each sq in the list of sorted cell ids and send to the device - sorted_sqs = numpy.sort(self.cell_sqs[:self.n_cells]) - self.sq_inds.put(numpy.arange(self.n_sqs), numpy.searchsorted(sorted_sqs, numpy.arange(self.n_sqs), side='left')) - self.sq_inds_dev.set(self.sq_inds) - - - def find_contacts(self, predict=True): - """Call the find_contacts kernel. - - Assumes that cell_centers, cell_dirs, cell_lens, cell_rads, - cell_sqs, cell_dcenters, cell_dlens, cell_dangs, - sorted_ids, and sq_inds are current on the device. - - Calculates cell_n_cts, ct_frs, ct_tos, ct_dists, ct_pts, - ct_norms, ct_reldists, and n_cts. - """ - if predict: - centers = self.pred_cell_centers_dev - dirs = self.pred_cell_dirs_dev - lens = self.pred_cell_lens_dev - else: - centers = self.cell_centers_dev - dirs = self.cell_dirs_dev - lens = self.cell_lens_dev - - self.program.find_plane_contacts(self.queue, - (self.n_cells,), - None, - numpy.int32(self.max_cells), - numpy.int32(self.max_contacts), - numpy.int32(self.n_planes), - self.plane_pts_dev.data, - self.plane_norms_dev.data, - self.plane_coeffs_dev.data, - centers.data, - dirs.data, - lens.data, - self.cell_rads_dev.data, - self.cell_n_cts_dev.data, - self.ct_frs_dev.data, - self.ct_tos_dev.data, - self.ct_dists_dev.data, - self.ct_pts_dev.data, - self.ct_norms_dev.data, - self.ct_reldists_dev.data, - self.ct_stiff_dev.data).wait() - - self.program.find_sphere_contacts(self.queue, - (self.n_cells,), - None, - numpy.int32(self.max_cells), - numpy.int32(self.max_contacts), - numpy.int32(self.n_spheres), - self.sphere_pts_dev.data, - self.sphere_coeffs_dev.data, - self.sphere_rads_dev.data, - self.sphere_norms_dev.data, - centers.data, - dirs.data, - lens.data, - self.cell_rads_dev.data, - self.cell_n_cts_dev.data, - self.ct_frs_dev.data, - self.ct_tos_dev.data, - self.ct_dists_dev.data, - self.ct_pts_dev.data, - self.ct_norms_dev.data, - self.ct_reldists_dev.data, - self.ct_stiff_dev.data).wait() - - self.program.find_contacts(self.queue, - (self.n_cells,), - None, - numpy.int32(self.max_cells), - numpy.int32(self.n_cells), - numpy.int32(self.grid_x_min), - numpy.int32(self.grid_x_max), - numpy.int32(self.grid_y_min), - numpy.int32(self.grid_y_max), - numpy.int32(self.n_sqs), - numpy.int32(self.max_contacts), - centers.data, - dirs.data, - lens.data, - self.cell_rads_dev.data, - self.cell_sqs_dev.data, - self.sorted_ids_dev.data, - self.sq_inds_dev.data, - self.cell_n_cts_dev.data, - self.ct_frs_dev.data, - self.ct_tos_dev.data, - self.ct_dists_dev.data, - self.ct_pts_dev.data, - self.ct_norms_dev.data, - self.ct_reldists_dev.data, - self.ct_stiff_dev.data, - self.ct_overlap_dev.data).wait() - - # set dtype to int32 so we don't overflow the int32 when summing - #self.n_cts = self.cell_n_cts_dev.get().sum(dtype=numpy.int32) - self.n_cts = cl_array.sum(self.cell_n_cts_dev[0:self.n_cells]).get() - - - def collect_tos(self): - """Call the collect_tos kernel. - - Assumes that cell_sqs, sorted_ids, sq_inds, cell_n_cts, - ct_frs, and ct_tos are current on the device. - - Calculates cell_tos and n_cell_tos. - """ - self.program.collect_tos(self.queue, - (self.n_cells,), - None, - numpy.int32(self.max_cells), - numpy.int32(self.n_cells), - numpy.int32(self.grid_x_min), - numpy.int32(self.grid_x_max), - numpy.int32(self.grid_y_min), - numpy.int32(self.grid_y_max), - numpy.int32(self.n_sqs), - numpy.int32(self.max_contacts), - self.cell_sqs_dev.data, - self.sorted_ids_dev.data, - self.sq_inds_dev.data, - self.cell_n_cts_dev.data, - self.ct_frs_dev.data, - self.ct_tos_dev.data, - self.cell_tos_dev.data, - self.n_cell_tos_dev.data).wait() - - - def build_matrix(self): - """Build the matrix so we can calculate M^TMx = Ax. - - Assumes cell_centers, cell_dirs, cell_lens, cell_rads, - ct_inds, ct_frs, ct_tos, ct_dists, and ct_norms are current on - the device. - - Calculates fr_ents and to_ents. - """ - self.program.build_matrix(self.queue, - (self.n_cells, self.max_contacts), - None, - numpy.int32(self.max_contacts), - self.pred_cell_centers_dev.data, - self.pred_cell_dirs_dev.data, - self.pred_cell_lens_dev.data, - self.cell_rads_dev.data, - self.cell_n_cts_dev.data, - self.ct_frs_dev.data, - self.ct_tos_dev.data, - self.ct_pts_dev.data, - self.ct_norms_dev.data, - self.fr_ents_dev.data, - self.to_ents_dev.data, - self.ct_stiff_dev.data).wait() - - - def calculate_Ax(self, Ax, x, dt, alpha): - - self.program.calculate_Bx(self.queue, - (self.n_cells, self.max_contacts), - None, - numpy.int32(self.max_contacts), - self.ct_frs_dev.data, - self.ct_tos_dev.data, - self.fr_ents_dev.data, - self.to_ents_dev.data, - x.data, - self.Mx_dev.data).wait() - self.program.calculate_BTBx(self.queue, - (self.n_cells,), - None, - numpy.int32(self.max_contacts), - self.cell_n_cts_dev.data, - self.n_cell_tos_dev.data, - self.cell_tos_dev.data, - self.fr_ents_dev.data, - self.to_ents_dev.data, - self.Mx_dev.data, - Ax.data).wait() - # Tikhonov test - #self.vaddkx(Ax, numpy.float32(0.01), Ax, x) - - # Energy mimizing regularization - self.program.calculate_Mx(self.queue, - (self.n_cells,), - None, - numpy.float32(self.muA), - numpy.float32(self.gamma), - self.cell_dirs_dev.data, - self.cell_lens_dev.data, - self.cell_rads_dev.data, - x.data, - self.Mx_dev.data).wait() - - #this was altered from dt*reg_param - #self.vaddkx(Ax, self.gamma, Ax, self.Mx_dev).wait() - #self.vaddkx(Ax, alpha, self.Mx_dev, Ax).wait() - self.vaddkx(Ax, 1/self.gamma, Ax, self.Mx_dev).wait() - # 1/math.sqrt(self.n_cells) removed from the reg_param NB - - #print(self.Minvx_dev) - - def CGSSolve(self, dt, alpha, substep=False): - # Solve A^TA\deltap=A^Tb (Ax=b) - - # There must be a way to do this using built in pyopencl - what - # is it?! - self.vclearf(self.deltap_dev[0:self.n_cells]) - self.vclearf(self.rhs_dev[0:self.n_cells]) - - # put M^T n^Tv_rel in rhs (b) - self.program.calculate_BTBx(self.queue, - (self.n_cells,), - None, - numpy.int32(self.max_contacts), - self.cell_n_cts_dev.data, - self.n_cell_tos_dev.data, - self.cell_tos_dev.data, - self.fr_ents_dev.data, - self.to_ents_dev.data, - self.ct_reldists_dev.data, - self.rhs_dev.data).wait() - - - # res = b-Ax - self.calculate_Ax(self.BTBx_dev, self.deltap_dev, dt, alpha) - self.vsub(self.res_dev[0:self.n_cells], self.rhs_dev[0:self.n_cells], self.BTBx_dev[0:self.n_cells]) - - # p = res - cl.enqueue_copy(self.queue, self.p_dev[0:self.n_cells].data, self.res_dev[0:self.n_cells].data) - - # rsold = l2norm(res) - rsold = self.vdot(self.res_dev[0:self.n_cells], self.res_dev[0:self.n_cells]).get() - rsfirst = rsold - if math.sqrt(rsold/self.n_cells) < self.cgs_tol: - if self.printing and self.frame_no%10==0: - print('% 5i'%self.frame_no + '% 6i cells % 6i cts % 6i iterations residual = %f' % (self.n_cells, - self.n_cts, 0, math.sqrt(rsold/self.n_cells))) - return (0.0, rsold) - - # iterate - # max iters = matrix dimension = 7 (dofs) * num cells - #dying=False - max_iters = self.n_cells*7 - - for iter in range(max_iters): - # Ap - self.calculate_Ax(self.Ap_dev[0:self.n_cells], self.p_dev[0:self.n_cells], dt, alpha) - - # p^TAp - pAp = self.vdot(self.p_dev[0:self.n_cells], self.Ap_dev[0:self.n_cells]).get() - - # alpha = rsold/p^TAp - alpha = numpy.float32(rsold/pAp) - - # x = x + alpha*p, x=self.disp - self.vaddkx(self.deltap_dev[0:self.n_cells], alpha, self.deltap_dev[0:self.n_cells], self.p_dev[0:self.n_cells]) - - # res = res - alpha*Ap - self.vsubkx(self.res_dev[0:self.n_cells], alpha, self.res_dev[0:self.n_cells], self.Ap_dev[0:self.n_cells]) - - # rsnew = l2norm(res) - rsnew = self.vdot(self.res_dev[0:self.n_cells], self.res_dev[0:self.n_cells]).get() - - # Test for convergence - if math.sqrt(rsnew/self.n_cells) < self.cgs_tol: - #if math.sqrt(rsnew/rsfirst) < self.cgs_tol: - break - - # Stopped converging -> terminate - #if rsnew/rsold>2.0: - # break - - # p = res + rsnew/rsold *p - self.vaddkx(self.p_dev[0:self.n_cells], numpy.float32(rsnew/rsold), self.res_dev[0:self.n_cells], self.p_dev[0:self.n_cells]) - - rsold = rsnew - #print ' ',iter,rsold - - if self.printing and self.frame_no%10==0: - print('% 5i'%self.frame_no + '% 6i cells % 6i cts % 6i iterations residual = %f' % (self.n_cells, self.n_cts, iter+1, math.sqrt(rsnew/self.n_cells))) - return (iter+1, math.sqrt(rsnew/self.n_cells)) - - - def predict(self): - """Predict cell centers, dirs, lens for a timestep dt based - on the current velocities. - - Assumes cell_centers, cell_dirs, cell_lens, cell_rads, and - cell_dcenters, cell_dangs, cell_dlens are current on the device. - - Calculates new pred_cell_centers, pred_cell_dirs, pred_cell_lens. - """ - self.program.predict(self.queue, - (self.n_cells,), - None, - self.cell_centers_dev.data, - self.cell_dirs_dev.data, - self.cell_lens_dev.data, - self.cell_dcenters_dev.data, - self.cell_dangs_dev.data, - self.cell_dlens_dev.data, - self.pred_cell_centers_dev.data, - self.pred_cell_dirs_dev.data, - self.pred_cell_lens_dev.data).wait() - - def integrate(self): - """Integrates cell centers, dirs, lens for a timestep dt based - on the current deltap. - - Assumes cell_centers, cell_dirs, cell_lens, cell_rads, and - deltap are current on the device. - - Calculates new cell_centers, cell_dirs, cell_lens. - """ - self.program.integrate(self.queue, - (self.n_cells,), - None, - self.cell_centers_dev.data, - self.cell_dirs_dev.data, - self.cell_lens_dev.data, - self.cell_dcenters_dev.data, - self.cell_dangs_dev.data, - self.cell_dlens_dev.data).wait() - - def add_impulse(self): - self.program.add_impulse(self.queue, (self.n_cells,), None, - numpy.float32(self.muA), - numpy.float32(self.gamma), - self.deltap_dev.data, - self.cell_dirs_dev.data, - self.cell_lens_dev.data, - self.cell_rads_dev.data, - self.cell_dcenters_dev.data, - self.cell_dangs_dev.data, - self.cell_target_dlens_dev.data, - self.cell_dlens_dev.data).wait() - - def divide_cell(self, i, d1i, d2i): - """Divide a cell into two equal sized daughter cells. - - Fails silently if we're out of cells. - - Assumes our local copy of cells is current. - - Calculates new cell_centers, cell_dirs, cell_lens, and cell_rads. - """ - if self.n_cells >= self.max_cells: - return - # idxs of the two new cells - a = d1i - b = d2i - - # seems to be making shallow copies without the tuple calls - parent_center = tuple(self.cell_centers[i]) - parent_dir = tuple(self.cell_dirs[i]) - parent_rad = self.cell_rads[i] - parent_len = self.cell_lens[i] - - daughter_len = parent_len/2.0 - parent_rad #- 0.025 - daughter_offset = daughter_len/2.0 + parent_rad - center_offset = tuple([parent_dir[k]*daughter_offset for k in range(4)]) - - self.cell_centers[a] = tuple([(parent_center[k] - center_offset[k]) for k in range(4)]) - self.cell_centers[b] = tuple([(parent_center[k] + center_offset[k]) for k in range(4)]) - - if not self.alternate_divisions: - cdir = numpy.array(parent_dir) - jitter = numpy.random.uniform(-0.001,0.001,3) - if not self.jitter_z: jitter[2] = 0.0 - cdir[0:3] += jitter - cdir /= numpy.linalg.norm(cdir) - self.cell_dirs[a][0] = cdir[0] - self.cell_dirs[a][1] = cdir[1] - self.cell_dirs[a][2] = cdir[2] - - cdir = numpy.array(parent_dir) - jitter = numpy.random.uniform(-0.001,0.001,3) - if not self.jitter_z: jitter[2] = 0.0 - cdir[0:3] += jitter - cdir /= numpy.linalg.norm(cdir) - self.cell_dirs[b][0] = cdir[0] - self.cell_dirs[b][1] = cdir[1] - self.cell_dirs[b][2] = cdir[2] - else: - cdir = numpy.array(parent_dir) - tmp = cdir[0] - cdir[0] = -cdir[1] - cdir[1] = tmp - self.cell_dirs[a] = cdir - self.cell_dirs[b] = cdir - - - self.cell_lens[a] = daughter_len - self.cell_lens[b] = daughter_len - self.cell_rads[a] = parent_rad - self.cell_rads[b] = parent_rad - - self.n_cells += 1 - - self.parents[b] = a - - vols = self.cell_vols_dev[0:self.n_cells].get() - daughter_vol = vols[i] / 2.0 - vols[a] = daughter_vol - vols[b] = daughter_vol - self.cell_vols_dev[0:self.n_cells].set(vols) - - # Inherit velocities from parent (conserve momentum) - parent_dlin = self.cell_dcenters[i] - self.cell_dcenters[a] = parent_dlin - self.cell_dcenters[b] = parent_dlin - parent_dang = self.cell_dangs[i] - self.cell_dangs[a] = parent_dang - self.cell_dangs[b] = parent_dang - - - #return indices of daughter cells - return (a,b) - - - def calc_cell_geom(self): - """Calculate cell geometry using lens/rads on card.""" - # swap cell vols and cell_vols old - tmp = self.cell_old_vols_dev[0:self.n_cells] - self.cell_old_vols_dev[0:self.n_cells] = self.cell_vols_dev[0:self.n_cells] - self.cell_vols_dev[0:self.n_cells] = tmp - # update geometry - self.calc_cell_area(self.cell_areas_dev[0:self.n_cells], \ - self.cell_rads_dev[0:self.n_cells], \ - self.cell_lens_dev[0:self.n_cells]) - self.calc_cell_vol(self.cell_vols_dev[0:self.n_cells], \ - self.cell_rads_dev[0:self.n_cells], \ - self.cell_lens_dev[0:self.n_cells]) - - - def profileGrid(self): - if self.n_cts==0: - return - import time - t1 = time.clock() - for i in range(1000): - # redefine gridding based on the range of cell positions - self.cell_centers = self.cell_centers_dev.get() - self.update_grid() # we assume local cell_centers is current - - # get each cell into the correct sq and retrieve from the device - self.bin_cells() - - # sort cells and find sq index starts in the list - self.cell_sqs = self.cell_sqs_dev.get() # get updated cell sqs - self.sort_cells() - self.sorted_ids_dev.set(self.sorted_ids) # push changes to the device - self.sq_inds_dev.set(self.sq_inds) - t2 = time.clock() - print("Grid stuff timing for 1000 calls, time per call (s) = %f"%((t2-t1)*0.001)) - open("grid_prof","a").write( "%i, %i, %f\n"%(self.n_cells,self.n_cts,(t2-t1)*0.001) ) - - - def profileFindCts(self): - if self.n_cts==0: - return - import time - t1 = time.clock() - dt = 0.005 - for i in range(1000): - self.n_cts = 0 - self.vcleari(self.cell_n_cts_dev) # clear the accumulated contact count - self.predict(dt) - # find all contacts - self.find_contacts(dt) - # place 'backward' contacts in cells - self.collect_tos() - - # compact the contacts so we can dispatch only enough threads - # to deal with each - self.ct_frs = self.ct_frs_dev.get() - self.ct_tos = self.ct_tos_dev.get() - self.compact_cts() - self.ct_inds_dev.set(self.ct_inds) - t2 = time.clock() - print("Find contacts timing for 1000 calls, time per call (s) = %f"%((t2-t1)*0.001)) - open("findcts_prof","a").write( "%i, %i, %f\n"%(self.n_cells,self.n_cts,(t2-t1)*0.001) ) - - def profileCGS(self): - if self.n_cts==0: - return - import time - t1 = time.clock() - dt = 0.005 - for i in range(1000): - self.build_matrix(dt) # Calculate entries of the matrix - (iters, res) = self.CGSSolve() - print("cgs prof: iters=%i, res=%f"%(iters,res)) - t2 = time.clock() - print("CGS timing for 1000 calls, time per call (s) = %f"%((t2-t1)*0.001)) - open("cgs_prof","a").write( "%i, %i, %i, %f\n"%(self.n_cells,self.n_cts,iters,(t2-t1)*0.001) ) - - diff --git a/CellModeller/Biophysics/GeneralModels/CLFixedPosition.py b/CellModeller/Biophysics/GeneralModels/CLFixedPosition.py deleted file mode 100644 index 87d6e7cf..00000000 --- a/CellModeller/Biophysics/GeneralModels/CLFixedPosition.py +++ /dev/null @@ -1,88 +0,0 @@ -import sys -import math -import numpy -import pyopencl as cl -import pyopencl.array as cl_array -from pyopencl.array import vec - -class CLFixedPosition: - def __init__(self, sim, max_cells=100): - self.simulator = sim - self.max_cells = max_cells - self.init_cl() - self.init_data() - self.n_cells = 0 - - def setRegulator(self, reg): - self.reg = reg - - def init_cl(self): - if self.simulator: - (self.context, self.queue) = self.simulator.getOpenCL() - - def init_data(self): - """Set up the data OpenCL will store on the device.""" - # cell data - cell_geom = (self.max_cells,) - self.cell_centers = numpy.zeros(cell_geom, vec.float4) - self.cell_centers_dev = cl_array.zeros(self.queue, cell_geom, vec.float4) - - # cell geometry - self.cell_areas_dev = cl_array.zeros(self.queue, cell_geom, numpy.float32) - self.cell_areas = numpy.zeros(cell_geom, numpy.float32) - self.cell_vols_dev = cl_array.zeros(self.queue, cell_geom, numpy.float32) - self.cell_vols = numpy.zeros(cell_geom, numpy.float32) - self.cell_old_vols_dev = cl_array.zeros(self.queue, cell_geom, numpy.float32) - self.cell_old_vols = numpy.zeros(cell_geom, numpy.float32) - - self.cell_growth_rates = numpy.zeros(cell_geom, numpy.float32) - self.cell_growth_rates_dev = cl_array.zeros(self.queue, cell_geom, numpy.float32) - - def addCell(self, cellState, pos=(0,0,0), vol=1, **kwargs): - i = cellState.idx - self.n_cells += 1 - cid = cellState.id - self.cell_centers[i] = tuple(pos+(0,)) - self.cell_vols[i] = vol - self.cell_old_vols[i] = vol - self.initCellState(cellState) - self.set_cells() - - def initCellState(self, state): - cid = state.id - i = state.idx - state.pos = [self.cell_centers[i][j] for j in range(3)] - state.volume = self.cell_vols[i] - state.startVol = state.volume - - def updateCellState(self, state): - cid = state.id - i = state.idx - state.volume = self.cell_vols[i] - self.cell_growth_rates[i] = state.growthRate*state.volume - - def get_cells(self): - """Copy cell centers, dirs, lens, and rads from the device.""" - self.cell_centers[0:self.n_cells] = self.cell_centers_dev[0:self.n_cells].get() - self.cell_vols[0:self.n_cells] = self.cell_vols_dev[0:self.n_cells].get() - - def set_cells(self): - """Copy cell centers, dirs, lens, and rads to the device from local.""" - self.cell_centers_dev[0:self.n_cells].set(self.cell_centers[0:self.n_cells]) - self.cell_vols_dev[0:self.n_cells].set(self.cell_vols[0:self.n_cells]) - self.cell_growth_rates_dev[0:self.n_cells].set(self.cell_growth_rates[0:self.n_cells]) - - def step(self, dt): - self.set_cells() - - # No change in positions, just growth increasing volume - self.cell_old_vols_dev[0:self.n_cells] = self.cell_vols_dev[0:self.n_cells] - self.cell_vols_dev += self.cell_growth_rates_dev * dt - - if self.simulator: - self.get_cells() - for state in list(self.simulator.cellStates.values()): - self.updateCellState(state) - - return True - diff --git a/CellModeller/Biophysics/GeneralModels/__init__.py b/CellModeller/Biophysics/GeneralModels/__init__.py deleted file mode 100644 index e69de29b..00000000 diff --git a/CellModeller/Biophysics/__init__.py b/CellModeller/Biophysics/__init__.py deleted file mode 100644 index e69de29b..00000000 diff --git a/CellModeller/GUI/__init__.py b/CellModeller/GUI/__init__.py deleted file mode 100644 index e69de29b..00000000 diff --git a/CellModeller/Integration/CLCrankNicIntegrator.cl b/CellModeller/Integration/CLCrankNicIntegrator.cl deleted file mode 100644 index f14f3b2c..00000000 --- a/CellModeller/Integration/CLCrankNicIntegrator.cl +++ /dev/null @@ -1,329 +0,0 @@ - - -void userSignalRates(float gridVolume, float area, float volume, const int cellType, float* rates, __global const float* species, __global const float* signals) -{ - %(sigKernel)s -} -void userSpecRates(float gridVolume, float area, float volume, const int cellType, __global float* rates, __global float* species, __global const float* signals) -{ - %(specKernel)s -} - -__kernel void gridCells(const float gridOrigx, - const float gridOrigy, - const float gridOrigz, - const float gridSizex, - const float gridSizey, - const float gridSizez, - const int gridDimx, - const int gridDimy, - const int gridDimz, - __global const float4* pos, - __global float* weights, - __global int* indices) -{ - int id = get_global_id(0); - int base = id*8; - int4 idx = 0; - float4 p = pos[id]; - float ix = floor((p.x - gridOrigx) / gridSizex); - float iy = floor((p.y - gridOrigy) / gridSizey); - float iz = floor((p.z - gridOrigz) / gridSizez); - idx.x = (int)(ix); - idx.y = (int)(iy); - idx.z = (int)(iz); - - - - // Indices of 8 nearest grid nodes - for (int i=0; i<2; i++) { - for (int j=0; j<2; j++) { - for (int k=0; k<2; k++) { - int4 offset = {i,j,k,0}; - int4 ind = idx + offset; - // Is the neighbourhood node in the grid? - int inGrid = (int)(ind.x>=0 && ind.x=0 && ind.y=0 && ind.z=0 && ix=0 && iy=0 && iz=0 && ix=0 && iy=-1 && iz=0 && ix=-1 && iy=0 && iz=0 && ix=-1 && iy=-1 && iz=-1 && ix=0 && iy=0 && iz=-1 && ix=0 && iy=-1 && iz=-1 && ix=-1 && iy=0 && iz=-1 && ix=-1 && iy=-1 && iz threshold - self.greensFunc.shape = self.gridDim - inds = numpy.transpose(numpy.nonzero(self.greensFunc.reshape(self.gridDim)>self.greensThreshold)) - self.greensFunc = self.greensFunc[:, min(inds[:,1]):max(inds[:,1])+1, \ - min(inds[:,2]):max(inds[:,2])+1, \ - min(inds[:,3]):max(inds[:,3])+1] - print("Truncated Green's function size is " + str(self.greensFunc.shape)) - - - def addCell(self, cellState): - idx = cellState.idx - self.nCells += 1 - cellState.species = self.specLevel[idx,:] - cellState.signals = self.cellSigLevels[idx,:] - self.celltype[idx] = numpy.int32(cellState.cellType) - - def divide(self, pState, d1State, d2State): - # Simulator should have organised indexing: - - # Set up slicing of levels for each daughter and copy parent levels - d1idx = d1State.idx - self.nCells += 1 - self.specLevel[d1idx,:] = pState.species - self.cellSigLevels[d1idx,:] = pState.signals - d1State.species = self.specLevel[d1idx,:] - d1State.signals = self.cellSigLevels[d1idx,:] - self.celltype[d1idx] = d1State.cellType - - d2idx = d2State.idx - self.nCells += 1 - self.specLevel[d2idx,:] = pState.species - self.cellSigLevels[d2idx,:] = pState.signals - d1State.species = self.specLevel[d1idx,:] - d1State.signals = self.cellSigLevels[d1idx,:] - self.celltype[d1idx] = d1State.cellType - - d2idx = d2State.idx - self.nCells += 1 - self.specLevel[d2idx,:] = pState.species - d2State.species = self.specLevel[d2idx,:] - d2State.signals = self.cellSigLevels[d2idx,:] - self.celltype[d2idx] = d2State.cellType - - def setSignalling(self, sig): - self.signalling = sig - - def setRegulator(self, regul): - self.regul = regul - # Use regulation module to setup kernels - self.initKernels() - - def initArrays(self): - self.gridIdxs = numpy.zeros((self.maxCells,8),dtype=numpy.int32) - self.gridIdxs_dev = cl_array.zeros(self.queue, (self.maxCells,8),dtype=numpy.int32) - self.triWts = numpy.zeros((self.maxCells,8),dtype=numpy.float32) - self.triWts_dev = cl_array.zeros(self.queue, (self.maxCells,8),dtype=numpy.float32) - self.cellSigRates = numpy.zeros((self.maxCells,8,self.nSignals),dtype=numpy.float32) - self.cellSigRates_dev = cl_array.zeros(self.queue, (self.maxCells,8,self.nSignals),dtype=numpy.float32) - self.cellSigLevels = numpy.zeros((self.maxCells,self.nSignals),dtype=numpy.float32) - self.cellSigLevels_dev = cl_array.zeros(self.queue, (self.maxCells,self.nSignals),dtype=numpy.float32) - self.signalLevel_dev = cl_array.zeros(self.queue, self.gridDim,dtype=numpy.float32) - self.specLevel_dev = cl_array.zeros(self.queue, (self.maxCells,self.nSpecies), dtype=numpy.float32) - self.specRate_dev = cl_array.zeros(self.queue, (self.maxCells,self.nSpecies), dtype=numpy.float32) - - self.celltype = numpy.zeros((self.maxCells,),dtype=numpy.int32) - self.celltype_dev = cl_array.zeros(self.queue, (self.maxCells,),dtype=numpy.int32) - #self.pos_dev = cl_array.zeros(self.queue, (self.maxCells,), dtype=vec.float4) - - def initKernels(self): - # Get user defined kernel source - specRateKernel = self.regul.specRateCL() - sigRateKernel = self.regul.sigRateCL() - #kernel_src = open('CellModeller/Integration/CLCrankNicIntegrator.cl', 'r').read() - from pkg_resources import resource_string - kernel_src = resource_string(__name__, 'CLCrankNicIntegrator.cl').decode() - # substitute user defined kernel code, and number of signals - kernel_src = kernel_src % {'sigKernel': sigRateKernel, - 'specKernel': specRateKernel, - 'nSignals': self.nSignals} - self.program = cl.Program(self.context, kernel_src).build(cache_dir=False) - - - def dydt(self): - # get cell grid idxs and weights - self.program.gridCells(self.queue, (self.nCells,), None, - numpy.float32(self.signalling.gridOrig[0]), - numpy.float32(self.signalling.gridOrig[1]), - numpy.float32(self.signalling.gridOrig[2]), - numpy.float32(self.signalling.gridSize[0]), - numpy.float32(self.signalling.gridSize[1]), - numpy.float32(self.signalling.gridSize[2]), - numpy.int32(self.signalling.gridDim[1]), - numpy.int32(self.signalling.gridDim[2]), - numpy.int32(self.signalling.gridDim[3]), - self.sim.phys.cell_centers_dev.data, - self.triWts_dev.data, - self.gridIdxs_dev.data).wait() - self.gridIdxs[:] = self.gridIdxs_dev.get() - - # put local cell signal levels in array - self.signalLevel_dev.set(self.signalLevel) - self.program.setCellSignals(self.queue, (self.nCells,), None, - numpy.int32(self.nSignals), - numpy.int32(self.gridTotalSize), - numpy.int32(self.signalling.gridDim[1]), - numpy.int32(self.signalling.gridDim[2]), - numpy.int32(self.signalling.gridDim[3]), - self.gridIdxs_dev.data, - self.triWts_dev.data, - self.signalLevel_dev.data, - self.cellSigLevels_dev.data).wait() - - self.celltype_dev.set(self.celltype) - # compute species rates - self.specLevel_dev.set(self.specLevel) - self.program.speciesRates(self.queue, (self.nCells,), None, - numpy.int32(self.nSignals), - numpy.int32(self.nSpecies), - numpy.float32(self.sim.sig.dV), - self.sim.phys.cell_areas_dev.data, - self.sim.phys.cell_vols_dev.data, - self.celltype_dev.data, - self.specLevel_dev.data, - self.cellSigLevels_dev.data, - self.specRate_dev.data).wait() - self.specRate[:] = self.specRate_dev.get() - - # compute signal rates, weighted for grid nodes - self.program.signalRates(self.queue, (self.nCells,), None, - numpy.int32(self.nSignals), - numpy.int32(self.nSpecies), - numpy.float32(self.sim.sig.dV), - self.sim.phys.cell_areas_dev.data, - self.sim.phys.cell_vols_dev.data, - self.celltype_dev.data, - self.specLevel_dev.data, - self.cellSigLevels_dev.data, - self.triWts_dev.data, - self.cellSigRates_dev.data).wait() - self.cellSigRates[:] = self.cellSigRates_dev.get() - - # Put cell signal production into diffusion grid: - # - Using a convoluted way to reduce by key to get cell prod rates - # into grid - gridIdxs = self.gridIdxs[0:self.nCells,:].reshape(self.nCells*8) - order = numpy.argsort(gridIdxs) - gridIdxs = gridIdxs[order] - cellSigRates = self.cellSigRates[0:self.nCells,:,:].reshape((self.nCells*8,self.nSignals)) - cellSigRates = cellSigRates[order] - cellSigRates.cumsum(axis=0, out=cellSigRates) - (u,index) = unique_stable(gridIdxs[::-1],True) # first occurance of each key in reverse keys - index = len(gridIdxs)-1-index # last occurance in forward keys - cellSigRates = cellSigRates[index] - idxs = gridIdxs[index] - cellSigRates[1:] = cellSigRates[1:] - cellSigRates[:-1] # difference in cumsums is sum for each index - - - signalRate = self.signalRate.reshape((self.nSignals,self.gridDim[1]*self.gridDim[2]*self.gridDim[3])) - signalRate[:,idxs] += cellSigRates.transpose() # add into diffusion grid - - - def step(self, dt): - if dt!=self.dt: - print("I can only integrate at fixed dt!") - return - - self.nCells = len(self.cellStates) - # Check we have enough space allocated - try: - s = self.specLevel[self.nCells-1] - except IndexError: - # Could resize here, then would have to rebuild views - print("Number of cells exceeded " \ - + self.__class__.__name__ \ - + "::maxCells (" + self.maxCells + ")") - - self.dataLen = self.signalDataLen + self.nCells*self.nSpecies - - # growth dilution of species - self.diluteSpecies() - - # Do u += h(T(u_t)/2 + hf(u_t)) where T=transport operator, f(u_t) is - # our regulation function dydt - self.signalling.transportRates(self.signalRate, self.signalLevel, self.boundcond) - self.signalRate *= 0.5 - self.dydt() - self.rates[0:self.dataLen] *= self.dt - self.levels[0:self.dataLen] += self.rates[0:self.dataLen] - - # Convolve (I+hT/2)u_t + f(u_t) with the Greens func to get u_{t+1} - sigLvl = self.signalLevel.reshape(self.gridDim) - convolve(sigLvl, self.greensFunc, mode=self.boundcond) - - # put local cell signal levels in array - self.signalLevel_dev.set(self.signalLevel) - self.program.setCellSignals(self.queue, (self.nCells,), None, - numpy.int32(self.nSignals), - numpy.int32(self.gridTotalSize), - numpy.int32(self.signalling.gridDim[1]), - numpy.int32(self.signalling.gridDim[2]), - numpy.int32(self.signalling.gridDim[3]), - self.gridIdxs_dev.data, - self.triWts_dev.data, - self.signalLevel_dev.data, - self.cellSigLevels_dev.data).wait() - self.cellSigLevels[:] = self.cellSigLevels_dev.get() - -# Put the final signal levels into the cell states -# states = self.cellStates -# for (id,c) in states.items(): -# if self.signalling: -# c.signals = self.signalling.signals(c, self.signalLevel) - - # Update cellType array - for (id,c) in list(self.cellStates.items()): - self.celltype[c.idx] = numpy.int32(c.cellType) - self.celltype_dev.set(self.celltype) - - - def diluteSpecies(self): - self.specLevel_dev.set(self.specLevel) - self.program.diluteSpecs(self.queue, (self.nCells,), None, - numpy.int32(self.nSpecies), - self.sim.phys.cell_old_vols_dev.data, - self.sim.phys.cell_vols_dev.data, - self.specLevel_dev.data).wait() - self.specLevel[:] = self.specLevel_dev.get() - - def setLevels(self, SSLevel, cellSigData): - self.cellStates = self.sim.cellStates - self.levels = SSLevel - self.makeViews() - self.cellSigLevels = cellSigData - self.signalLevel_dev.set(self.signalLevel) - self.specLevel_dev.set(self.specLevel) - self.cellSigLevels_dev.set(self.cellSigLevels) - cs = self.cellStates - for id,c in list(cs.items()): #make sure everything is correct here - c.species = self.specLevel[c.idx,:] - c.signals = self.cellSigLevels[c.idx,:] - self.celltype[c.idx] = numpy.int32(c.cellType) - self.celltype_dev.set(self.celltype) - - diff --git a/CellModeller/Integration/CLEulerIntegrator.cl b/CellModeller/Integration/CLEulerIntegrator.cl deleted file mode 100644 index c38665c7..00000000 --- a/CellModeller/Integration/CLEulerIntegrator.cl +++ /dev/null @@ -1,35 +0,0 @@ -void userSpecRates(float4 pos, float area, float volume, const int cellType, const float effGrowth, __global float* rates, __global const float* species) -{ - %s -} - -__kernel void speciesRates(const int numSpecies, - __global const float4* pos, - __global const float* areas, - __global const float* volumes, - __global const int* celltype, - __global const float* effGrow, - __global const float* cellSpecLevels, - __global float* specRate) -{ - int id = get_global_id(0); - int specbase = id*numSpecies; - int cellType = celltype[id]; - __global const float* species = cellSpecLevels+specbase; - __global float* rates = specRate+specbase; - - userSpecRates(pos[id], areas[id], volumes[id], cellType, effGrow[id], rates, species); -} - -__kernel void diluteSpecs(const int numSpecies, - __global const float* oldVols, - __global const float* vols, - __global float* specRates) -{ - int id = get_global_id(0); - float factor = oldVols[id]/vols[id]; - int base = id*numSpecies; - for (int i = 0; i < numSpecies; i++) { - specRates[base+i] = specRates[base+i]*factor; - } -} diff --git a/CellModeller/Integration/CLEulerIntegrator.py b/CellModeller/Integration/CLEulerIntegrator.py deleted file mode 100644 index 3db4d153..00000000 --- a/CellModeller/Integration/CLEulerIntegrator.py +++ /dev/null @@ -1,176 +0,0 @@ -import numpy -import scipy.integrate.odepack -import pyopencl as cl -import pyopencl.array as cl_array -from pyopencl.array import vec -import math - -class CLEulerIntegrator: - #Simple forward Euler integration of species rates - - def __init__(self, sim, nSpecies, maxCells, regul=None): - self.sim = sim - self.dt = self.sim.dt - self.regul = regul - - self.cellStates = sim.cellStates - self.nCells = len(self.cellStates) - - self.nSpecies = nSpecies - self.maxCells = maxCells - - self.maxSpecDataLen = self.maxCells*nSpecies - # no need to scale up signal storage - storageLen = self.maxSpecDataLen - - # These arrays store the level and rate of signals and species - # in a contiguous form. - # To avoid reallocation, create enough space for maxCells - self.levels = numpy.zeros(storageLen,dtype=numpy.float32) - self.rates = numpy.zeros(storageLen,dtype=numpy.float32) - self.makeViews() - - (self.context, self.queue) = self.sim.getOpenCL() - self.initArrays() - #self.initKernels() - - # set the species for existing states to views of the levels array - cs = self.cellStates - for id,c in list(cs.items()): - c.species = self.specLevel[c.idx,:] - - - def makeViews(self): - # Level views (references) to the data - self.specLevel = self.levels[0:self.maxSpecDataLen].reshape(self.maxCells,self.nSpecies) - # Rate views (references) to the data - self.specRate = self.rates[0:self.maxSpecDataLen].reshape(self.maxCells,self.nSpecies) - - def addCell(self, cellState): - idx = cellState.idx - self.nCells += 1 - cellState.species = self.specLevel[idx,:] - self.celltype[idx] = numpy.int32(cellState.cellType) - - def divide(self, pState, d1State, d2State): - # Simulator should have organised indexing: - - # Set up slicing of levels for each daughter and copy parent levels - d1idx = d1State.idx - self.nCells += 1 - self.specLevel[d1idx,:] = pState.species - d1State.species = self.specLevel[d1idx,:] - self.celltype[d1idx] = d1State.cellType - - d2idx = d2State.idx - self.nCells += 1 - self.specLevel[d2idx,:] = pState.species - d1State.species = self.specLevel[d1idx,:] - self.celltype[d1idx] = d1State.cellType - - d2idx = d2State.idx - self.nCells += 1 - self.specLevel[d2idx,:] = pState.species - d2State.species = self.specLevel[d2idx,:] - self.celltype[d2idx] = d2State.cellType - - def setRegulator(self, regul): - self.regul = regul - # Use regulation module to setup kernels - self.initKernels() - - def initArrays(self): - self.specLevel_dev = cl_array.zeros(self.queue, (self.maxCells,self.nSpecies), dtype=numpy.float32) - self.specRate_dev = cl_array.zeros(self.queue, (self.maxCells,self.nSpecies), dtype=numpy.float32) - - self.celltype = numpy.zeros((self.maxCells,), dtype=numpy.int32) - self.celltype_dev = cl_array.zeros(self.queue, (self.maxCells,),dtype=numpy.int32) - - self.effgrow = numpy.zeros((self.maxCells,), dtype=numpy.float32) - self.effgrow_dev = cl_array.zeros(self.queue, (self.maxCells,), dtype=numpy.float32) - - #self.pos_dev = cl_array.zeros(self.queue, (self.maxCells,), dtype=vec.float4) - - def initKernels(self): - # Get user defined kernel source - specRateKernel = self.regul.specRateCL() - from pkg_resources import resource_string - kernel_src = resource_string(__name__, 'CLEulerIntegrator.cl').decode() - # substitute user defined kernel code, and number of signals - kernel_src = kernel_src%(specRateKernel) - self.program = cl.Program(self.context, kernel_src).build(cache_dir=False) - - - def dydt(self): - self.celltype_dev.set(self.celltype) - # compute species rates - self.specLevel_dev.set(self.specLevel) - self.program.speciesRates(self.queue, (self.nCells,), None, - numpy.int32(self.nSpecies), - self.sim.phys.cell_centers_dev.data, - self.sim.phys.cell_areas_dev.data, - self.sim.phys.cell_vols_dev.data, - self.celltype_dev.data, - self.effgrow_dev.data, - self.specLevel_dev.data, - self.specRate_dev.data).wait() - self.specRate[:] = self.specRate_dev.get() - - def step(self, dt): - if dt!=self.dt: - print("I can only integrate at fixed dt!") - return - - self.nCells = len(self.cellStates) - # Check we have enough space allocated - try: - s = self.specLevel[self.nCells-1] - except IndexError: - # Could resize here, then would have to rebuild views - print("Number of cells exceeded " \ - + self.__class__.__name__ \ - + "::maxCells (" + self.maxCells + ")") - - self.dataLen = self.nCells*self.nSpecies - - self.cellStates = self.sim.cellStates - cs = self.cellStates - for id,c in list(cs.items()): - self.effgrow[c.idx] = numpy.float32(c.effGrowth) - self.effgrow_dev.set(self.effgrow) - - # growth dilution of species - self.diluteSpecies() - - self.dydt() - self.rates[0:self.dataLen] *= self.dt - self.levels[0:self.dataLen] += self.rates[0:self.dataLen] - - -# Put the final signal levels into the cell states -# states = self.cellStates -# for (id,c) in states.items(): -# if self.signalling: -# c.signals = self.signalling.signals(c, self.signalLevel) - - def setLevels(self, specLevel): - self.cellStates = self.sim.cellStates - self.levels = specLevel - self.makeViews() - self.specLevel_dev.set(self.specLevel) - cs = self.cellStates - for id,c in list(cs.items()): - c.species = self.specLevel[c.idx,:] - self.celltype[c.idx] = numpy.int32(c.cellType) - self.celltype_dev.set(self.celltype) - - - def diluteSpecies(self): - self.specLevel_dev.set(self.specLevel) - self.program.diluteSpecs(self.queue, (self.nCells,), None, - numpy.int32(self.nSpecies), - self.sim.phys.cell_old_vols_dev.data, - self.sim.phys.cell_vols_dev.data, - self.specLevel_dev.data).wait() - self.specLevel[:] = self.specLevel_dev.get() - diff --git a/CellModeller/Integration/CLEulerSigIntegrator.cl b/CellModeller/Integration/CLEulerSigIntegrator.cl deleted file mode 100644 index f14f3b2c..00000000 --- a/CellModeller/Integration/CLEulerSigIntegrator.cl +++ /dev/null @@ -1,329 +0,0 @@ - - -void userSignalRates(float gridVolume, float area, float volume, const int cellType, float* rates, __global const float* species, __global const float* signals) -{ - %(sigKernel)s -} -void userSpecRates(float gridVolume, float area, float volume, const int cellType, __global float* rates, __global float* species, __global const float* signals) -{ - %(specKernel)s -} - -__kernel void gridCells(const float gridOrigx, - const float gridOrigy, - const float gridOrigz, - const float gridSizex, - const float gridSizey, - const float gridSizez, - const int gridDimx, - const int gridDimy, - const int gridDimz, - __global const float4* pos, - __global float* weights, - __global int* indices) -{ - int id = get_global_id(0); - int base = id*8; - int4 idx = 0; - float4 p = pos[id]; - float ix = floor((p.x - gridOrigx) / gridSizex); - float iy = floor((p.y - gridOrigy) / gridSizey); - float iz = floor((p.z - gridOrigz) / gridSizez); - idx.x = (int)(ix); - idx.y = (int)(iy); - idx.z = (int)(iz); - - - - // Indices of 8 nearest grid nodes - for (int i=0; i<2; i++) { - for (int j=0; j<2; j++) { - for (int k=0; k<2; k++) { - int4 offset = {i,j,k,0}; - int4 ind = idx + offset; - // Is the neighbourhood node in the grid? - int inGrid = (int)(ind.x>=0 && ind.x=0 && ind.y=0 && ind.z=0 && ix=0 && iy=0 && iz=0 && ix=0 && iy=-1 && iz=0 && ix=-1 && iy=0 && iz=0 && ix=-1 && iy=-1 && iz=-1 && ix=0 && iy=0 && iz=-1 && ix=0 && iy=-1 && iz=-1 && ix=-1 && iy=0 && iz=-1 && ix=-1 && iy=-1 && iz0: - print("Errors in reading SBML file...") - checkSBMLConsistency(document) - model = document.getModel() + print("Errors in reading SBML file...") + checkSBMLConsistency(document) + model = document.getModel() if not model: - print("No model!") - return model + print("No model!") + return model # load SBML model form given string. @@ -124,7 +124,7 @@ def pythonMathFromASTNode(astNode, kineticLaw, model): return "1" else: - raise Exception("Un-supported AST node type: " + str(astNode.isName()) + ", node: " + str(astNode.getType())) + raise Exception("Un-supported AST node type: " + str(astNode.isName()) + ", node: " + str(astNode.getType())) # constructs a python program string from given SBML model. diff --git a/CellModeller/Signalling/GridDiffusion.py b/CellModeller/Signalling/GridDiffusion.py deleted file mode 100644 index f863e897..00000000 --- a/CellModeller/Signalling/GridDiffusion.py +++ /dev/null @@ -1,163 +0,0 @@ -from math import floor -import numpy -from scipy.ndimage import laplace -from scipy.ndimage.filters import convolve -from functools import reduce - - -class GridDiffusion: - """ GridDiffusion: - Signal levels/rates on the grid are stored by the Integrator, and this class writes -into that array data. - 1. rates() computes the \Del^2 transport operator for grid based diffusion. - 2. signals() returns the local signal level for a given cell, and given signal -level array. - - Other transport models can be implemented by replacing the rates() function with -something else - e.g. a bulk flow term. -""" - def __init__(self, sim, nSignals, gridDim, gridSize, gridOrig, D, adv=None, initLevels=None, regul=None): - # Data organisation - self.gridDim = (nSignals,) + gridDim - self.gridDataLen = reduce(lambda x, y: x * y, self.gridDim) - - self.gridSize = gridSize - self.gridOrig = numpy.array(gridOrig) - assert gridSize[0]==gridSize[1]==gridSize[2] - - # Scale diffusion/advection rates by gridSize - h = gridSize[0] - self.diffRates = [d/(h**2) for d in D] - self.advRates = [a/h for a in adv] if adv else None - self.nSignals = nSignals - - # Initial signal level - homogeneous distribution - self.initLevels = initLevels - - # This is the volume of the grid element. It should really be used - # to calc local concentration to a cell. Need to go through and make - # everything consistent. - self.dV = reduce(lambda x, y: x * y, self.gridSize) - - self.regul = regul - self.setCellStates(sim.cellStates) - - def setCellStates(self, cs): - self.cellStates = cs - - def setBiophysics(self, biophysics): - self.biophys = biophysics - - def setRegulator(self, regul): - self.regul = regul - - def flattenIdx(self, idx): - print("idx = " + str(idx)) - print("flat idx = " + str(idx[2] + idx[1]*self.gridDim[3] + idx[0]*self.gridDim[2]*self.gridDim[3])) - return idx[2] + idx[1]*self.gridDim[3] + idx[0]*self.gridDim[2]*self.gridDim[3] - - def idxFromPos(self, p): - return ( floor((p[0] - self.gridOrig[0]) / self.gridSize[0]), \ - floor((p[1] - self.gridOrig[1]) / self.gridSize[1]), \ - floor((p[2] - self.gridOrig[2]) / self.gridSize[2]) ) - - def trilinearWeights(self, p): - x = (p[0] - self.gridOrig[0]) / self.gridSize[0] - dx = x - floor(x) - y = (p[1] - self.gridOrig[1]) / self.gridSize[1] - dy = y - floor(y) - z = (p[2] - self.gridOrig[2]) / self.gridSize[2] - dz = z - floor(z) - w = numpy.zeros((2,2,2)) - - # Calculate weights, giving zero if grid point is off grid - w[0,0,0] = (1-dx)*(1-dy)*(1-dz) if x>=0 and x=0 and y=0 and z=-1 and x=0 and y=0 and z=0 and x=-1 and y=0 and z=-1 and x=-1 and y=0 and z=0 and x=0 and y=-1 and z=-1 and x=0 and y=-1 and z=0 and x=-1 and y=-1 and z=-1 and x=-1 and y=-1 and z PyGLCMViewer QWidget -
CellModeller.GUI.PyGLCMViewer
+
CellModeller.gui.py_gl_cm_viewer
setSavePicklesToggle(bool) load() diff --git a/CellModeller/GUI/PyGLWidget.py b/CellModeller/gui/py_gl_widget.py similarity index 100% rename from CellModeller/GUI/PyGLWidget.py rename to CellModeller/gui/py_gl_widget.py diff --git a/CellModeller/GUI/Renderers.py b/CellModeller/gui/renderers.py similarity index 99% rename from CellModeller/GUI/Renderers.py rename to CellModeller/gui/renderers.py index f5dc3128..7935e57e 100644 --- a/CellModeller/GUI/Renderers.py +++ b/CellModeller/gui/renderers.py @@ -191,7 +191,7 @@ def render_gl(self, selection=None): glDisable(GL_TEXTURE_2D) class GLPlantSignalRenderer: - # Render signals as chanels rgb + # Render signals as channels rgb def __init__(self, sim, chanIdx): self.sim = sim self.wallcol = [0, 0, 0] diff --git a/CellModeller/Simulator.py b/CellModeller/simulator.py similarity index 98% rename from CellModeller/Simulator.py rename to CellModeller/simulator.py index c2b5eeb3..57ca5ac4 100644 --- a/CellModeller/Simulator.py +++ b/CellModeller/simulator.py @@ -1,4 +1,4 @@ -from .CellState import CellState +from .cell_state import CellState import copy import pyopencl as cl import sys @@ -166,7 +166,7 @@ def next_idx(self): # and have the user-defined func initialise the 3 modules ## Specify models to be used by simulator object. The four inputs are - # 'phys' = physical model of cell iteractions + # 'phys' = physical model of cell interactions # 'reg' = regulatory model of biochemical circuit in the cell # 'sig' = signaling model of intercellular chemical reaction diffusion. # 'integ' = integrator @@ -191,7 +191,7 @@ def init(self, phys, reg, sig, integ): self.reg.setSignalling(sig) - ## Set up the OpenCL contex, the configuration is set up the first time, and is saved in the config file + ## Set up the OpenCL context, the configuration is set up the first time, and is saved in the config file def init_cl(self, platnum, devnum): # Check that specified platform exists platforms = cl.get_platforms() @@ -378,10 +378,10 @@ def importCells_file(self, filename): for row in list: cpos = [float(row[0]),float(row[1]),float(row[2])] cdir = [float(row[3]),float(row[4]),float(row[5])] - clen = float(row[6]) #radius should be removed from this in the analysis + cell_len = float(row[6]) #radius should be removed from this in the analysis ndir = cdir/numpy.linalg.norm(cdir) #normalize cell dir just in case #this should probably also check for overlaps - self.addCell(pos=tuple(cpos), dir=tuple(ndir), length=clen) + self.addCell(pos=tuple(cpos), dir=tuple(ndir), length=cell_len) ## Write current simulation state to an output file def writePickle(self, csv=False): diff --git a/Community/contributing.md b/Community/contributing.md index 106868e5..01027608 100644 --- a/Community/contributing.md +++ b/Community/contributing.md @@ -10,13 +10,13 @@ Write yout first issue [Here](https://github.com/cellmodeller/CellModeller/issue ## Fork and Pull Request For people that may want to change the code to solve a bug or add a new feature for example we suggest to fork the project, implement the changes and make a pull request. -If you fork the project and adapt it to your usage we strongly reccommend to make a pull request to implement this usage for other users. +If you fork the project and adapt it to your usage we strongly recommend to make a pull request to implement this usage for other users. ## New Branch and Pull Request For recurrent contributors we will add them to the organization and provide authorization to edit. To contribute make a new branch, if you dont know which branch use as base create one from master, implement your changes and make a pull request. -With this we avoid that the project diverge from forks and incentivate a culture of continuous contribution. +With this we avoid that the project diverge from forks and incentivize a culture of continuous contribution. ## General Open Source Guite to Contribute diff --git a/CondaRecipes/appdirs/bld.bat b/CondaRecipes/appdirs/bld.bat deleted file mode 100644 index 87b1481d..00000000 --- a/CondaRecipes/appdirs/bld.bat +++ /dev/null @@ -1,8 +0,0 @@ -"%PYTHON%" setup.py install -if errorlevel 1 exit 1 - -:: Add more build steps here, if they are necessary. - -:: See -:: http://docs.continuum.io/conda/build.html -:: for a list of environment variables that are set during the build process. diff --git a/CondaRecipes/appdirs/build.sh b/CondaRecipes/appdirs/build.sh deleted file mode 100644 index 4d7fc032..00000000 --- a/CondaRecipes/appdirs/build.sh +++ /dev/null @@ -1,9 +0,0 @@ -#!/bin/bash - -$PYTHON setup.py install - -# Add more build steps here, if they are necessary. - -# See -# http://docs.continuum.io/conda/build.html -# for a list of environment variables that are set during the build process. diff --git a/CondaRecipes/appdirs/meta.yaml b/CondaRecipes/appdirs/meta.yaml deleted file mode 100644 index e6c3d6fe..00000000 --- a/CondaRecipes/appdirs/meta.yaml +++ /dev/null @@ -1,60 +0,0 @@ -package: - name: appdirs - version: !!str 1.4.0 - -source: - fn: appdirs-1.4.0.tar.gz - url: https://pypi.python.org/packages/source/a/appdirs/appdirs-1.4.0.tar.gz - md5: 1d17b4c9694ab84794e228f28dc3275b -# patches: - # List any patch files here - # - fix.patch - -# build: - # preserve_egg_dir: True - # entry_points: - # Put any entry points (scripts to be generated automatically) here. The - # syntax is module:function. For example - # - # - appdirs = appdirs:main - # - # Would create an entry point called appdirs that calls appdirs.main() - - - # If this is a new build for the same version, increment the build - # number. If you do not include this key, it defaults to 0. - # number: 1 - -requirements: - build: - - python 2 - - setuptools - - run: - - python 2 - -test: - # Python imports - imports: - - appdirs - - # commands: - # You can put test commands to be run here. Use this to test that the - # entry points work. - - - # You can also put a file called run_test.py in the recipe that will be run - # at test time. - - # requires: - # Put any additional test requirements here. For example - # - nose - -about: - home: http://github.com/ActiveState/appdirs - license: MIT License - summary: 'A small Python module for determining appropriate " + "platform-specific dirs, e.g. a "user data dir".' - -# See -# http://docs.continuum.io/conda/build.html for -# more information about meta.yaml diff --git a/CondaRecipes/cellmodeller/bld.bat b/CondaRecipes/cellmodeller/bld.bat deleted file mode 100644 index 87b1481d..00000000 --- a/CondaRecipes/cellmodeller/bld.bat +++ /dev/null @@ -1,8 +0,0 @@ -"%PYTHON%" setup.py install -if errorlevel 1 exit 1 - -:: Add more build steps here, if they are necessary. - -:: See -:: http://docs.continuum.io/conda/build.html -:: for a list of environment variables that are set during the build process. diff --git a/CondaRecipes/cellmodeller/build.sh b/CondaRecipes/cellmodeller/build.sh deleted file mode 100644 index 2e8b221a..00000000 --- a/CondaRecipes/cellmodeller/build.sh +++ /dev/null @@ -1,10 +0,0 @@ -#!/bin/bash - -$PYTHON setup.py install - -# Add more build steps here, if they are necessary. - - -# See -# http://docs.continuum.io/conda/build.html -# for a list of environment variables that are set during the build process. diff --git a/CondaRecipes/cellmodeller/meta.yaml b/CondaRecipes/cellmodeller/meta.yaml deleted file mode 100644 index 4dec2631..00000000 --- a/CondaRecipes/cellmodeller/meta.yaml +++ /dev/null @@ -1,84 +0,0 @@ -package: - name: cellmodeller - version: !!str "4.3.1" - -source: - git_url: http://github.com/HaseloffLab/CellModeller.git - git_tag: v4.3.1 -# patches: - # List any patch files here - # - fix.patch - -#build: - # preserve_egg_dir: True -# entry_points: - # Put any entry points (scripts to be generated automatically) here. The - # syntax is module:function. For example - # - # - pyopencl = pyopencl:main - # - # Would create an entry point called pyopencl that calls pyopencl.main() -# - cellmodeller = CellModeller:GUI:CellModellerGUI:main -# - cmbatch = CellModeller:batch:main - - - # If this is a new build for the same version, increment the build - # number. If you do not include this key, it defaults to 0. - # number: 1 - -requirements: - build: - - python 2 - - numpy 1.9.2 - - setuptools - - scipy - - pyqt 4 - - pyopengl - - pyopencl 2014.1 - - reportlab - - matplotlib - - mock - - nose - - run: - - python 2 - - numpy 1.9.2 - - setuptools - - scipy - - pyqt 4 - - pyopengl - - pyopencl 2014.1 - - reportlab - - matplotlib - - mock - -test: - # Python imports - imports: - - CellModeller - - CellModeller.Biophysics - - CellModeller.Regulation - - CellModeller.Signalling - - CellModeller.Integration - -# commands: - # You can put test commands to be run here. Use this to test that the - # entry points work. -# - cellmodeller -# - cmbatch - - # You can also put a file called run_test.py in the recipe that will be run - # at test time. - - # requires: - # Put any additional test requirements here. For example - # - nose - -about: - home: http://www.cellmodeller.org - license: BSD License - summary: 'Multicellular modelling framework' - -# See -# http://docs.continuum.io/conda/build.html for -# more information about meta.yaml diff --git a/CondaRecipes/cellmodeller_dev/bld.bat b/CondaRecipes/cellmodeller_dev/bld.bat deleted file mode 100644 index 87b1481d..00000000 --- a/CondaRecipes/cellmodeller_dev/bld.bat +++ /dev/null @@ -1,8 +0,0 @@ -"%PYTHON%" setup.py install -if errorlevel 1 exit 1 - -:: Add more build steps here, if they are necessary. - -:: See -:: http://docs.continuum.io/conda/build.html -:: for a list of environment variables that are set during the build process. diff --git a/CondaRecipes/cellmodeller_dev/build.sh b/CondaRecipes/cellmodeller_dev/build.sh deleted file mode 100644 index 0f82cf5f..00000000 --- a/CondaRecipes/cellmodeller_dev/build.sh +++ /dev/null @@ -1,11 +0,0 @@ -#!/bin/bash - -THIS_DIR="`dirname $0`" - -echo Installing CellModeller python package -$PYTHON setup.py install - - -# See -# http://docs.continuum.io/conda/build.html -# for a list of environment variables that are set during the build process. diff --git a/CondaRecipes/cellmodeller_dev/meta.yaml b/CondaRecipes/cellmodeller_dev/meta.yaml deleted file mode 100644 index 79d6c428..00000000 --- a/CondaRecipes/cellmodeller_dev/meta.yaml +++ /dev/null @@ -1,79 +0,0 @@ -package: - name: cellmodeller_dev - version: !!str 4.0 - -source: - git_url: http://github.com/HaseloffLab/CellModeller4_private.git -#git@github.com:HaseloffLab/CellModeller4_private.git -# patches: - # List any patch files here - # - fix.patch - -#build: - # preserve_egg_dir: True -# entry_points: - # Put any entry points (scripts to be generated automatically) here. The - # syntax is module:function. For example - # - # - pyopencl = pyopencl:main - # - # Would create an entry point called pyopencl that calls pyopencl.main() -# - cellmodeller = CellModeller.GUI.CellModellerGUI:launch -# - cmbatch = CellModeller.batch:main - - - # If this is a new build for the same version, increment the build - # number. If you do not include this key, it defaults to 0. - # number: 1 - -requirements: - build: - - python - - setuptools - - numpy - - scipy - - pyqt - - pyopengl - - pyopencl - - run: - - python - - setuptools - - numpy - - scipy - - pyqt - - pyopengl - - pyopencl - - reportlab - -test: - # Python imports - imports: - - CellModeller - - CellModeller.Biophysics - - CellModeller.Regulation - - CellModeller.Signalling - - CellModeller.Integration - -# commands: - # You can put test commands to be run here. Use this to test that the - # entry points work. -# - cellmodeller -# - cmbatch - - - # You can also put a file called run_test.py in the recipe that will be run - # at test time. - - # requires: - # Put any additional test requirements here. For example - # - nose - -about: - home: http://www.cellmodeller.org - license: BSD License - summary: 'Multicellular modelling framework' - -# See -# http://docs.continuum.io/conda/build.html for -# more information about meta.yaml diff --git a/CondaRecipes/mako/bld.bat b/CondaRecipes/mako/bld.bat deleted file mode 100644 index 87b1481d..00000000 --- a/CondaRecipes/mako/bld.bat +++ /dev/null @@ -1,8 +0,0 @@ -"%PYTHON%" setup.py install -if errorlevel 1 exit 1 - -:: Add more build steps here, if they are necessary. - -:: See -:: http://docs.continuum.io/conda/build.html -:: for a list of environment variables that are set during the build process. diff --git a/CondaRecipes/mako/build.sh b/CondaRecipes/mako/build.sh deleted file mode 100644 index 4d7fc032..00000000 --- a/CondaRecipes/mako/build.sh +++ /dev/null @@ -1,9 +0,0 @@ -#!/bin/bash - -$PYTHON setup.py install - -# Add more build steps here, if they are necessary. - -# See -# http://docs.continuum.io/conda/build.html -# for a list of environment variables that are set during the build process. diff --git a/CondaRecipes/mako/meta.yaml b/CondaRecipes/mako/meta.yaml deleted file mode 100644 index 1d0579b3..00000000 --- a/CondaRecipes/mako/meta.yaml +++ /dev/null @@ -1,66 +0,0 @@ -package: - name: mako - version: !!str 1.0.1 - -source: - fn: Mako-1.0.1.tar.gz - url: https://pypi.python.org/packages/source/M/Mako/Mako-1.0.1.tar.gz - md5: 9f0aafd177b039ef67b90ea350497a54 -# patches: - # List any patch files here - # - fix.patch - -build: - preserve_egg_dir: True - entry_points: - # Put any entry points (scripts to be generated automatically) here. The - # syntax is module:function. For example - # - # - mako = mako:main - # - # Would create an entry point called mako that calls mako.main() - - - mako-render=mako.cmd:cmdline - - # If this is a new build for the same version, increment the build - # number. If you do not include this key, it defaults to 0. - # number: 1 - -requirements: - build: - - python 2 - - setuptools - - markupsafe >=0.9.2 - - run: - - python 2 - - setuptools - - markupsafe >=0.9.2 - -test: - # Python imports - imports: - - mako - - mako.ext - - commands: - # You can put test commands to be run here. Use this to test that the - # entry points work. - - - mako-render --help - - # You can also put a file called run_test.py in the recipe that will be run - # at test time. - - # requires: - # Put any additional test requirements here. For example - # - nose - -about: - home: http://www.makotemplates.org/ - license: MIT - summary: 'A super-fast templating language that borrows the best ideas from the existing templating languages.' - -# See -# http://docs.continuum.io/conda/build.html for -# more information about meta.yaml diff --git a/CondaRecipes/pyopencl/bld.bat b/CondaRecipes/pyopencl/bld.bat deleted file mode 100644 index 87b1481d..00000000 --- a/CondaRecipes/pyopencl/bld.bat +++ /dev/null @@ -1,8 +0,0 @@ -"%PYTHON%" setup.py install -if errorlevel 1 exit 1 - -:: Add more build steps here, if they are necessary. - -:: See -:: http://docs.continuum.io/conda/build.html -:: for a list of environment variables that are set during the build process. diff --git a/CondaRecipes/pyopencl/build.sh b/CondaRecipes/pyopencl/build.sh deleted file mode 100644 index 9f635d9b..00000000 --- a/CondaRecipes/pyopencl/build.sh +++ /dev/null @@ -1,15 +0,0 @@ -#!/bin/bash - -git checkout tags/v2014.1 -git submodule init -git submodule update -$PYTHON configure.py -$PYTHON setup.py build -make -$PYTHON setup.py install - -# Add more build steps here, if they are necessary. - -# See -# http://docs.continuum.io/conda/build.html -# for a list of environment variables that are set during the build process. diff --git a/CondaRecipes/pyopencl/meta.yaml b/CondaRecipes/pyopencl/meta.yaml deleted file mode 100644 index 2160ee6d..00000000 --- a/CondaRecipes/pyopencl/meta.yaml +++ /dev/null @@ -1,75 +0,0 @@ -package: - name: pyopencl - version: !!str 2014.1 - -source: -# fn: pyopencl-2014.1.tar.gz -# url: https://pypi.python.org/packages/source/p/pyopencl/pyopencl-2014.1.tar.gz -# md5: f89d26676aaff01312116caea114f06c - git_url: http://git.tiker.net/trees/pyopencl.git - git_tag: v2014.1 -# patches: - # List any patch files here - # - fix.patch - -# build: - # preserve_egg_dir: True - # entry_points: - # Put any entry points (scripts to be generated automatically) here. The - # syntax is module:function. For example - # - # - pyopencl = pyopencl:main - # - # Would create an entry point called pyopencl that calls pyopencl.main() - - - # If this is a new build for the same version, increment the build - # number. If you do not include this key, it defaults to 0. - # number: 1 - -requirements: - build: - - python 2 - - setuptools - - pytools 2014.3.5 - - pytest - - decorator - - mako - - numpy 1.9.2 - - run: - - python 2 - - setuptools - - pytools 2014.3.5 - - pytest - - decorator - - mako - - numpy 1.9.2 - -#test: - # Python imports - #imports: - # - pyopencl - # - pyopencl.characterize - # - pyopencl.compyte - - # commands: - # You can put test commands to be run here. Use this to test that the - # entry points work. - - - # You can also put a file called run_test.py in the recipe that will be run - # at test time. - - # requires: - # Put any additional test requirements here. For example - # - nose - -about: - home: http://mathema.tician.de/software/pyopencl - license: MIT License - summary: 'Python wrapper for OpenCL' - -# See -# http://docs.continuum.io/conda/build.html for -# more information about meta.yaml diff --git a/CondaRecipes/pyopengl/bld.bat b/CondaRecipes/pyopengl/bld.bat deleted file mode 100755 index 2d6c912c..00000000 --- a/CondaRecipes/pyopengl/bld.bat +++ /dev/null @@ -1,2 +0,0 @@ -python setup.py install -if errorlevel 1 exit 1 diff --git a/CondaRecipes/pyopengl/build.sh b/CondaRecipes/pyopengl/build.sh deleted file mode 100755 index 6308b482..00000000 --- a/CondaRecipes/pyopengl/build.sh +++ /dev/null @@ -1,11 +0,0 @@ -#!/bin/bash - -touch requirements.txt; - -${PYTHON} setup.py install || exit 1; - -mkdir -vp ${PREFIX}/bin; - -#POST_LINK="${PREFIX}/bin/.pyopengl-post-link.sh" -#cp -v ${RECIPE_DIR}/post-link.sh ${POST_LINK}; -#chmod -v 0755 ${POST_LINK}; diff --git a/CondaRecipes/pyopengl/meta.yaml b/CondaRecipes/pyopengl/meta.yaml deleted file mode 100644 index a54e484a..00000000 --- a/CondaRecipes/pyopengl/meta.yaml +++ /dev/null @@ -1,31 +0,0 @@ - -package: - name: pyopengl - version: 3.0.2 - -source: - fn: PyOpenGL-3.0.2.tar.gz - url: https://pypi.python.org/packages/source/P/PyOpenGL/PyOpenGL-3.0.2.tar.gz - md5: 77becc24ffc0a6b28030aa109ad7ff8b - -build: - number: 0 - -requirements: - build: - - python - - distribute - - numpy - - run: - - python - - numpy - -test: - imports: - - OpenGL - -about: - home: http://pyopengl.sourceforge.net/ - license: BSD - diff --git a/CondaRecipes/pyopengl/post-link.sh b/CondaRecipes/pyopengl/post-link.sh deleted file mode 100755 index ea6fdabc..00000000 --- a/CondaRecipes/pyopengl/post-link.sh +++ /dev/null @@ -1,5 +0,0 @@ -#!/bin/bash - -cat <> ${PREFIX}/.messages.txt -This is an install message from the pyopengl package. -EOF diff --git a/CondaRecipes/pytools/bld.bat b/CondaRecipes/pytools/bld.bat deleted file mode 100644 index 87b1481d..00000000 --- a/CondaRecipes/pytools/bld.bat +++ /dev/null @@ -1,8 +0,0 @@ -"%PYTHON%" setup.py install -if errorlevel 1 exit 1 - -:: Add more build steps here, if they are necessary. - -:: See -:: http://docs.continuum.io/conda/build.html -:: for a list of environment variables that are set during the build process. diff --git a/CondaRecipes/pytools/build.sh b/CondaRecipes/pytools/build.sh deleted file mode 100644 index 4d7fc032..00000000 --- a/CondaRecipes/pytools/build.sh +++ /dev/null @@ -1,9 +0,0 @@ -#!/bin/bash - -$PYTHON setup.py install - -# Add more build steps here, if they are necessary. - -# See -# http://docs.continuum.io/conda/build.html -# for a list of environment variables that are set during the build process. diff --git a/CondaRecipes/pytools/meta.yaml b/CondaRecipes/pytools/meta.yaml deleted file mode 100644 index 1d507c58..00000000 --- a/CondaRecipes/pytools/meta.yaml +++ /dev/null @@ -1,66 +0,0 @@ -package: - name: pytools - version: !!str 2014.3.5 - -source: - fn: pytools-2014.3.5.tar.gz - url: https://pypi.python.org/packages/source/p/pytools/pytools-2014.3.5.tar.gz - md5: 7f8e9d6a88090a601e96a9ee095d3512 -# patches: - # List any patch files here - # - fix.patch - -# build: - # preserve_egg_dir: True - # entry_points: - # Put any entry points (scripts to be generated automatically) here. The - # syntax is module:function. For example - # - # - pytools = pytools:main - # - # Would create an entry point called pytools that calls pytools.main() - - - # If this is a new build for the same version, increment the build - # number. If you do not include this key, it defaults to 0. - # number: 1 - -requirements: - build: - - python 2 - - setuptools - - decorator >=3.2.0 - - appdirs >=1.4.0 - - six - - run: - - python 2 - - decorator >=3.2.0 - - appdirs >=1.4.0 - - six - -test: - # Python imports - imports: - - pytools - - # commands: - # You can put test commands to be run here. Use this to test that the - # entry points work. - - - # You can also put a file called run_test.py in the recipe that will be run - # at test time. - - # requires: - # Put any additional test requirements here. For example - # - nose - -about: - home: http://pypi.python.org/pypi/pytools - license: MIT License - summary: 'A collection of tools for Python' - -# See -# http://docs.continuum.io/conda/build.html for -# more information about meta.yaml diff --git a/Doc/BacterialBiophysics/BacterialBiophysics.pdf b/Doc/BacterialBiophysics/BacterialBiophysics.pdf deleted file mode 100644 index db10c9d2..00000000 Binary files a/Doc/BacterialBiophysics/BacterialBiophysics.pdf and /dev/null differ diff --git a/Doc/BacterialBiophysics/BacterialBiophysics.tex b/Doc/BacterialBiophysics/BacterialBiophysics.tex deleted file mode 100644 index 1888be8b..00000000 --- a/Doc/BacterialBiophysics/BacterialBiophysics.tex +++ /dev/null @@ -1,355 +0,0 @@ -\documentclass{report} - -\usepackage{amsmath} -\usepackage{mathtools} - -\usepackage{tikz} -\usetikzlibrary{shapes} - -\renewcommand{\vec}[1]{\mathbf{#1}} -\let\oldhat\hat -\renewcommand{\hat}[1]{\oldhat{\mathbf{#1}}} - -\newcommand{\deltav}{\Delta \vec{v}} -\newcommand{\deltap}{\Delta \vec{p}} -\newcommand{\deltaL}{\Delta \vec{L}} -\newcommand{\deltag}{\Delta g} -\newcommand{\MInv}{\mathbf{M}^{-1}} -\newcommand{\IInv}{\mathbf{I}^{-1}} -\newcommand{\nT}{\hat{n}^\textrm{T}} -\newcommand{\w}{\boldsymbol{\omega}} -\newcommand{\rx}{{\left[\vec{r}\right]}_\times} - -\begin{document} - - -\begin{figure} -\begin{tikzpicture} - -\node[name=A, shape=rounded rectangle, minimum width=3cm, minimum height=0.75cm, rotate=45, anchor=-12.12, very thick, draw] at (-0.05cm,0) {A}; -\node[name=B, shape=rounded rectangle, minimum width=4cm, minimum height=0.75cm, rotate=0, anchor=west, very thick, draw] at (0.05cm,0) {B}; - -\end{tikzpicture} -\end{figure} - -The velocity of a point with position $\vec{r}$ relative to the center -of mass of a cell with its main axis along the unit vector $\hat{a}$ -is: - -\begin{align*} -\vec{v_r} &= \vec{v}_\textrm{linear} + \vec{v}_\textrm{angular} + \vec{v}_\textrm{growth} \\ -&= \vec{v} + \vec{\w} \times \vec{r} + \frac{1}{2} \frac{\hat{a} \cdot \vec{r}}{l} v_{growth} \\ -&= \vec{v} - \vec{r} \times \vec{\w} + \frac{1}{2} \frac{\hat{a} \cdot \vec{r}}{l} v_{growth} \\ -&= \frac{1}{m}\vec{p} - \vec{r} \times \IInv\vec{L} + \frac{1}{2} \frac{\hat{a} \cdot \vec{r}}{l} \frac{g}{G} \\ -&= \frac{1}{m}\vec{p} - \rx \IInv\vec{L} + \frac{1}{2} \frac{\hat{a} \cdot \vec{r}}{l} \frac{g}{G} \\ -\end{align*} - -This expression is linear in $\vec{p}$, $\vec{L}$, and $g$, so the -velocity of the point after an impulse $\deltap$ is: - -\begin{align*} -\vec{v_r} &= \vec{v_r}_0 + \deltav \\ -&= \vec{v_r}_0 + \frac{1}{m}\deltap - \rx\IInv\deltaL \times \vec{r} + \frac{1}{2} \frac{\hat{x} \cdot \vec{r}}{l} \frac{\deltag}{G} \\ -&= \vec{v_r}_0 + \vec{M}_{\hat{a},{\vec{r}}} \deltap -\end{align*} - -\dots where: - -\[ -\vec{M}_{\hat{a},{\vec{r}}} -= -\left[ -\begin{array}{ccc} -\frac{1}{m}I & \rx\IInv & \frac{\hat{a}\cdot\vec{r}}{2lG}\hat{a}\\ -\end{array} -\right] -\] - -\dots and: - -\[ -\deltap -= -\left[ -\begin{array}{c} -\deltap \\ -\deltaL \\ -\deltag \\ -\end{array} -\right] -= -\left[ -\begin{array}{c} -\Delta p_x \\ -\Delta p_y \\ -\Delta p_z \\ -\Delta L_x \\ -\Delta L_y \\ -\Delta L_z \\ -\deltag \\ -\end{array} -\right] -\] - -In the above, $I$ is the identity matrix and $\IInv$ is the inverse -inertia tensor. No confusion should arise from the use of $\deltap$ -to signify both general momentum and specifically linear momentum. - -The inertia tensor for a rod of mass $m$, radius $r$, and length $l$ -centered at the origin and lying along the $x$ axis is: -\[ -\mathbf{I} -= -\frac{1}{12}m -\left[ -\begin{array}{ccc} -6r^2 & 0 & 0 \\ -0 & 3r^2 + l^2 & 0 \\ -0 & 0 & 3r^2 + l^2 \\ -\end{array} -\right] -\] - -Therefore the inverse inertia tensor for the same cylinder is: -\[ -\IInv -= -\frac{12}{m} -\left[ -\begin{array}{ccc} -\frac{1}{6r^2} & 0 & 0 \\ -0 & \frac{1}{3r^2+l^2} & 0 \\ -0 & 0 & \frac{1}{3r^2+l^2} \\ -\end{array} -\right] -\] - -Suppose $\mathbf{T}_i$ transforms from world coordinates to local -coordinates for cell $i$ --- i.e. it transforms the $x$ axis to the -main axis of that cell. Then the inverse inertia tensor for cell $i$ -in world coordinates is given by: - -\[\IInv_i = \mathbf{T}_i \IInv_\textrm{cyl} \mathbf{T}_i^{-1}\] - -So we now have: - -\[ -\vec{M}_{\hat{a},{\vec{r}}} -= -\left[ -\begin{array}{ccc} -\frac{1}{m}I & -\rx \mathbf{T}_i \IInv_\textrm{cyl} \mathbf{T}_i^{-1} & -\frac{\hat{a}\cdot\vec{r}}{2lG}\hat{a}\\ -\end{array} -\right] -\] - - -We assume that colliding capsules --- those that overlap and are -moving toward each other (the dot product of the velocity vectors of -the contact points on the two capsules is negative) --- collide -inelastically. In this case, the relative velocity of the two contact -points along the normal $\hat{n}$ after the impulse provided by the -collision must be zero. So: - -\begin{align*} -\nT\left(\vec{v}_{\vec{r}_a} - \vec{v}_{\vec{r}_b}\right) \cdot &= 0 \\ -\nT \vec{M}_{\vec{r}_a} \vec{p}_a - \nT \vec{M}_{\vec{r}_b} \vec{p}_b &= 0 \\ -\nT \vec{M}_{\vec{r}_a} \left( \vec{p}_{a_0} + \deltap_a \right) - \nT \vec{M}_{\vec{r}_b} \left( \vec{p}_{b_0} + \deltap_b \right) &= 0 \\ -\nT \vec{M}_{\vec{r}_a} \deltap_a - \nT \vec{M}_{\vec{r}_b} \deltap_b &= \nT \vec{M}_{\vec{r}_b} \vec{p}_{b_0} - \nT \vec{M}_{\vec{r}_a} \vec{p}_{a_0} \\ -\nT \vec{M}_{\vec{r}_a} \deltap_a - \nT \vec{M}_{\vec{r}_b} \deltap_b &= \nT \vec{v}_{b_0} - \nT \vec{v}_{a_0} \\ -\nT \vec{M}_{\vec{r}_a} \deltap_a - \nT \vec{M}_{\vec{r}_b} \deltap_b &= \nT \vec{v}_{\textrm{rel}_{a,b}} \\ -\end{align*} - -Write: - -\begin{align*} -\vec{N}_{\hat{a},{\vec{r}}} -&= -\left[ -\begin{array}{ccc} -\nT \frac{1}{m}I & -\nT \rx \mathbf{T}_i \IInv_\textrm{cyl} \mathbf{T}_i^{-1} & -\nT \frac{\hat{a}\cdot\vec{r}}{2lG}\hat{a}\\ -\end{array} -\right] \\ -&= -\left[ -\begin{array}{ccc} -\frac{1}{m} \hat{n} & -\nT \rx \mathbf{T}_i \IInv_\textrm{cyl} \mathbf{T}_i^{-1} & -\frac{1}{2lG}\left(\hat{a}\cdot\vec{r}\right)\left(\hat{a}\cdot\hat{n}\right)\\ -\end{array} -\right] \\ -\end{align*} - -This is a $1\times7$ matrix which when multiplied by the $7\times1$ -matrix $\deltap$ gives a change in velocity along the normal $\hat{n}$. - - - -In block matrix form, we can write: - -\[ -\left[ -\begin{array}{cc} -\nT\vec{M}_{\vec{r}_a} & -\nT\vec{M}_{\vec{r}_b} \\ -\end{array} -\right] -\left[ -\begin{array}{c} -\deltap_a \\ -\deltap_b \\ -\end{array} -\right] -= -\nT\vec{v}_{\textrm{rel}_{a,b}} -\] - -More generally, we will have a system of equations with one such -equation for each pair of colliding cells. We build a larger block -matrix with a row for each constraint and a column for each cell in -the system. If the $i$th constraint involves cells $a$ and $b$ (in -that order), then: - -\[\vec{M}_{ij} = \left\{ -\begin{array}{ll} -\nT\vec{M}_{\vec{r}_a} & \textrm{if } j=a \\ --\nT\vec{M}_{\vec{r}_b} & \textrm{if } j=b \\ -0 & \textrm{otherwise} \\ -\end{array} -\right\}\] - - -A sytem with four cells and four collisions might have the equation: - -\[ -\left[ -\begin{array}{cccc} -\vec{M}_{\vec{r}_{1a}} & -\vec{M}_{\vec{r}_{1b}} & 0 & 0 \\ -0 & \vec{M}_{\vec{r}_{2b}} & -\vec{M}_{\vec{r}_{2c}} & 0 \\ -\vec{M}_{\vec{r}_{3a}} & 0 & 0 & -\vec{M}_{\vec{r}_{3d}} \\ -0 & 0 & \vec{M}_{\vec{r}_{4c}} & -\vec{M}_{\vec{r}_{4d}} \\ -\end{array} -\right] -\left[ -\begin{array}{c} -\deltap_a \\ -\deltap_b \\ -\deltap_c \\ -\deltap_d \\ -\end{array} -\right] -= -\left[ -\begin{array}{c} -\vec{v}_{\textrm{rel}_{a,b}} \\ -\vec{v}_{\textrm{rel}_{b,c}} \\ -\vec{v}_{\textrm{rel}_{a,d}} \\ -\vec{v}_{\textrm{rel}_{c,d}} \\ -\end{array} -\right] -\] - - -We can transform this into a square matrix by multiplying by $\vec{M}^\textrm{T}$. - -\[ -\vec{M}^\textrm{T} \vec{M} \deltap = \vec{M}^\textrm{T} \vec{v}_{\textrm{rel}} -\] - -Consider $\vec{A} = \vec{M}^\textrm{T} \vec{M}$. We have: - -\[ -\vec{A}_{ij} = \sum_{k} \vec{M}^\textrm{T}_{ik} \vec{M}_{kj} -\] - -\dots where $k \in \textrm{constraints}$. - -If $i \neq j$ and there is no constraint between cells $i$ and $j$ -then ${\vec{M}^\textrm{T}}_{ik} \vec{M}_{kj}$ will be zero. If there -is a constraint between $i$ and $j$, then: - -\[ -\vec{A}_{ij} = -\vec{M}^\textrm{T}_{\vec{r}_{ik}} \vec{M}_{\vec{r}_{jk}} -\] - -\dots where $\vec{r}_{ik}$ is the vector from the center of cell $i$ -to the point on the surface of that cell associated with contact $k$. - -If $i=j$, then: - -\[ -\vec{A}_{ii} = \sum_k{\vec{M}^\textrm{T}_{\vec{r}_{ik}}\vec{M}_{\vec{r}_{ik}}} -\] - -\dots where $k$ ranges over all constraints involving cell $i$. - -In general: - -\[ -\vec{M}_\vec{s}^\textrm{T} \vec{M}_\vec{r} -= -\begin{bmatrix*} -\frac{1}{M_1M_2} & 0 & 0 & 0 & \frac{\vec{s}_z}{I_2} & -\frac{\vec{s}_y}{I_2} & \frac{{\vec{a}_\vec{s}}_x}{2l_2G_2} \\[6pt] -0 & \frac{1}{M_1M_2} & 0 & -\frac{\vec{s}_z}{I_2} & 0 & \frac{\vec{s}_x}{I_2} & \frac{{\vec{a}_\vec{s}}_y}{2l_2G_2} \\[6pt] -0 & 0 & \frac{1}{M_1M_2} & \frac{\vec{s}_y}{I_2} & -\frac{\vec{s}_x}{I_2} & 0 & \frac{{\vec{a}_\vec{s}}_z}{2l_2G_2} \\[6pt] -0 & -\frac{\vec{r}_z}{I_1} & \frac{\vec{r}_y}{I_1} & \frac{\vec{r}_y\vec{s}_y + \vec{r}_z\vec{s}_z}{I_1I_2} & -\frac{\vec{r}_y\vec{s}_x}{I_1I_2} & -\frac{\vec{r}_z\vec{s}_x}{I_1I_2} & \frac{\vec{r}_y{\vec{a}_\vec{s}}_z}{2I_1l_2G_2} \\[6pt] -\frac{\vec{r}_z}{I_1} & 0 & -\frac{\vec{r}_x}{I_1} & -\frac{\vec{r}_x\vec{s}_y}{I_1I_2} & \frac{\vec{r}_x\vec{s}_x + \vec{r}_z\vec{s}_z}{I_1I_2} & -\frac{\vec{r}_z\vec{s}_y}{I_1I_2} & \frac{\vec{r}_z{\vec{a}_\vec{s}}_x}{2I_1l_2G_2} \\[6pt] --\frac{\vec{r}_y}{I_1} & \frac{\vec{r}_x}{I_1} & 0 & -\frac{\vec{r}_x\vec{s}_z}{I_1I_2} & -\frac{\vec{r}_y\vec{s}_z}{I_1I_2} & \frac{\vec{r}_y\vec{s}_y + \vec{r}_z\vec{s}_z}{I_1I_2} & \frac{\vec{r}_x{\vec{a}_\vec{s}}_y}{2I_1l_2G_2} \\[6pt] -\frac{{\vec{a}_\vec{r}}_x}{2l_1G_1} & \frac{{\vec{a}_\vec{r}}_y}{2l_1G_1} & \frac{{\vec{a}_\vec{r}}_z}{2l_1G_1} & -\frac{\vec{s}_y{\vec{a}_\vec{r}}_z - \vec{s}_z{\vec{a}_\vec{r}}_y}{2I_2l_1G_1} & -\frac{\vec{s}_z{\vec{a}_\vec{r}}_x - \vec{s}_x{\vec{a}_\vec{r}}_z}{2I_2l_1G_1} & -\frac{\vec{s}_x{\vec{a}_\vec{r}}_y - \vec{s}_y{\vec{a}_\vec{r}}_x}{2I_2l_1G_1} & -\frac{\vec{a}_\vec{r} \cdot \vec{a}_\vec{s}}{4l_1l_2G_1G_2} \\ -\end{bmatrix*} -\] - -\dots and: - -\[ -\vec{M}_\vec{r}^\textrm{T} \vec{M}_\vec{r} -= -\begin{bmatrix*} -\frac{1}{M_1^2} & 0 & 0 & 0 & \frac{\vec{r}_z}{I_1} & -\frac{\vec{r}_y}{I_1} & \frac{{\vec{a}_\vec{r}}_x}{2l_1G_1} \\ -0 & \frac{1}{M_1^2} & 0 & -\frac{\vec{r}_z}{I_1} & 0 & \frac{\vec{r}_x}{I_1} & \frac{{\vec{a}_\vec{r}}_y}{2l_1G_1} \\ -0 & 0 & \frac{1}{M_1^2} & \frac{\vec{r}_y}{I_1} & -\frac{\vec{r}_x}{I_1} & 0 & \frac{{\vec{a}_\vec{r}}_z}{2l_1G_1} \\ -0 & -\frac{\vec{r}_z}{I_1} & \frac{\vec{r}_y}{I_1} & \frac{\vec{r}_y^2 + \vec{r}_z^2}{I_1^2} & -\frac{\vec{r}_y\vec{r}_x}{I_1^2} & -\frac{\vec{r}_z\vec{r}_x}{I_1^2} & \frac{\vec{r}_y{\vec{a}_\vec{r}}_z}{2I_1l_1G_1} \\ -\frac{\vec{r}_z}{I_1} & 0 & -\frac{\vec{r}_x}{I_1} & -\frac{\vec{r}_x\vec{r}_y}{I_1^2} & \frac{\vec{r}_x^2 + \vec{r}_z^2}{I_1^2} & -\frac{\vec{r}_z\vec{r}_y}{I_1^2} & \frac{\vec{r}_z{\vec{a}_\vec{s}}_x}{2I_1l_1G_1} \\ --\frac{\vec{r}_y}{I_1} & \frac{\vec{r}_x}{I_1} & 0 & -\frac{\vec{r}_x\vec{r}_z}{I_1^2} & -\frac{\vec{r}_y\vec{r}_z}{I_1^2} & \frac{\vec{r}_y^2 + \vec{r}_z^2}{I_1^2} & \frac{\vec{r}_x{\vec{a}_\vec{r}}_y}{2I_1l_1G_1} \\ -\frac{{\vec{a}_\vec{r}}_x}{2l_1G_1} & \frac{{\vec{a}_\vec{r}}_y}{2l_1G_1} & \frac{{\vec{a}_\vec{r}}_z}{2l_1G_1} & -\frac{\vec{r}_y{\vec{a}_\vec{r}}_z - \vec{r}_z{\vec{a}_\vec{r}}_y}{2I_1l_1G_1} & -\frac{\vec{r}_z{\vec{a}_\vec{r}}_x - \vec{r}_x{\vec{a}_\vec{r}}_z}{2I_1l_1G_1} & -\frac{\vec{r}_x{\vec{a}_\vec{r}}_y - \vec{r}_y{\vec{a}_\vec{r}}_x}{2I_1l_1G_1} & -\frac{\vec{a}_\vec{r} \cdot \vec{a}_\vec{r}}{4l_1^2G_1^2} \\ -\end{bmatrix*} -\] - -\dots where: - -\begin{align*} -\vec{a}_\vec{r} &= \left(\hat{x}_1 \cdot \vec{r}\right) \vec{r} \\ -\vec{a}_\vec{s} &= \left(\hat{x}_2 \cdot \vec{s}\right) \vec{s} \\ -\end{align*} - -So we are left with the equation: - -\[ -\vec{A}\deltap = \deltav -\] - -\dots where: - -\[ -\vec{A}_{ij} = \left\{ - \begin{array}{ll} - \vec{M}^\textrm{T}_i\vec{M}_i & \textrm{if } i = j \\ - -\vec{M}^\textrm{T}_i\vec{M}_j & \textrm{if cell } i \textrm{ and cell } j \textrm{ are colliding} \\ - \end{array}\right\} -\] - - - - -\end{document} diff --git a/Doc/Maths/cellforces.pdf b/Doc/Maths/cellforces.pdf deleted file mode 100644 index 6e7126d9..00000000 Binary files a/Doc/Maths/cellforces.pdf and /dev/null differ diff --git a/Doc/Maths/celloverlap.ai b/Doc/Maths/celloverlap.ai deleted file mode 100644 index beaba9f6..00000000 --- a/Doc/Maths/celloverlap.ai +++ /dev/null @@ -1,1658 +0,0 @@ -%PDF-1.5 % -1 0 obj <>/OCGs[7 0 R 44 0 R]>>/Pages 3 0 R/Type/Catalog>> endobj 2 0 obj <>stream - - - - - application/pdf - - - cellforces - - - - - 2014-03-07T21:11:18Z - 2014-03-07T21:11:18Z - 2014-03-07T17:08:10Z - Adobe Illustrator CS6 (Macintosh) - - - - 256 - 136 - JPEG - /9j/4AAQSkZJRgABAgEASABIAAD/7QAsUGhvdG9zaG9wIDMuMAA4QklNA+0AAAAAABAASAAAAAEA AQBIAAAAAQAB/+4ADkFkb2JlAGTAAAAAAf/bAIQABgQEBAUEBgUFBgkGBQYJCwgGBggLDAoKCwoK DBAMDAwMDAwQDA4PEA8ODBMTFBQTExwbGxscHx8fHx8fHx8fHwEHBwcNDA0YEBAYGhURFRofHx8f Hx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8f/8AAEQgAiAEAAwER AAIRAQMRAf/EAaIAAAAHAQEBAQEAAAAAAAAAAAQFAwIGAQAHCAkKCwEAAgIDAQEBAQEAAAAAAAAA AQACAwQFBgcICQoLEAACAQMDAgQCBgcDBAIGAnMBAgMRBAAFIRIxQVEGE2EicYEUMpGhBxWxQiPB UtHhMxZi8CRygvElQzRTkqKyY3PCNUQnk6OzNhdUZHTD0uIIJoMJChgZhJRFRqS0VtNVKBry4/PE 1OT0ZXWFlaW1xdXl9WZ2hpamtsbW5vY3R1dnd4eXp7fH1+f3OEhYaHiImKi4yNjo+Ck5SVlpeYmZ qbnJ2en5KjpKWmp6ipqqusra6voRAAICAQIDBQUEBQYECAMDbQEAAhEDBCESMUEFURNhIgZxgZEy obHwFMHR4SNCFVJicvEzJDRDghaSUyWiY7LCB3PSNeJEgxdUkwgJChgZJjZFGidkdFU38qOzwygp 0+PzhJSktMTU5PRldYWVpbXF1eX1RlZmdoaWprbG1ub2R1dnd4eXp7fH1+f3OEhYaHiImKi4yNjo +DlJWWl5iZmpucnZ6fkqOkpaanqKmqq6ytrq+v/aAAwDAQACEQMRAD8A715n8z3P1mTTdNkMJi2u 7sULBiK+nHWorQ/E3boN+irFJLO3lYvOnryHrJNWVz/sn5HCqLsr3UrA1sLuSFf98sfUiP8AsHqB /saYqyCx89yrRNTszTvcWtWX5mJvjH+xLYFZHp2saZqKFrK5Sfj9tVNHX/WQ0ZfpGKozFXYq7FXY q7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXktnI0tsk7msk49aQ+ Lynm34thVWxQ7FXYqseGNnWQikqbpKpKup/yWWjD6MVTWx8z6/ZUX1lvoR/uq52entKor/wStjSW Q2PnjSJqJeB9PlO377+6r7SrVB/sqYFZBHJHIivGwdGFVZTUEexGKt4q7FXYq7FXYqkeh+dfLmuX mo22l3S3A0v0jdXCkej++DFOD1owola9KUIqDirUvnnyrH5qsvKrajGdd1C3ku7SzWrFoYiQx5Cq g/C1BXfi3hiqEk/MzybFfajZTXkkM2klxqJltrmNYTG0a7s8ahlb1lKMtVYVINAcVZFZXlte2cF5 ayCa1uY0mglXo8cihlYexBriqD0nzLoerXV7aaddrcXOnOsd9EAytEz8uIYMB14GmKquk6vZapBL Nak/uJ5rWdGFGSa3kMcisN+61HiKEbHFUbirsVdirsVdirsVdirsVdirsVdirsVdirzHUtPfS9Tm sHFIyzSWbHo8LGoA90rxP9uFVHFDsVdirsVdirsVbtXubJy9hPJZsTUiI/AT/lRmqH6VxSn1j541 CGi6hbLcp3ntvgf6YnPE/Q4+WClZJpvmLR9SPC1uVM/U271jlH+wejfT0xVMcVdiqCjKXd3dB45V S2ra0ZiIpRIiSMyqDRqcuPI7ghgO9VWAP+Wx0SFNPspLrUtCv4ktNXjkW3eaGy020lFjFb0SPkQ4 RKsrsxpUjfFUYPyl0fSK6poclwNVsVSfToXMRha4toL+OAOipHUE6pJy+IVou4oaqqusflu3mCM3 NzevpM+q2NvD5ht7WKE/WJYJEmTmzB1K/wB5HIpU81IWoUEMqhdIg8/6zez6F5u0uKXy0JtRhkuW 9NHuIIriM6dIRDJsWiBZuKip24rx+JVR1TRvP/lO11CPyeG1y51cajqE11fLblo770wbWL4GtKrJ 9gMxYII1XiAahVmXljQG0iHUDLIJLnUr+51CcrXipmakaLWn2YkRSe5qcVTnFXYq7FXYq7FXYq7F XYq7FXYq7FXYq7FUJqelWGp231e8iEiA8kapDI38yMN1PyxVit95H1CGrafcrdIOkNx8En0SIOJ+ lR88bVILpLiycR38Elo5NAZRRCf8mQVRvoOFXYodiqjerdNZXC2jiO7aNxbuwqqyFTwJG+wbFWK/ l5p/mGzhuBrEN/C7Q2yt+kL9L71LlEIuJYVUymJHYjb1KHsid1WYYq7FUHq17pNjZNd6rNDbWcRX lPOyoilmCr8TUp8RGKpxY67rlhQW92ZoR/ui6rKtPZ6iQf8ABEe2NJT63/MLTI4y2rRPYBacphWa GpNBRkHMVPimBWQaWrLp1sGufrj+mpe7FKSsRUuKEihPQA7Yqp3jRz3ttZLcPFKh+tyxx1BeKM0C s4pxDSMpp+0AR0riqOxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KrZI45EaOR Q8bCjIwBBB7EHFWP3/kfSJqvZltPlO/7neKvvE1Vp/q0xVj995Y1+yq3orfQj/dtts9PeJjX/gWb DapUk0bO0YNJU2eJgVdT/lK1GH04oX4q7FXYqx/zl5d0nWrSyOrvEunadcm8uEuEV4XX6vNBR+RC qFM/Pkf5fpxVR8gXMh0NdPm1G31STTeNtFd27xsZYI0VIpXCPLQycSdziqaaxfC3a3jaFbhZGLek aFi8dGj4gnaj0bmdlp40xVU0HX/MNncehHdJa2ty21vGgcRybmoaSv2u9FG+KU9tdZ8zM800moj9 4wELJFASYlHw8m4b1Ysw8K4FRH6a8xf9XJv+RUP/ADRirv015i/6uTf8iof+aMVd+mvMX/Vyb/kV D/zRirv015i/6uTf8iof+aMVd+mvMX/Vyb/kVD/zRirv015i/wCrk3/IqH/mjFXfprzF/wBXJv8A kVD/AM0Yq79NeYv+rk3/ACKh/wCaMVd+mvMX/Vyb/kVD/wA0YqiLbzVrtuwM4ivof2lC+jL/ALFg Sh+RA+eKsr03UrTUbRLq1flG2zKdmRh1Rx2YYqisVdirsVdirsVdirsVdirsVdirsVdiqD1HR9M1 FAt7bJPx+wzCjr/quKMv0HFWOX3kSRavpl4fa3uquvyEq/GPpDYqx69s9R0+v6QtZIEHWcfvIf8A kYtQv+yphVSVlZQykMp6EbjFDeKsE80wad5VigfQ/q+nX+r34VUaUwRl3Uc347x8UVOR5KQOw5MA VKjpEusPqOpalPKmrJPKY7MqEhnS0iJWMBa+m4duTcuS1rX2ChMJ/MWlRXFjbTS+hd3l3BbwW0pM MrO8ig8A1OXEVNVqPDFWd28EVvBHbwrwihRY40HQKooB92Kr8VdirsVYhp3nyRtdvNMv7CdIF1Rt Ms9SiRPq/P0FlSOSspm5tv8AEI+HQVrirL8VdiqQea/NdtoE2jxykV1K9S2YEE8Yip5ybdAjFKn3 xSxPyZdeavLOo2Ok+ZDc38vmJIro3E09vIYL8o5voURGDeilIyvEcBU0NSFKr0vFDsVTHyrctb66 YAaQ30TFk7erFQq30pyB+QwJZtirsVdirsVdirsVdirsVdirsVdirsVdirsVdiqSah5O0S8ZpEiN ncNuZrY+mSfFkoY2+lcVY9feT9ctatblNQiHZaRTf8Cx4N/wQ+WG1YzqpT0zZzH6nfTVjgFxHR1c qTyVHG5UAkdsVYT5W8m6X5UvJrOC4mmeOCKCAzFCWgDM6EBFXfm7A0+ffFCaa7pN7dafc3lpbPda pp600+zj4pJHcylOM/qOVClI2PJQeXBj0JGKpz5b8yaa31LQ2uri51VIXWd7lP3he24LN6jpWLny k3Csd6jqDirJMVdirsVSOPyT5aj1ltYW2f6805uzynuGh+sGP0vW+rmQwepw+ENwqO2Kp1J6tF9P jXkOXKv2a70p3xVL9Q1OWxST1fTeWQ0soEDF3p15Dbp49MVYr5j1rzV6mkz2trZKsNwzXUUnqTSP GLeX1FjC8RyZa8RvvTFKN0PzkdX06HUZbaO3SZibK5kDGMLyKVYkBk5U+Fvskd8VZUPrfrJ/d+hx /efa5cv8ntTFCn/uT+r/AO6PrHL/AC+HH9dcVTTyxb3lx5laRQhtrGBmVviqJpQFRW7fZ5nb2wJZ h/uY9GL/AHn9bkfW+3x412496/PFVHU9SfTLW8vr6e2trGBC8c0pYUIFfj8fYLucVR1tcRXFtFcR OJIpkWSN16MrCoIr4g4qlp83+VF0qTV31myTSopmtpb97iJIFmST0jG0rMEDc/hpXriqIs9e0S9l 9G0v7eeblIvpRyoz1hdo5PhBr8LoQfliqIu72zs4fWvJ47aGoHqTOsa1PQVYgYqsutSsbWCO4nmV IJpIoo5eqF53EcQ5Db43dVHuRiqJxV2KuxV2KuxV2KuxV2KuxV2KoO60+C8uFF5bwXFtEA0IlTmw lPJWNGHEDjQDvufpVS7UvKGizwhrWCHT7qGphuoI0QrXqGAC8kPcYqxi30HzPbwhrrTUe4lo872b xleRAFCJGRiVUBa79PDFUNB5TeC9e+h8vmO9kLM9wqQCQmSnM8g9fi4iuKo39G61/wBWy4/5Jf8A NeFXfo3Wv+rZcf8AJL/mvFXfo3Wv+rZcf8kv+a8Vd+jda/6tlx/yS/5rxVLtXuNQ02NBJp0xuZqi 3grECxHUmjmijucVSBLTVBNJcXFpNcXci8nlX0wu3SKMM4oB2/E4qkXm5pDb6ba32mXJt9RuTbXC rLDE0ccsMkZZmWZTT4/2T+OxVSp/IHmhdZWaK4vH0O1mt3g0uVw54QihSN/rFKMa8ua/ZPHFD0Xy 2NbkiayGl3U31YgCQNAeEbryQPWUEkbr8IPTFKdJpHmidGI0uS1UMFJkktnkKn9pEWbgf9m64FZf pNnHpiCxt7Sb0+PqyXjtEfUlIFeVH58z/q8ew2xVEC+ujAkn6OuA7vxaHlb80H87H1ePH5MT7Yqx T8yPJ935usPqkStA9kLj0muIobm2n+tWsls3GEzxH1IxMWjZyoB26HFUk8teX9c8zR2t5fXU2lJo E402G1iFyiXUVmVPqujtBTmSU3VgQOQ2NAqoeVvJQ8l3+meR47ePU9D1Uw313cJDLaLBPpdlaxiU CINFznurJZmBkDMZDWvEl1UPJ5c8w/l/CfNk1pB5jfR7RdL03TLC2k+uei8/D1hMCR6sq8HmJiPH jwUndmVRp0nXPzI8rXF1OTpEl5cC2uNOvFuZrV7OB+TBbeT6q8Mkv920g3KVpxLfCql03mXzh5ui fySfLn6LieV7Wa/KTwRJDaXKUntw8apQRL8CczVuhoN1XsuKuxV2KuxV2KuxV2KuxV2KuxV2KrJ4 IbiF4Z0WSGQcXjYVVgeoIOKr8VdirsVdirsVSvXtet9Jt1JX1ruaq2tqpozsO5/lVf2mxVhX+kTX El5eSetezf3knRVUdI4x+yi/2nCq7FDG/Onl291lLB4Xt2g0+b63NaXEDTeu0Y5RICroVAccqftE Cu1QVUH5I86a35gumjv9GfTES2SVjIJlb1S3EqPUjjBU7keA69dlXp/kiJi2o3X+63kSBD4mFSWI /wBlJT6MCWUYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYqlev a9b6TbqSvrXc1VtbVTRnYdz/ACqv7TYqwn/SJriS8vJPWvZv7yToqqOkcY/ZRf7TvhVfih2KuxVU sbG71S7NpaHgiU+tXVKiIHsPGQ9h26n3Us8sbG2sbOK0tl4QwrxQdT4kk9yTuTgVXxV2KuxV2Kux V2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KpXr2vW+k26kr613NVbW1U0Z2Hc/y qv7TYqwn/SJriS8vJPWvZv7yToqqOkcY/ZRf7TvhVfih2KuxVUsbG71S7NpaHgiU+tXVKiIHsPGQ 9h26n3Us70/T7TT7RLW1ThEn0kk9WY92Pc4FRGKuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2Kux V2KuxV2KuxV2KuxV2KuxVK9e1630m3UlfWu5qra2qmjOw7n+VV/abFWE/wCkTXEl5eSetezf3knR VUdI4x+yi/2nfCq/FDznyLZ/mJb+bbuXXLW5i0ieK4HOa9W7UzCdXhcJ6zCNfSZlURRJ0+JehxV6 NiqpY2N3ql2bS0PBEp9auqVEQPYeMh7Dt1PupZ3p+n2mn2iWtqnCJPpJJ6sx7se5wKiMVdirsVdi rsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdiqWa7rsGlQKSvrXc1RbWwNC5HUk /sov7TfxxVhTGea4ku7t/Wu5f7ySlAAOiIP2UXsPpO+FW8UOxV2KqljY3eqXZtLQ8ESn1q6pURA9 h4yHsO3U+6lnen6faafaJa2qcIk+kknqzHux7nAqIxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2Ku xV2KuxV2KuxV2KuxV2KuxV2KpZruuwaVApK+tdzVFtbA0LkdST+yi/tN/HFWFM0808l3dyetdzf3 knQADoiD9lF7D+OFW8UOxV2KqljY3eqXZtLQ8ESn1q6pURA9h4yHsO3U+6lnen6faafaJa2qcIk+ kknqzHux7nAqIxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2Kqdzc RW1vLcSmkUKNJIfBVFT+AxV5yJri7mfULre6uaMR2jT9iJfZR95qcKr8UOxV2KqljY3eqXZtLQ8E Sn1q6pURA9h4yHsO3U+6lnen6faafaJa2qcIk+kknqzHux7nAqIxV2KuxV2KuxV2KuxV2KuxV2Ku xV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxVAeYIZJ9B1KGIcpJbWdEXxZo2AGKsFikSWJJENUd Qyn2IrhQuxV2KqljY3eqXZtLQ8ESn1q6pURA9h4yHsO3U+6lnen6faafaJa2qcIk+kknqzHux7nA qIxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxVg+seX7v TJ5JbSFp9MkYuEiBaSAndl4DdkruOO46UpviqUfpLT6Em5jFOoZgCPmDuMKo3TtOv9WkVLRGitT/ AHt860UL/wAVBvtsexHwjv4YFZ1p+n2mn2iWtqnCJPpJJ6sx7se5xVEYq7FXYq7FXYq7FXYq7FXY q7FXYq7FXYq7FXYq7FX/2Q== - - - - - - uuid:59629770-09a3-cc47-a7cb-246e202d9cef - xmp.did:F77F117407206811822AF4FA08899B87 - uuid:5D20892493BFDB11914A8590D31508C8 - proof:pdf - - uuid:d099f02e-66f4-2e4f-92d6-7d724bb83a97 - xmp.did:CEFFCC408520681183D1C415F6245211 - uuid:5D20892493BFDB11914A8590D31508C8 - proof:pdf - - - - - saved - xmp.iid:0880117407206811822ABF15CCA4F0A0 - 2012-10-08T12:55:32+01:00 - Adobe Illustrator CS6 (Macintosh) - / - - - saved - xmp.iid:F77F117407206811822AF4FA08899B87 - 2014-03-07T17:08:10Z - Adobe Illustrator CS6 (Macintosh) - / - - - - - - Document - Print - - - False - True - 1 - - 5.854167 - 4.055556 - Inches - - - - - Helvetica - Helvetica - Regular - TrueType - 7.0d20e1 - False - Helvetica.dfont - - - MyriadPro-Regular - Myriad Pro - Regular - Open Type - Version 2.102;PS 2.000;hotconv 1.0.67;makeotf.lib2.5.33168 - False - MyriadPro-Regular.otf - - - - - - Cyan - Magenta - Yellow - Black - - - - - - Default Swatch Group - 0 - - - - White - RGB - PROCESS - 255 - 255 - 255 - - - Black - RGB - PROCESS - 35 - 31 - 32 - - - CMYK Red - RGB - PROCESS - 237 - 28 - 36 - - - CMYK Yellow - RGB - PROCESS - 255 - 242 - 0 - - - CMYK Green - RGB - PROCESS - 0 - 166 - 81 - - - CMYK Cyan - RGB - PROCESS - 0 - 174 - 239 - - - CMYK Blue - RGB - PROCESS - 46 - 49 - 146 - - - CMYK Magenta - RGB - PROCESS - 236 - 0 - 140 - - - C=15 M=100 Y=90 K=10 - RGB - PROCESS - 190 - 30 - 45 - - - C=0 M=90 Y=85 K=0 - RGB - PROCESS - 239 - 65 - 54 - - - C=0 M=80 Y=95 K=0 - RGB - PROCESS - 241 - 90 - 41 - - - C=0 M=50 Y=100 K=0 - RGB - PROCESS - 247 - 148 - 30 - - - C=0 M=35 Y=85 K=0 - RGB - PROCESS - 251 - 176 - 64 - - - C=5 M=0 Y=90 K=0 - RGB - PROCESS - 249 - 237 - 50 - - - C=20 M=0 Y=100 K=0 - RGB - PROCESS - 215 - 223 - 35 - - - C=50 M=0 Y=100 K=0 - RGB - PROCESS - 141 - 198 - 63 - - - C=75 M=0 Y=100 K=0 - RGB - PROCESS - 57 - 181 - 74 - - - C=85 M=10 Y=100 K=10 - RGB - PROCESS - 0 - 148 - 68 - - - C=90 M=30 Y=95 K=30 - RGB - PROCESS - 0 - 104 - 56 - - - C=75 M=0 Y=75 K=0 - RGB - PROCESS - 43 - 182 - 115 - - - C=80 M=10 Y=45 K=0 - RGB - PROCESS - 0 - 167 - 157 - - - C=70 M=15 Y=0 K=0 - RGB - PROCESS - 39 - 170 - 225 - - - C=85 M=50 Y=0 K=0 - RGB - PROCESS - 28 - 117 - 188 - - - C=100 M=95 Y=5 K=0 - RGB - PROCESS - 43 - 57 - 144 - - - C=100 M=100 Y=25 K=25 - RGB - PROCESS - 38 - 34 - 98 - - - C=75 M=100 Y=0 K=0 - RGB - PROCESS - 102 - 45 - 145 - - - C=50 M=100 Y=0 K=0 - RGB - PROCESS - 146 - 39 - 143 - - - C=35 M=100 Y=35 K=10 - RGB - PROCESS - 158 - 31 - 99 - - - C=10 M=100 Y=50 K=0 - RGB - PROCESS - 218 - 28 - 92 - - - C=0 M=95 Y=20 K=0 - RGB - PROCESS - 238 - 42 - 123 - - - C=25 M=25 Y=40 K=0 - RGB - PROCESS - 194 - 181 - 155 - - - C=40 M=45 Y=50 K=5 - RGB - PROCESS - 155 - 133 - 121 - - - C=50 M=50 Y=60 K=25 - RGB - PROCESS - 114 - 102 - 88 - - - C=55 M=60 Y=65 K=40 - RGB - PROCESS - 89 - 74 - 66 - - - C=25 M=40 Y=65 K=0 - RGB - PROCESS - 196 - 154 - 108 - - - C=30 M=50 Y=75 K=10 - RGB - PROCESS - 169 - 124 - 80 - - - C=35 M=60 Y=80 K=25 - RGB - PROCESS - 139 - 94 - 60 - - - C=40 M=65 Y=90 K=35 - RGB - PROCESS - 117 - 76 - 41 - - - C=40 M=70 Y=100 K=50 - RGB - PROCESS - 96 - 57 - 19 - - - C=50 M=70 Y=80 K=70 - RGB - PROCESS - 60 - 36 - 21 - - - - - - Grays - 1 - - - - C=0 M=0 Y=0 K=100 - RGB - PROCESS - 35 - 31 - 32 - - - C=0 M=0 Y=0 K=90 - RGB - PROCESS - 65 - 64 - 66 - - - C=0 M=0 Y=0 K=80 - RGB - PROCESS - 88 - 89 - 91 - - - C=0 M=0 Y=0 K=70 - RGB - PROCESS - 109 - 110 - 113 - - - C=0 M=0 Y=0 K=60 - RGB - PROCESS - 128 - 130 - 133 - - - C=0 M=0 Y=0 K=50 - RGB - PROCESS - 147 - 149 - 152 - - - C=0 M=0 Y=0 K=40 - RGB - PROCESS - 167 - 169 - 172 - - - C=0 M=0 Y=0 K=30 - RGB - PROCESS - 188 - 190 - 192 - - - C=0 M=0 Y=0 K=20 - RGB - PROCESS - 209 - 211 - 212 - - - C=0 M=0 Y=0 K=10 - RGB - PROCESS - 230 - 231 - 232 - - - C=0 M=0 Y=0 K=5 - RGB - PROCESS - 241 - 242 - 242 - - - - - - Brights - 1 - - - - C=0 M=100 Y=100 K=0 - RGB - PROCESS - 237 - 28 - 36 - - - C=0 M=75 Y=100 K=0 - RGB - PROCESS - 242 - 101 - 34 - - - C=0 M=10 Y=95 K=0 - RGB - PROCESS - 255 - 222 - 23 - - - C=85 M=10 Y=100 K=0 - RGB - PROCESS - 0 - 161 - 75 - - - C=100 M=90 Y=0 K=0 - RGB - PROCESS - 33 - 64 - 154 - - - C=60 M=90 Y=0 K=0 - RGB - PROCESS - 127 - 63 - 152 - - - - - - - - - Adobe PDF library 10.01 - - - - - - - - - - - - - - - - - - - - - - - - - endstream endobj 3 0 obj <> endobj 9 0 obj <>/Resources<>/ExtGState<>/Font<>/ProcSet[/PDF/Text]/Properties<>/XObject<>>>/Thumb 55 0 R/TrimBox[0.0 0.0 421.5 292.0]/Type/Page>> endobj 46 0 obj <>stream -HWM7 ϯ[`dEKXHntg.zha`liGJzo&W7Ǖ]bz; oc!׿w9:1u`nsェdnOqf]ә+gG.C;R!vzHLbwݴhv(<>MCCG%{9"/E > !A. X1®Su UgU>vޥ1Lb` NU`\+ L.Y_;)Vĭ)jj$&;$0'' Y\s - -p8"ʒ-6Yg{nƤ˜ -^їkOMQT?!ѵݺP0K*(3 -?6#38Dd&٣XQ@//'J/pZ`UyNK LN*ځ7tdϹP -]=YZbR>kОGLQHTb W$j#LPur 2>t۫odf72-!/01S2 ^ްZ6~އܞQS9mEv'V9лijzשtuJ"_.#ftPKg%,z(yNj~M%<1zsVMIs:Y NDֿJ9NP\R@ȌEa"D X27E!nW{46(1.Z (tv(s|fHOx-0 -}hw_͵2RHPb50g -? L~Y_cJ?|Pփ~pO> endobj 55 0 obj <>stream -8;Z\t9+HS.$q,N2m,gLGcZI^Tpcc5`o>)iR9u*#tF\tY3_=2\m+Qn5c.S5UgbjK(4 -"u9r[X7-T8ABENJ@AjKpBh[np.)*=Hr,)b%c,_i#7QO,+cFK3s.J,IVY[0js9mirI -XVhEJ`6]>ln'B.XKLEfg endstream endobj 57 0 obj [/Indexed/DeviceRGB 255 58 0 R] endobj 58 0 obj <>stream -8;X]O>EqN@%''O_@%e@?J;%+8(9e>X=MR6S?i^YgA3=].HDXF.R$lIL@"pJ+EP(%0 -b]6ajmNZn*!='OQZeQ^Y*,=]?C.B+\Ulg9dhD*"iC[;*=3`oP1[!S^)?1)IZ4dup` -E1r!/,*0[*9.aFIR2&b-C#soRZ7Dl%MLY\.?d>Mn -6%Q2oYfNRF$$+ON<+]RUJmC0InDZ4OTs0S!saG>GGKUlQ*Q?45:CI&4J'_2j$XKrcYp0n+Xl_nU*O( -l[$6Nn+Z_Nq0]s7hs]`XX1nZ8&94a\~> endstream endobj 52 0 obj <>/ExtGState<>>>/Subtype/Form>>stream -/CS0 cs 0.502 0.51 0.522 scn -/CS0 CS 0.137 0.122 0.125 SCN -1.5 w 10 M 0 j 0 J []0 d -/GS0 gs -q 1 0 0 1 16.9644 209.4238 cm -0 0 m -121.86 -47.053 l -133.055 -51.424 145.63 -45.821 149.991 -34.665 c -154.279 -23.478 148.726 -10.902 137.528 -6.588 c -15.707 40.554 l -15.707 40.554 m -4.529 44.92 -8.064 39.333 -12.413 28.151 c --16.678 16.957 -11.161 4.401 0 0 c -B* -Q - endstream endobj 53 0 obj <>/ExtGState<>>>/Subtype/Form>>stream -/CS0 cs 0.576 0.584 0.596 scn -/CS0 CS 0.137 0.122 0.125 SCN -1.5 w 10 M 0 j 0 J []0 d -/GS0 gs -q 1 0 0 1 169.2495 152.3472 cm -0 0 m -130.625 0.013 l -142.644 -0.031 152.356 9.727 152.405 21.704 c -152.374 33.685 142.663 43.416 130.663 43.405 c -0.041 43.489 l -0.041 43.489 m --11.959 43.536 -21.694 33.786 -21.722 21.788 c --21.667 9.81 -11.997 0.084 0 0 c -B* -Q - endstream endobj 54 0 obj <>/ExtGState<>>>/Subtype/Form>>stream -/CS0 cs 0.576 0.584 0.596 scn -/CS0 CS 0.137 0.122 0.125 SCN -1.5 w 10 M 0 j 0 J []0 d -/GS0 gs -q 1 0 0 1 193.9482 38.6372 cm -0 0 m -92.357 92.378 l -100.887 100.846 100.855 114.612 92.42 123.115 c -83.927 131.565 70.179 131.58 61.702 123.086 c --30.722 30.78 l --30.722 30.78 m --39.241 22.328 -39.23 8.551 -30.766 0.048 c --22.258 -8.384 -8.542 -8.422 0 0 c -B* -Q - endstream endobj 61 0 obj <> endobj 51 0 obj <> endobj 49 0 obj [/ICCBased 62 0 R] endobj 62 0 obj <>stream -HyTSwoɞc [5laQIBHADED2mtFOE.c}08׎8GNg9w߽'0 ֠Jb  - 2y.-;!KZ ^i"L0- @8(r;q7Ly&Qq4j|9 -V)gB0iW8#8wթ8_٥ʨQQj@&A)/g>'Kt;\ ӥ$պFZUn(4T%)뫔0C&Zi8bxEB;Pӓ̹A om?W= -x-[0}y)7ta>jT7@tܛ`q2ʀ&6ZLĄ?_yxg)˔zçLU*uSkSeO4?׸c. R ߁-25 S>ӣVd`rn~Y&+`;A4 A9=-tl`;~p Gp| [`L`< "A YA+Cb(R,*T2B- -ꇆnQt}MA0alSx k&^>0|>_',G!"F$H:R!zFQd?r 9\A&G rQ hE]a4zBgE#H *B=0HIpp0MxJ$D1D, VĭKĻYdE"EI2EBGt4MzNr!YK ?%_&#(0J:EAiQ(()ӔWT6U@P+!~mD eԴ!hӦh/']B/ҏӿ?a0nhF!X8܌kc&5S6lIa2cKMA!E#ƒdV(kel }}Cq9 -N')].uJr - wG xR^[oƜchg`>b$*~ :Eb~,m,-ݖ,Y¬*6X[ݱF=3뭷Y~dó ti zf6~`{v.Ng#{}}jc1X6fm;'_9 r:8q:˜O:ϸ8uJqnv=MmR 4 -n3ܣkGݯz=[==<=GTB(/S,]6*-W:#7*e^YDY}UjAyT`#D="b{ų+ʯ:!kJ4Gmt}uC%K7YVfFY .=b?SƕƩȺy چ k5%4m7lqlioZlG+Zz͹mzy]?uuw|"űNwW&e֥ﺱ*|j5kyݭǯg^ykEklD_p߶7Dmo꿻1ml{Mś nLl<9O[$h՛BdҞ@iءG&vVǥ8nRĩ7u\ЭD-u`ֲK³8%yhYѹJº;.! -zpg_XQKFAǿ=ȼ:ɹ8ʷ6˶5̵5͵6ζ7ϸ9к<Ѿ?DINU\dlvۀ܊ݖޢ)߯6DScs 2F[p(@Xr4Pm8Ww)Km endstream endobj 60 0 obj <> endobj 59 0 obj <> endobj 44 0 obj <> endobj 63 0 obj [/View/Design] endobj 64 0 obj <>>> endobj 43 0 obj <> endobj 42 0 obj <> endobj 67 0 obj <> endobj 68 0 obj <>stream -H tOWߖDޟRvjߗؗ BE,! Pbz"RZ]:c̙w|s> FCxwّ3tKH7 -]m@x,b7Ot\20@6}D=~_. 5{' P]\ɱ=m_$&v`BҶߧ_(~2F%=>h׾Qݟ/d~K8.`Oj yt_[|yN?;?{ y?!!}ܐP?H3nfoKJmyy̶V+xyǗ_eWYptJ3UmaMc@[@G6ńDI0@2| a,%A -, -VX `=l 6 -  ?n{~p'Q8sp^E -\k \p n?7!<?9/ 0`6́A4ba,c)KGX+`%ձ&ƺasl-vHO1p4/pN¯p2N8gL1B\+p-7v܁; x=|1SArȐRY*OդTP#jFԂZR+jCm=uԉ:S$u(N=(zR/Mԏ? xHh0%J0N#O44/i}ESiM flCsi%Q2-%Rh 6F?nC 4Q:F3tH -]tn-Cw>=szA,Ǚ8rvAܜ9?\ab.Ź r\+pEU*5&\r= 7܌ù9܆rQܕ ycyx2'bN弍SG>ȿ}N?$YHV&%4pi.-FJ;i/$B:J',]zJxT̔$Q|Y*)BVY'dlT!{r\Ni9/!<~d8Q3LN;D8N;6g/䛐!3C<1uLִ7nVfjT2s2is֜3ms5n^h&ͬ94Hsj.ͭy4k~-5G k 0-%~#-嵂VZEj55ZWim6ѦLõVFjv]8k:Wi.źD2]+u5E\vwln^7p]ㆹEwn[٭6rHw;CO''ȓӓS)^`¡54(4whЂCU V9W}J .\IHΚ3@xg9OO9\V=w_yӫ3 bv0=XK`Ieճ"VƪXka 1Vag]CpW?{ NsWﬞsV\gW]Vsx]Q! -zY=+P%Au!5z6г3??A|z9os-까[=dJ^=f3y"CVK^=m1=߭`zfl>=syӳ =+[=qҳճI-zىX=@gV1^=[='K+yWo3zvh%q2@JL2M92Wd,RVZY/esz9&'䔜 rIM-䉼 gkzt:ǩtr>=S]!sϨo}zFQfkz0}zc>=/eŕӭFE x#LtU`TkzXč1ovx+뙈7* -ޠD9/D*Uy77?j*'|^)SdO"{V)ggڳ3٤؞͊ZسS"]سgB{ZhQ>3gs"{*l.A3XhO{Y 7h?UFthhh˄=؞wdPVc|-8uV:|霎|V<)$qh, gY|E8X^x1,HdqdT] NYh>e0]I r]Y0_<S6Qw7%ߐo)s]iT Nr@ _o%c7.Y;|i "V <+xԇ 7ypO^ kQd鸸:#%waRZj$rM$JVCjlzՄ%/y.UIuL)QWH)T9B $IUr[1m/p3 3;? `Wd/fRNpT:"&?AHͶǨl\0nhy#pe,TN0KČ4SL1#E{9\Kѽ,m7B#~7 xD 萝6R/}wPnhϭ4qsɝIyTrZ4 y/7y7ә<L?Cb]mGmv=mwfifvZ6NU{jS5TmvU;[dg7~ u5TVF:jMA D(>  0!1a$>țoc [1a""0 1S1 1431 /RbKsyB{,,2, -*) -E":l&6c bc 0pGqIiA"p琌pT!LXa+$,$!9/S&1x,Nv q~][[ܢ/A䂥%~}k(5۫vCD㷤sې#Ӆ- -G6uv[GC!hEYVDQc& !Zz=sI]2 -{9]1;;MvS^c#.kq[aj$RY|?ΆfFsSB @M[S u>̼JWS{61PKx2@ ]B=.[͹q_n|OxN{W 3w3[̩DXEv%FTx7S7}D~'.rǐ#SD.ҹm\?:&. GX*rfS%7Z^SY[ƵA>}\ձ@謮ŷ:5}݀ZA58ji%mMȻq}.bkp:8_W{=ABbk€;H\*֊knqo/W ; }gύƭ^Dmh\&m ez~'_eC Zw|;Úۏ"D Y,m/H[:?6ONJs,91"M3g s2+))^EH++3CoRWGz7ijO;zn|}}'V!9eIy!KZWFe쑔a\glinwH -y%l;GXf8lfXa微v3.Z';EvxתջxՃ6451Ff&O/UnV5Q8f+2]J쎛WKI7]@rj^Ԫ%zGauݢW23;xe˴kռsɋW\&6\?i> g BPny +4VShw:p Zwy7-0o%ßNml;L+j -;u0pf]os.Ph>+:U礡7j6`d296Z{>` Pw~[̭ny4 qEX L& ^2-'\5_zrN!\hɄ[N1.aǴ;N'Gr -G^>p5]^Lp|8:R#\7L!h«&^ oW<&kC=-ž^=&6p@cG4 9ve؇^ό!H,Dg)EZep2x5aE5;'/9gcPs$zsX -fH'>C!CC,cm-9=v?:XiiNvtH>/b(d4?\~hYJf*Y+4g乶_ tVG\5w*XOq"bNZOWj0bY5c]M#0Ƹ+w)".,"y|"z<Eʑ~y(oG{}ma*$?`쨽@p k͉$HC/q!i!,-/X^Hx"dfY@L-Js&[i,5y]s UȚo `%KJ#bרH9 %2#jV* mL%0J!1c&㷋/*Rd(l͍m4D ЮE +R_eS7X0HQno[sW{PT} X]v t*PDķV- LbFٙЙREB4613bRj3il36c5'NUYs%G w]噩m^YYҶcq)J`elM!wArjXjxђEPvݏ(i#rL뫯>lTM5qEd1{ChKN=I>KP*ʯUT]ZgT7r,CWd|CMn/{ K-vt -ߎ4[nFA@BV(Ex^ΐȂ*G1WLSFOv9$?}N?|)d Ac~zYiURDJ_W-++7ՎE8"A.Ui,eO'Jw>]kWMꝓ~ۙi-X(HOw?7^-ex+{Ƹ0֕}!ܺ4E"OVWVv|GəWpV6ulЩΰEKGGw1skl+޻xRUy -w'#>cmd5$LL]}@mkӶ6Uۧ&1Um&TYeRH52h!cdPk dy9ɯ9$ 'y/PqOQawQ:`(\:kRtLC/F!XH_iYZ%Y騐.頹xd7i3D sBOxL @D+ԢtIuիkh-Ai_}ԬR;֎8(&`nzAc]Y:IWSnИa%(|6"b~_+$h]n8Ly/.){X@—$}/Ψ\ 4` o)<]|ڽ8y>T}T=>']haKK%;X=d~Ï>~ݦa6pV2oms52M{>WVƾD&OZMԎv֫}``l\M;0@;nBKbIST-JgўgïDx|0ֈ.y:9yB6ܳ53#mڀ5ƽRsfIo7w! BJ硫@݁t.x r+ 8]~?ݸη 0m'~߈ߛn1Ν>rN=$wA|_2q\)}vYԗ2Z+gf\ {.Gc{OBwB/K-Yo6%S\{0W/d#S?<~__)Ҥ"'C^MO'6(_0> $^]Kr+j) 1`#JUtDka-\ 5нۀq#ۣ8#̡8lTx|M1塦~ ],7~b>9̝&ktòzsd$*C:Ju"T9?z_jwhuI||+k*/bS{Xt!zyLs8載zi..6ďWPy v[jrG(X މchXE{3ʍ}r7c 9^mX6_SE3cLn̽F4pG7Kbď 1_~ޠt c@as8diͶQH.!1,w5HQU?szƶ{1315bÿmmșsocbo ]v~Bۉv3:'jßkwj֬>78H'E+$|uVom=\kqH>^O7Z{ؘ9p~}/Y+WNA>OIݝϸ煼{ m+}qV|$vkdQj-n>uuQyd$srM峔Yu-w;Dc+?êe+f{9{?s9x=$;.Ih0Q/s~|Vrrˈ$U|wz'?{WdϻI'Z𵞔CnfA0ʘ) #RcUU=h.W\#g-0??UR{  $.!ѼF8Lc0|qUy%&I^GHCz!#ķ5u{0 -}S*zYI5\u݊g ; -ƩGGc?\dbM0Zoca_ZG!&Doucce^ѻ*O=q5у$\ޜv~ڛu>,K|G+Jƞ5IvC3op`LU#r%7-u5ϗlB_qt_b2s#[<#ihSދ-":rw% iy5cvQfq7 RO>!5XLE H3ᚾ:A -& -lm .v5]-&27oď!1dI#C*oKd;f̑~[GJv( ʷOJ=kq_Ԛ{<$p I̻3(8?E31t z45Fޕ tNо^Y9J>!g9Ԓca/7ۭ2q #!绩p1,SR> -5fWơvTsV߯f*ź{_3gOZ`%rBj @9]甮oi+= -hK}wrF->S2eSK>c{; /Бgy&W1=F=dkV6$ǰ:af)v *8ż+L`>z7.DI\Aܧ~7qKj>5`M.Th%Vc:\? u%6W͔\lШ؇|Ļ1g>?f!Zq,"fS*$yJ1z+6fHr6"vLƣN-ށ (ԑYG-^Aq]L ]јg띆+u .CA0 C5lڍhtw0\,eǐGp/azvk^;}0ozd+3>\D= =̯NM5C?w^b8μ|}9y>, `Hs9j -y5`q1+ -eD90*031+ d*/k]G zR<ɇyTPyG6d`|{R{(峐T,m/"\R{,G~@ߔ37)Gg"תG `VH_q}<-[O(y!7w0XR378s]F h'=%//親-N\2^汐(PZ(6MJ Ψ O|*'"PT QEQŝP-[?n_9svr'9`#ST Qr47WrcQ\f#"WsdgL}܎ }31q -8=Wql=Ӯi)j"l@GasǪ]C WɎ_xn5׹R -ف5NIJv!¬9̑aB-99bzӴ8\aC=;Je)'I_#BcȐU;::S8B8rhC#1&ױ[\W9Ƒdqlh~G1-oZ|B^[Ceӱ05Xjq5fz#!9r%KM#WV^4F`dzrfMq_iE,f3)p5*J\.3JHww>YP'` Y B#wenyª,2=E` V|^芲|XN-}ݥFeW` h no?^@Ш.vi.-yփTd꾋L0&w)(6j꿰(䧠 B|WdǚН2S=bag}E+KLc暋O7Ru[+tW}X!/:1-'fٶx|YqUk" ~/P ^F)D*< 4]G]\\G\wxצsf(vp&83izM>'Ϣr"#:DtyT&3|PB*Jl jj^yfzW!1M B3Vh6hvhN.xtCwz} b(a80 db$K+Pa.ZոbA+",ƍXTk2ܢVJj:ZQ kq7:ܫu>'c=xcF<86 >|qn|i>í|۸; |Kɗ -_k|op[|{]?~~ď SgaWGy[w'IğyWogBqSIDJDKTRSjIm#u%VI}i 48i"M4R i%v^:HG$tx&% (=$-}$YJ?/d ,C$U0.i2BedHђ%2FJ+dL2E4ɓ2Cܒ/R(̔")̒)2Oe% A90}j[W۶m۶m۶m۶m3=Z?ol 6Ć0n#l68olM6Ŧ4n3l -`fڜY67` A"[lKl2 V*[mkl6&l[lmv.m{lv!;lGvN);mg쬝v.%lW]vn-mwݳ#{lO=^+{mo쭽>'l_}~/mCB#$B!4 ,!<" ""!2 *!:b &b!6 .!>C$D"$F$E2$G -D*FE:GdD&dFdE6dGD.FE>GD!FE1G D)FE9GTD%TFTE5TG D-FE=G4D#4F4E34G D+FE;GtD'tFtE7tGD/FE?  0 (8L$LL4L ,<,",,E !˱+ -k [ ۱; {qqqGq q'q -qgqqq qWq q7q qwqO / -o _ ?  A#Hΐ ð Ȍ¨،øILL¤LLLLôLb,l\<l,,,¢,)R,,ʬªڬúlll¦llllöl®þ¡ñɜ©ٜù\\\¥ 2q9Wp%Wq5p-q=7p#7q3p+q;wp'wq7p/q? 0(8O$O4,!1)9_%_5-=?#?3+;'7/)@!d(RZaV^QYQU]1S[qW_)*+*+R*R+*+2*2+*+r*r+* - -JJʪʫ**jjꪞ꫁ZZڪګ::zzkjkjkFjFkjk&j&kjkfjfkjkjk*PZZZZڠڤڢڦڡڥڣڧ::::::::󺠋˺뺡ۺzzzzzzzzt{H=p#xD=GhcxL=xybOI='GJO=t>"=g,ճyv9x^B^؋xQ/ŽR^xY/彂WJ^٫xUսZ^x]7F؛xSoͽVx[owNٻxWݽͪ l -]w(d3Cnjin kb+bEri23y혙=|Ozg>Jh:͠4fKh>-ZJh9VӉtLЩtNgЙtMйtOЅt]LХt]NWЕt]Mеt]O7ЍtLЭtNwНtMнtOЃ0=Bc8=AOS4=Cs<@/K2Bk:Ao[6C{>}@G1}Bg9}A_W5}Cw=@?O3Bo;A_7X1%(`!8(G*Qjb#lM)6[b+lm-;b']+F`7='b?p 80("#PHa р#ш&QhF Zцq1888:F2:E -nhQ$0aF&c -zч阁٘XXXXXX8'dSqN8glsqb\Kq.Wj\kq 7f܂[qnwn܃{qxa a_k|o?g_~ox=ȃK\1s˹+øoƼ oʛo[ּ o;μ #x7ޝ=y/ޛ}y?ޟ >C0>kx$ZN\ǣ9cHn&;`̀|7s r|4Ov>x' Yα]gYc < 6b{x2O^< ɳx6<^ȋx1/᥼ -^ɫxuBW35ݒ'ْZ钂dXfrvwd)mU4Kw!et1P0)^mC&NTSѲjd#=U+:P- ][0$ϠFꚜbNUO -)5+!զ%7d3H3LI?XRDCd1[Je"d#ԉXr]Z(*q(+mK \2C2Jr,EȤxb#JѦE*3P銏D2A ^zu5\V=kͩBF?h bhAF? Iݴ TB/K,gʛr [l\2js~ lsiw-ü:A+?ny==6LlLڊ]..lϔGPjm: mœH#xB -L~} a%;_sQ%V;\$uݞ(w]^H(ʨHi9|mTmꪒMUײzlRuzCD]l4D%Q(Ѣ9Jj5d9_>ɖMX;\khʦٕȻK*imZ5T&)5ӹRd皴lC3+A[\<8WD  JjA W޲thc#NZS!焻=C `eJ1lVT/0 --9VN!l 7ΰ\7jF-bOyK.-XhȘJ6,1A6ZӌN&EB˄fTD}";:ENY/ e!: ",䗅B|D~+":"'n]{/G~ERA%.QRVTԱ1b9"7H5#X8q׊CNB!E"EW{]*~4Qy\{1캞_^R,!J6玂jh1} 0sw`ai~5Enz/H]捶u+m, -FXHs, y-`C 7xto98*}bVw;n"P(,GM,;x|h92w˚͸ٮq%|N8q;c a&}L7VƱ ɯ$yCUKO$a۝:asF⫘U1"kbD !c !pXB %@Ǩq^^vԿ^A &"xD;"!&1= U׀Y|~F6=y9 qI)%LŁFք n"'qIVxK:5wX21rd,6|"$h+Yך3ҎR'< q$H#\2q[P5 TÐ,m:6b$uyW(<cKIDNTw#1bJbA8rtޜYdwD؆4<:#^#^ ~C#^6Ȕc#k4Z.Ș' O9ⅻblٞQat uτS.R8~x7shX$M_1*h ^Յܴa;+\-T.a#~O$g>mTĵ# "!b o}K+x'|X"57+zss$Q{j*2]3qTW8Yٴ܋P[yQs XYE$_t{ "6Le4t܊]۸1i!blԦ|ψ]1|GwՇbDWBIq%~6@dv񞙀ƳFR &TCs)KmjM ԨjC3Ԓ"svνNt)/"k.pXrV *W*ћWp `* 4滺i^5_U0TU]WvI^oE@P ;g`yvP՜7H2T&s:f_@C UQ}};m-}su%9Դ-hŭiL| o14-i1̷ElZ<[#"5-FiNun`*}Jy!#^ ~C#^"^!=D8̏y^oA>i77zX ^%J lqW-5/j՘ND|Ig՚{bcL쉉='F0Z}BoPxe&C6*7(= ->SZЬּ:^эɑo}J!֍}t|{?YNu~a377bxZA^oHٻ+MP08?ckgh {Y{YO,̢<+^-ne:.ϩav2̮`Q_ /;>f -3f#⣍Mh?3=ִ,OVL,''1d}*oR0{iNm2;.roT(nR+wGM7?yWnj]Ko~êYmΗmmfMa=&\bXbژ^|m'ѝUWU]b#Yn}}9y&1bo@ ECC6 2&'Ř&2K3>)Z}u:"fdäK:S]n]SEPKlm|QULuZ̺-t[ֽbi1ޖӲykƌ(.: HC#qzh[snX:/\b.rbX/b%|K.hb(Qr4ZTVxp#jHU= iq -_/=u[MR#*C<[^>k5}ډҐƼE4s|! Lbc,2;y L)M\k)SԠLzIBlL+tL_^*ײ+-cŕUްL閽Ve[e˒=*(l#uP@ UbqHCڀNƽ:Q :WCio-CBm]m#WZKر x'?4EFRP-qM^RrR_h/2c\}4ڎ3)b;ϫ,Ms!s<ثZĞ][u׼J4y՝wLm.C34Dh'φj.{'b>J JlQzĞ٨j& o%\7|@}]P]\\uQjui\_M7U4ky]NRme*j[u;Q-|닏;kY[-|-|-aq۰ςgYl86džo÷m6| ߆o÷%_Q+j~Zd5RIحZ<=*7 UY\`Ǵ,œH}ύUū4pS9YGjWsY%U-i~ʧ{ ˒U6+8Kf?N2IyV;jou>5sU"P*:j&j6.>[ۂos -|_W+x -<O2?Tx*< -OmyOe~| _k5| _k5:|_tx:<Ogoooooo0?p ֗DŽc2|L&g·[-| ߂o[-| ߆gólx6< φgólxvc6u;|߁w;|߁w].| ߅w].| ߅{=|׃zp=\?????????7??777777////d!;777//////.n.Β*pM:IZptV<Ǣ {){ ~a>~;~ 5kȃy܋0_'qpDT>4ΓYn6Y|e:WX>KCYǸqo{[/ǒ~'qv\+ia6ٺV(m.8ģ z75W䨰a]qa@[C\=BOerXFQ(vmvX.Ot`5 ܰ_ QU7Z^REdc7ߛi~ vq`fP7La7#d߹wG;~];ΎkeǏCw:ޝxwQǻstra/Q/:~9Q/:~9a/3vr˙_N;nT̰&m|;M~㧩CM:i:vݸo&ٲ\v$3-^UJJ"6PEsBw 6E=}~),Kg@^&Bv TSR_}kqr8 ţ#OMIƙViwt8\e~%]e]3v3͘})TAUTCu@ME,?<ڨ׿MR|`$~}}\OsL.f<3L즹kne3ɳv[;Na=3ͦ'P.޸u7ntϟx0QҏnQknU\nE.ƙz5îs՜$_;{s0C&Pvqv_K ̫t]2oq7߼̦.}m0fmKut>/otvsSXUP#XX .>ix)7,[Gys|TEMBuq.oWɷY\cy?JiԈD: -!19sua:zhi5ƣk(ĨfquVpi(t櫇htZ+ʈTF2"5$ݫ}'+\&z'zC*R1"y)Km;W{tQ^߿02-r'zl]<|Rw_:L$U*4Y @.nH&˿;E"\(jZ:>!IU+ -|>SP_ _g=mrZld_Ky}ߊ;M\wr׭Wooo÷Uژ:v=vAWtNvǧI/GZ{E:z~88x%TƬ#Jиۻs(ewI!B+lXcSc;^rhQTm$&RK#JeLn8Kojg ){{3v,'g<܏c+?u>><<5o_B:y@EQۮ}Zglz -hߩg2V(cX2V-?-a &ھL05T:!3DI~za e. - *Y-4q`oL]UJx$ `@@hzHK `50CBBBBB~UBcJy@&Iڡ/q#}x -FZz(b(bX}@}2 -q'W׸^t op~78 op~78Mor~&75a3)\#Ϙe(䆰:/[̾'7j>1, SVtKli~sHӃ;m.'r|%L Z%ˆOnmIZ]c=!)sTҿuHM1R/K?H?fּǝI7r&}pK|A9>VigVd VII[}HXxt*Â7uP:)`wOn Z)kH8͑~2ҿ20;pF0X/U?6%q"!Ԇ-& ײ)6- :'Q;'<"t8dAbMM/|nm gy )J>uO^ u}0i/r:Irzb~`qOYsKY1&{ dFez- n\^pjԬic=zp#uӕ}C/ndS^*FOZhʼn]Z׷dKVt2{'t՚p&\L*õ41mVgаOcw߿X ucAb endstream endobj 65 0 obj <> endobj 66 0 obj <> endobj 69 0 obj <>stream -H|_HQgZn꺑HYm7X q\C RgwhRP[,BA/AEBR=h/EPQowf:w>w.vquHrUvذ;> endobj 48 0 obj <> endobj 70 0 obj <> endobj 71 0 obj <>stream -%!PS-Adobe-3.0 %%Creator: Adobe Illustrator(R) 16.0 %%AI8_CreatorVersion: 16.0.1 %%For: (timothy rudge) () %%Title: (celloverlap.ai) %%CreationDate: 07/03/2014 21:11 %%Canvassize: 16383 %%BoundingBox: 29 -261 444 -39 %%HiResBoundingBox: 29.3604 -260.4097 443.9658 -39.7861 %%DocumentProcessColors: Cyan Magenta Yellow Black %AI5_FileFormat 12.0 %AI12_BuildNumber: 682 %AI3_ColorUsage: Color %AI7_ImageSettings: 0 %%RGBProcessColor: 0 0 0 ([Registration]) %AI3_Cropmarks: 27 -292 448.5 0 %AI3_TemplateBox: 298.5 -421.5 298.5 -421.5 %AI3_TileBox: -165.25 -425.5 617.75 133.5 %AI3_DocumentPreview: None %AI5_ArtSize: 14400 14400 %AI5_RulerUnits: 0 %AI9_ColorModel: 1 %AI5_ArtFlags: 0 0 0 1 0 0 1 0 0 %AI5_TargetResolution: 800 %AI5_NumLayers: 1 %AI9_OpenToView: 6 48 2 1444 867 18 0 0 -4 37 0 0 0 1 1 0 1 1 0 1 %AI5_OpenViewLayers: 7 %%PageOrigin:-8 -817 %AI7_GridSettings: 72 8 72 8 1 0 0.8 0.8 0.8 0.9 0.9 0.9 %AI9_Flatten: 1 %AI12_CMSettings: 00.MS %%EndComments endstream endobj 72 0 obj <>stream -%%BoundingBox: 29 -261 444 -39 %%HiResBoundingBox: 29.3604 -260.4097 443.9658 -39.7861 %AI7_Thumbnail: 128 68 8 %%BeginData: 5676 Hex Bytes %0000330000660000990000CC0033000033330033660033990033CC0033FF %0066000066330066660066990066CC0066FF009900009933009966009999 %0099CC0099FF00CC0000CC3300CC6600CC9900CCCC00CCFF00FF3300FF66 %00FF9900FFCC3300003300333300663300993300CC3300FF333300333333 %3333663333993333CC3333FF3366003366333366663366993366CC3366FF %3399003399333399663399993399CC3399FF33CC0033CC3333CC6633CC99 %33CCCC33CCFF33FF0033FF3333FF6633FF9933FFCC33FFFF660000660033 %6600666600996600CC6600FF6633006633336633666633996633CC6633FF %6666006666336666666666996666CC6666FF669900669933669966669999 %6699CC6699FF66CC0066CC3366CC6666CC9966CCCC66CCFF66FF0066FF33 %66FF6666FF9966FFCC66FFFF9900009900339900669900999900CC9900FF %9933009933339933669933999933CC9933FF996600996633996666996699 %9966CC9966FF9999009999339999669999999999CC9999FF99CC0099CC33 %99CC6699CC9999CCCC99CCFF99FF0099FF3399FF6699FF9999FFCC99FFFF %CC0000CC0033CC0066CC0099CC00CCCC00FFCC3300CC3333CC3366CC3399 %CC33CCCC33FFCC6600CC6633CC6666CC6699CC66CCCC66FFCC9900CC9933 %CC9966CC9999CC99CCCC99FFCCCC00CCCC33CCCC66CCCC99CCCCCCCCCCFF %CCFF00CCFF33CCFF66CCFF99CCFFCCCCFFFFFF0033FF0066FF0099FF00CC %FF3300FF3333FF3366FF3399FF33CCFF33FFFF6600FF6633FF6666FF6699 %FF66CCFF66FFFF9900FF9933FF9966FF9999FF99CCFF99FFFFCC00FFCC33 %FFCC66FFCC99FFCCCCFFCCFFFFFF33FFFF66FFFF99FFFFCC110000001100 %000011111111220000002200000022222222440000004400000044444444 %550000005500000055555555770000007700000077777777880000008800 %000088888888AA000000AA000000AAAAAAAABB000000BB000000BBBBBBBB %DD000000DD000000DDDDDDDDEE000000EE000000EEEEEEEE0000000000FF %00FF0000FFFFFF0000FF00FFFFFF00FFFFFF %524C45FFFFFFA8A87DA87DA8A8FD78FFA87D7DA8A8A87DA87DA8A8FD74FF %FD04A884FD07A87DA8A8FD70FFA87D7DA87DA87DA87DA87DA87DA87D7D7D %A8A8FD6DFFA87DFD0FA87DA8A8FD6CFF7DA87DA87EA87DA87EA87DA87EA8 %7DA87EA87DA87D7D7DFD69FFA8A8A884A8A8A884A8A8A884A8A8A884FD07 %A87DA8A8FD1BFFA8FD07FFA8FD42FF7DA87DA87DA87DA87DA87DA87DA87D %A87DA87DA87DA87DA87DA87DA8A8FD17FF7D52A8FFA87D27FF7D277D7D7D %FFFFFF7D52FFFF7DA8FD36FFFD1BA87DA87DA8FD14FFA87D52FF7D7D5252 %A8FF52A852FFFFFF7D7D7DFFFFA87DFD36FF7DA8A8A87DA87EA87DA87EA8 %7DA87EA87DA87EA87DA87EA87DA87EA87DA87D7D7DFD11FFA8FF7D7D7DFD %04A87DA8FF527D52A87DFF7D7DA87D52A8FD37FF7DA8A8A884A8A8A884A8 %A8A884A8A8A884A8A8A884A8A8A884FD07A87DA8A8FD0DFFA8FD04FF7DA8 %FFFFFF7DA8FFFFFF7D277DFFFFA85252A8FD38FFA87DA87DA87DA87DA87D %A87DA87DA87DA87DA87DA87DA8A8A87DA87DA87DA87DA87DA87DA8A8FD09 %FFA8A8FD04FFA8FFA8FFFFFFA8FFFFFFA8FFA8FFFFFFA8FD3CFF7DFD14A8 %5352FD0BA87DA87DA8A8FD0DFFA8FD4CFFA87D7DA884A87DA87EA87DA87E %A87DA87EA8A87D27527DA87EA87DA87EA87DA87EA87DA87D7D7DA8A8FFFF %FFA8FD05FFA8FD50FF7DA87DFD05A884A8A8A884A8A8A87D5252FD05A884 %A8A8A884FD07A87DA8A8FD5AFFA8A87D7D7DA87DA87DA87DA87DA87DA87D %A87DA87DA87DA87DA87DA87DA87D527DA87DA87DA87D7DA8FD04FFA8A8FD %54FFA8A87DA87DFD16A852F87DFD06A87DA8A8FFFFFFA8FD58FFA8A87DA8 %7DA87DA87EA87DA87EA87DA87EA87DA87EA87DA8527D277DA8A87DA87DA8 %7D7D7DA87D7D7DA87DA87DA87DA87DA87DA87DA87DA87DA87DA87DA87DA8 %7DA87DA87DA87DA87DA87DA87DA87DA8A8FD32FFA8A87DFD05A884A8A8A8 %84A8A8A884FD06A87D7DA8A8A8FD067DA8A87DFD27A87EA87DFD32FFA8A8 %7D7D7DA87DA87DA87DA87DA87DA87DA87DA87D7D527D7DA87EA852FD047D %A87DA87DA8A8A87DA8A8A87DA8A8A87DA8A8A87DA8A8A87DA8A8A87DA8A8 %A87DA8A8A87DA8A8A87DFD05A87DFD35FFA87DA87DFD0DA87E5227A87EA8 %527D7DA87DA87DFD1EA8AFA87D52FFFD0AA87DFD36FFA8A87DA87DA87DA8 %7EA87DA87EA87DA8A8A87D5252277DA87D7D7D7EFD10A87D7DFD0CA87DA8 %272784FD0CA8FD38FFA8A87DA87EA8A8A884A8A8A884A8A87D527D527D52 %FD047DFFFD0FA87D277DFD0BA87D527D52527DFD0BA8FD3BFFA17D7DA87D %A87DA87DA87DA82752527D7D7D527D277DFD04A87DA8A8A87DA8A8A87DA8 %A8A85252527DFD04A87DA8A8A884A82752A8A8277DFD04A87DA8A8A87EA8 %7DFD3EFFA8A87DFD07A87D27277D7DA87D5252FD10A87D27527DFFFD07A8 %FFA8A8A8FFFD07A8AFFD06A8FD3FFFA8A87DA87DA87DA8A87D27527D7E7D %7D7D5252FD11A87DA8A8A87DA87DA8A8A87DA8527D7DA8A8A87DA87DA87D %A87EA8A8A87DFFA8FFA8FD05FFA8FD38FFA8A87DA87DA8A8A87DA87D7D7D %A8277DFD18A87DA87D7D7DFD0452A87DA87DFD05A87DA87DA8FD04FFA8FF %A8FD3EFFA8A8527D7D7D52FD047DA8525227A8A8A87DA8A8A87DA8A8A87D %A8A8A87DA8A8A884A8A8A8527D7DA87D7D27A87D7DFD06A87EA8A87DA8FD %07FFA87DA8FFFFFF52A8A87D7DA87DFFFFFFA8A8A8FFA8A8FD2AFFFD07A8 %7DFFA8A8527DFD16A87DA87EA87D7D5252527D52FD06A8A9A8A8A8FD08FF %7D52A8A87D7D277DFF527D7D7DFFFFA8A852FFFFFF52FD2AFFA8FFFFFFA8 %A87DFD1BA8537D7DA87DA87D7D5327F87D7DFD05A87DA8A8FD09FF7D527D %A8527D527DA8FF52527DFFA8A87D52A8FFA87DFD29FFA8FD06FFA8A8A87D %A87DA87DA87DA87DA87DA87DA87DA87DA87DA87DA8A8A852FD067D5252A8 %527D52FD067DA87DFFA8FFFFA8FFFFA8FFA8FFA8527DFFFFFFA852FFA8A8 %A82752A8FFA85227527DFD32FFA8FFA8FFA8FFA8FFA8FFA8FFA8FFA8FFA8 %FFA8FFA8FFA8FF7D7D7DA87DA87DA852527DA884A87D7DA8FFA8FFFFFFA8 %FFA8FFA8FFA8FFA8FFFFFF7DA8FD04FF7DFFFFFFA85252FFFFFF7D7D7DFD %30FFA8FD19FF7DFD06A8FFA87D52FFA8A8A8A9A8FD6EFF7DFD09A827527D %A87DA884A8FD6DFF7DFD0BA87D27277DA8A87DFD6CFF7DA8A8A87DA8A8A8 %7DFD05A852527DA87DA8FD6BFF7DFD0EA8FFA8FFA8A8FD6BFF7DFD11A87D %A8A8FD6AFF7DFD13A8CAFD6AFF7DFD05A87DA8A8A87DA8A8A87DA8A8A87D %A8A8FD6AFF7DFD13A8FD6BFF7DFD11A87D7DA8FD6AFF7DFD11A884A8FD6B %FF7DA8A8A87DFD07A87DA8A8A87DA87D7DA8FD6AFF7DFD06A87D52FD08A8 %AFA8A8FD6BFF7DFD07A8522752FFFD06A87DA8A8FD6AFF7DFD08A852F852 %FD08A8CAFD6AFF7DFD05A87DA8A8A87DA87DA87DA8A8A87DA8A8FD6AFF7D %FD0AA8AFFD08A8FD6BFF7DFD11A87D7DA8FD6AFF7DFD11A884A8FD6BFF7D %A8A8A87DA8A8A87DA8A8A87DA8A8A87DA87D7DA8FD6AFF7DFD10A8AFA8A8 %FD6BFF7DFD11A87DA8A8FD6AFF7DFD13A8CAFD6AFF7DFD05A87DA8A8A87D %A8A8A87DA8A8A87DA8A8FD6AFF7DFD13A8FD6BFF7DFD11A87D7DA8FD6BFF %FD11A884A8FD6CFFA87DA87DA8A8A87DA8A8A87DA8A8A87DA87D7DA8FD6C %FFFD0FA8AFA8A8FD6EFFA87DFD0DA87DA8A8FD6EFFFD10A8CAFD6FFFA87D %A8A8A87DA8A8A87DA8A8A87DA8A8FD71FFFD0DA8FD73FFA87DFD08A87D7D %A8FD74FFA8A884FD05A87DA8FD77FFA8A87D7D7DA87DA8A8FD44FFFF %%EndData endstream endobj 73 0 obj <>stream -%AI12_CompressedDataxr$q&u~ȌU25&rh:1 -hC-Ia(deFf/7o6ooxƯUwՊ~_~I҉tuuG___ݧ?\r_7^\wW77?]\|X_\RJ/v8kkrݯ:txǏq;ӱo_ܴznBX}?wqvm:@gǭ]ǏۛۻZ~xZmo..=?n~?]_O7wz{mߝ_\_usm?]߼ͧwG;~ggƅn ?lץ~/tkwwJ׺sr4:Z۫wnh"Ә7u#KvesnXqygiOZY!/_{ndP~}ηo.x,u9ۋi9|>h+Nn?c -jU7rov./}\4C9zCu~rpQ_ſIc_OMkhbM_Cw=}a G=;>4>_}nVSOW^dz;掾>]^8;\\~:=-䫳vŅr]\^ъ.9rw~_ٕ\zU\ze^Kruqεon[98νG$~S?SOvۋ~;{KxuuvI}$%?\ݟ}|xwohxRoo.o?3ڷoSvo?ξxs} z|ٻOyW+|~w .x}|{gW~ys?"zxCU~? "ss}KFWgMZlk[zw2 1wHW>.^tbfc ç[~R)wל}M/-ugxeЩ?~HK9KP|8dh_+;+9k9?}/|3EZ&;z>7liُpqŧ{ڇ k=0o?Ȍd"V-xￜg!>fݧopq^OOqtBa KO?ֿt}(˪տ}?>6Ie4۟?}ǒه۷.8]S 8}ꇋUMh򪛆tƳ U iо?\\hq oo;ՄDhKL͇|ӇB"J?ޮ?HFeXo;|;wW+?Wﯾ'._.GPtkGhO݇ǻ{Z(|zkbǿ}cOĒ`K?n WO$eMh}˟˱Bj{㏫oooo+=8/ ^NH }_r ,X\v'sz*ꛟI|]'"wb?x7xGՃ@-o>]_}*/>\kxg~cFpywjyH Ͽl?-.za胟bbӢ~|=wׄ}+\¡ҕ+rW[#1pYҷ{^'ۏ_tg. {2X',&dv2)icP}_tZwyݹ߅]a76n}nqnQsxpg:sEn!} -}{>싶[hۅYhC}>w}GSs48őVZc Ŏ<}wa6a -cBb6g[l'ͼ5םMS t?bg~18ӸajnSO4Mi7MK6q3lfhpϷѣmvn%7lX¹ߌ?jC>5Wjmn?irS;zvHcG7vc;z!7D8n膶?4n~omϫv8pj¬V拖|^{Mټ[_g#-=ˁ:hCXm mmsڀ.zڊ=mʉ疶9mZG76hx64PZ;OxN4;o;ߞoΧ|8#y=DwD'^u?TP^Zc$ ~Sb=@vݮ[hnhami wۖӶl&æhӻMihvUC$:'GCRk=ڮ\Q?>un=qsZ"sλࢣt6nvnVIx> ˔̞yp#!5_<;V1cΆjQ-fi3BGC"xݴ[gi9(<[e9s\CieG{CAG;pc -\jh))۰܄ '>ny!M d5.cimY OZ/ymb/6^>s:q执%f&Vg -21/kcٲ+A߄mif7BáLkʣ+&?6ME6,7'&"HӲniQv7DgV7~:f *9b (Ҍ{OX$'\>I />q]z~*eg#Fص#b `j륯urg.?'Im#:[ub[n,5Ͽs4o>}psxB۰*e* -!AP.HžaϷĵ@݀{kvttu#i6Ɇв'#k-Ы'R9qГgh;}v zH gR$ -HR; I ^3 QTaXX1ZAvXyQQ4sbA߰!op5ş!`Y$ mvch1&v~-uXnkQseÖ1) - 78cd`m'Z[ZV9#l6 e;0gmJx>!n]ofqWȂ.:\xțy=q'͎ !u2qpmYJ߰caj[AѐQ?Њ- `7nveɎYc,5~V$GWm?\δ;+PN6BlF O\:Ҷ_ ID4`XK#fZD[K>Hp'H,gƶxqM_=## `a'B aCVyɀY>I(?+$غ.;6#F얟L`0%dnd(],q;r%Ku-;XHtNdx (&6P@hɂP0TT!)7t X"#+v*'5&;nI 6oH m1`#\`D UDMn =>B SS`hb\t`4@'P!׻  RW]6@جۥi4~:pN  '@gܭ%^ lb~6@"Cr_'vhc&. y6p%-5neӖb/F -{^j -Tp$wsC2 jæZUy5ڐ(:e!'9TQq-yT|ɢ! xB!S" Y9gH"L`fv36322zgs`<*9<$pȜg40KM̩mgI#:0U³qfc7o,e%ζl鵮O s ǫQ> ;LEHv {USУRPYyi8BGSeNr<<[̖&M|=<^O CG,FƠ fwJf, isjf&Ck\ŷMq`DcrosۣE[:-J|ntXC@Nu1V'nHgvvÞUpRMې|\ԝaHШ:28_K:1&)4 C`iϛ刁s.7؁mcHڞ%ҡ >.KYJ^ ήۢmfm7MROC|HQ3A=Ӥ(9B^KyZ$jAR;i`zvzZNާШMHX%d9RK=z&B6q3ߍrol#j=U - &cp/A]i񌶄[Hb^+,3m5\/uz B۞hmMX) hKeX+.ZmBB fت-@I\r tShR<9}or:io,.sz:"(>"Qo9+]=8ubf [G%y[pgߛdѽl~j~3߰䑜j;zl$ L$UF Md&E4ͨ5toX'G蚧&rE{0 1vGر0BujY!Y_!w,- nuYtv%5G[Dh" -lKrZofxI(;MVZ` <͢#frB I |EϮ9N?sѧ|$}%XHK۔sIVy0Y*Ui -QSƦ@#x,;p݁/` +bP&7ic67̅yH1v̟<1sv-L?!`IT*HGd7C?)+E #jM^ USѷp3+||&\ٻ-1|Mx9K3u3*&w1{4>dًl|%/h6IH.9R3s9RR4%Lks#Yfm{s\?x&6آpMe,>"lZӊK5u݈\G$쁌}.E&vUִ Kv*OIqC -G^vء@ GF^hyf~L}f[a%FH@FL0b7\ϼb mDh L.Ha %Gd#WjBTo=A9r9֚EFWy7HD6 R/Oa*r b$G/;3mͭܦ=ێ]Yv=.$6?ܗ7kfNunfI&[i{I)yo!rYkء Kٗ^ !1w2e]&2$)J:#FSЎA̹OvP|q1a\88]梨 بI#u -$bLPDI(QAVK1gE -Oӥ,sP[+32LU4!NJ?50*t`!Q7&lMiܖr}qǭY:7KWSa_ebcq==MCe-S_C6}uv4i쵠ٕ~jʎ5Ġߵ~yZE~r+]+tl),MK[k.Oa D2` Nȯ6\)I`AG^gv Wn? 3 X+P=3mM5/y޾<ϕR-W]Aw6@טpxh -ܫO-'˭Uf$Bq&}=ضOlE:yܞ޴_;T=ye㐂[#[9p)z! ;f;,sq;" +{f:/l=D0f}'禞L=JCSC2l$O&r}3nZ&ɳ=7ت#o(D #Ɏy̥ !'\YmuԦ'ng5K;>eWPoNRNĚS[sPc-MLNO^[3鳩,jlW6w4v6'익Sm\i1{A%*vv$۔?SƢ^&}玓Wd]/ZS=S)Οߚy0[:nEn).FI&`| -iKM};$d!ctH}~U0KV}PZ,f~yƖq2ļļļļļļļļļļļļļ<篢טט11sGabm,^RΟP/fp Jr͞3Quc`j3 ؇.~vj`}<#u<;^~f`M8xvIC]r鼆%aB׳#y"gp\_,0. 8G20Ed[Ҷxsb?2g95!3IrtOަv%%nh1%Hny&֖؂!kUnqέ 0Tse<|p)⑝M,{~Rzξ}!oX -,0;U|\ORg/55 {p,T҇~WhHyqZ[9b !iQ|F{0 e}pZNV l~k9[.]cIZVV<gsnꭥz.{=.lS)y Jc@(&2Z O61eDꅔ5&nR,)%uI5P!6DG%?bմD6'.ÁIB: ۀ RO.e4>-[?DɼzkަG4Ju FИ/>I[ۤU:yo%ysϼ2D25=kЗ]ъTi %2omw?73|g|+'I+7U%xog Sfw`ƀ:0ӰYdUםK=|;|곢r8Lj\T0`ktÚHS(>$  N^3Zivy<Ų1^yԳݙWLjBM /{;5_鵗]#xϮv37-5h֘Ħ(8%oL¸h_]YzZ;ouNlm m'V~I+tPG'S5i9dåqsf3\og)1(S#\L(mSm>񏎙X&ըďea = 2R10q4O%,%BC0\RTBa-jP5O vRE)u09/=w(kirVwc-0xx{wmNpd:BfƐl13p*g8ɅMiJLݦ*'צ^m)' Z wg" `Z5:B0f&[O"jIua/}fkd}~%[TxJd -\򊨜&nܪOz,}ZXOXPffK] -U8Czh:2S|~AUcd=DP[?Hmj[Gxz=qANi&S'lI#3$-tL\[Lz`فY;vj-a*!1*-8-:mbqGGf|1)OGةTd RlAޓ40IVB y R7~$Z!^"Z8Has l1}zЇ$qBp)TE7K 32B"r8 -dE!?^l҇h(Z.Ax`FK%`g7Քs6.`YY Ӽa9X|ivcln4y@<9?$$ǁ.'SϒHx,ETsw:<ժ ->X}fw6"yg{N} &94}(@c| ~VEg9 -䐧%hfy>+mRe+u"PN OSt'镥:htM钦J<>B MԌ#EY$钚S%W$X&M*?hqOnJ7gU(^,Y J<1آIx×k3T2BMl ]K1 KF˦/"3 CIp[sChXJ3LLw<:2˽,'6̲EJ<g` ?sP҆hjsYZGTYJgy.zZeidmt.xZ)VXGi%VRVY3=Ew}WXzSۗ<{zR u>ÂPw}JO͖BQmNh5l{>)/]AeNu~fOmO/2=C=ӗ:K$?,SǼQufthT. tP4hzfX -ϙ%KxXz2#b-HgDߚ[Kɻ'ƕAs9Hk_C4t0h2֚?Ѣ&,Zvz?;)K0Y_гIE+^fyK&Y-蛴MOVA6SFv; f'J`Y_UՔ4q{N~ҵKhh1g2Ι7g=WMA̒.ToCqTIZZo]ϵykjEс0kcs3|9TvW,>P?k5zt9F濢sԻکw'ڶ(mHZprңє|V[s/m:_ښ/ÿ,e/Γ[gJ\Pa0CoW\V"=oMU=z*Ec>GcӮhFڛ=8æs\ylBQl+ι_Lљ#áK験_VS7@ 54jÛbUdE_-Ί㻻 InQykW3ZbIr1EeoY܊ȳ시nv$$U9e󥭩\Uۚ/Ì귩u>h{OԱ8xYDbG|ׂAe~l<˜Zzou鋾[Ádúb[>~^W ϰaq~yhQU"HX& FO+~ු{9O9K)&%Sj@ :=AϿ8"ybZΓk])fSQ;n3 4v8CNB*uӫqmvۀl=|$5Lm2Nɋ5~!Qv9x}ή<^5[>@,QE@hj=u垜X8]{f|7?}.Ɩd]#ͥdZ[95Q&̊m=2SD F7aUiho}ckOU-gcs`f]f{.;Ib=2itY>Lm"&YBm92۔QƱ:eaӘ&<;[F6F_N{޴-mޞJamj-'H^bWcyh{VͮfB$5n\ӚXɯi+?k"?ß'إտvV.(zGG>?,O6ww?~xfWi<;nKZ/w^\}_.韽׼>.3dHVSV{Cz+.VHaM^#-0CHY$!7#$aՎ::kݷJzjq\H׍ : 'QkC;HX=?iԮ/pg~ttԭHa=ۯI#.=It$!#n#p: Dkp|Dё^υB1]״p-Bt Wb8ݳ_A鹦/ -oQ}}9s@ i"e}S-=NxM/S3t;Nnu+. P"[b4TXB[,ESK]Ӽ"NH:]bЈ;l_PIƐ-A%@l'*h+c-kalE\&)xAH'v -B@hC9ZދTrG?dlqiTd@jŰWNzEy,I9"wNҘ L߈ -P/S".Nra(%&CwO7Tʍe;0YVt2#L`2/R26@2S ˕5ddGj(pD,-*a"K* 0-Xʎ0\078 ӺY\-fR- kX*vDy9x#,n Hʤl:F338ITf.J8/qTUT!zRF@CƔ Z6C#0Y >h68S )H0joUR XǪNF,C uIΏ*% u-v*2^TW侢TA{puU:;zHU5eb:k=˔\d0h$DB'Νjp4oX(T!<)RqwPXbco,V 1Ѡ3vd -tyѾ=B/'8:x)T E: L1ĩFt+veK IH0lV-VlQ6g ?x0϶ /u3vw'K"aL%TzbphIv2hpU`VPZ*4"  68i+Rn|Ũ)mcWb 7NwsXS3 b~40a5Ӏ1fGJ&0 -̦Qf0l#KG -Q8$3ƘPd6Jx2N>O?&e+Q)%I:34gJ>4ɑf2Y `DjV2\͐f­*r&+l+n|nB͞X fvT} 2,iAMI1ci̘IUu3ZdBy2Xf55LfcS̨+1M4[wItl6W6K5kO\GUjZR!R q*:q5)KVKuN^#t0LEOAO7A DxĿ `8 b XZЏ2HJ=)ܒ侮ed -7P͓P(Y *UɆ_)ŲT+Ϸan!\WZ}V=wcJ[z ;\ '6Ճyi$V1&42#O=5Ű\H?CVFPNu‰ ^[^%; -Smwg|Z"+.%ʏf+E+_ GQߕ=l`cA|/ΨA>+܏ntˊy?o`g =K-dY*^l @vl*%7&:d.6kJHDi9J x1T]+1xMW&{]FBI5J}G@ő3hD.v:HpGBX '6ԩih- b)FFB/D)84b8GBFU8 '؂== .T[hd;F$BWQP+.dW8jЏ,?Pe<axDׅ=D|:.k"#޴Y,먃C,^RC yأb:jiX6y(Br5BK~:0`³ELB*WhG631) -f+ץ܇c1ʡį%?9@B;v (+$V|F7Fu3@Lu+7A:Ly󗣙z&$:3Tʩ&Lt5(WM&圪^.cX - !74$w!Nk#("/_G#FGJj!M將Ps%q'6mRcI 6HGmP-}B֧(Alߎ}rHe,'Z9@!civdQ 96'2S0[5.J  Glĩ;ϱeJ8 ғ'w˰za8'@O2zq` &GI,$_8||CKd&zl~4 t1v5q+N:Fm̴$ἉQow! p -"բ#^8C.ǯ1=zv_r W^ ~A [ZO6i:S<0ʕqS6*GRrlX atX$0F;XʶIdΩʔ܋!oX`PS.|^ RT4mwx4gB V|ojY8w:glV FWAXщőxC }e ̾Z6XD;rP.|L(l8Lq(X⯓o%7e -`,!n~GB6FcޖGKf-U}'F5uZH c~"2<]/]<=uge_Wkm\]_Yd" .3XK|Ƞ -@Ⅲӿd/$AW}Dֲxj*QF9"J4(`)왩3rUw -'U% 5=hj .-h?LZFEs -V5x$~ }eFc -L1)߷I!Ȅ d>z]ӟӁER8qJ$I??ىcR`YIy&H2 UЬ<|v<Ɣ$'偟dѬ3XA?юƓ=p.rH摬:G#PH8ʨӍf/20tlrX -dV!(M0ػhq F_F{Y -.%^)j;el).K@HrMcTC*#YA9U4oƌ-2?4, hh-Ƿk-Ԉ e*SyIh/F -Т&A&UP4n<@U1 }zE75DO=ҕ¡AqK 6" ,hxv9  ,AkW1P[YCˡ N=-H9z2D%sg7rB2> ,#(쮌b|x/cAi]1M!HpkeB+Ҕ}C [@BSLNRqx>| -` )u0b  p TEd @@p).I0A&f,JDch g[5$ ʉ2Id96^tLɁ튔:{f,`9Pk=Fi2و[J́ۯ&-aziڄ ,bLjh,ؖ]QM*;ұ E2i b~pWR`UM+ 9M!c&&(*Rt Ũj$&J؁23"^3BT$-=Ln@-== 1n{TlβQOZpXٸIE);D*l:pfH.K|K&l \/ uy~ƹt%eBA kӔ|2ԺrМne'I71՝<&s')dWռYě}E%@,;G !#4CĬ%aiYX0nIKTH.6)bKi's:ggF;#J C:YW eiVe<&IVQŜ =):+NY4 N.fܙÝ6H0U:0!x_W& bgI%8)~\%bvLj k%wao@e5 7؏Tb^eTUi&Ru!qR@\J!_ʮ*? ͽ,)PI.~-kN/hIsR ,[ʜAy'(j1i4f/d9DTq,gxRxKJU"b,I[0:)= ʋG/gzHeӈ ;YaGz8eI>H8c^ubS(\[-Z5)=8W9q:yK1Z,XhW[k̈́["KǞEc,8r}iu2oҌY4 U^( ԳX`ˎTlpW dꇤáJ1]5tf@"hj+싦d TV3UQi=f-T#dUӰ -[af5u칪ЙշRiG32WZ٢MjW]TkY8|G5d&<8`4n;o@fT#wo$<: pT_J2 &Emf*r$9B%ׁEsVఓ(Db+C)ܒLbc(Mv`OTlG)&FEL+duHbm]%?VR8$)-f1+G@F ]@(SYⴔ"w/-$<{|Mqkb1mEVil}&>ؑ"L>g8<뚝&]fd2iysW|]K 0 -Դ@C){%uzC| -1%Hd'ihvcٱfuHzZ)^) JH`c5CMMc6 g.ݤ]Y$c)LET^S -=K+-}P]EeN;UoS}l&)ln) RC J+oBTE~2ygo+A4 tE^eZחkpTeAȗe&0[ΰ΢Tjz-s$u }uR'XJؓH: 9:56~b1T q60]6,CğirQT4Aa -!?Li;Xh"Odf"Ox>OEKO}ϴlZ^Sz1.LgiUsd9b/|J&LE+ŏ" -ދ] 4B,,Y\4]8aYX4U'}W}*-k滂$f|W(ęX-U EiNwJwSXv^+i+=|U,"9kB^ ^`w缽 -ҌWpq -q,2^ fh6w2^q18 Zbii(botWMWo08f],+ʂ(Xf@e& ;M/6P=4NkA.t"rHN'$@3ێ9 <.%٧GN&!=× h6 T|BF.N8[ k\6&i.%S^:t@x;άp7&CbiMhc"GL;Tt|(|;biJVa挴1 A (nB -A` -!R\E_1U-8ykZ$ 6 (_ 9l- .ߒXN CREhl&S(jz^I7 \x](2InZs>²V DOZ#NY,? -8EM.$Y!jj5ՍfGIjmHc:[ vLR1!ߢJ(i!l^ZMf*Phyo[d+k$ hO|C-7FTR:A|V^0So\pn\#(\Bls9[FKy 86B-CcRU}i%qЪMZ/ |R99!4j-.V˻Xf5*K<PՑ>,r^Qq$& lxx,͵劁(0rV`;V|p å\E -G7h Gx.<oZs2>XDdLDEWo5#JA1̽#A+IsXyH#9$4jI8vDʕ6#VSiL곈j CԄ)k9$nh99S+ecsP&ޞ2U g /WH.!;yQ}\TU"Yʩ֗)YV{~:{O]6V VȖ皴:AVFqkmupmIXzhY][bVz7/C-[-W+ke-bm#iY%jKźusQc޹qIFR\FY)J\R\Y)TܬT*K?tUAp7sI#zj!4R$;i-"|A@qdT 05IH0Pj@:4>2LrP0D&MOc O'Ij,c <٪ƘRKJ,$46O$- lק^!-!tEFXiI?M F9Őd}¯ *ah aH]2 ?l|Nd} {瀹mj`zH**,!ߏ l/  Yz(K"@*#*=X"h89oqE(, nX"xܤ6W*#psy*HRp*)DKK=HaoiS!J؀,Ī8=7&*,L_L؅ JBx MX1$VB}!b?R3gS'?D[2d#a(bQՐ&>Z65{UShXjl96[6 e-Aj0-i -m'@;&2dRf4ӶA 2AF& ~5Jb0mEq 5dQ/+*gQCE`]UmLn_t ؕ7H@,(W3A̲`LҬHJQ1\3fc61|d -jc1yL1\a&?̬peI1S Efr'3M|eX6sL3cI~fT$D3$ t*mJg«M5a%e3CL͕mVMibYH+q,U55VYn]SS\3f(6njɦѹR8mU3+w1ܔ;3hJQ%},r%RMol -P%7{pe4C0QVFT{z4E5m)+TLJGNS~V@<ÀyOǔFq &(&y%1 J!OF\A% =h/r擐cx$:e7edzX ejd8eG -md[#=ši)_^ZG$oJ3c0u>FgONu:jX\ .$HgO> 9mG.mJ~bG׭&;Hzl|}w,P~0=+?{"g!D8@E|Waf?82)=(NK[1.KFwʶ9)tХP#yB_l)@|,vң9OE1fnaS[лuMc-rPqh@0x[/u x @OwU)w3D 0,OuMcêu|=lE3:/C8(ދ曓|ws 6OQ+tղ"! $iC0fL7Oj0.%jx݊_bn"XWȲY:|'d>P/O8:8},ɸYƋuø -ԩ=vF3D*b&qõc-=ľX5V -zZL.JLE_TiX(O%=\~xVl's}qľkc(Ύ`ծ)b6ZgrUS9wkĸv>% ҭ??g^/y(S *1TöyKB49:9J H\b2?,K@D -c zm%z5R J6Bиp|Q(y@fiW/$V#YpMV1xg3$= -2v-^HgKZL40¾>3")IM{dcX|}UC )EU -FTp0IP/V(4mY-ը>Grɭce~Q89w{6* *q޺}{j>~{N+4iڙkB}Eg}U1kۏE>w 뿂'35a2DeFͱiDpNB$`aX׹ZS\5޹Dvah2kUr}f  lpe# VAN(n]4,=LoqZ {tߋK ƻ:c;7wY1UopFZ -59ϵ>C:BGh&|QĠpDM^>,:jϼ=p`;(VӇty}h5$vhVCTؔe(b̿Y,`̅k?Gad^k[FlWnёc]*Rh0. -wZ(OPVI!lj\,3*aF | okB󛱴Twv:2$,zJQ3yrԟ3GPﴞ\wS*1WԥR;a0:ͪZ3W.ޖssx$5t'&v/ 7WGvݚrju lfʢ ٨_X%q x`Wn/_B( nuD~ji#ֹxup0'Q,"q -#-Վ6"jtY4Z`jIQpݲH6S -ڹ<|B-KP~jGN{W;ԩ,>'r*:l* 5rX{X c F'3a9FMxZ K -%r*T?r/]i=3@eUND#s_~2-O\V jl O7(ʞst=A2/ WU߮gofnۧ5ÓZg)v-<Ҫr[؃v)jro!UU ^J ɻ%':n-!aUCr^zz8k`0 1[efpo"{*Ԥ2Sj [Uފ`r;@ӿN+&sEҿ¿T-|];Xߒ8O_5Lm[16?6l74 8{Pm;݌8€kJξQχ\74D]sD!]^\>&xRB`},c_h(b+;H:ോ?Z(U^amUT І̻C2 Bc"n4շX9XI~$m ذ͟5Nݦ((h]y !P? Ѐp W:"l20:7,h/ 0a$aڈ*"qYlJ (06oG1p0č fNA|r_q!ncZ^l'DpT6`I`+oE%5Bݜ=Op^W3H IJ`?q%EJd1/$FQ'х \A>t ^b'4L)&=*KsRjNK9iՙO) &R%pwFΒwWPqR92"\Cr qd 6q ֆι,JW?@%Ӕ'-E!< | U_kt8߭k K,$QЅM(^J\ ~ Z%]Ydm]EF ֙[pZTf[I4s`c#A$=sO!ZVPk#+IP@y.eyzE: ib#>t׏?hI9 Ե\,LX^`,@9οaqXPMusHn4쑬8/GzpmWe;1NIHFc3#C<DžpJ{]UlXe#qvNRJLia-ߜtnDk,ˑhkh7JiPAduW$|9[>\d=3ю6.CJS`Vz:AxjYB|[}+p5(6aUYf#iS=4ڱy_[9nf.>#9ϰhKmsz8Gw3,),uDG_k>)'+M[joװX9J~ftS0`* $Cykvr 4 [3w}ͼP4 =# .ħQNe= UzE@h=F-5#^*PL3rO]т(ޚYXXm}tJI?`RSvQ/L4O-yNm>~0y*ʹ~z Rq,nay `i"v}S._V8,۹_O n ׅ=AW`溄Vf W". WqH @R)Qr/!Q23m2kC@a)6G.3$}iVVݛ'P?ӪdY ,j {;DV׹]|ra;e91aQQNk-h#zb^Caӓ@;h:PnFUNIt{:/4T)!u&zT8BӜKU"mݯbM; ;&]h+ -—:pwϴ*]^רs /7/dOrDpVY|Yvve2h3Q@{|n܋gz#ܹ>0G@\9zMА/.i!IO!| dރ&Ui"y?&ӯ0_*B=#$4_ 8؇*PF}Dk ZM 'cr"nk0{J0` ϐ72[(29mƌv͈hnN?㫡&2$Cɐnj 20#ͩ/3"=\v ONA(_1>7AK}l# ?BU}ƐV}9ػ ;0!qYHk7v"q(lR -տhؐNZ_G?N VZ%i.nT -eW(>+k_ͺ=,ƅNTw,sn|m%ݿ1inEi&ށ|8 -!?G1Qobb@SߨH(sI%v 6!ZMV^G3~InzM_Q~+P47G-?iO/ؖ -ȍ$_QWчB32|c -IQQ &JCpXJ$TCţ^vx"He+5 %;rIok ]!\T C$'f0šXJTTx(LE+;F>QyG.us(yg .fYg ;` -a'ɿf5*$ͶfY툂⽷vUhMT8?z1V[`VHhޫ3*oWgO(PIWͅqi vȴV줯EBj%x[Y[yY.|Tn'c/n˷]9}e1`qMJ%(4rSȗOXgoֱ??';=^:HUOxOnBnBn|www-[ȳ-[~ ~ȧ~l ~l ~l ޲<ޢ<{޲|ylxle-;ȇ/Z޲|jylyly-[{[!Zޢ<[޲<[޲|jylyx{Oa a);-u5Jz#;q*q!, 4XPV -M5*M FG`֖bU";'֦ abcKXQ9@-~8Z: ZC4!hT]B呛;!ݎxb 5iUe |DYÞgв/ޫ>"'Dd ґOO!}au*~X ?` U`ëݺSԟ ^_At CFS:Th4RBLF -TH15JuS:Ԩb*QBL:JI%T2cLcL>S:Ԩ:T裎1ڧLL>(S:Ԩ:T4~>#:v}@yzL /Qhg)Nx1Evm -cj5}>ۻY6ڏ`{~;%ڨ8:O>a$~ P3N@s) Ha WY͌)wWw}sx[b"&W5߶oQ9/ Vݹ%0$&*<-G_RPx% *<)LqY\۞Crj{6d{Gg#AjãəZۄѷu;m4F[!qq#Gq]~{O?x"svS8Oafκ6uCT(ҋfn(oytV]5]e#AE*LMOcV:aj]rVFɠmUp@jO~e42" ^h5;{oQMfh/UNVS&T.>!,iz란eątUAPw4`\hV -^Kp1ق{_ +vv -B,&~̮e] -RW7)^3Bh7T;翟IOw -{L|{QTW>>(>\0#:N_Cz%VZ 6َ\g U, HW'-`zߣ ұbFP%թJ:/{ ֠֫=ԮWE]4]%^q:sjoށP(ۅd*UVWBC2ǵ3ŕ*|r9H(z*63 鰟-,b4~qѨS{OvFC?`(u"A6Gg+6lYia4JK$yvji `oa"U! `r/HC-OSmfAHiwڍt`k8a_R,CDAٗaR+W-{[\,Q4FƳ$8Vk؆3cUކ[RP WU .B!GciUl%+Cyt@z;Z)"}ŕֶU𲷕cz c֏i\T‘ӓ9sƫ/!,{9֞[ 0`q57]TtSfoaz~dq@D A +$ Q ֻ ;Bͥh-sι*[**b_Ӓ$:<,Yn=UBuasw+Ҹ)uLO\vMR ->kcRJ\$s0~G`?uQ/JJiCGV ccfޣFq;'Pҁ#mfBob3+wp>[TV~P?E>^/9:y J LbInΘqHA5Ao KgKj U2sV\E]EP,~],"oFW/;rܹ9sR L"' 5JNQ(i&S=ń50ԈZ\?~RNh~ѡ?0 `_~ uh0FI#P|xP%K}-LC -2c3 00'yҩ |h޽Ǎ9& * -ܖ20&ٗ4Xa ;ES h?wO(&u99#2ZKW: ]bV*  E=ReģN'?v p/hL fJcO/'ws1*TqܞdQٰh46'yKINbu%qњLH#& ; Ǫi-BDk? 3\5g{E*Ţ -`۷&m20Fݻ"gǒjNF*'?@m}R eeVk<-ͣjaCQ-XLm}NnFLs@m`<@"UhlLxsk=9+U@P+ ! $;Gҏc 47[[dmηKl\@*s?_,0lV0l _;0W̗mʂ! 柧]@a?McBM!M~B=>NQ@R4Ӌ/AQ4Υ[!.iչ -3 -_Y rTOE  -@2OYXhϾ/V{C4xnK  o^V A{ݫ^QWR ' Շ-:Fozx;m=խ:M3xo[LáI u}hf1Z}}5/&|6yY,X?}}ݹ/~alo KO/__կ׿K/W/7?[+<|+1C쑈s?38Jo?ſ?/~iMx]3[K_|||§~7_Ìk&ϼ>P:bbˆq3DweXm3IOi+fXޔֈ+z K|9R --tJV(Ng!)ZNwRzؓZ4Qt)N_-yu'3M5H iH]v| -pޫ~ɑIX:UP:̙1^`gn_\μP -+tP*QG1D[ܹt)q I1haJDN}UfՃo법[wɊkDR `I@ץxwp pkč~u^ˮgmNg" tHW~n[ahкQRTPw -+%qy+]H kDUͫFqÀEqnK4JpZBါ>v""Dp!uWx>ױʱwjmL3RW^^/5N`uyI7ń|7ϪZ+H0H)ed׾o&b -xzn؝^3l.i"RTÖ -\ $]3ܚ1gj>:oh%Db<ǟ(;wqJq8h;NE%ؗd b_2Tl(T:jAZ>l3ب#X,v]MlI4#~5|Ѳ Кr$$ŝxt50 @TiwRiƪ;i4v=a:L_>c_z3W)T{zEAȈPi< ']v[lB5 nE)Gok%~J.R M\ \/rR} "kW(r0/ƯmѽΩvԫj6`FۋiA\Um8)ȉnM^zQ=o45n/.Z"(~9R](hw :n:XDŦ,ȥQ!+^Bt@hyvZP7ΪsPi:[ەХ W0!zKER2įvΙ\;*ooPz -{ plܯṁaԷv+H._S)diF듺m%[Mdv!ۡ-ʹ&Id.9iKۖ z3TY/.DmsRgƭ -~٤4xnUi]PE;y/l 됒fMw^$?vl{ 1UK.իXqܥ=T@uAb}b֕씲ZQv ]G?E͚!Lm|+8"HINb\?!7&ng̢FbtmlBM_P:.߈"s0 {B(4Nz&嬆`)U&=;,,TVÞ"d0ݞ' 1K ZOau)љj}e{-"쒸mX ~ص'^ደ7+sG`$0¸DFYcO qoPfXA||gV -@UFx5~l>ҋG愦!&?c7drXEaqw,͑*I`Sg;UXm'Rm Upqu/yVC'$m{yfXrs\Ծ1nچEUOb8cshB,[qFEH~6%#XE/Ua N cͽUB^.@m!{q,0>4WywPZ_i/nV-CrHo?dsi,DTcb13=I'm},tH`f%5 9~$j.e!m. -9¹)U咛uBji4X y<ţ*ebaՔu `UidxVFl ~ڃW[4-%YrLM6sx hg'> c8Oľ,I"v׃z)8$XŊv{2z%W1rPC` Εq^*b&¢)km}쒏Gد㕉A cGHs( -I^@qpaBjED(M -vReDZ bB>t)vݽI n~ "8)({\6vdC@V6%{dY,@};6*sNKV]BSPxQi[n5m]0e*`9n m,Qjh]DUi5U):jg/;K ~)} ^*pӦ>FLhI%u{`:Kٖ5>z ]yKa,٨jc^tlvAS"e\3kVH1Ufث AbbUUYԹNn#`~l/7L(o-fs3. ׃6Z]7lV`rk:A *9OGӬRaQ7jV%̀1b`5wb(u(ՈI66Ӥb81]Sx/(d7/e5WuT0~@F7tiܣxc zɫz(|NeU`58v~@ YQI^qDb묒, U󑅠 -F' 9 -ws; *pj/,XD D ͻD2*lf%b6DUC=l*_1z߹(dbBbz5:VU=s^U3:xmkEIKfM&)Ṅa`]5U#XQ@E-1BuVm},m -Ildt)i5s*42,גHL|}k+3$ ---Fs픪:ywZ#4cmTO1scQoFBN ihŲOnQ$YZ bd_)hH>v%z\eoh'KޯڴugCA  -l Qrj+εA6 :!^cbQ3;ࢲ]vZE,W*CVg)P,jy두@U@9U`yUSlT>tYpe(WMN~ eR!%Sd0H^*_*C2(M.̈́nmڡ<1U1*!ҁ%kv3fWFWA1ej-zy#US*4ŝfI!/*UUwZ-zVvqZ#YdpR` -av/XQ Glޘpap% *“,FZ~1J2d*i݄ۼ/R{K_Pux&2-]R T7/DW;-#X`:Pq@A=|Tllq78VmN5AUL^{ qs; 'L&jdr?m0$1 -*Ə)n]ڋKиH, g,aM:g -/rJ{bB|H2l l3n -f*(́ Pz Jlez YxNE&hФOΩVS/8-բŨ -ֻgd, - T-{ٽ%R5#LZ>!G),Tl^N(",|D`92S6+iF:/q9| CftáOkKm?4Q$'Բm^ƳqB(PAzLV՘RS<=qH+uU&hШ `aOXRyrdl\k~rWE¾U^mwKFzY`ugNQp2| eNMosDbrϪ?ʹa"MDKzǻ$E6ŊJ3!T7TJ3N>]iJ'k<\Q!;9:aojMh*ZWaT,.1lD ~ D%BVPbsPu-]׀nj8tR_Wk[1|" -6)EPt^С"q=n3'vl%jv( hx  fӱNgd,̒j|Zv27p8{G](ŵ:a3D@ΡHi0=IX@G.*fz薡XF6{zUq2Acȣu5Q-?m6KjS=$WжZ-A6.nRPd muSC,]C_e|CoJOS_."U[iaNY=2Ai4 -[z$} J  p/1͡~E?g8 4 \j#f{Q^U6k U[)t*I/FՇĂI(EoۦʇԵhWR a,38bT6*I-[hU/z:y[i'n%YúL-%?z8 ®V`LR i)b'Yg'-q6b%s2_<]F(2*߂) -PA6$*@,i&b2ϱX-Xw4 Y63# aVuZew$K #'gUǸ_ coRAW/UTlGH2IЀDVY/FJh(T!øsIӞ!*%NjLRQV}&]۪#NVl":)Ɉ,lJgί )[HȚa_|t0o&fz^[u !CĬsC5\9el^a^jZD#b8l90@ԓ*عV#ʬRD.c\2C- ߴI2TNt)ivUT_],@[MYHl:KשC0]@e08BsPMڬ&i\Ti|iqJSyYefeYxBڧ -j|UJ:۪$'@mݫ=@D8ҺĀ|!U{9ŷR]P[ӡCI"m]3 WVFĤQ硪`W(v'7K8UR -@`節">ۜGq9̮PN7vfq5onN!Ÿ0+U6UB;sJ&eR qY3=ozw \w#}uiԝ&qY1MbK.9A LFzϧOw+*{UsE(¿BlޢSqɅO8C؏m ۊ~b -Ϗ}& s,{+hAV߮ĭ[x&7E(HLT2'Kd=\}B `dGZN#g1P[ -(coR;eK )8#*Pf9x^ԗ(;DHR 1DErb9q@nK) -/V[e9s`' G#mߥFVw ['fFcL_]ܷQco[UEQNdd&2"ݙ`LddWo22g22I&22f&#&22$37Y6d"#+DX #+xz '#LFVz 2BDFvΛ LFd/m #CrÃL҉L ddzV+YIh #l=(LF6HAdd@@FFMFv۵22k&#[/ AF&Z22I&22$o22 }?,C?75u@F #g22no22Vu7dd]2HJXLF\]q\dM\dL\d.i$= Efe -O.2Zf.UAݑ狋7R'.24ዋL‘ =`w㼴R((\d.􉋬:sU~N\d5LEV^Ȑ\dH\dc~"|p[ѾȪ.f"l"d"C"jȐ\dH\d.*=|+5O.2N\d&.[[Ȋ:YQ-EV"+x\dYkg.2uv.2 F.R7k\d&.2 \dEDG"+$G.B΃>nPn"KEօ+A(,cO.2TEVDXw..\d)s.2}EVhzr\dԭs'YQ#EVDҹEVjȊJ5..R\d<|"F{q0F.Bz"KE"+BVvȊBYx"+x@O.B"EV"C8q.˛ E`"B?~p!$$xpe.2ERuqQ"#;9qQ3q"C8q >h"ГL‘L\dz Gy")H&.29O.29#yE?\d\d\d_;qY -.1":(G.J{EV"㪉L_\d,#Y -L)#Y `בk"G.\d]\d_t"!E+L\du[g.2A<$$V\d'.2YUڃwDb?E&E;G.2=E'L\d;quE"+:.r7YEҘR0quipcYa"Ⱥd"EVչ1/.2I'.2$37ҙLL҉W\d*EK?rﾹ\d5N\dD_\d G.2G.L\d]j\d~ݑ`› Ed"+ g5r!$t狋\E\d]2ruipf.ro.2;hG.2b43 I.. &2 5"ӊfY-"C:sI2qYEEƫ\dlE6H.. .r.2]o..2Y_q7\dX3AYi"+ {>rrq\dL҉ EEyȐL\dX>Y%1qm}s^\du>EF x"#R3sxs!tEE&EEEEfqY_^\dN+\d6~r ~"wy">hfE#"C8q!c"Sxm"d"Et"SCE༹`M\db`Ƞ|s8sa"c\_\df.2'.2㛋a|"#d"C:sf.*'ҙLL#/1sq㛋.2摋 "3=9pIN\do%qYEjcY=ڋ E`"E&Efu.2~qI\dUā -Et\dEVUpQ4"+B:s|x" -qۈa‘w"*EPE@`E&#u["pHwP{kO.2≋Y{plF.r3ѓEEFJEEV["c -_\d -\dEűP.2&.2E꓋ E+M\dr O\dxK-3չE@EVݹ~EfL7s1iE혹Ȉ\dq'wpJ\db&.ZˁL!'u.2Fu"+ ?ؖ$>ipaȔ -dE2s)6q%"+Al\do.23Y9OpRm#]DUE&E&EEt"+pȐ8@g.2e'.27 E|EEa1s!0H\dE-&.23Y\dff.!=\d3ȪgF.2I&.2"C:s!EFEEViyq!ȪX}F.2$/.2q"EVH\dUd3'.2VE2YQ ~"ΙEV >sz7sY-˃;g. -܋5q3/.23I."t"C2s!ysՀgJ.oMpE\d*圸YL#'.2\d耉 3qQ"_2rhx .X`#E6"t"C2sUp>`1qYy"EFEFEᓋ~F.2eo.26N\d׹"#7s|ȌEf|#b#?"SyEvHΟ\dʮM\dL\dE E EV"撑lʛLwN\dU J71sUi#/.*և'.2^b"EVE2r1#ڭ^\dֹ5p!ȐȐ\djH$yq)g=qYk"SƓ 7Y('x7Ig.23|"S݋E&8߉LO.2fv"c Y/.2 \dԈN\dO.2*&.*"ԘȻN\d\"ȊRO.3AL.2rGB +b9r\d*xq@`"S9E&y"c1N\d4N\d\dvŃLL\d^\d]EVs"CP["E?qQJ2q_\d/T52r!xqI8rI0r9O.2p'.2JF.FoɓL`B읋 J.t.2a:ϘbhDq V#P\d\d\d^\d'.Ed\dS\d@\d,En:EĻB #`-`BP.L"3\d .2SddB$?$s62ֹ2IF&\`#C bd#c(ldLF&r'F&`d#ScውL҉ FVXz62Bg'Z##n{!Ԟd#Spd#ab#FDFLMaO62 G62 F62H|E勍ЙLMldHldNld -bNldEf铍FVLld/Ԓ;Uўldo62I'6*(䑍 ɛLЉF&}b#pIldU@#etY -F6.|'6gw`#ʉld*Y ->gd#Ci$$ȐMldu?f62ȪvF/> vK7!&62F6.Ⱥ4Tk8#wldMldUш'!‰FF FF&lb#SVF&Fdf#Cf#Sub#db#kldg623~񛍌퉍ǃ7ҙtJ`#td#Ӎb#FV7>1?=g62r3YIőLe+$<$$/62*gf62df#뒑̤#Y1;ƨ} kd#F&HL5r%(/6D%ȫ`#3F`#S]FFϛJG62KF6Alde``FV,u׭62U=$$ȐȊ"#YQlsd#Cf#Sid#(FfFV`=13 "ub#tF&׉Lx#Y -F6Xo62F0uFfґ҇FFFV% Ȅb#F&|ljL=/623L׼Jm62UOldl`#Cld*КF6HFƓf62~FȐldL:I2W>ȊbG62ۙl ld]ldEF9 hwd#F6ȄX:q:?NldTld]2)Y?ȬFfB##7!ld!0Jg6*^7IG62ld&ya0ldLldȔ{f#<Q2x Ftf#C2ɵ{ Epb#$4׍/62-#Q'~ޟ$K4ەTb)UY9KUTWHJP w8`{UJ#JhdF/D#cVL?42Fus[F&$GȰ\42% -L3B#Phd>42D#L#}idmk~idE#d4l(Ҟhd6*l)FĠiWhdTHShd\L#[Bmid\و BehGiC#ThdF_޸*l翡w&B#[J-1hdF642\7LQ/LaJ##ZhdK42jL#[v}id LBF&2l@X4qB#׉FRHg -FidTI&~hdKN[i<ȸ2LO~)I,42D#_bI(42 >ҦڝhduhdTk&_)2 #L#Ȱr42- -Llw42j~id -Y< -l FEQ idL#Phd42L#}lU]e¿FFPm!ȶ49)Qid -٠FK#{D#[, z52LCQ -LB#3FĠid|hd*L8FF/LB#F֦B#S+T)$id -)4%VFyFK#s(v?4oߌ?_6=$:T24׽!gvs~"^@d3-jC&v2 S֪. d1 {i׻qT#z+"!NDKi'xϊ̽6~켬;c! -|LfhFiU4߫mi -׊6c^c=6tL9ve@")+0Niuݴ%dkL7b*??1-ltc,ʘ 2ƤYy!`g71~utUXwwEtn-$.Ok]0w+l13!Ȏ;?Eg)z<2.b AusUOTG~arv7 Rlx0{jz 6ury!ʹ↩}| [N鹇uH5 ^а1f5+XC|akpFfms1øTah-ho00.h=0G+4V=v4Lu*4 <悆=sSø~ojRgfl"065L]L oaRk,j9|媔%gۺa [ذO%͛a-.0o0 a8Cv -j6- --Q5si0ڴ;2f 9%bd0̴r^ާ”&Ր09+z`@2 Rz -(#R1a}A|u-SV g[A&]A Bc ^oh]%̫MO F= -[I[, iHg02&qق3 ,`:dG8LqaڃPlkZLAFL#OPT02FN0a&AxEk&.! @وkQ4N -gK#Ef -PL%2DP&q2LbSzP0)`̦!@g:Ј贈3C?< ` [C]uÄRN 2xBfV=`JX Ag -BuG!h`lliӶah/UmG`J!3㔊:Huꤺi8Xf`{iL ]Ke2ló^U{5 U1jzYYk 3lijB'ګ1O/\G=U؁48."s 0F #0$3I`|/ ]a/ md/#Y_*P>tT]-$N=ULi/7SQk $R0^leL_Y;ׂ^e717&'{QW.ľwna2Ǣu߸/ ,!2pj%qv4 z dHfƾji^uG%$v leWz 7 weu$HM$40K"+m!.w=v_ץbD偯!^AdDZK>CyP3](9uN*+:,6((/@^K( p ߗf򢄔+@^}qyA -ynyz@^-姖krV2kғ0܀.=5͚=B^/W(Q %H3./4o8 l!xm͞^R}C/ӡ^J8Bx}͍BXk!0z/}6?3lMI&+) @xf@s})0&i+Vrw!DcлHzKn.Zev؍EhraN^6qp < -eQ]K f2Z/f6Re5+kT۫ v]Ux]H;q8Uo gT@>$I][3P2`peVT KI]I K~$3> W{ҵZb0ݭ&E@ce q3JFtm5]i0X^.W~e60@t)btaotba|FK0P{1HNkoEtYa!dDEF[GtޫO]:3]jУ*/]n{.voZQDW D х)#pFtqta9K(OBt[GFtζ ]t+]R+B"e+ -B,_,@֘%FtO6iK]]K *\ KZ @KQ​ͥAjxa$yfs ׄ7,Uh.)t P?kXX\Ճͥ]wqKEg:ih.uZ)BFTu6.-52K*%`sa:<ӹ~7]t.M΅"ӹ[t.Y0KLRɊAx.(!.x.t/<6ҵn+|.,>Wgjhs2JMsi~0O2j'Ǹsx* -RB8P o >>cTtUEd<}p<Lb`џ\6HsHmp@wtY@hХ 3tiW~xF-zKt!(f]zeGBtIPX+JuK? e.A貊Bq t1) Y{ dㄮF,BEa=ׯ1]0DtiWYe_-|Gsɚ؝ \k6 %&sQs -ڗ_p4iG`KONT.労_P.+s&E[\؆s=NѢ>;e.X<.l%wTe;n^GqQ[qɢp^ Bb.\j^.u "$n,0\D7Mf ѧKx<|p)R0\D.)0 JpET5(\(\i…vHCE!L/8gCo9&&ٌ8AakARLpɑpbp$ --d];3[E iU(uJcR<큉sbo=WzBozLz#-[T`E8ҋӫWɓEܺ/[Qpw7'Z}4d1lKŊd|20e[aDiZjKc*ҖDˠ-YYy .\-ōNQЭ{A@[ZμĖlx'`6sOk|-)3f\x-~,tK˒g,NyNz.ƣ?Zbm.ݝ`"p|‘Z˗>stream -v gM U iRMcsgcMKfU,c aU\+~V{EB2^+Z~J5sz)T ֠S큽|N)D^iAD~q>½8G^^54UW8\+ˁ Q QUmQ;!g^AL¼VR̀#~fD{w"^r9('IZ- wk+*Z٧0 ܕ9]]pW&]I`F+/U{Q^uFJ-{̻Ҡ!xWzEafޕ&}*Rq:xWzO_.O wEe$R(˸+D<.pJxhmMo.U^ N| -j E]a6pWX4DfUn+leN+4 RBЌ+ 3y~E0*8hWkdU Κ\ayWu]-1xW]DûH<]xWK(W>]I]u(+3J>b]!$ޕ^ -o̻]v)+`dld?YHAoNwE+$/ t+)v:ShDb鯙/hWڇu sB`W&+b`W-h+☔mqI"x veWs8_aWBؕ6vE*]-îv0 evEl]O%yHLaEP;p6λŷŏ>BEkH+e_+BpCw%E/ ֕#ZJ;'J_ c0>1]#c(W'pWXH] ܕBN]-͂&pWl:.f+M9ERWழaPpW\]&#lλJ^%細 -SWxw7Rg|#^0h]̫~:Wގ̼Bh;W( 4b>3خi^uvL̫s{z -{*)aҟABEj&Pa& PY#w@H KLQ N"\DHP@ 2?:yAeT[t%)Rkz3AS5̤X)*D] P>:?T)#0 薍bUG@Pm!!K)[[&=688@P7Z -Q5#^@ŚΗ#TK v7, ;D+5Gw#.% -:[%_ BEVAR>1VƕT6T g}/@xmքfIT -!,rMb[S\M洩6>V~AVQADgMoMMJD)ۖ* F'\YF=H>;k,B2yz$͜C(5#jr_?\@Jǎb541Vzjj'^0DŽءU=|m-SϹSSٶil̃i FdY;!c}jA5bƲo]ut;LR(6s/j#11em6S05hTs9lapjam Eox& -c@z'H=Qd%u*2V)gQ2+NgFj<|2?xY}vBJa~EYQ@pn7Յnb"/mFՆ%_S4R)"q9Rڪ -NAN"r1hYM(uw"NO=|%,x)y>|yRe Tj e\vNӫ0RԂTPx`Ref{o[؛SU>8JnJk. 8w_5`s$x:kʛ$ҞJi=#9LZ̽IY:X3dz Ȕn}d.4<˚j]xT\u)߬؍̒2\.S0nMYNìJ5K*Rn򷰴{/|NS%9)VXѺɤ@e;~5$=Y|˘0OkF:`$z -ljh Y{[PrT+>n'vx1-eUZDQWBoܶ™7ǔjV 6Wc(Hzk -%. ;FOS_34]-TP]7JCub|z][-Ou()}W8RS{gKn݊Eڙӈ{ۜDa`R VUɯMi!VV8E~qj ?URV;6/ZSݤޜsCt#T Q;95s7D N&?'x?iBOeR1:uIeŬ\{;) g-CkṘf-i4=s%Ie<[l:_ uK,%01$ Xe֟{3E~6x\6n~묆9QR]oǺ7K+#]\f52GRx6+<=٭fq,E.A}t;runѭ7ǟiB by^T47bCܪ6S^tٶz)yت"8LѾ>dLb vMX'Жc2P3clhăM|"Z2%,/(xThR[Z eL@ag˔KI+K -z-] )\NƋ0^SY0e#{/:.e QqxPH`c0|!WMzFzMPt=r7: }2)%VVJQxFuS.BB* ߝ)nݖ#m61GQ5 PR[VL+F#Ig@y -軙 -kpKåJaxCobP΋{!+Q!KEw/hOs፥h(e68QeS&!N^ʘ", -=ICfFmU1u|?#I7xZuzt;>-,o! !q8,řZ砬p\5 hf3[vݪ -Q4ßX26s-7瓔`nz > !& Ýx]V,N:uu:ӆ%ED KʵڽiXW{/KZfkgK_~ZE(ҾuE3t^( 8_0^9!HFJ mI9U%K\ <ϯsNQzk (Э} &snogYJ" h'elVOxMV٠Fɩt`(1i[ND|״AlU  YZ }\]0ugK7)8(uOpcj7L'ZvV7_{ym+~٦8۞+&tB- ~;{+a[Wi3S)#דܚ64j=jGc3 4tFأRz8ĥP"!X]AIV>b*Y2]CeUGuϿޑ"kX5NJb,zcϤksV(07ALw2ǴSI`E|an"7m(;0b/1b -F{<5Mx_'scNeQO4+ܮB7$5s]msVo\1<.n6(b~ "vusSBobuڳK& C@I} -Ӳ%: -5|)uk@NU<0N l`^M!'ƈj5Q[<bUd_L |Qh*Y1X*M$X'7/&1x!,ذ:S[w@2E ܘQQۿd_Y1y|b_[ay[1v.S;[%MF;|jԥ)@h#PY1mSASaՋJyZb@Nlg!E;E0~ ->ш@\}m RKOCR37اІw: qQ&@$wB4n~=!쭟S,hB9/ߗ/dJyk̀~3tlmޏQ؁ -qS0cn WzQiTUt4ékR}S1+S%9[ 1#J;G^6D+Kk׽q!3 Wujzk΋B@8*T*S 6h\*q\^cT0^{8'Ԥ>khQlN22EM˸KD1xwU}vbhgSQ('9m;Ub0Z-fl! C2A2E-7 2H^N.~Tk -k~aK( ->u&T.."6),(|4oxT*Aޝ!o>KelU-|^s󐻊io>'" a"ц' yl;jwGڝ(U}Qt 2ý5Z%`vNk/-PY4FJa3%9SuQP(>ӺTvc&Üwyfu۵/wgJTk4). ೾_Û<)GObyB#;mZ{l ]M4;|hTpQ𸙻mFQ0RpD` Br!-̨E [i-c8yB{B*ul|Cac J) 6,MAQnY}XwJQ8q RKM4Yu![D# -p+W{i Ra&4H+展Vk~է(ˤ㌡so)jR47Wҕ&RXZ,J:5XbTtC/Z8Q^w¥hvӝ.X$\v1Ȗ-Yl5l!~zc6W&%)7ĚNL kfBUS]Q,۪a#4x a>Rv-kv:Ef fR&K+ kÄƶWâ2Viyl@tgP.]͉bI!D'؅ΓdҲ -y opclpQ܌/eDic,X1=p4KGx֎T_϶?5c(CTQ>(36u`el% *hŧzA7]` 17/ F =SA^f=OUL?Va(6Bg(UΙlc3Nz } .<% ُᢷmxeld/}YLuX* !QE8M*Z6#X[t;"SC0Py5X95#֬kMiB+ OHr눘tH*Ow(Yj!jv+hhNEⰑR'^^c iY\=`bֵ4-/f"ֲ{/ۉ!Iz+\VHc Hl6i>v[%C!OKЏ8lJ^`MfKS@l0ᐥt6~ph.op@Ҳ1Ş ;,5|KX)H~TJ] sGldx*o2N7.*V":hHR9b )zB/\<T+-PIz'ф&K4 pҵz|m+Ӭ#\n7@m67I+jt14"F< {>oaE)-jXyu3xEQL>&3Ymqe73<{պEJ@^ɻwYFI2v;g8 6gn=ܦf2t_%1v ZqMx/y mxNS^UmU*w*xL )b9}gFM5wS-4/èwIւ[i'U- -0Ԇyay9v%p϶E}0s!SW,:$RΜ5}AJH4fMPNNBSü"vA3'-@/jv{;9pO1ATt=+NW/RQӼCɿV0)9,wV x;iEj&"B4֋Ꮌ[/[0p\9ٲvi )ǣ9VJ`t+IJd;H!y ̪RBEW@/k64-_2TD{bL>D{#f7qo|XʭQ[/f32bt߮"s;gqv-sUS7TR>PLwPBpJhDP!a<R-;d٣ZاhK_[Hꢥx@]R2כ㰲^V!i=8ԗ#5c+6JY&l3nϭYsN -7vl%LYjd9{Z/8P=^ A\3*T'p1ާq$V5nv-\fKL(S[~7$=3|\ i|W.6GM:U(4Zߎ9FT@*h'H3cاfb5a){ w[QDLxnu[;UuыJE*:d:AښG'u1>FZ>ma9c,539;nutS/aM -Rܜh0vʲG/݋XjGU֗l7 jŀC% Ad5>nDj t t:fR記_]'*s\aj;PU)ݭ,.p Hu~sVz8xښo{ٛ͝GpF;DҚ; Vѳ0cIͥC겴}5Δwmধ -kN *b޴imH2e[WzOz8Nope -/"^O:=k-(bP~7<2 ;nJTBĬ'Wb{BU%~xNYH._bGa-ž䴾{T t1<|!)}Ӧz:x<>*ثR؇ 6q9Xh,%Ya&bmK7 P-iXǩT,߾|̡WC__հ[AGk0bܗ[6+t_Us5Es.*oV -?߱lf Kq`W}m[(T!\|nN<Ǵ(8vN x\o5UQKy.C3{(q[饔 T,O@.=gvd ͞3&za{{yNveȃnIe]7Tc:-{{n-ok0΍H/| %- bTv{=/†q;]$3%ߞZZǽ4=G0; Z׵ x?3JOiCHr! /Z1.42/uҍNWFn%[Kgx}|^e>tmA -uOi@VX -yOL&k'óbD65Ҿv\eZW -8L6UNo= - - ӄvgǛӽlRdK5~ka69z8-6Ͽba.l< LbKT7'6Saa_xM Cm=P -Oʗ'$T6YԪXe6oӷlh4^xxgvGOB}ߘ7vKCOUx3FT/4ݝg/OHE٣xdT?hhh<ԂC)hq'T4/ƃ]xvT>^x h$&V#fr;!hh< oxfgTx4ƓE,h<)1h<P+OP'S8_x[h:OgEO~x|ƓRx(}xf4'4}_4&[x[h:o[Oh<#x"WA *cx_4fc#WxLU4V0@QYx  -AEhh G'cAO -(hhh<ƘӉ_44ƃA ,*x[u4WGiA QwOx#Z: oq{}Xxn+OC-h< -OYxR -Ęh<&OŠƓeCEE)x -T4"$_4Ԃ㰌ƓE4ƓE(h<+Lh#h<xP -Om7H6G^x|e$4#VWx(AIhh< %~xx4XA(/h<ǭF>{T41Oah<%5h%hiE9gcAQvƣ ,P zs&4" R -gGסg4Asn4ioAQK]xL(D(.h<'LJz6~xލӜUxJ}xx4g4 hhB ggf4l_h<:rǵ*hūhhE',hhN: 0++hEAY/zFхPx4 T4G@cSx=o,?ch<=GCZxR*OGIAY -

h^p<),L -O7 |x+%Gѓ8 -Ù GcQxW8sgPRxI-ppp<b -J B]p<=Ygpp<pp<+oo+TQSx_8ǓRx(8j^* -Cǣ2xIu8X)QpVxW8<p<OWx43/[b*p<@MxZRV8)pǃ1Rx+ּO -ǣM.UQIl; 7ڎZ2n5r5"@cap jB!-q!tT|bϖy,س`vB\ٶtXx|p찹9H٬./zvޒ;HMB-1 v~Ŧͅ DzJŤFI}V"dQ@ӻu]wH"gi E@psz1E 5e܄x`薐(t[3Jȫ=ݱ&뱢mEYω9rԠ.hEԺ7\Q.95Y[B&msQZyr5>sK̹-:rNQH A{ d[p. n\PM]L\66נL@4ѽ}PK9 mU)ܨ šH'b͡k k$Ehj{^᰹S > d؜\>lN=dlP¸FIm cI?W`s>\N>țk.9Lx/Ѣcޛ5CLaѸ/ѯzÖמфcMB͡`9 6"R"͡&ٛ:YId4Db洫XTAN*6-4M8Ԝ~AL 5ژ@٤u5qUW{涒Qs[ f1Bᜫ:kϺvdM[B-18sB>YB"q8s(q-c:+́ 3j3cZ4,\{S`ZH 0spxT3heRfOaAN9?3'p o_6OJKm5bj34-|>}3ʨ8}P$V3h8ZNdʜ9@3_fV37B/|:P\мxv̱!s˧.Sj][Ӭ[etv9S|I{Q8<ռ(sBqfIg&}Km%S9FmoE1vc1ܿ!s6h:rVD3cD!؃1yl1gߑs1bm%3ꌹ~[FwVg]̘P7DesZ)9L~_qѵΈ9vcZcJŹkeWsm^PͱC X7ͷ-\4+4 p`1J^GvD j0v@8_a`- kךר `-'Oj1zyCuʙ?)]eӎU&]~ -aI1F'%hrK!LNP ƚ̒{|-XrIy%D[b䨎#`k@r-YTHNH} 9HNf8"V@y[䚂)%\c+|n#[̑Cvv[9Gf9rq/nVvnj\c¢ipݶи/M^GtZ'C.dbH9݈wtis[ĸ$bV״xH|Fyf"ơb"'er21G"ơLb -KLB9q%8QtuqJSd`Vg6NxRv85⬰mۆ“'eO kܼd^VצIS,2/NC$8xqR;㗌‹#PpJ%q,iaŋE<Od^VGbּ$lvUB{f-9O*0%pnI8n7P8U RBΜN88qq8p^"š ȗܭNt'L'5H)n+ ŵu{ *Nt=2-QlTݞY8&DXNh6Ai]]Gܟ.n @)+s\TVp+66NQBܔfQ.E.(Vpb? -l Ҝ@]*y3tv4'cqܛ_; n @a>{dLVe7 Hp[$ N#1ۋ0]DSfrASHɸ+SʤS3ɐPpڠQPpJA[7YRIp4UR+2/%$8W-Qe:PGK5lnU{g$o9S{vצ ( gӕ$8ܦl]$8]}Tgl‡tl_} -Ĭ?@pRH|ЙLNHNtM"hypDܧCg@ڼ B2f8*wV p8h"dqoˆ;d a^cn׵phW(8LP8i[:4/'QZkudtϷ఍#p|#̬*3* p4<,|2HԩwlE\V )0pt X9N׮& §Q贌JfaȤQ`8jXGd R[ r]G |`!"\'X"ר^mS j;qn)EpCprG8f r8hq[ cqP,8pFNS-Ap ٬N:.nA.cF"P 8() 8/q\ CQ~? Ud0->> ŁyоR% pT&w343N8MpwygimL0o# ]QsI#Tuq;߹o6cp߮櫀φIo̷1Bi6odFZɗAޢ*hoM%2MauA{k>_78wFZވNrhQho8m9)7ttM $ZCgPqgd؛>`z {zk8:ot[SfebjuN3ekšlH*&ɴ6PG갶'jS+զ E@m˧Mp8Bg 9ǠI8Hflc Z^PNH<3nO,>g ³Qt6Ҏ 3lVM4a҂F_c Y8mשe,yMX{"ʦ- e#dk;&}F21!ԫɽ "[|6F8*kƦxhc;+f͐AbpQ侕2te)M.0lB˱ -ۡgNkl}k^2״5xXI׬ׄD5{7gSJh2;-bŀ l+j Z;]9k$AfS֗X¬i)0kfY)kO=dM+fLgZEIEV -YkͧY* -mu8eEU$  -ՠ5jO[5 Z1R=*SZ.{KVMpt e &ZIm@knsY!kR,j!kmx*gA֤x(3FZܰs2di A֔ -ȚmZٜTփR8cngƚ0 Z8cM%)ΌF_2FqqUšD Hx[-X?eu`0 UXO/\kRʹ}n^yBC5*ebR~sGDXkQ5ͬr>k 8賺mճk 6aRI2au_5=^F箄GYc԰zԈgV0α k:S|ibKdZS釯"!Z,)@k,Y&WEXbpsr&y6A'ILXo_-ȅah_$5ešk0 -štšl*ʄ56&BRnk S1 ƸchgE5kKqM5TYbMf k4\<~Xd k(ˠHaMuh5RLX=6aGc")Sf㙰$ DAXskt0dKӽTL,FEfل5{:'B1FQ uš!^ kH š >&q&LXƄR֨ Z{W klSv{%I!q&Y=U a+`MÖ)X,ڮg%G1QI2ߤ&`sՌtF=f5 -J*|em f(IAm=xR&IhS"5_,V 0$WYW϶;ǫu x5eA]JR -^  XSTJXӃnAXEd{Q>a |5n\7jXRVjz?_t5-l]t56חzOmx6j*eAjꭑ#TVD`<5ј,7o ]Mx7t5mFܐ)鑆bh5h}Qjt$?d5XYS:VT (l^!\~5 oWzUM ?T5  -^AUcNo$Yι̂aFEc&BUkwhxcªi@U/eCf 7U#Bƥ1˸`ӤS((9E&!SPϨ(LMg9mc:~)'F!(o VjD%%qT53U _BUhSp&jU ŬFJk!ʢ=j[(jRljzԱj[;@ -!cՒb+X5EX5 Vmcm܎VV /VuaP V %cŪ!fxUUTj4F?qôbU.ۛj#4j7T= -FtUk z-ޘZ@՘rCP5RgslƉZTT#~zfD03Ո7v>YL5V,L5g~.j񈯑 L5TPTC^'2F^ i=E`tGlX|^3$cY"g3`ZLZ #SXL_cSմ Zj8cUM -ݢIDU/NUcK>&j݌{ #T4EUnnƀNeSPTՐUJ%SwkQU - ]gS0 íAhW!~4ZKFRh5> &ž}FGoPX3WpV뼽",İ@%%nl5j۵@$Yðj[dz+T9ctUXg\/ /&0 B7+ʽՈSj`5xXm؜Fbֆۻoi5vUSEU{sޞ^Yjs4ڙjGXRp?BT;N= #ym᭲Ӡ,,vacFo}/2qQ;Ǘf@Ԕz13$\F#O' ӌ~Pf>>M? vxvB(4kc4٘ D+v$ŬY2y;o[)K[V!,t K mTr\fw=:oRNVxdRVC4< DD yE")iwdJqI? ->)nUi[X itbVq£Ѳ,4M&C@H'o!`w 0w-bfXKT7)ƃ E6PhbAіRhh*h܆Dif1Zt D;ͲŘލJS*};&Wo&W[B;G%$>AS:z=pBA;te16m D#QP -L_i~&~&Usf!s9^3~X|ymٴDſ3,  n=V32SLmtkN3p)e.p3 s2A:S͝t}ʤ3V3).ҙ -f*@qf${EI!5*>̠}\[ӷUoYSLT2λ0dVtME0ڠt0]*Am!aΖ3,Y[D9C<r֦ML_L3 QrW8(g o|v\ 9=m%Sζ3xxv$XA*VkD9SpA9#:/mAt'!gNl+ s9#N$eM9c6}w<8g[Ȝ".e=8gEOZbig[&?V;}o To8{ |j?Bm& 49P2o/~.>}КM6 T5!Uǡ52JI_E߁|҇C -;7g#L[IӵU& Ԯv{?>0 4z@'a'%h<3ȩba6xjh tcHo$GFs& T -Q2+}83h9sXś~>OQF2kxX<5߉y ;yrIɽHR>U73#Uͷ25ML}YD9̸ݲH4ScJ>Uew>쿵Ů:4$<:\Ƅy`Zlۡ`# :U6@R'rh c<\R[k>XL[=Xt 5W3}PƢOתA9|:5p=lH,P'UD_}'c0N o}NہRÅߊ!o-oݗ5"QE>NpM?M"owx s/e*rynwNR( tT8T}j֏`ae͋IɡV *Ky(I9p71=(XKUDs ΙobS>npk'ĩ{@omU@m -5DtHzi -%.ɄSxQ[>1l6 ~,xRM* T*MR<(1˖Hm۟4lbvæXa9ؙ!s9BŤ$Nγf=lTӗpb'R<3RT kBV]{PA`"[ڗ?öUֹq{B^rdzyV|*;:䰨u,'4 )fm^&>{IzK -m9/S@ӓ\tRTl_oTЄ`/m[twSn=[7mWhuᓰ՛9._W9Kda5ꍓ?p\t_ךĦVF&_[\F mUhv,ﭖFs*9qE_΢/,,p3\aFP] n{C!O>< ysL{QϺ< ,Uz3qԘL?vGv>Pl+p$eVҪ`a4h%ˏKqِ< *LZ~,Xl6Q)pe2CqT'gr0?VҴxMd=}JLi)Ivq> fK".'Sf1xb6Rr1M9C&TJ\fۤºW6t/HVNijDI}xcAڤ fe)C!*b͓C! aQlhS<в笩gt @R-Y_N#) &3:\vK)P(>+(moOGs楑C*VBP׿*|'yڰM_olE"ު\T.5nldۀ}<Ⱦ;<+Z -ntsSkدC?)] (Po,@m[3<]c[8h[C=ZDQY | --E_PömRY_ٺJ$ o:N}R{:qKm+j𬿠F"4^PlNq -Z,!N-3B-؊ǓP/(8̾m[UV8D&^=j&It;qK)$'[*wBOϮ$8S< iަhw۵xVRbhra}p@շo>axk)ټN++X9II῾̺/v};cGvt56*y?6fI2SCDC -kRb~Z+^+tUґr=g3̪J)m)#5㛿0|V-5C`i)viU/qnu4U,l#<|lO0HAK[>m&G]xy{ͦA Z|Gxb]hݥȇmm(>΄Ӻɯ|xe[g Ėx:AauE3TgAp%ٍst+2O8K\ ʍ<9}GV.%E6Ԟse#hºwR^ڀ)Ze^cxe7ҁĤMNw{60F BUͦ}z&3qM rg'<'"Y>Sp(uO c;$ěN|X#o -ӌE6]/W)&c07[M茅Z#pڊb~*d߫Xf\٩yCz1]#Nӆ&CpcjG?dld@fIhF -S&<3*7I=ҪxҖK{Oی7TV"X8{E+ ~hܕ#TݹTH-DɾmR79+hH2*XWP#$SH2f"bQol kFWE-|`Ss}oK'}zJzP,fiyHRAB~zu?? ֛(h!ц͢<ʐzr:0Q5*T4(@^[u"7DOUOZPAm!٬z;O8kP/7Qw-uYh77C7eEmh7:~ZӞsm&zCcޤ>\R%!?  nZC y;4ʗy;䈩7ٙùu]G:(W8!zz[iʁCɝ"+0oMWQz@!yJ DFuQyhmyʀgAv#R؋\A$zVKP7R'Z92yn5Fܼ?SECE K%5DS@`l[j(n ߣYjȵ)ozxd42ď;3Rڣ'E-<Dʈ^6FzӲx/SY2^TWL`fo oԉ :5%x)Iه29OKgX)/Ū yN}CԒ@Y/=mŤ@~2E K <+8oo,o@xDlk'.6FzuxeO-)o_V$"}㬌Iio=cssZbgUkx u^ H㫾m-0 fdl<=xO.{ՐE%Y%i[xj?!pf5AX>"죏XI%'urA۰Nئ')4N (""}q{j18E;~yc:8F{nﭙ5OYr牯"` Nߤ7λ%ߍ`(Z7NA|e$wI-6AJTY4hiEE$/>c͊dQeJ"p?,{yw[[b}zd),Ϻ>F!wCU=BextYnp7/8I#I^ra>SyM{aI Nφilm)wGψA"*EX|ZMIDHl 8 ZC%@t *]ј+zJgg6+t` b]tmtxѢ:QjiQcY;[{舮r= 65kTςi^iԩM -Rd6>`tvhWQ B,W# sjXXYvwVlHWgPO2qq$BWbCg2iYqDN2~RbF=8-Q%076" nĤ.<k{ph?0lV>j FD#EVY Ժa.|AIȋOAI>Ӛo$QD[(;mIb&qtYJXVk\n6Fʔ9Ӽ2 S^Zl`)V-j.+蹡JXKXW3)i]~0}|F/bk al`<]yjU8LU,]IԲМ8%V %TY);H6OT; SD -kֵ,dg!f=tH5샎]* -HyV:HY4:r}N]m Ya"WR@GGr"JZC{YΨfUbsG`и3մV{b'6: 1Nk[0iEj|Ҁ,qy<9\6C U]6{8tf!m`]C8nc?K|6V*1VC]{r6aQgp >t{{?ylO7R=!X{Mx[j%BÅ!׭M8a$42,:~l׿tk[N+x8ijfJGe\T:*xCwQce>DZ9;,DՇoB }X]"&(jd 1wD`b6(H\AK(xT6c%3af+'t#lݡzI} T>[nMKn2Ԏ.4vZ׬S&jThk@'yX!CN@pN4ē} --(Фti>!q2l-E_IM"mgЃֱ-9ڀG - 9N"^n?6`w qr0`_rt>T|s@I -TT  R}ޗ+CSu.'%ݍ>*r9yBpt۴^fjcc#Ymq}@(>T:f; ,W,EZB+%tz[kk5cz8a*+yf{1}},NÚMN1m"NI@UE;t᜛K6cN2ok lF5syiD< #԰Zrl(#Rzz,0TbV GI H 0q:oO*솽 L  -sn$1l0jN$ #E!N\\:ڤ?hMK̋JP𰐄4RO YuJ;sfUE1ҡ>NH+:qgZXojj cCxyi. -Dkâcş Ӟ*-q^ Sjj]is>f%*9<ϰ `7H}o">M5w Kڽtao~.Kɥ"Ix­NQB[gә8s#Xǁ ߠۂr/sEz:Kw:.m,`Y=azv};|@uS/&"dn"0l>KtĈkתvyJds[eAP 'exuЩklۡO 13\McJ˲U:åo[dzoۚpw7i}fi5yt6-*k7Yg%L3zz8szq!>ߑ[3c~|0f wJ;sX^k=?+<gRP+Qpl9um9Ey(j/fE {RArƪC9DXuIrxRV?v# ʙESn79')Ddž;7O1x\\uxv;jM`IP!T2̍jΔ;ae\:odszsz7.ۊUzU1v91>GJ>k=`(bP>7 4w`u;" -30^dϷB#TfLN!:sp|5J"5#M<$PGNoԡagAMʳW[%9,&eK/ nq ǜƶ7nf [Hv'/%Zɥ&n.}۬16cq7?n$NO<2\o i⦙ݍwyV)+cΉ -lYު^><,6:VnZn\SOa>̅/;*[($W@ῲYbޱ#dZl͠wDQJB#v,I-518hWرY;YnP -Fqe<Ǚ56G̱(8OIxm֧24Cاo8;r|;2,UesG7U(rlc͹)xf4c -Oe%2b1;Q4Mm -U%Mzfgu^~1\BB۪_QzfByop -ivI 0~Kx1f ލG(k!j͍@AXP-oi9=dTD[TpR 3&6O]3Pz$r-pƞk3q[.sǭ32'}ªBf݊bFQf4#Y1LF6_LD ToЈ}9LƞCCe2Ouf\%<,jHī1N2kwۚ' Q;nR$Cϊ"TTYlj>'{Ee¾Pvs*rz*ǩ̄Rmf8skvڿmv:һ0n6o}0R56 -匢Wpg[S#+G2Y*6-*yV*`I?Ҽi K-3a)rQ-`g}o^r9}¡hmug;P(Ss0emN۝'Ӻ&P^a81-3k[IIvRKK ܈`C$,TJ"_dگ]D[g\n'2} p0c츌ٵ0Jӭ!mmb-Avfi>:vw &RyI}^R#F5zUŚ^[Y>8|<+F}?b;ӞSy[sBRUUs`+f -owug7'H'jiK:.ըqY/x5"Jc-]=ǩ.ѣRz%G79#Rn? Lx3$uQd#R۪.,$;5I!ؙtH V -ynj.>\ qZz=T%Nfi{#\n5fZ?w<hV`aʓ }RQ1%wPrq+36~EBa"$f7yⴰ7~VLJ։P"@j1u+(}a,Ƃ*Q?Fƣ۪d3XxO}7%ǓZx 8*p2 j(p<dzc*O+p<)g_8@'e 5 ~K8O~x}":Sx_p<c|/Uxr̾x|- 8 }?pv/я 2Pl[ 8^ӒjW;xp<UxMEm[hȗ_8^;Dr*Ow?wCx@g82oӯp't_6RR ׮08^״H,p ->"zLߟ6^?k$2al?:)l<l<+OSde}oX4?l<^lNf~x _6Ũld6Rsa[xCȅ7I)ld6V'LUe㩭7lq61/6ja68?V6ƓfU68Ƴ嗍'Ve0<񒒠XIH/fl/6R>K:?z/䪰x*Oo67O7 [Jam5x]rׯx+O[Jam5x+OOS̪yl:$x]~xS6/t^ycxR x(Ow%bRͥ4xR0ө(f6>:OVe)kfiyU:F/:t<\ o+X$Nӟt/OZd:‹OtOQ7o~x[ :D~ES9TY6~Jt<"L35(G-tOjI)t<Oj:ހKӭ,t<]B[B--x oh1:ULKj(U]]xt<B8Qx -xR+%8EC-t<)'MWKt<3o gjQx^t<:>G+׋EoiQx o:+t.N6KN݇fv=^کn솺_[ lN*ڭ#)u[b!ّ'Cx)s -)vu_׆ؽFɘݬªicKb5sa׎qkGء;b(vBZ9/ָ b'e|U!vΎkg}X(ql]Bצ5:cxnQ6N׭PrSN -EBXص Ůatc[y2N*8bm<>"InP쾯qk2Ůu^pJb;-QNwGawj?J眬gn~i^GQqmx]wz" / )h]=Sĭ#}8Ïbpu[柅Uug(BT)yu[ظNd%OFTha4Z%D;>=z:9uZ8sSe^a萺Wn Q iiu) Ut9(9:N ۢ鴾!xhN?LGIau\0uG$SrO1<5t_T:)JLPڈ=sI0k#:Ak8M_ -N"c JP:B JHR ^1ҽGUs@tw7N@ *)Q:^fml*^L%T:cXu 3-EvI C!8A>hJV. n:B'(zih&t*|tvI6&뉅{99Z6{NJ=T=wiyX9F's.7OY9ͥgo:wFQL̡sIЙs[Hȹ%qN=84]0g 8p!o{U?Ϋ罉sR(b[ĹF7/syqNf 8KsMHr}+k!Z!5pNkk -puUԙڔpfs {Q3Agbk z˵~Z{5,JrK 6dT-d\S9ꂖk*o݊܎ӥQm咒r[ \h9~L#,rڮ/" -'er2ZN*Bˡܟr(ZJTUv+ʋ(C~Yn+, _8GNi: -Y1k|sVؑMbqPxk^8Xn+,U5cs֌rRo[夜Wǝl^SrRm}=,ǙZ\뇅XN6cJ-uJ`ZsuW/\{C\Y@(4)NcYBq#kܼr - TC92G3?]r97RN -qη LG5c[JAm5rǃB(|l{NYqr -X"irW$u&'q%wY"i'iHfȝx>]<>A[Bmr -qirڜ=g+9` ϧoB'8}Pv*ۂǝ*;Nп'Mۚ4L8L*s39jdp]89Uϵq: aN @8Ey}B5PC1Y}[JAm5qq^8Q$d2k> dBJ"8E0>>q -8 0J(~1dmdKR>#hVeJFmՑq$ݗ% -63G%u[2r`cϧevAƵ@Ƶ[8) -2)}8dO[;2NWK\2uM`) 5QqLF I!8Bg2Y8=B91Dxm`\>蝹+Nڤ+˘@kŠSx[ +N!bqŠ8Ȃ -U PXqKםe'rAő PqVw 5j]Pq+܃1,Xq=+YqPTF8PSNFx**NMդu*_witmőaqR|\8)- xPI=]8FI%Ҷhqvkݸhq<_Y|q'@*VKADtmy -/N/ -?(xq ^\58͋ST ‹Jf&aۺxqRXG^TFŋCcPγH`ht\8} Q נ̸v?6@,\\ʹpHLl1xY*0NF.kO$o?K8@ơ(Uq+gc_Ǡz K鐝SEӀ[!Ƶ,b3 )FO!I~h ơqRq0? 08-`0i[8}}[}/t>dR{aT&8U&VDVpgyfimL08q# ]&ry*%N{bVSOEi0 qf NG| l X|8}t85gT8y1hQ;w4}Lp[:/.{\X }µȟ/,_ NcJEk G0b`Up͈mcE)X8}o,"k p-:?EYq\ -/ӂz (S Sf@Bmkp:rA½©-x_ppz&&'"5@8S_q%448yG5*N,8L{_S,J($'ӿIFN)8.#Ȣ?%Ypwd^C ;)xz icu>Mt̨[FД1E.zMFȟG}Sjo6~N󴭘oO0H`6Z:+zwсogeޛ -z3Gdol/7֚A]@%m]c<3:t%Zz)hV#~uAilj TgxSDxSTAxSExkrxӸ"oVઑwSFj̚)&vb)SUGm; UIMOh:pJfn*ꦈ^f^_n`'A9]Z@7Qx`ׇ`U8΍f$wVfyRHn*:;JQP -䌥m^0n?禸 !nzV/ -tonnZ&s嘶Ep|n~Np|Rfw6%oI'fz}RoyVxlbf]X6FM+gnۼʱm{Y ja_0ێlpQ$)4wB^_,\lbe -Spm۽? 6> V[dAp\G~X';&Xyƴ j,Jt)8mGm}mh#mr4g(1>tZm1we[lʱ+ fzjP̦'Nrنw,.,X6Ŕ,@m\lʵ$5v?g YyEck -Q<9+Mⱑ49V،wmV̖46kyՠնaZiتwM֢ªP.dž;plR,͘qlR)_8F36MGeOeWS8udž]$PL46 -uamc#-<3w5ilR<)#-I nH5XƦ4=RNcS0(ݦѰE1ؔkzNe0,fm'֨Gp^066$V Fb? JRٜ-qVhb8ؤR] 啗ESA Ŧ= ؉iQl Ŧ3m[TO_"%fAb_[Ep5;M"f -.+'.*K@IlZ -Q dNmdge6x;oq(ƅbPl/tŦfFyŦ11bӠc@bccBWvZt,[%RXl;v^jf䈃il4MJO,6{\x4H-?mZ@) -M$Mt%,9CnnFYlF -d%~}ؠ3dy Mqv= RFx6=@b0Pl0O(zPl]4kbE֣vؚqeFET^(63DJ\i+%(6oMi$J&MĦa˔ um׳Il$(@lʼZ 6o 6u;J6(H;@W-lĦVE.+Rf*(_objbO"bC"]?Hlٺ7n b϶raQ sP$6)]$6=趙=zԠgìĆِ8ZŘ SA`Z01c6P0lZٺ$0l _)TM,MS=5æ"2l8lZPF8lʽb.EP;+Mak 6[ vv% -=mH_ˇ`wvz~f!;WLol -t'- :K_h^װE!/r -}M(}+Cyפ)5j[h%`G$$V&_AK}UגoRf.A(5ykk^5_#QkR5=My~wRk-i%k!U,PG_B2kߝUS5kx&bd,ZkS[5\S3Ec0<'jEXkR ^|)_o S |?|Mfzk0SԀьFSZ<fPC, r)'󱘻调563m!UyS8MwVY_{ESk I55͹kk(ZmT^_#~D>6}3eM4?VMQ^6ic״h~ kI3#7QѪݔ3ذ#5`뼽 6m-p ҍ:M`l5]j2 ; -R0t2-vJ>M/Q;q7^L`S"80+B`#:lVN`cǖ4lD 9\z) " -F`bG|Zů)lM]5Gʿ9oϨ5)n7*5e*h> {e wMb ˺%:Kߢ,52/5jӨLxt;xkrZJ:v+mMv [p9C?3֎@iM9f:iMi&3X;>]%djj7 iW?7]3&l5M0 p{iC2sՖWA[vGh--jv!yP;6yN9Rm+@=w4Q:)MMU 9Ʃa,M6Ra<*KMMJ-y My*HvGMif!SwpA#DMZb7XiIXm꒍ [-$|v¢ ;Ri/5/XdzZ EOSEM}:x>df1z: LN;-4ݩo[ -5-8Ͷt;31$diF :m7w]Y6kK[BfmT\`(Z/I;m %M ICfIh.Hㇵ^ i8ўMXxw-h`[㫝q+v¢]+P4 >FAܛt+>6iTxѶ_{kCvyX<43 yh2]V +BD3"7Q`b̠EDSgjfju^~[D[ 厲3Z@4B9Fflw"U3EKM;,Ù$&Twp&ҍ(#Ѱl~ (< ]Ӌְ^nʦԃ̓H4ĭHd#Ѵ=H4)Y $ZRTڟB t!Ѩshy-.L4޶L4fMf&{aM H4he(X^H4،hfDB=B5A?OE &g{[Ja2WTM-wVm(d">.h=۶S]ӏ~m+@iSf@m@{".:찞DB-1ph -8Y8CC<֦7N M_6&1hh͏⯠84}Cvqδ#JeaNjCjECh$ɂxA% 84mqh -"ph-,-.g+fF=(#CkŬ4Ф7ФXȊeT6rdH-̜;ph[I<-$;5 bO@4f_\[qJ<5=2-2eJq4 -:#xc\ǩԔ@e<4O;7 aϦ،tjZEd)cfxh[<4SGz%pP5;' Z_t9~L62֌E>͔#%dcc4&qF}/qȬnK2#32_{^=(z`r܈",Pm7A3 F|k79[htHp͘2O.DZ÷眂GۅhBjo5M69ٍh >0ͳRޜd5߈F*gnDc[TͮDk+v%1J=ٕhJjW1:x) -;AJ4 ɕh1 ݈F=S+FNj9[c"j v 4V4Kj ]wv+XnER4(İMDCQ&Ry/W /ъ3dB4J4y8S -%h`&]~%"dN' o9^|_a0/]]~w߿N=/ϯ7<׫/˫ysѻo;]]|Ϯn0W_?8ϖG޾З{_/Y*˯Mpo"o_cj:?G@ݭYJ8褯i}WFH7@WW[\ݲc>r_=3PnHtw>/S&ŧg;"Q8+Dx$fA)KJ{ƴ٧ -"Lgd+҃,Liʐ>+DWup!i[TJIWJLrrxIJ.s@D.vb2sBd,5O=VwAڭ;W e@CtٝG2TIBzBÅ}#軮VYc!>J! ~0L>KP>`nmO;dIYH[.HNs3^Id ۊX#G+sI@lljЃxD"fβ"mBE/;Y|k'Dd[#پ= 9CbPY= bɧ^/u{ e{.3puؑwxoS.RF$YKW:5IA$Y" -}p*k mD26a:΃N H8znhb'@W1`r7єj'o>5Ns2eThTFJ}kh՗N/+x焜$kܢUGS#yp|3y}4^h[?u* ˏNӏ.6o:Z~o$O?l{]?Qq^#ؾHVqxSapI[ӈ -R{wM -;XUwN!zBZ"Q29*$_ )WU_|jg0 YhP>ey|@$yQ]mndQ:²kȌ)` 8Ϭ~@^ncdT0}Y[f{cm: :6Mn%=GNp- x tIƇPX8iˤ hng#\aLJo:0aŏX 9h \H4Ϣ(6ֻ0h/PF[c`mmM:kNsvX3XY%Kɼgeu93m!vvQEO/ pkۗbl#hkǦCq|")'h 4}D4wћdzžeP#%őJAK/tgM69 ,CtR|},t*#$jX!^7~ͺQ&2 nV‰YgY.oDIx_~ φ6 (=b{9冄bc>h.!MXYZpDq]l!Bv ՘>I.4 9 (9Ĩ3Eo_餲js#:r=oNu`UEXYnE=%i!g@/:3)8Uۃ"M B[u­\V]v&(gCe n2͍%X> J֮"̾gbX5=8kڹb-jNJkp99;F Qn.6t-?KJͽ3br;6PL#ს3P#]uO G~A$r{T/Va_0$؄kz'3}~TسQ{AiZ/RZX*ghN_2N;:d΀*2Yz;&P=;rK\9+3:dozND.LnL)cH/>nz~t672ʼ~u&%z/,@0z 1M(,w]36fSw9ԶhǸ[tfڊk# bsf7UH.?fz_(f5Q] r -)'֟p,o:|gGF^>[7brvg$'T,agi<5۸d1U#f7 1Iӏ{o+8x(Mie='+J0NI!f2l D#mx[ՂsSSrR7+0h.ѵPcYKgp*lJrFUChh!XN?Qj\"2 -",M bm[1շ"n\\[uEOQrN ==v6bވyJ b*cD#;\(Ԁ!6ZĪɸ>fQ6>׵{oJi]QI*XAe(Usu3Z5 tk0 3e̜`|{PwLڶߦH(GCY$[gm -tayړ>In6uD3{$Ʊ l˘SC׷ꛎ2v:SS>dZQӆ3lɛnM6;؏y0yyNaÊlX7 ;d {㆝xrTmi4H%0Z6ϡe'FѕXL0ǢcǂNdX%%B4[=45oBY(,}&4oaHSO5W)Ѵq0SoBݬ vo]'XFN0;Щ(`.i ƛnק{NFR荅5[8z11q]9cg(hY67bG7/Ep@M&[)9E^js#:." QrY+N̉ lt1lW' )ͳ7F#*|"zdSP,A9 -"E56O 者hC#B]i\yL(ŷЖW؉ D͜곱cc\l{}t♗ū좿Ur G_{S̋@UohFUۀrQȖ{W+轆ơYXZ. G<I: *%,KM/~JlQ)Q7X}}# .# rnlW?29>J,\ 2H̭Z/Bs ufzca -ֳ葛DsxQUt\ʭV2GlS_agnsfU"@ ֩fMZDY F!7ӵvX\]/ CT>PJ՛l7#>r nT[UH!plu~PIl#D)B B=^B,UmRDPY!lϊ귩ֵ"INnQ-ۣL];^؅AuWδbKXG^j'' #1P*% ,^>ؤ@ n9$JyhP5XtckMz>#=Y@u*97F]h -k13k l#qg{0yNO\]}@H:5Hߦm>?5~u /t]o5ŀNC[!(6'A X`ZjCkqG!C -,h׮)I +7n=ꃽJrlʨ:Q(]QrP(E%kl-QxA@4$U9D)sn쀩^Zp]20Iʞ(1 @HzY|l5nA0/G+>>UkeU{Wh3BII?8U9?^SBFrݍR]l셍 C*_x[P6H - kĮ3Wwv^>5+4HwCYE^Qkx/*v Jze$ O6L55~Y5rr7/\hu]wVV`u4n 'SȘ|.77dPo FŞ7=ZZ)Z@%mnr/ l%*! LD23 w ,l!^!dLN&eP,ǻDR;q}[Ζ2( MdQ`oŘN! UPD+(hq'8:YN25a2uㄘrޖ -!+Q!ZxIgVy7V×wCQ[UP.WRi 'DwlDG" Ðp^%4ԵR!"\lQ4;ծlA%*:5E͂cNgIIbK*K&=aF>aظhZId1!ϼm8EݐEћ" -Ldh9؝j%d7!bU7 UlM~!M ObIO87T-a_^Z)kNg$ZQCo5`&!Yho $w(r-4тeM58QjQJ7:zց.-;@ЬKmbLDIt*@qMAM!6Y T :р}쨪X+)9d9Mo~T/VP|3. rcbÈ= zfIbR"㭋B -V<9[Px5iG=@YE"ƕmc $֦4=8ȅ S[5Ƚy{E+'yΈk ^j 'e/Dۓ۳*j&ќrZ9 Kk`!xԢh}C3/y5k hMWpZYIC띋vdL#7].1ʽTA! -uZxZH^d/Ofe? gYԓLHCWsE3x#یJ$2JxKU/10f&Nk-)_Nz:Q !0WC7i,N=4*f;:{6؞ EuKgۄ$ 2l?TV(6&1}̲Jt]ަdT84ᐕ;ѩ۱()b -[Phpv".HԥJB&mEa3 f%PQ6 хFV(*7 K3^22ӅH xώN8Jԛv $|P1;('NʶZ^n:.iW@HNɣ\SF=U%IkQ[җy[CM5ol0\iWʹ]Dz)1; ~\N*PRWc8"N/ثkym 80%drvA#Mm5*eyKsm6[qtd9HԛP74#Z/@bi^PlqR7XCml J vTZmstĂ#SuH5Ӻ7ų c7)*F5XmV*W-#bIH]nBb M%vM6q1&!a )uAR), -IJybj1` Gخ~ - -BHo1K׌ά/mn{GTĂ(HլJ,M4bŎ[MuEXX.A-; .<4F-zv<qXc#0& - Mjha#t)胮&3FK /v0oPpA]K.*[Xr&PI;˨H:ôE a%V㴄AabB8{ÒŮeR}:&[Q ƮldjJ̅F-qܺ>g X!m i@RcQ bj/"`]gP!ͨmѹf;S8X~d\(Įp'183nv - neHLb6@yc ,.-7o;5GbۓK@AT@.4dڦ%3jժlJ`x:x,wePE"'Cl1MΆ(eIud¸:BրN\wcr4/"}C-S-BZg LR54yu Jkwf_r[N>. :c\c7f, #9C$]nYEhܞ5H.r8[ft.[-^Q 1O%&)^ Dq:bjOR[VEV#k2&Z6z-wogZm2XNqր%{q| <*ٽe5~PZ@ NS"&Ҏ`(^7 KZ}8n8[9+=s;|9fVjY;{t!B+`5f(P I[YߓrBV% g$-w-;>!ԉ -m6<*,Bza4Ǽo.JXZ o>neVW C?5&umfVk!s؈mwfφyLJLaQM,WC "R[^$k?P1X5b׵)2F\4_tb055ߊ|YAg ->|3ꭳq+p X-+|Cfͺfuf+7t M(nR o.6Ҙl$ -Ćxe9̽W/k*ͥg[*xB pg VbPJ͒qTDj5K_y'\?LM2: 䏅iI>\`Ҳiɞi} endstream endobj 75 0 obj <>stream -}7f  Z@a9tpYBzH\6h`Q\ -Sly$O'i>XYet'6Ў/yIQ=mPaV/S -quegK I$KG ׏"N >ONjz\>$860'f^&v{o/ԕLM`H7$ǔa) =6wS%k[uCK)(MxurJ/-^QZ.-'q_#bzk2Nc!&+aziKg12ɮXгM`F5-.XYԈlHNA"ʝ3l&v4k*$&h:DkMxc\Zu@i%mX)a^)i*;"8ʱoX<ࣩ 0 S"&UYMcA<5σUblu~,bOr=c<١kGvJKLyoc=s`N;欔=ʅ6do倘?9b b}ڷɹRbSI=@*ڬx6BhTHu6y񊺬 -82\IM^,{$M I}S!ڳmZIw~sg?Q$#Fn]&ܓmjL ya<m(- "dnO;-C-&9Qz#-{j9Ʃ }0@:Il.ĢZf~R cL쥜42hK ->B@Q4P8@sK>u™<Yt29#Z}cEcEBT21πnؠs#tJb{j  5`ɕI4*` bIjM:Xg̎vB tX*  ;0yg$ $DXd/ߓ>kκ,ߐn.):6"o{l$hR+KhSж#Mn0r-^0X2-W!ڙd,WXB Ż}WJѹ qvIrXVe5A'0ىo) vb$:+8]K` JMCJ|U?i߫b!ZD|PzzkZe/\  Lw957E{HOuah.(hp wIcı6S&@'9mG)\=P6T5 i_\p`573{Dc 9E 214dr~+Fy]cA -4Ce(m4 -g^!W>Y[9:EI6]w6j"9ܲlŬްEkoJrא hJ`6TjC\c2汭V0= [7p&u%")Oh#hI?NMHfdY( 8GS<7dJ%]ZNAԊKI" -0'm˚Z2v+ BHʓ:-ZCġ<Ƅ$Q2udq -!|Q7?M(3- ꥳRl9X*U?hVgy⫢3>Z!Ů&AP77dm{Db@Z3S´~qQ-BΖku`·%\#4Ǣ6Ya)zǬ4IoX gn*W -(Or6%aXDIa2pYڍ9cl3Esʔ͐/\p둥%{kRb phږOI+VtJQIY.bxb鸩m£@fara\й4f) -t}vP|[$MFq4|H1_liZ}܁Z,S18* ɖjї!.\FÌNT9x1|\ɭl߲ӧ Z8vN#%"Cd˚hUbTM<>)16׿kST-`xZ ~P\]z0/Ze&2B.F Se{1NV!AYfHFdMUoE#* /~ RyZ(9Z0OD-"lص*qmcXI XL~Ԣ8]5%x;5njb4Y%Mӷ LH/J2jg9wJLVKDmD[[o8|@eٷŖe@1ߥŋ=Mde/yB̃з ސV~$,A irX.ߜAV.C.;&1̒w tu { -Ǿ*s -qٱq}ӒMyBz/N$]#[djD8E7#NI)#r`7X^HX%#o %b-{7 -2QHGI[F'ϷРeTZxJCYתׂ8zYtL[N|h*Rf9 - .Y tbblSVnj,ٸv|քWKnSAuZ^&Bm<δuϰ%)zٯz,f%XCl.?ߑ1sHkGѶ3QadM*xPLon .buZFf5-ü%#%Z=:v |g>pƎY9ஙrZFɮ eQnU%Iص2q,y[+ ̅4D/7J[aSZQVx,rكve3[<) k䶛eljPإV1ZI=2 -af#+!N,+&ʾosATpf¤v;/[=8תcbQ6+1X~ֲ -Ќ̐TVx$HG$yhXEgoK XLQVaWyQe+iwbԄ41r?Yx~:vл/[V|<(ghWrIXY4VFnˢ`N(4RjύbL7שw`uSZmnC/%F%MJC`HcP[xsV|n;I=c+\xMou{{*nv܀GN锼Z'^nYMH*np߽^Q x -Î՞VCJG C"CqJ^}Q'NYk> -p`B@\L]elu:IR[D2:yBG?g=kJ$ĖFʎ K"z)HIVugFnՑփ)vlum\9Xe&Pd@Ӊ".jk N>xׄ %SDc^oAm}g[XUBn%͑0ώ̳s??Z2$N2Kڂ\>*::J b)X5jx4Ӯ yH, -,DN|,n݅ŐlHu! G:J|φTِ&Cȼz|mPj͚B?!SO/?}6s\%~7ǿmIW._\]p0 zK헮~_ꢒ~wׯ^<|9}<}sy7[1m?Ozz./>{}vӻwvKëΣ?|ߜՋ;Ƅg=~*bW/o/.yu%<}}狇.+/gNؾ:us֣w(_^]ﰄk<۟6 ]wof79.8uvU?z]4]ݾCpN:<Ͽba0yn{u)Al.˗ǿ9OoD`>50M՞իgengn8؀pl x6s㳳wѾ؀'Xiہ8/9q;J&Gmşyѫ]~wu]O_z}u׿?STfKC輷5._\2Bˋ?~$cۅ[_WmG:ۻ>Y*v{YaK]iH_nV8~_cWcv<5yч2Qͥ<iw"&Gb@G+!Ol/177ǁygDݳw#tx*}AKDng$?]?GrvSw0n=;y埜]zy[GC#ʝn l?ھ>>ĽOf3m=} o2/_-O[Ol9H=nFeOu@ӳ> uXgovnI'{\kaO|o ?޿j[kχjoǭvϾL[h_N}ds-g'x>W[sG{@1ooo/#|ŏv}v˛ۇ?gymj>Jݱx[qQX{) ʧ~mۛClڍ{!C[(vX'Uϧ)[Fl=@z)gz9ȷ[9˷ovo{%~{_ YKAAQt;Ht{nm6r3r[GUvDym=&:li -twʰ? 8yUN_r|g&/oUdj\ݾ|yu+QXo/>ۡL䍏Ww5w^};ێljly{}5CŝCŝo|wRww\M7?y>G1[v.dTTgxZɏ }IeL?ӄG7G᛽Iih81\ډw{&GnBށ=$| a끼cӁ'"} q|~G; O}SgNҟ38J'^K70C!|?eO"[C>ğ]||9ğx<ğDuhf's~>m9Ĝ1Cq3_T>~흧xqWgwU~-{!py}}㼾 Wz_Z̿Ymݘt-y⹝Z;_K|p\pA#^ {?7UM=㮾wWwח|wǮH/kK; -x{y>©3v6@Lݕ=e6᭙P'agŧմZ~Q/9gsp ̙sp9[hp݈3G=;9Oۖ=8s>ę1KzB/N_s.ҊqsE='[ ≗~ Oۻ/."_wXwmڗ -TۏPLPPPPil{//pK[pqsw7۟|x_)$uX{j<ԁٛl=qGv VϳC0}Am?A~ ^ʗC[*mH^o?sl Ķ -ܩ+`>BsVSV\l[ד?;p{f <3pF/f{..#9Oww/?v೼bkKPidT=`On -oȡ*_a㣌ɴ^c{'WWͱ=z?wzz{7>]qߗMӠeO[y:M?:S{GvX19=p 8AYX{[[JrI-lC*\'[(= Ƶz}r7]`Xvlx_]P~uaֵ./;y'o:,W9zz8BGcOucnN͵w>^!׷Pyvvw?v>>p#Uh!緯^n9y\4yt4nY's<' D4'O`iʔ`яۇu_E -ʗKmNW?[O_p/}~uRG>h?W%}xow~q|;ɧ)_Oq'ttZ:߇t}ԟzsX_tsN}!ا4ԗiHC( ԻPIC}*7ꏥ;M⏮XI|.>8g9֌;)ؾjwJN8-w>>u]^ ߎ~eݾkR_vǿu_n-߿z!_P>o /t}I_~y~-ZWR?^#_=#<~G/u=aayU%x[?1ʧ>v+SCbឰ67oٕΧB%}!;.Sʃr,sl\ꆾݩO}44|yyfɧrIen8}?Ӿ+1O\+t/Yb,Jm;=(Ne<a):xP]r4|TF_r|[wg,@wZC)n0]_u9"й>0q{icYIuX]^ٻc~X-yNj}$f|)E1&v 1A*\|Վ>KKcpUO:Gr@UR|,]d]a]i*oڇCķ0TʪR"GRr=N_qIBR9uR)Pb]*?rOsh%tp;[aS~VNuF*u0 y?x>`h]X*dXtU|GeZ\(=*g;ϟ#[y/z738hꗆ>[ u-)+u5V]6mRҹzTԳ+lpux]WQw -&8'c*x*a{u;UOd]儿cuI$OΌaUBWP8A.|B^(.Օ)B)>L~*Mm' jK&\+#P9" li`21$\ VS  rɐ$z.q*2!50uɦ*>HEʻ$U9IfS\# -Һ.> -2Z\qXNVͨlHd~iKUGʐ c9OTȵ f'8HU4w}KLAmi1x3P^%E-:*uґZ{ksơ6} z獒W55<)!C)jMQ5&~g*ac*3ݾj=N'ثL$GGj[8ݪ֮:D?NE'|FLI' -}(8*!q8}9 "85dl>\@D߬a -vrB2W#pelK@)#Qb'Y29Tv@)pz 0Q)=9CFi BItg*LR8p֍S[c:Z -Xkz5[{muU;ĩ`jTyQU3Mj'wQ~1`:$oa`\+XϬn# OP22hn; y 'qy݅ΘЍLWCKrF:|]/Τ9Dnc ׅ|lezY-!H><cby=o+O|{4y/>P%_86l9?7G=9#p t4>zA7+YPHGsZUe*)<iSj tޏ{|%+p{*[Nԛ^{I15DCJXHXu?˩)'Sㄇ"E #?vYh{_8Aje {O۱u7_-|7$!Rկ M'==!<ڪu9Lхȭp:@nF+*I=-^t0>/zqŌ-fyd_Y\yOAq@*8]F<\ .!kU{:: #bES\ -P"BXg5?!Eh'&}@/|` -tˉ»J?TU']ւΎL̨kS2HcC\A1+-İe|EP g B;baƞ(QEbLC\g~zoy 31gFƝwGX覈"M|RIX68Bdu8C1؛A;,]Tg Yg $V~Tq6/>0}x`npiט 8dŭ{Si`k@0¥Ey0upE6GCAg3JMZ=~hu nDT鿣ߞq"R1ڂO>r'wz.x^ AkYpBe"|PmuIbdM0 -zSQ9j9,0|f ,y#pXj@Z6v4، :1Ly~D:ݩq݀*~Z܁s&;aX4iȷ++ ꯬{GR?OA$r:SJ=RU|.|)khQǰqWf95G&p9`P+ze*)% -O2IJ ,T&kYy `%``v'{STH AƳz~hxP4_.ϞrF ~:Nz{U"6Z0:wm`żP^A:Pc%{h HZ1_\0҉"{4RQ"|!n:e:G8\-aK<ˣ'ECG s F30@Ic -NVr -RD@\gtZy+bwQ::FVPf@>hNwsGD =Ґjs@h.iؙe;j9Ԅ -["?$$Ϡ 2P Ltjs2f-gɕU?̚Sw- N$OQyLH\)(՜/!9 -u9K0F3P66[=zBJIhw("JoZZ,|#6dQL?Eө' -8j!d%dCI S`(ZѥT@D,BB0CpyU>(2\"(Gj) Js-;́&1<7kS"Ѕ7%F|$ZHrh:}H.08ejSS  +E mď1;X]&|>4HjpUyl ^&$8Q~w̖DdP(}.E? CCxAvl-ksTsȐW4MEe~''!eԉXbfb>P6-Pu&C2hX :X ,DUYhӸ#_% D$Ѹc LEA l h \Cn㽧b *9n@jzPEbV2E4E32I$cR5 Q=GhDW,+ B38@^!Y DWxM9pI<[s݇m8}i1d M<_J(&U9yq4IQ( -wTO`:0B]DMyh$ni8DP\i|EO(/HmnЌ!ċl A=:D|1Qg9|Pd]A>p)hB"#  - q6\x6)[0 g9 hjπ-l1IŅTa:{+I)Ҳ,p1("+G;8 x>9=NlF$ ܁3e#D6HhIQ1+}a(0 -CŵXA_gS闚/*BCYge86nG㬔%h ݀% 4.@4#1jhEY͠^xi[f,|[ ׂ!s]0l=Nh@`@:ͺ,uT  ADY1G@4KC >DN$Ǯ3ý '% a/6`hK xYz=uNk~[ˠ2= gJC0XU78=|IcҍU"̓*s__' ?s6mpGG:N{kRgHZ$;;fxn)p]}NF/$HfN0,uynCHE,+l,)n Ifh434]Ltlʨ1{qԆHa-g)UhL4O6ZF"ȞCeIB_YԚZ׏bU#11 u^x. -D6*쪞7hFт{r?} M6@w/!׌֠XTYE!,XEVд[ѻf#q#tHp!L{WjbI}ge( =ejP0 L֦RȋETUj>O%E41IJq69ɝ͜k J;Lqœ(UqBSa,VE!x@Stl"S*V='c4~'PpFN ]Hakg6"CW1s.8z'DSE~"P6?F*PjcothCAfʉ Gtǭ٘8C?7 nD5`9E)%"PU"Uk؞j6|% -/%@cy՞|DV74)I-{&\aS*\rG D4F1yC&uBNiٚ]-ÒtAÐ UX/Ա'J,.kNSuk7}y|}e쓷Jl.‘@AU](AsI&$O_ _] ~>)6,L[Rԯ<5>˓){5Zn{N?Z~UDudPqM5HtNE{ʏ4vCj^P`5[)'++$ܔU^{QW/T8CˮƧ"x9Ĝ5=A!k} {Xƍ|p\f)qNx(g}`s N 8UNq8Y(]{}b+WF=PYuV0(KA)E|[Lh{-p@d0U?c1p}Ｆd^lOW)ʘ~Cwמ뛫?r u3(sV̞wV|6ZC1xzmJSxr2dپ`Th?؟GEJZ43~UEU_ߟ}8Ws$d#i1'qI?t|Z=ܹof^L^E6"[}hUS[GAAJJxE8:ؠ5~ϐ\ va3HpV8lƴQӝNN6LqQj ^Ė/W{ >>>mH$ə֗z "`/ x 9a{P0[NLXo_#יt^?PyGdj\!&{$24㰦;r K+B$?>EGN}w?rlXˍqvܥmvl;tL+qVEwk]ٸp@Tp:bnK0f?>YgYk -|J妁w_{_[7?>/|ˋj\mngۅ5B䲚8$!*K]"4&Z]]' %Ib)3${-ʊ|:cR}kgϖz -S;өDKH+5TwN5Tpf -wSuLNsMWpy?pqliGk+}\[7Dp{.4o6W}G\zW9I@,ֆU`Ɨ76k -$-ϯc͜?4[vlxUvR4,H nU0ؤA.^O _ ZvPͿP5CjFbYw7o|M;[8tyCP{6J R)L$ԗd -f\˥. -KK-"弎%`3GA5sY-U - Rԣ@䃢Pر'> ܒS(lAxHEUQL@>L -3IRk^Pf Iw10~Ȍ%4r_X@4b(N^+`IQ}ggtY2@a}]'-mAۉG -'U{d䤌\AdEOR7?I%?f{"y111댇M,@I*Y% -$aJQKY5X@*Z̹S W>fqvZJ%q؏-QpbAv3LCPY -I < zi2 ɜ\LCJN7}jC`ppE<@uQ /yO*~1,& )PRG$_eUqLR)b9ᆀCٻNXojJ81E8pz*JTt/{2EZ-^2@RͲHIH=6$,9.^*%JEJSudl^D)~ ^p7"r̭z CNEq.?'ܒIO;vb8ʋ(Us';zBK%  YrbwiQuƣnmJzh'8nPxrOb3Y{)S(FN8%g d$0$_ψ@C/,-lf]9 'TN q'T9UrQvRW -7:tQ1Mk{K.H=Nw]l ";MCMV_7 Īari=w+|,h=rYŕ8rAww3xh;)'COޙŢ),3JiLLqY܁n/`D_6C]L+c3F<YM28UW;*L*xT5X/Kxx" :E$ 8=kRMkr3ki]z!QY5jr!Jig-H*dX̂92UȘ+*7 hG-8TL>UbCUDg /6ju bSP,W͋!)<敖\VȎcN8 LE8_0|ng2,Ͳ'V,bza[1?|\TgF z -,eJNTÍ -I)%X\! v)P7,֧n8֨d)i &$|e)R:)bG} >EJ T=:}*=9<+c3MJcu~ -\lKY1Zdm`Ah|f`WoVAR((_o b~1>wr_J:5k*dDTΣ/* C,Zv2A4zЏő:uM$^J=8< 2wr|J5 vN z7G~G㙔-s#6Aؑ(2(S-#YTÞgdʋNh?z %@L8w0u,  v+q @$Rvʶ#Ib_=[fgLtA'*S D2&2Ty1J>\NXΚ eP4H)_DN,)ibJvH;ҏ DAMa&)P/A6 `U24 -xL{(,se40Sp%Ɣ8 -|N1V!sb\"eJc=jK*e@ګ wCպJUGE&Lg_0UVJ~>PhQZ(PBbrLlTc:r6adMɥP9]o]  " sj#̆+bh$8K\$sqx䙒Sdy`H̋1q7̌%)ΐ0'DA(a9ERCbbȤr+q5fS ASJFېÊ jpHDdOd6Jk}*BODOa -*䪭TYa\RZ002(,9o p@!昮 0(%)7t)x G쀭01.V`Y5X+Ӑ\,BB[ ^4J)EՆ7m""v%LQk-693bI b -:,4Z|ReL -n, 5kHH=]&z4E"dSkMr͓GҊEWN89<糌nf.y `n9r;G3>z]QKρz L8zZ0@"7&zEC祩(6 /G_b~*;yoG,BBIiSEgVW WtwXk x+T3hsJ&sl$@X AO)"? })9  j H1<]sц?Рf^šzTFH"65r2|@U@K+iL;+ iD$$Xkg -jGilXDAn/L!k0{AA -CҪxa @j!ZPT@mhvxT 4JS iq(GԂ<ؗbTd$T?* XҀi2,x@^S̍jz_4_BG $})s#PjJQwAA)UA1IC%`-DP98. fDڙ8 UyWI.$Ad,+wˌEiyײ@oT O#NbvQOKM1HVx$y zܘwF ,OiG$OGRl){cCMzrPL2O%>ae8rT(vw cdpiDB>Zm_o 4 AʉAjwx+?]* -lp$*SWJ3t LK4|2Ied ˸FDŽ( 2I2]D*ɠ`D -1])|mD|*$(ލe&]bXdBF"0dBA -_@է@Q*y*@PHTJ?HSvzp]EUs,NfR5Qė B0[[pX8!PL2<9N'+nȇ͟ q@0e rYN#;STy &L `r)@<*^hQ5U).p_ZQ䈫 - GL>-A-HV(jT,7\*kx0ЅMCJީLzt]-|LrkΓQ(`2o1;`1Tu@x J'∐cIz"2VTҁS*֗%HA[U^ r^,vqN4bPwoǢ(7g+|HO$t8qJ$ z8aP!j4촅5נN0i;HT>ď@eS98St0~Wa9##9J:& -%ǂ+>LJ1Kg<djQG\"Pu~EIEb@S$A /b /Œp0hr!kHbjzU@ drb)*,HSjz!t#"41Se+N$;mP;5t -ZjDS)(7CȎ, -H*N26/"y}EP>3q3sKE;RxrTmLAtZV*q G~yΑ[^/CPt&zD3lIE@":/]g N(mx5UX:X7<U޳jၐgy lF i(ě偙~ -ʉF\9@ @(\8A@ `ɑ8>܁vk(A rց -KX=RMM9KCqz&$Ze8J2qPm74dS1y^DNK-IKS$C;o$ tmjŋPQ&(AQ>nsQ`i,tcW3]ǀJ:Bɰd&#=3*TbUE"ǝ, ؏o.]X0唚Ԅ/@= |&ؼvPUo;!Dڏ+MLU$pXvr%4я|OO뻏rxD9Z [-r}WVKS_[-H  -pNǃ iOvp t5Q]וيAr+jQn Vo4P0 -( -@! -Z=7\N@wXk׳jŁTU]u\w(p$mPEs\ Iy -]p9 @|)<W 2Օwr PnڎJ|ts&pb rDDqyPqE@wDž!% EHtW\| 2 g*Wi3*D IWud)Tr{! Sto4+^_Wm umi@Q掂A܁|\%.JW/jQnJ]%['.?|+AΘGS{r" e(*O{:]c* :f8fS呮5cpvel a"'kJy6pT#9p 9'n} VdVY5ĠhG V0} A7i&=- ǡ¨2N!0WRNMLtt!*p 󞞊`# s:E= #SAO$~zhcC/ǀhGݎ+ -H - - ;K )A /b 27呸|kIGFٶ4 YÁO'І$C'fSNT@b*'z2ϣ؃).e u!LΔ)HβP Q%&q ̻"""jL>.P<N8.ZXJ_=ЅBIq1=Q=Iv?=^HNsa-R)J DL$:D䳆p32လz@&`B[ɨOZ2LkLL{e9RU" +ɩW!9>;.օVGJ E"GNV(vlF[:ƪJ!M@2'9]B'ލH pd`R)a2$Z,$"?7N7h';:E Heƀ'^R9^I8̳"sKe)y@]gјa~OH>& ^`Qp[Ƽ,nQRB64L[=DIIP A6 -k_;HTx ch^@G?oOO[H3"X4c+2~WH3"̈́]H3!pEiW"M=pEz -X\UfiW"X44.xs \f,pEi&$rFn=p#'L-pEiW"X4c+L\f,pEi&$(pEi&H3"XWdx́+RW"Xc+1UH=""Xc+RO\^."$-="xc+R8'} CW \"W \se -\z,pchW \z,pE +RH5"ՄuJ=H="XWH3"̈́iW \fB4c+ҌH3!pE.pEi&#+!8 kǬt:dJ~YJzZXXd'C^ -є-,[OQg5+=ңqVzd;Pl;X7!V%VzX8Yҥҝ*XApլtխt֬t<1+JSZ"eJI1+Mt^JeV:.6YV8+=2gGt&Jn5fWUQ3fזVzZИ8Nt܉JwVIb';PkEVzBv+i8(-u:5ܥhyK=j㿤lRg RwFVk'* -( -@ah0)gN"Td N5oy / WԚQfcn8-uҗP uCN uQX ] u r-_,ܵø3sxXE Q~N Dܜ%N  Abo>D_b=l&E`{r6z8{lNmSKt;=wۡ1`[4j!%1ܳlJnb(TOn,n\rm(Mlt$B&!\N%!![E98 -Lk6i,K[T.NUѫ4e s@g|,L`AUt K:`e ,wEfd`yŠL.ɜ>d0orga"81H6gʙ+>t؝npX Y! (Xe48&Gg/nLQ;B,D -(jP8QDI!S3yP5.jl4!A-2ӆ,p8B7!gKT~G1Y"M dILVaNq/)T_:"V3vocS4)WbFMY\DatJWJ"jIykqR0iV0gG7f#Pz"@zƎqscTsOXg79Sz. 72 CѬHOD؝ zP2NsBD#7*=Ro5iUK?6A%\81Sqa],UfCeE{S,T??{]I)Vc>5atX*Qpb{Į9~d7Lp SrKg'_B-;-y( ?|a}=KǨ#rY9圷LijFz;SF *G0 ׀{3ø\/ˀt\1^,GOP@#J˄Q޼ /$$N7֯!l?JJbݝ1ڡw$57}NA3<:\n * ፈ)y@\,׏oYA [*.#"`/#򪠲GUpxZ7ĊaߗԇG} "C -twPdC/#Z)@OXKH@CN˛dw]u@t@$ZXSGS_֯AV#jƕ!i3Fi& _*Qn@C(y0x$,tG )0U> Ec2rOdt>0ѣÛ$BdS w8 -Ϥ,?ֵs;SVhp"2⦊߉ՁcZr0#$e2ooJa}`8)&Q8ye c-H@ -sxwWLa'S8Îטw:JhK򘦔 0@] 5)I?H a|ԡă+c51h(DHsLqCE)j]Aj\]Q\bKW.U\z"eq+/]7W' 1 l+O{W_ eO#5bb0hGђcgȅSGS)aSJi)f1IQRJc)yʁa %$$ݿѶRG*4w.hSRH+2F~-^!p#&;0yG=zN{Џد-,Q{RHW~Rox^$kesDo1W$-t /I@̻7Ab}o1f2&:)s$BS|MьWXeW5q4mT -1)&qZQ8= JOeTXqJN(=25 -#B'Q]B@0N,5r' ye}Y|U_@^Q[y}cSϦ/4.ѸaAYca6fnG;jmj1۸n[lFA;쵇Ճ(mq0zqT!EML,l[ǭѠmSmw;V;7=rS3 Cߴ?U5ff/_LM-=<vݳMV^ayhhALly5,H(t 'y(>Gg} r#o-gMe QcSmyjNd&#!/#o^@>xr8 9(wy -|&,L<rA<!fWRUSRSPl&fx1؊_Y`ZɒYTbY9$bKOX ggP(K5b貅LQbVWyg[!\م%2V볨Q_q!^+.(!Uc5cMJ86\<Eb1$"ˠ/tA-G%fhׅZE~ vϵ ˅\|IAU)@Ӄ9QA  琑1 (~s@e#|d)wBY P`5> |rEBK2uOCp:,Pc'1J)9ɋβq @h&)֍Ԅ75s_$[j% P}AdB|JK!LsN*WUk^ii۽2T@"d, -H3b0:vEo(d1 ҍp2%TeWJ>bߌ B$qHP:52?TXJ>Ϝ%T?|9$*(+Q[䪶̎jT)zIEϺ5΄q`Rs:x x..aw7 -_Q9}$^ly-,` @'D[<1eFe *Q!R* L #jẘ9  N!8&O5?>VQA$|)P"ކt"%3Qa4K`ŚrzZ;j@NV@$=~ A BB(ACհ)oVƄ7(,!-)H % oUDڕf@dLlYR`ǀqO@l@" >ey730I4P@tZIjhFrx:xttl?&sEH,g%ozXt!mj-d2ʿq TM`kScy -&J =!| xD!Ȗ+ "eLA; n%1d ^ҋd,aPP)}̆)Q9FlT(=Ln% ŏ-VoA3S0R", 2pT '/m[vTMWQjV+.rX@DUVlEcD*PeԤ.*G Τ!]H92 )@EoDNI"i ]Gu[@֭N<hV\)-r3[KJm -ի9% 3RA*W[kh`'Qҗ×/ Ē"$K/)- p%0Ca-eC*G"fƋq|T:$p!\%[ EaA*sH&@%kp Q1G{r"Çr+HJ\nJ`%ş?aĮ)rKg99QɆIJ[n\͌ حlY%4Rb9aF.JQUEPpyθ 0)4*WAh BOhF/*r @G׭bE'3{H Uqޅ6\Rrtoi~YJhOd qۊ F*WۈqWNX&ɫMN-VQB}xeXA]I0J0X5OzG \H$сZ$hYTTGBdY΃K;eyB9Gvi}=:EjpLIHWީSD_/%Ul[ -Ɍp)|W H@p924KprZ9I(0Q(~G%#WL X==1 -BU\(.Z*ǃՏ3 -KbA<7\L/wJcZIn7f Ӵ$M fDF̘8*:vB`뛦^''|ߏE<_ G Jh&(;!?(KKr&Xl/E/.jtyBLSĠx$'bph(>эDl Q-r\R0&25"Gn*w(fxfR6C<@\A@[ܓ)Zu \ #\w| 8 "}H砻r /$+Pm ŵ*)( -p=}Ylm>6`{ -4jIEw rQh۽QHYPzbL"c"7АAGYtYr.\%ݜR *^)P! {&`I[KT8A/*7SpBԞ4lD")k) ;u$t+Zh./s wKXšKv)] [+{2DHZ,ckTZ@J/ \Q"Hr +t`zĢ!7D)3/N|7&=P9Д;tᘆHԡ*!$gPODQ>\;+Ӵx ]cQHrQ -@ -d^ȆS j\A/rHEȌn ЍwsY -xW q)1\Tj6N /a\Hc14HzSUD1Zi_螔QzJ0HnBD_t #rŢQ@nu=0MA C:$  C׷"(𦴁~YPBBe9 - (ZN],E.z$!c:N&CBG xJ +3`DJt"ۂ~Y^[!2RndAn z?Z"aFVd? -9y|}t{Tq=hT+5?i$ǰ701#XA(O3.zw*Tӂ& DInA 1WivHI*;:Xp׵9S5- zsWTAmf7X3)psQaZQeFEyӴ<w [6@}=^]%)LRKb"pb 2(˄LnK۹ -!`g>vYYKOy0U=LB)3l\  U?i2\![s#1ΐ{n.-1W/-Sڃb](tOz{a8q_%*x4m{/oۖ=lk.Uۣ?£^bլfo9vд*دmׅeV:]hoɲkPʸu/< ;V{v?Zn4~o3:ϧ7 hB/ۣASƀ?=E`[iH J V'۞,MoO\dses> þ A{vbTc&78F5Ab,mۣY)ԃֱGm͙ƺ>̃ްl=4 ؆)[ZqYcJpZ-mRm ߙd[R =2oJ@ _ |6lm!yC?í_M-Xq*,{5K\]Zi"oJ#٬SsѢWDwDğ:S wO`v6_W]6NFEwJ -+8[X\CM!ǂPIꍰM)AuZq ve_CA$8jp2Tb6/TO"S\[Ne8xli{5 -pp@)7:;%A~]527[{~Hd_:A%PYLRVg2wNOq3`fL`4=9ip4^ip 079nL9Nd{vno/)=7חg{[H(ߏ[.v#_}ЌŜO@ \) -F 6gVf{kqL2k-!koF$mZja/O^{86hL֨L36GwzΤ%=$h}0hkb {'GN?y:ZA?sw_|Gb*UP 6?q07a|q?&-7q \%dILC#ABYckE`dM&.0ʼJ`, -w`,:XT!2Y[9/T+uD!/~[ xe߸W^wAKH)ޠ',9i -K)Pz>mc?, -un [UPg - U}EWHm~0`T|7T}[TLȬ7- mO?8_v:j'광࿫~Ko?5yy4wcV $^jZ9$.7?t1c?Æl5d -_Ku'g^Eַz?dJjY  mtGo#v9:zvuwivqrQ, !X_bӚ>(m$( KRD"Uge".^gG̋ΨMo[}e&Gj/TP Uemȱǯ5{?U9(;b3jw*Fr]`%N'$ԊsW?YKq4NZh,ΘKȹH/rZ -7Tt>S:Yf2S⢲ܛ#;\Ꞵ=rs̈Dl'9V0gxSO5ƒa \4h/-7G0 +bx:ȿ-0ŋC:0O N9`4^K .t,ȃh d;hS U"ee$H+4R*{nY309jي0[rW[m] k0"L2^4oxX)SXJpš<*Qa 2+A\kKJ!~0N52^X\qve]fUnMΙokbD\*fƋ95dl6wz`}ӿ }[OyУ$g Zwn+XČ,0Eӕ!'QCa‰n+߫*j#P 2Q)S ՄnK2J%}m}Zev9i eFse*&={wk-aJO$="DbP\b12ouIm9@D5^qfW뒥H[JuGcyqİ#'GZx٬(owkW%UJ"Gʒ^:ŦtT>w(RSjҎbmK$3]V\I1+[4lzu';a;1]tG}WU8su?{Ziy곤 3ޱܠvW=E9AG柷_þU JaUBWp"Db|ݕUBexb!ChTxCcR$ǘr_Y XZ3_h1)H+rt]r6 =n.ys(v&^x%K9OZ 4s$J]҅C7ώ5ﶇC;ݑPSyI#.:֨ Eabt:Gǭa㗙:F5Dtvv=ý`=h>0~*+ݓvo/7-?w{b#{#| - 9;>lV8 unmz愿>G[xx^{"t~?ZѠs2jzW߸jq.ѥ+k1#gro`x3*L75 S ?;~}t{kkSDcm8ۣq_^_+mĄ8Zm𿸫~suh){2/'vtxc؂j؆3S7o;!h]B[̰<s˂ &i:l~ew]s2oZŅq5#+/-sqoȪƠcj|o2m/+ڣ֞U<9{t9uEGJ Ƨ5'r|fΰmڍJIq܂a褋{)Ek0{~?H9,vs޼FjYWCڙFȝҹ1ʜRDbh_l' rw- n5xmviQcu3jt>C0umb&w[<<Ρ³^gמw.Hfs"]Λ\ ݧ-'v`UWɤ -PFԘ."q{srjuq>z>Nk]xس 7xԈ*9=ne4}䋍ѱe g#'٭z'vcއ`xFRgOn?;?nãi-vMR14-E%TwۣqRyRwڿ--u _vv7N%-="/0IŒup˛Qq,MLN{bD7W`bz:Qb5<}mKEs/ ܟ9)'cA -FF?N#[e[en"sNw-ȿ`8m 9mNU-4O3Jp4m-ž./KoЧh0 ;9XJgp*Aov{:_5x9.{I⼋_ nؼ8ߎ݄/c窿5Ljf60>Y͏{h>8KO4D6|n|x|Ecus5"Yq!4УwQ?Q/ ۱tk iV̐Ru^mg18Gl~sk w:Yg揼tZ ASu[_;cG=0jR]|r9p0%dɜZ7E'/;leҠi gcX偑x9GQK?m$cS[Ax:s48GhN~o4=Q~wfÓa[Lmh]wq8]&A+܄h>7]2;[Vo%hϥg7fboibx>Z~dNiyPoyJ;=B;7ݲ9eo%) ǻgpl0T;K$Us,msD,d^mD><ż7x{@tpDZ~ϕbt}U7}s$ȫg1֟WW%r[l)7˾~U@_l~m?wnN/F&q;Y|ܮO xQ T\Yc SNcw"uƭ&݄̌eqln/?xP6pq͵[/n_zy18wtxwڅ3W;gY?5Z~deb}ycp|X :>\^oݽS.;x׷?]`ekdj8smwuojNז~gk퓫w?xxsw ~\[_?E*Knt=[N߽27Is}g͇jj:b{7_nwbaڧpܢ.^lFgyeW<=3w-6h֧ܺbzev_/)zܹӛ _[&?,}4g+ [.\{=Qr;LMg;?=;k[/VQ3J>2vur6{~;'lX2o}ͧONƗVl/\Wl,W_Mdk,*$[nXzRzW߫ƺ ʹ{8(W}0۫{@P]K8|p:,n>jl>OjҖTڏO]NӤb˨ݽWž=42qmnvoڝ{榦úvVWLmUk__4Mv[Otˏݹ[т f>wn3ouʒYlduAj)yfT鵷^~vpr݋fIt4?<\V/&[.~yI>y>y_cp8ؽqv+> nX[3bݳ|*?΍]- -.+\|{]>ަ[Κ -3%߿>^&125~(0^ŢMl)6q"SӸLZ0Lؼ)nbga좎"7oG_77︌GX|Qܪmt&l_؈6( +@<踍 -bg~{8q-w%4eHYXaJxݯ*Dd,%#6OCfh1 x0V[&Ft6~dڠ8:Ka]&M?Mڶ`ן..rᆝn۳5klk@nan铼}!{vc福6=Ll|i/b۫V{'T$ʺ~iMY?\zhūy'O~~ËqܿNv6F{POem=Դ'ɵ]fvjA%}φ=xY|4T4[8׵eW/}s}g Rxk]oœko^XW}D:Dcsa7|W(MN5˝a'ܛZn\۝^e՗G]lrCο6js|J6~QuON,߿Hh<9{ⶹpxԝS4ʷM?y݌X,/M[LT@,: r7h^?Rv*eqKWm켷M`8ײ_zzbߋt^]\uG7K擫ͭ׬eqobĪ - +ެ_ec X|k{˧/mxʾRt} *7&q0DKۇVn W]c{u~Kyn|e)kZ鮛&xaeC%c [o4{w' Fz 7V-\:5o٭\umW D&Vqm`my`AZԜܤyZkVFl,'xX*Լ[)ݷ뛯F)(WbOOOVoS=Z-Ջ?`.Y闠JwCu[踿qrpr}gmg_}^:ڸcOV|}z M1cӅkeG |0|څGF+lrP#TK/?v2i>ܻ3ݶ*Fṽ`\|\'5!{ڗ;߳=O{L]{bCj`VvAˉZ!kn?|0Ž:o%4%"3˅ s~ l=P3Eb{gu'u%ǜp+q.kV}r}Ӕ>YGSZ2k:7._fN6>tYs)Roy,gXAӓ23 -f~C~ g [TLs%VώG}cB- SE1ܢ/1&A@Uh'0e*:P됙E`q3 td<;Q6NFTe?ܟ ) -숭L% -wY. -4+Km)fiE*-u-V9RZ`\8,^&kd]GaC]P~̅m9_4$+e~}YW n [x_dO_[8lB?dYU .F0lD''7r]־Ne>z_SΰNb -KB]?VV_es֯/jIӕd)dIэ`Ă_'V{db!Go ]~e}E]ZN-ډϕxș185EV u)W@d#2{ΒC&'sd?2(7 5?1ocyb/|j*_չ.a/M*3FތLm{g+2b spbnu5|& $籵~ɢ*`VĸgQ:9L<;KSQ)Ɓ]E"rWp9yҹ0<;,;f]<3oH/Sۗx r+!OU1됻7PJ*1/JHGpq:mՏ -h-^Z~%Eш -a)̚kU*oўp@gO+$ŪԵdHT PdSĕҾ0 ˜brQ*İ$] -U1l1;*[_럾\ybe0IaVc{ʙڿ?`V7XE{0xV(·!6IC1F6 ·36oP;¬c'xe-!gr&~I3xe_gRCߢzWpi6m֑G xtޢʼ <Dyw_i fSIcV*r!IZIk 3a҄!]:QC2LJc@%t.P2Ɲ~z近̑t}myh /:bxxO7CSFpЇ"ئ4Wjtj#ʭև%hGIBmJS+O #Y[ -k*nXz[{{E,6~>qcǦ&6&Lg{0^y ߣqݰm|6in6d ։wc|0k ƜS2Vz_chqnMwƓ5]ɱpLi -5Bdi6j͹+4<}UL޾ʹ)F:`fggAs4g4?>&3+|LSr1RW.G-is=􊩮eJUf=VCfuuV gkk/ vboCga]vnXߎlvjKO[՞u+m=lvԾ4yKlj;!f?S٘7uסmC Gu~>r?8-p-^qzgkfq:殳S띓R;)E*rN]JCW-x\oٜT[cI/:Lwi`^P05Z\Di" -B>-wH*An3?d)5=3GUGu&ʒnR^eL<6U% S߭p:lHgt6g݋>PǶ=OɥROUxf%[}^5qޛMksgp{}< ܰu7o-ZwR*ECUjq2@.J@p`zAZ X._|킫V$1mȝeCjм[4:O8^_Bx>GDsK:EF})+z=WG# Z-Y [~tcGjVXmW&Y{:MqW-'|)4|%`&Df_&g4Jdq$K;|&sn?i )gJd9j4I{yWŚәtݸ̸U&Z2,YY7}Ȇ\_lung!- -*%70*?eT>]߯L4, V)ZHX,߅,UEˉ l} _EdJa4cˑMSZW,֩DWT^d|˯j›yv=juHלld]{2kSǩ>: lyj[m04Ƨky5kv.6] csNÚe´ As<~NYGNf޷Bg!:hi|w-ɦ[c&ߠ?7?lPoOa[{kك۷MR~'>χ%2>Rt`Qch֏oxu9\푳Ό -f7lcp~x~M$t'ozsr*k>;:}ǎ0kٶT̽1MݲpqϢyK.~RO*7u{gZR$UX֚r}b_T7Uwm:_?~Vv}[-[nYƟNև'i'b6M^jiL,@4) 셨J擞dzp]r&`pW Ajxv*Nj9Ix{M -f\↵vI܈b&;̢I=+=icL˅fZ/_ɘ[jR\NdSѤpf!^5'-JNv/9iBd'-%7+[EfӱYν$'ǕhR4 3mkQu}MZ;CSTzr1c՘]Gu{&!ܤ+JOZ-,M -t:nT[t1e&a-=iͦvV%:zfI%=il} 'IQq8+ȸM?1W:fu*oѤ7; ~ --IN3LzDЀG4ѐco1>hL; 'u^BfZ}}0i$S#.G4FI5mآkq N_C}|a+gl;.02P䞋RC-H==shݸ5 YϿv.{5bR|<Z~ -Oz'bxu(<$2[ۚG;yrK~ ,S'bϻ^ì4^Bn`m?=g Å?uwg[bD2v?F_0q3R^T_O a$Dd3 -kDO;KxSa=$j\cVzMb7[阭;0 ՁiJe{9!t& YZEp W<גHA^PA"LHE9}*_P={'x@ KM -48H.RLA=g 3icj;J~RN -y7)Ԓ˜WwSpC&:xNJ &|AB'f'NI/5)ҒF^!G -^Iϓ(*Ab"7xԤg>e -s;KֈK.}ock0bD$jqZn<$\NRt8L4HS /@PbsYԞ7G?{-=TUWih7ȠE L߮F7NL[Mݸ0_j'`Dwy8/elhIH?::V)[{My$ьclEKaEeB!mm.Bs y̜)1?^ӫGC46I }v:yg]AFX_|/:~[;*]sX-rcF1+|"Fj9) 2d>V!ɈY{YCK}ѷd,d=H e@] JzF'; ; rpJٶ U89l #k[`c)L^?9} ޞH;3Hc:K<7?DŽھ,]y`n餙AHuxOwd-Pi0Y6g]v^;<^s=g ĈgB|&ĨG6\ˬ~.4<"kM`{4;0ⵆrP1QQFXI%aC/jcT|aIJQ[ )$O/K/D'Z3K$"-B$dk0Bbp=FxE&dtj2P3x[&3j|8ZBbr28x%AuQ3[6pLvG6}_~TӪl<$пb lT'`,#?hV",s\]y,Ń)}`w:}ݺ) -g%[J,}WDIvSUIK_˷}8m糸aC?JVHbE}4)Ĭ@ `c2 ζ0 w%(-9^sůB6݃ەxwzTbI#4.B+ @P+ym D˖*ѥ{X`CKl`mw -.s$$fe#eCYR*aFL%)Sl44O19mU낄UPlmpAkr. -El#T$[ a -DTph 9|{{ &t -kF[Oʔքs^/}|2BTJibB^ |Ga}!<}֠ -8XU -VhmH/])r4ǹ   +Gd-&>2E#u(cRuBVqĬQf`Re&{{ݦ4Jsョ޷ɹsԤ4FO*]&[^͗B8d%acG?W;SVzeOZ_(>(9ȥpBуbP& vyJqP#P,8$!' Iƅrp-+V EcrFRzܕ!!ב͈cAEsS,n4ȧL{>ʚwD(prU"#$H0J-#v$ibtEF6:pEF$E.qs,2> -qԦ,2(H.=(cӃMQ"QczihWbS*>#Xd-090EOp.X-x-anדʫbW:Euʇ%/ -|#TɇIc͇{0[Pe>z\Frw3<7N#|8.&I]T,7_YD-)-DUD^zȄl*#!#*kq ,8 -tqkbG<:yB:awI3d("B'%pcFwaGmY -2N8dpL0G-*h8HZ7hjZap0yU-A\$Q拕/0u'ԙ Ah3nH%HeZê Beh=##2ROH/-cٔRe PgHYm L%^ ؍:Sg‰ "7Tw©+ -cM -3MOTݥPaU_?Y!鱊BylzxRA54DLEQET ^(dx rfe@IFWl WC+/kv]5Rˁo~a8Itf΀f 3#A 1G1i ҋ=`S̀=Ph+A@J`/Z2; kJnN_! tϻ\ۛR۷rg)WHG3IJXɦ -'Jv}-8(N7Nn} ;| UI:unawpO;n_J&Iv-L^1aI7ӗoծb:aGB$4fP˞$J<w￧o -pRH"BUӯb[PnܢBY~kU$'$S:ɩ¥PSʡ>M䤛p7?^7ɞ*wj@WY$kU?Nk%%]r$-ed;N*N'dImR6 -{e=!N7F~F6T.6l:BɦF78'YW>9N3l:4؞{C܄鄧K]pG6pyz6ԒD某M'Kw!)=M'%-ɦ:?NyV6T.DO餆R_yS6U=%N*A] !v6s1ʦ e˛җ˥coeIyKhItrs=#Φ_M' Mxj604OϦ"<+0u -@ؕƻ*~1Yk [DEVxB:vIkvGIjz9cNɯ*BJRYn^ lVh1 -cUqy)БMVSlŻE˛zbU@0سufvk YP΍OIjb0/(.PwwNy򻾱aM-dljt]wg>>.Nm - jh'T @<ܭrZ%IeXտ$"+`&^Jj- ZD|"w7ÝT-锧>HSd(f=ck4jCp'ҫÝʪ0UE YbΝuGa;eÉ =!:dk׹B^yYs\{dbNo|Ӕ0k)D=y ^7יȃzk#Ek%a6|>… a;~˛>lu-Nlx6LH. o&坾 /y'}vRq{A@!B?m$<ϗ5޵8/NÓ]ⲓA^nJ3]ܤ6wxPvaYEއۖ#hWi(:S'@ @I߫*1hm]pBpof#RJvګDTRdݸyU -wwɚ,$?q!m%IF˶$G;ԍWKZ$Xu4GbuM!hJrUfTEa0sj$5zQ -x.*)ۉo\9JKkF-+bW}]ژoҷ'Ff4pbC -pߡU+^*;^v#nWf5u3[Q(| 4|Z L>JK}L5{Y+.{gK3dܤ#g9cr5`^op'3Ǩ}rV셝/.v@0] u_ܧg1(%] w 9V75Z}`fNQv|U.I`$؍R9 }Ndk̿oZZoص\6)bQntayܟ6Z!n'ސ6T9;WTlڛ@~Ó+YjsUfȃCUBUsYjs|pIiCl!?)lh+Q70{V)LG'7clʧu|gmʧ-YMW>ДO$qaD+Pw6ݙ\Oʊ]UJhk}T)=|O PeW?At}舻) 2D7.M־~'QeнOyk4&?O }7ĻrU)G$>R8[Տ`'f{NVJ+SVuQЏA[x}}$GaGs0$q-zߞ׏!C~:$SvE"B_?j!Th_?b5_O1Lgp?O%+zG_?4IN~Z~|V8{J_?e!^]6⢯hۻI]DODdAx_?e3"xB_?bWqُa2ww?ti }nk'J\Q޾~(BߕG}ꬴ+/!Ob]~Vm7~JtwMVۏdx[^oKwctپ~,R]-ɉv9+]} vO.}n[O^~]n, -}CIO})xFnMUޕSͮrW?U$-- ٵ2y yO_? %zf8MrELY..2w廒iJ0m1+2i 7 -ml 1͘ Xxz["Mx2d6w̗F~!o >7f -Y̺m602جB?-mҗ Tw dxv09/xmWp.x3dQ,sc;ezAm]Ggje:LCb<t䧓*OLfr[5av@Ӣ뼵߽+k$ݣi akeh#T@S~qop$,L{s`e*HܗK-fq7- a?Io AI`!`q@;dj x,g[,m;Glrhq9P/J-|m~lLS G>ȎOd$`dO3fτٵn3;&Zb[BfsC(i8MDK3c܏*ٖR;S֜/#{ te=0@|[Ä=y ;@[lYྶ÷vmDKetzy*%S]Q9!+p% oq=|`?(fh[Y&0e\}FXSDr.eG4D0= -`a}^ R`! +oӥ ?D C(s3G_rHb+@476&upf4'iqatYMJZb%DZG%Kk>,K1;63%m Be(IZ07x/Ir19ͿL4OUm^WK`t D!Б3ܼc>Y@2Hʿ]ٻ`Dgt{o _Q]^!2 öYK/o8fLWռQ/_w=罼yi-z?N4 {2Ƌ;7d6aD1ɧhA~+ ?sKwof3apqӠb҇cuޮs_Q2ٷel|d4nI7:qњ<0x.]] <ӧIDbـuum4EiI -YWB cU B; lqK=fT㳢xM7jN!~4WW\A(~b)?i9ʲU3FZH¶G|<"Ǚqǵxfj;&iH8,D^)[,Dq<" .pYՁtu a>X 3=E7F${!NQgi!?q/?\8jom"+Cw=,gTB ~z_jXWARRmZ@:i)X36so([+k$׬_h=.~]iWOCPd/GACvpN>BI68($8FG^$eT -tZwZ2  =49SE,,ԝсs9apR>E# Nڣcv*R bIK5Nw N| H\%'{BO{jzA 6AUBu wV=ߖϘ= fR^) Ơ :%MJjkPt1֕O9 Y2x`hcc)DB 9YroE@cP^@s|t8fYRiiaŃ.3ZPڝm0D۠ b TA -N8hs`*,V?Wڐq8nBbqC%ͤ~[[vv $h~7lӖ/pDΟ`v\>H \G8 9c!XK F8q'N=̜y ˻nx' yec>!MrDnI%mG@F-xqK8reʶzF `Dk:NaIΏ#ai T3$s,F>Nv,kR|=4(=qkeZMw6m :B&rD -*$Y!@/GVi*aŀ4NUK]_0 e[@= -v0[c)<]h J2JWS{C |eh -@8tnjxĻMRI0 V"fP<)# ۺ< '2}MEd~O{i$fNO]u!Qp >:R!Ot b:&m>f0Y* yD߽' -|oxDܾ1*Gzkk|Jo2vjc\u6d8i$}p.'p4}dG mqR[`!MkUa eBɲ?^uYlU{9|zRd&TB\ B{H"UC~&Ì3@O@9CY+xR6{!7(B90]0`jt-d:fumEB#_BC&I gľ0" +AM^b.&{ܤEqq^O2pL`)0`#`SE4^Dsb|~D@l>Bf#X'eȥO(+x8;H()Q@Qߗ1xJ -2fb{^Y ;T Q6:+c)2jE)h0.>{SpY/{^?8?,"yTL DPԑ$q_M+lnF#Tc'&ZHHXN1 -1 L0@SIr\Jˆ 4οA,1yUޟ]U0QV\fΒlz#L<=qX"ygWG/rL8ps8ibdNZ6'=<4sx? SU5t?yC@(#'if}pREGо }FHzDB?"aL]] d̳ׄUkdWYs X8 +3 iռ蚡hתy1fՔ ϰj{Ɵe}6vMeyHnjĹ-ήyU㒰jYɮƠl|UֻPk>Ǫn1s^ڏ[5 ]xvX5_ú5;gK]9VM^]9VM<Ǫ 5 %s'+5cdj5jv~EVMcvX5R_ϱj|Lޮ&Pk>v;i=ê gQk>Ǫ NpQIϱjBίd|UuywJҪy'5_()[5_ɮk>(J&Cd|U!o|USꭚUn1 *k^Z5MI8^njFޮ&%ت &qhRHtKᥔo1g8to6H m0EIQj &]EZ_qjf 9Y0)>yO"/GR- \DI Ʒt t(ML/?61DӹtAܡ,,ٛD$xq1sN b}v=]>L!rTfCJ0b os"?|ThW E',`R*`bzQ+ 5Gw)%zu|X KCHuHz&4Z0+(Zl큂q/G -6P:wH32b^ iZze 8",sы˔P@ *O -dɪ2 9»?%Hu?#Hrp ny3A$?V#HDPGO <K$"GxO =N"~ 9 AP rA21A"r= DJy1)6"G\δ`{-c@TP[XE@Wq^⭜zu.xW<''cg=~b8@g'x  mKX7D>%`9<^ljBRB|I,ÖDTa -J)ު_čK#oPfp gHʸ`+#i_\V<,wt&|\&AUWz҄q~LfȣDE1jm=#ۢBx.m9 㼭 4#HPR  bv;h={}HK뇬W*]pz(u~Ղ:LvD\B4 Cc%P9%Yboi Υb,Ky)ʲDz/RLz;S>stream -. ̤G-I7ʄ@Fg `OCY2a @' 9/|Qggl,†0Oz=L{ -  I'0-ai0|T̄ kiA5b\tPJJC5(]8_<TۭY@s"? s.dJ -ý!<,cؗgk`яr)‚ Llw}ϏG o깒32>k]&ܐ:p[ԁX~@_Ւ(.XEwA<ے3&˸6"w#aߨԁ0uN xF+xW/8GtybKd9!QZ_˰*0fR9LX_acDCPJ(JKn7GZr9k}j4/"d.S6|+o &3 -BMZu>OoꖒQJVcGiRǡ4\:zxSu\"ޒSLZ0A6t+;b.@M2F։~ dsD{;;y2b;i -Dof(۲<<ӺC7aǬDo(fO;A?ȑ/Zo˖ Gp6^0>?:(]L+\ bwRcbg`{5 sp_%3p2 Ѽ)ē= ؇_`3`N`ZFZA0-r-+uсrޱKcP3OC{o&|?-oM9;ɞƘmU=k&-xLVl@ҳ"0&W!2ɈyE.=pp7'ף+3cGnh7v՚ -2b)t]mbdQS8p1e$t.:~]&elRA6%^[{= 3ewsl# ðxP4EVZ\퀴u3vdvpi@(]L.OβhL>K9az`/fayO֜[!`fFDfg. چWqś8Zpi{exv)ܬL \ -o֫;ft!L2o|1NP/>q~~\5!+Q |/{Log|q%BI/fⅮ8'))/g ^#'ޏ,Ml>gNf1;mb''B@BU^쓧R($q+Atqavo[ӌBM[țPn2u`Tc߅-8*_>ns^1n7 &XA?Pn_P&b|ш4rh /ԗ7[Ku~?i*qL.ˌAG q~5s;Y%uJv\1Xl8:`:^=F[Ҳasiff)X,5xi%{7@"}I.4_A>ׇ-NXf'RbY) Phq։L>) 2g -5\)\pzG'-A{\Sа(:}DF`gJC"-KŖa[ -:S!ɧ\rAܨ aeiI%WԲf{JTAbTQb؈ϻR3Cүڑ:Mfڇ>Î;D+ۚs󉍨FQ)t0CR>134@r*9ԃ/p>Ѿ6޵85'Øwͫl=hFCK.KfslV@9sRg0v*ajȀ6Rrߝx@@-f ]j^ił3!n4w {o1+v΅} !]װbBkSAm>7nt*큣FBhbj!͉kۘ@Ky+JRP Jo@|K@eq2d<+܌:Wv -g#+hZ7 Cnϲ.Vw:e,#+ʶW]Yv%=V^S_Yi5LuBT0z]W@į{oA6=`|QMݜH bmOn0BR<$F{|,7D0%!fHK>ٿFQp ϱ_oeyү2o:"8qWHvKnXd:f#PuF.{:i8ȥ]]}Ȅ6^3g\_+$s?Hg缗7 ~YØG.bR@(؀+zn u#;Siߒf*/O'kx->; `04xa-4xaPcPm_Tr]|\O;(X~˓{ B__ /xƌBX^ʿȕӫqy zr~ ^`5|<@p_4M;=$&&}~$/^8|! 7қQ^(^x}`@{|`'Nx(C{s  D-//Ryy/sޫt$yh~;@^x/w('O(0^7ةziH{/% E:8w>~qIl%IJ T fyq5ŜL&f ^ ..h -?$ hψ|H_ I?<q$=ï^'? ?pS&8(`kp-?is(tDHyq?r 8BMCwS$( PMS^vHQ<pp G$F@I}\`& 偃8(M" -p!1FC^w -xQe>WdN/a Mћ pCa?}">SrPVģG s+ĝ$ i$I!*NGnSGطt~R`[~C9~Bt^7kr^!_H%z -wUmIbh ` -Gl ''| #< #(( w3~  G~rHм K@.7m\%n椁aZ31} `^@!B|>IJ }75;*07 ';`>wO?C%8NW@ß])?Pf@/tShljz۸/؋`S m-Z @Uǀ,vѴoK\m9I393μY[0"VB$)u* %(Ȭ4RXBt3 Ryx՟V4x9{n>lU -jF|wz40ibDN`U9 W}ܹ۪E?9ᚤD-4FI-- Vv(AFLQhc\a*C *]r+c0xIvj!IF' 6s̜{y3fp Tμ6~+DȊڡJ#Ku0AQ^3Ẏ \zO֨7& O&~+%vt@"d׫3 -x'zW*6ȧj>kwolWᯛf c!-Q^#H%Q:jY?) @$ pcყ"@<*X)߭hT/ 4#T# ri-o=ZWՃPӒHJR #qc5aDenN@ƺ(UJw{v GFn)P為x*B03l=DaV딎P灺;9); V_PbmX\_\[\]\Y\Rk7+je{~{ݯTf ?wе>}f[? endstream endobj 56 0 obj [/ICCBased 62 0 R] endobj 7 0 obj <> endobj 27 0 obj [/View/Design] endobj 28 0 obj <>>> endobj 45 0 obj [44 0 R] endobj 77 0 obj <> endobj xref 0 78 0000000004 65535 f -0000000016 00000 n -0000000159 00000 n -0000042606 00000 n -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000285581 00000 n -0000000000 00000 f -0000042657 00000 n -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000285651 00000 n -0000285682 00000 n -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000000000 00000 f -0000050489 00000 n -0000050225 00000 n -0000050038 00000 n -0000285767 00000 n -0000043134 00000 n -0000044305 00000 n -0000075990 00000 n -0000047229 00000 n -0000075877 00000 n -0000047116 00000 n -0000045344 00000 n -0000045916 00000 n -0000046484 00000 n -0000044367 00000 n -0000285546 00000 n -0000044783 00000 n -0000044831 00000 n -0000049975 00000 n -0000049912 00000 n -0000047053 00000 n -0000047264 00000 n -0000050109 00000 n -0000050140 00000 n -0000074826 00000 n -0000074916 00000 n -0000050828 00000 n -0000051081 00000 n -0000075208 00000 n -0000076058 00000 n -0000076298 00000 n -0000077312 00000 n -0000083189 00000 n -0000148777 00000 n -0000214365 00000 n -0000279953 00000 n -0000285792 00000 n -trailer <<7EF4BF3AA73D410CAD3CA11AF0794393>]>> startxref 285969 %%EOF \ No newline at end of file diff --git a/Doc/Maths/celloverlap.pdf b/Doc/Maths/celloverlap.pdf deleted file mode 100644 index 91e51eeb..00000000 Binary files a/Doc/Maths/celloverlap.pdf and /dev/null differ diff --git a/Doc/Maths/cellvel.pdf b/Doc/Maths/cellvel.pdf deleted file mode 100644 index ec615c79..00000000 Binary files a/Doc/Maths/cellvel.pdf and /dev/null differ diff --git a/Doc/Maths/math.pdf b/Doc/Maths/math.pdf deleted file mode 100644 index 00d4aa18..00000000 Binary files a/Doc/Maths/math.pdf and /dev/null differ diff --git a/Doc/Maths/math.tex b/Doc/Maths/math.tex deleted file mode 100644 index 4be048d0..00000000 --- a/Doc/Maths/math.tex +++ /dev/null @@ -1,913 +0,0 @@ -\documentclass{report} - -\usepackage{booktabs} -\usepackage{float} -\usepackage{comment} -\usepackage{graphicx} -\usepackage{amsthm} -\usepackage{amsfonts} -\usepackage{pdfpages} -\usepackage{siunitx} -\usepackage{mhchem} -\usepackage{subfloat} -\usepackage{fullpage} -\usepackage{array} -\usepackage[toc,page]{appendix} - -\newcommand{\ecoli}{\textit{E. coli}} -\newcommand{\ecloni}{\textit{E. cloni 10g}} -\newcommand{\bsub}{\textit{B. subtilis}} -\newcommand{\pbad}{P$_{BAD}$} -\newcommand{\plux}{P$_{LUX}$} -\newcommand{\etal}{\textit{et al.}} -\newcommand{\invivo}{\textit{in vivo}} -\newcommand{\invitro}{\textit{in vitro}} -\newcommand{\csix}{3OC6HSL} - -\newcommand{\tred}[1]{\textcolor{red}{#1}} -\newcommand{\tgr}[1]{\textcolor{green}{#1}} - -% Units -\DeclareSIUnit{\molar}{M} -\newcommand{\ul}{\si{\micro\litre}} -\newcommand{\um}{\si{\micro\metre}} -\newcommand{\ml}{\si{\milli\litre}} -\newcommand{\nm}{\si{\nano\metre}} -\newcommand{\ugml}{\si{\micro\gram\per\milli\litre}} -\newcommand{\degC}{\si{\degreeCelsius}} - -% Misc -\newcommand{\tenx}{\ensuremath{10\times}} -\newcommand{\fortyx}{\ensuremath{40\times}} -\newcommand{\sixtyx}{\ensuremath{60\times}} -\newcommand{\hundredx}{\ensuremath{100\times}} -\newcommand{\odsix}{\ensuremath{\textrm{OD}_{600}}} -\newcommand{\Pspo}{\ensuremath{\textrm{P}_{\textrm{\scriptsize SPO1-26}}}} - -% Matrix/ vector shit -\let\oldhat\hat -\renewcommand{\vec}[1]{\mathbf{#1}} -\renewcommand{\hat}[1]{\oldhat{\mathbf{#1}}} -\let\oldcaption\caption -%\renewcommand{\caption}[2][]{\oldcaption[#1]{\small\textbf{#1.} #2\normalsize}} -\renewcommand{\caption}[2][]{\oldcaption[#1]{\textbf{#1.} #2}} - -\newcommand{\mat}{\mathbf} -\newcommand{\invmat}[1]{\mat{#1}^{-1}} -\newcommand{\deltap}{\Delta \vec{p}} -\newcommand{\deltaL}{\Delta \vec{L}} -\newcommand{\deltag}{\Delta g} -\newcommand{\Iinv}{\mat{I}^{-1}} -\newcommand{\Minv}{\mat{M}^{-1}} -\newcommand{\crossmat}[1]{{\left[#1\right]}_{\times}} - -\newtheorem{remark}{Remark} -\newtheorem*{note}{Note} - -\begin{document} - -\chapter{Biophysical modelling of rod-shaped bacterial cells} -\section{Biophysical model} -The measurements of individual cells in microcolonies of \ecoli\ -presented above are consistent with the overview presented by -Koch~\cite{Koch:1995} that cells have fixed diameter and grow only along their -major axis, and the findings of Wang \etal~\cite{Wang:2010} showing that cells -are equally bisected on division. The observation that cell diameter is -constant suggests that cells are \textit{rigid} except in the direction of -their growth axis. Following this suggestion, we formulated a simple model of -cellular growth on an agar substrate as follows: -\begin{enumerate} -\item Cells are rigid elongating capsules~\cite{Koch:1995}. -\item Viscous drag dominates inertia; cells are non-motile and move only when -subjected to a force~\cite{Purcell:1977}. -\item The distribution of cell lengths at division is constant, and each cell -divides in half~\cite{Wang:2010,Koch:1995}. -\item Each cell's unconstrained growth rate is proportional to its -length~\cite{Wang:2010}. -\item Growth is constrained by forces between cells and from viscous drag from -the substrate (figure \ref{fig:model}). The ratio of the work required to -constrain growth to the work required to move a cell is defined by a parameter -$\Gamma$. -\end{enumerate} -In a rigid body mechanics model objects cannot be deformed and are completely -represented by their position and orientation. We extend this formulation by -allowing cell length to vary, adding an extra degree of freedom to accommodate -growth. - -\section{Mathematical description of biophysical model} -\subsection{Motion of cells due to applied impulse} -Bacterial cells are modelled as capsule-shaped rigid bodies, that is cylinders -capped with hemispherical ends. Each cell is represented by its -position, orientation and length ($\vec{x}$, $\vec{\theta}$, $l$), and the -associated linear, angular, and growth velocity ($\vec{v}_\textrm{lin}$, -$\vec{w}$, $v_\textrm{growth}$). Here $v_\textrm{growth}$ is the -linear growth rate $dl/dt$. By extension of the usual rigid-body -formulation, we define the generalised position of a cell as -$\tilde{\vec{x}} = -\left(\begin{array}{lll}\vec{x} & \vec{\theta} & l \end{array}\right)^T$, and -the generalised velocity as $\tilde{\vec{v}} = d\tilde{\vec{x}}/dt = -\left(\begin{array}{lll}\vec{v}_\textrm{lin} & \vec{w} & v_\textrm{growth} \end{array}\right)^T$. -Similarly there is a generalised momentum associated with the motion of the cell -$\tilde{\vec{p}} = -\left(\begin{array}{lll}\vec{p} & \vec{L} & g \end{array}\right)^T$, with -linear, angular and growth components. -Cells grow by -acquiring growth momentum $g$ which causes extension in length. For a physically -possible arrangement of cells, this extension in length cannot cause the cells -to overlap or intersect, leading to a system of constraints. It is the solution -of this system of constraints, which is derived below, that results in -computation of the correct arrangement of cells during colony growth. - -In appendix \ref{app:eqmot} I show with the assumptions listed above, under a generalised impulse $\Delta -\tilde{\vec{p}}_i$ the change in generalised position of a cell $\Delta -\tilde{\vec{x}}_i$ is -determined by a matrix $\mat{M}_i$ such that: -\begin{align} -\Delta \tilde{\vec{ x}}_i &= -\invmat{M_i} \Delta \tilde{\vec{p}}_i \\ -&= -\left[ -\begin{array}{ccc} -\textrm{diag}(\frac{1}{\mu l_0}) & 0 & 0 \\ -0 & \frac{12\mat{P_i}}{\mu l_0^3} & 0 \\ -0 & 0 & \frac{1}{\gamma} \\ -\end{array} -\right] -\left[ -\begin{array}{l} -\deltap_i \\ \deltaL_i \\ \deltag_i -\end{array} -\right]%\\ -%&= -%\mat{M}^{-1}\deltap -\label{eqn:motion2} -\end{align} -where $l_0$ is the length of cell $i$, and $\invmat{M_i}$ is written in block form - $\textrm{diag}(\frac{1}{\mu l_0})$ -and $\frac{12\mat{P}}{\mu l_0^3}$ are $(3\times3)$, and $\frac{1}{\gamma}$ is -$(1\times1)$. The matrix $\mat{P}$ is the projection onto -the plane perpendicular to the cell axis $\hat{\vec{a}}$, i.e. $\mat{P}\deltaL -\equiv \deltaL - -\hat{\vec{a}}(\hat{\vec{a}} \cdot \deltaL)$. - -\begin{note} -There are 7 degrees of freedom for each cell, hence generalised position, -velocity and impulse are $7\times1$ vectors. There are 3 components of centroid -position/velocity/impulse ($\vec{x}$, $\vec{v}_\mathrm{lin}$, $\Delta \vec{p}$), -3 components of angular position/velocity/impulse ($\vec{\theta}$, $\vec{w}$, -$\deltaL$), and 1 component of length/growth rate/growth impulse ($l$, -$v_\textrm{growth}$, $g$). -\end{note} - -\begin{center} -\begin{figure}[p]\centering -\subfloat[]{\includegraphics[scale=0.75]{cellforces}}\qquad -\subfloat[]{\includegraphics{cellvel}} -\caption[Biophysical model of rod-shaped bacteria, forces and motion] -{Biophysical model of rod-shaped bacteria considers each cell as a capsule -(shown in two-dimensions). Forces on each cell (a) are generated by viscous drag -(red) and constraints at cell-cell contacts (black). The velocity of a point on -a cell consists of multiple components (b): the cell centre of mass (red circle) -moves with linear velocity $\vec{v}_\textrm{lin}$, the cell rotates with angular -velocity $\vec{w}$, and grows at instantaneous linear rate $v_\textrm{growth}$ causing all points to -move away from the centre of mass along the axis ($\hat{\vec{a}}$).} -\label{fig:model} -\end{figure} -\end{center} - -\begin{center} -\begin{figure}[p]\centering -\includegraphics[scale=0.75]{celloverlap} -\caption{} -\label{fig:overlap} -\end{figure} -\end{center} - -\subsection{Motion of points on cell surfaces} -We described above the change in generalised position of a cell due to a -generalised impulse, that is the change in its centroid location, angular -orientation, and length. Now consider the motion of a point on the -surface of this cell due to the change in generalised position. This point is -positioned according to vector $\vec{q}$ from the center -of the capsule $\vec{x}_i$, which has axis $\hat{\vec{a}}_i$. Its original position is -$\vec{q}_w = \vec{x}_i + \vec{q}$. -For small displacments the cell axis $\hat{\vec{a}}_i$, the associated -projection matrix $\mat{P}_i$, and the cell length $l_0$ remain approximately constant, and -\[ -\Delta \vec{q}_w \approx -\Delta \vec{ x_i} + -(\Delta \vec{\theta_i}\times\vec{q}) + -\frac{\Delta l_i}{l_0} \left(\hat{a}_i\cdot\vec{q}\right)\hat{a}_i -\] - -And substituting from equation \ref{eqn:motion}: -\begin{align*} -\Delta \vec{ q}_w &\approx -\Delta \vec{ x_i} - -(\vec{q} \times \Delta \vec{\theta_i}) + -\frac{\left(\hat{a}_i\cdot\vec{q}\right)\hat{a}_i}{l_0} \Delta l_i \\ -&\approx -\frac{1}{\mu l_0} \deltap_i - -(\vec{q} \times \frac{12\mat{P}_i}{\mu l_0^3}\deltaL_i) + -\frac{\left(\hat{a}_i\cdot\vec{q}\right)\hat{a}_i}{l_0}\frac{\deltag_i}{\gamma} -\end{align*} - -Now project this vector along the direction vector $\hat{n}$ of interest to get -the position change in a particular direction: -\begin{align*} -\Delta q_{\hat{n}} -&= -\hat{n} \cdot -\left( -\frac{1}{\mu l_0} \deltap_i - -(\vec{q} \times \frac{12\mat{P}_i}{\mu l_0^3}\deltaL_i) + -\frac{\left(\hat{a}_i\cdot\vec{q}\right)\hat{a}_i}{l_0}\frac{\deltag_i}{\gamma} -\right) \\ -&= -\frac{1}{\mu l_0}\hat{n}\cdot\deltap_i - -\frac{12}{\mu l_0^3}\left(\hat{n}\times\vec{q}\right)\cdot \mat{P}_i\deltaL_i + -\frac{\left(\hat{n}\cdot\hat{a}_i\right)\left(\hat{q}\cdot\hat{a}_i\right)}{l_0}\frac{\deltag_i}{\gamma} \\ -\end{align*} - -Which can be written in block matrix form as: -\begin{align*} -\Delta q_{\hat{n}} -&= -\left[ -\begin{array}{lll} -\hat{n}^{\textrm{T}} & -\left(\hat{n}\times\vec{q}\right)^{\textrm{T}} & -\frac{\left(\hat{n}\cdot\hat{a}_i\right)\left(\vec{q}\cdot\hat{a}_i\right)}{l_0} \\ -\end{array} -\right] -\left[ -\begin{array}{lll} -\frac{1}{\mu l_0} & 0 & 0 \\ -0 & \frac{12\mat{P}_i}{\mu l_0^3} & 0 \\ -0 & 0 & \frac{1}{\gamma} \\ -\end{array} -\right] -\left[ -\begin{array}{l} -\deltap_i \\ \deltaL_i \\ \deltag_i -\end{array} -\right]\\ -&= \mat{B}_{\hat{n},\vec{q},i}\invmat{M}_i\Delta\tilde{\vec{p}}_i -\end{align*} - -Here $\mat{B}_{\hat{n},\vec{q},i}$ is a matrix which represents -the geometric effect of a generalised position change on a point at $\vec{q}$ -from the centre of cell $i$ along direction $\hat{n}$, and -matrix $\invmat{M}_i$ is the inverse drag matrix for cell $i$. -The expression for $\Delta q_{\hat{n}}$ represents the motion of the surface point -at position $\vec{q}$ relative to the capsule centre in the direction $\hat{n}$ that -results from application of generalised impulse $\Delta \tilde{\vec{p}}$. This quantity is central -to the formation of the constraints explained below. - -\subsection{Effect of a set of applied impulses on cell-cell overlap distances} -Now consider two overlapping capsules $a$ and $b$, forming contact $k$. We find the contact points on -each cell $\vec{z}_{ak}$ and $\vec{z}_{bk}$ as described above (figure \ref{fig:overlap}). The -change in overlap distance $d_k$ is the difference in the movement of these -contact points along the contact normal $\hat{n}_k$. That is for generalised -impulses $\Delta\tilde{\vec{p}}_a$ and $\Delta\tilde{\vec{p}}_b$ applied to cell -$a$ and $b$, -\begin{align*} -\mat{B}_{ak} \Minv_a \Delta\tilde{\vec{p}}_a - -\mat{B}_{bk} \Minv_b \Delta\tilde{\vec{p}}_b -&= -\Delta d_k \\ -\end{align*} -where $\mat{B}_{ak}$ -and $\mat{B}_{bk}$ are as $\mat{B}$ matrices as defined above using the contact normal -$\hat{\vec{n}}_k$ as the direction vector, and the relative positions of -$\vec{z}_{ak}$ and $\vec{z}_{bk}$ from their respective cells. Viewed in block matrix form: -\begin{align*} -\left[ -\begin{array}{ll} -\mat{B}_{ak} \Minv_a & --\mat{B}_{bk} \Minv_b \\ -\end{array} -\right] -\left[ -\begin{array}{l} -\Delta\tilde{\vec{p}}_a \\ -\Delta\tilde{\vec{p}}_b \\ -\end{array} -\right] -= -\left[ -\begin{array}{l} -\Delta d_k -\end{array} -\right] -\end{align*} - -In a system of multiple cells, there will be one such equation for each contact $k$ between two capsules. -To solve all these equations simultaneously, each equation becomes a -row in a matrix equation. For example, with four cells and -three contacts, the -system might be: -\begin{align*} -\left[ -\begin{array}{llll} -\mat{B}_{a1}\Minv_1 & -\mat{B}_{b1}\Minv_2 & 0 & 0 \\ -\mat{B}_{a2}\Minv_1 & 0 & -\mat{B}_{c2}\Minv_3 & 0 \\ -0 & \mat{B}_{b3}\Minv_1 & 0 & -\mat{B}_{d3}\Minv_4 \\ -\end{array} -\right] -\left[ -\begin{array}{c} -\Delta\tilde{\vec{p}}_a\\ -\Delta\tilde{\vec{p}}_b\\ -\Delta\tilde{\vec{p}}_c\\ -\Delta\tilde{\vec{p}}_d\\ -\end{array} -\right] -= -\left[ -\begin{array}{c} -\Delta d_1\\ -\Delta d_2\\ -\Delta d_3\\ -\end{array} -\right] -\end{align*} - -\begin{align*} -\left[ -\begin{array}{llll} -\mat{B}_{a1} & -\mat{B}_{b1} & 0 & 0 \\ -\mat{B}_{a2} & 0 & -\mat{B}_{c2} & 0 \\ -0 & \mat{B}_{b3} & 0 & -\mat{B}_{d3} \\ -\end{array} -\right] -\left[ -\begin{array}{llll} -\Minv_1 & 0 & 0 & 0 \\ -0 & \Minv_2 & 0 & 0 \\ -0 & 0 & \Minv_3 & 0 \\ -0 & 0 & 0 & \Minv_1 \\ -\end{array} -\right] -\left[ -\begin{array}{c} -\Delta\tilde{\vec{p}}_a\\ -\Delta\tilde{\vec{p}}_b\\ -\Delta\tilde{\vec{p}}_c\\ -\Delta\tilde{\vec{p}}_d\\ -\end{array} -\right] -= -\left[ -\begin{array}{c} -\Delta d_1\\ -\Delta d_2\\ -\Delta d_3\\ -\end{array} -\right]\\ -\end{align*} - -and writing the system with single collected matrices and vectors, - -\begin{equation*} -\mat{B} \invmat{M} \Delta \tilde{\vec{p}} = \Delta \vec{d} -\end{equation*} - -\begin{note} -The elements $\mat{B}_{ij}\invmat{M}_i$ are computed by the \texttt{to\_ents} -(positive) and -\texttt{fr\_ents} (negative) arrays ($7\times1$ vectors stored in -\texttt{float8}) which are stored for each cell for each contact it -is involved in. We consider contacts to be directed from low to high index, and -so only the cell with the lowest index in each contact stores and calculates -these entries. -\end{note} - -\begin{note} -In the analysis above I have split the matrices $\mat{B}$ and $\invmat{M}$, but -currently the combination $\mat{B}\invmat{M}$ is computed. It may be better to -split it so that we can more easily compute other forms of $\mat{B}$, e.g. for adhesion (see -below). Application of $\invmat{M}$ is already implemented by -\texttt{compute\_Minvx}. -\end{note} - - -\subsection{Growth of cells generates impulses to prevent overlap} -Growth of cells during a discrete time-step $\Delta t$ is modelled by simply -increasing the length of each cell by $v_\textrm{growth}\Delta t$. This -causes cells to overlap (figure \ref{fig:overlap}). For a physically correct -arrangement of cells, reaction or constraint forces must be generated to -eliminate this overlap. - -A capsule of total length $l$ and radius $r$ -is defined as the locus of points within a -radius $r$ of the line segment of length $l-2r$ along its axis. -When two such capsules overlap, we define the points of intersection on each cell -($\vec{z}$ in figure \ref{fig:overlap}) as follows. First we find the closest points -on each cell's axis line segment. The line joining these points then intersects -each cell surface at points labelled $\vec{z}$, where it is normal to the surface. -Hence we have defined contact points on each cell, and the normal to the contact -$\hat{\vec{n}}$. The distance of overlap $d$ for each contact is then determined -by the distance between the contact points along the contact normal direction -(figure \ref{fig:overlap}). - -In order to constrain the system of cells to produce -a physically possible, non-overlapping arrangement, we must find the -impulse applied to each cell $\Delta \tilde{\vec{p}}$ that produces a change in -the overlap distance so that $d=0$ for each contact. -We have just described how these overlap distances are changed by a set of -applied impulses, and so we can now formulate the constraint system. - -\subsection{Constraint formulation} -To form a physically possible arrangement of cells after increasing their length -we wish to apply constraint impulses to cells such that -\begin{eqnarray*} -\vec{d} + \Delta \vec{d} &=& 0\\ -\Delta \vec{d} &=& -\vec{d} -\end{eqnarray*} -As shown above the change in overlaps $\Delta \vec{d}$ produced by a set of -generalised impulses $\Delta \tilde{\vec{p}}$ means that -\[ -\mat{B}\invmat{M}\Delta\tilde{\vec{p}} = \mat{A}\Delta\tilde{\vec{p}} = \Delta -\vec{d} -\] -where $\mat{A}$ is a block matrix $n_{\textrm{contacts}} \times -n_{\textrm{cells}}$, $\Delta\tilde{\vec{p}}$ is a block vector $n_{\textrm{cells}} \times 1$ and -$\vec{d}$ is $n_{\textrm{contacts}}\times 1$. Hence the constrained system is -given by: -\[ -\mat{A}\Delta\tilde{\vec{p}} + \vec{d} = 0 -\] -Hence we have formulated the system of constraints as a linear system. Given the -solution of this system, the change in generalised position of each cell is then $\Minv \Delta\tilde{\vec{p}}$. -However it is clear that in general this linear system does not have a unique solution. -To see this consider that cells may move perpendicular to the normal(s) of their -contact(s) without affecting $\Delta \vec{d}$. - -\subsection{Energy minimising solution} -The least squares solution of the constraint system is: -\[\underset{\deltap}{\operatorname{argmin}} -\left\{ -\left\|\mat{A}\Delta\tilde{\vec{p}} + \vec{d}\right\|^2 \right\} \] -%\[\mat{A}^{\textrm{T}}\mat{A}\deltap = -\mat{A}^{\textrm{T}}\vec{d}\] -where the expression $\mat{A}\Delta\tilde{\vec{p}} + \vec{d}$ is the vector of overlap -distances of each contact after application of impulses $\Delta \tilde{\vec{p}}$. If we interpret the least-squares -solution as an energy minimising solution, where the energy is -associated with the overlap of each contact. If the overlap at each -contact is $\vec{\epsilon}$, and if the energy is stored in an elastic -fashion, then this energy is: -\[\frac{1}{2}\vec{\epsilon}^T \mat{K} \vec{\epsilon} - = \frac{1}{2}\left\| \sqrt{\mat{K}}\vec{\epsilon} \right\|^2 - = \frac{1}{2}\left\| \sqrt{\mat{K}}\left(\mat{A}\Delta\tilde{\vec{p}} + \vec{d}\right) \right\|^2 \] - where $\mat{K}$ is a diagonal stiffness coefficient matrix. So -it is implicit in the above minimisation that $\mat{K}=2\mat{I}$. If -all the stiffnesses are the same (i.e. $\mat{K} = K\mat{I}$), then -this makes no difference to the solution. If some -contacts softer than others are required, the corresponding entry should be changed such that -$K_i<1$. We use this approach to approximate the -effect of a soft agarose substrate. This is a bit of distraction for now, so -lets just stick with $\mat{K}=\mat{I}$. - -As explained above the matrix $\mat{A}$ will typically be poorly conditioned, -and the matrix $\mat{A}^T\mat{A}$ will be even worse. So we still can't get a -unique solution. The usual approach is to use regularisation to `select' a -solution. -Following the energy minimisation formalism the solution obtained should -minimise the work done or energy expended by the constraint impulses. -Given an impulse $\Delta \tilde{\vec{p}}$ and time step $\Delta t$, the average -force applied over the time step is $\vec{F}=\Delta \tilde{\vec{p}}/\Delta t$. The work -done by these forces is then -\begin{eqnarray*} -W &=& \vec{F}\Delta \tilde{\vec{x}} \\ -&=& \vec{F} \invmat{M} \Delta \tilde{\vec{p}} \\ -&=& \frac{1}{\Delta t} \Delta \tilde{\vec{p}}^\textrm{T} \invmat{M}\Delta \tilde{\vec{p}} -\end{eqnarray*} -Combining this -with the overlap energy described above leads to the problem -\[\underset{\deltap}{\operatorname{argmin}} -\left\{ -\left\|\mat{A}\Delta\tilde{\vec{p}} + \vec{d}\right\|^2 + \frac{\alpha}{\Delta -t} \Delta \tilde{\vec{p}}^\textrm{T}\invmat{M}\Delta \tilde{\vec{p}} \right\} \] -where $\alpha$ is a regularisation parameter. In this case we can interpret -$\alpha$ physically as the relative energy cost of cell-cell overlap (e.g. due -to deformation of the cell wall) compared to the energy cost in overcoming drag. -Differentiating the above total energy, and setting to zero gives: -\begin{equation} -\left(\mat{A}^{\textrm{T}}\mat{A} + \frac{\alpha}{\Delta t}\Minv\right)\Delta \tilde{\vec{p}} = -\mat{A}^{\textrm{T}}\vec{d} -\label{eqn:finalsystem} -\end{equation} - -It is now clear that \textit{any} quadratic energy term can be included in the -system by forming the appropriate matrix $\mat{H}$ such that the energy is given -by $E = \|\mat{H}\Delta \tilde{\vec{p}} \|^2$. Or maybe more usefully, the -energy can be defined directly in terms of change in generalised position -$\Delta \tilde{\vec{x}}$ as $E = \|\mat{G}\Delta \tilde{\vec{x}} \|^2 = -\|\mat{G}\invmat{M}\Delta \tilde{\vec{p}} \|^2$, and the linear system is then -given by -\begin{equation} -\left(\frac{1}{\alpha}\mat{A}^{\textrm{T}}\mat{A} + \frac{1}{\Delta t}\Minv + -\invmat{M}\mat{G}^\textrm{T} \mat{G}\invmat{M} \right) \Delta \tilde{\vec{p}} = -\mat{A}^{\textrm{T}}\vec{d} -\label{eqn:finalsystem} -\end{equation} -where I have moved the $\alpha$ to make clear its physical interpretation as the -relative cost of overlap. Note also I have used the fact that -$\mat{M}^{-\textrm{T}} \equiv \invmat{M}$ because it is diagonal except for terms -involving the projection matrices $\mat{P}_i$, which are themselves symmetric by -definition. - -\begin{note} -Writing out the matrix $\mat{A}=\mat{B}\invmat{M}$ and $\Delta \tilde{\vec{p}} = -\mat{M}\Delta \tilde{\vec{x}}$ in the above system gives a -factor of $\invmat{M}$ which could be eliminated. However, this is actually -acting as a right-preconditioner. Similarly expanding -$\mat{A}^\textrm{T}=\invmat{M}\mat{B}^\textrm{T}$ gives us left-preconditioning. -Hence we have split-preconditioning. -I'm pretty sure we did some testing and the preconditioning did improve -the condition number. -\end{note} - -\begin{note} -The factor of $1/\Delta t$ is not computed in the current code. At the -time we were considering a kind of ad hoc regularisation term rather than -explicitly minimising physical work. Adding the $1/\Delta t$ makes sense. -\end{note} - -\begin{note} -In the current code the viscosity from substrate per unit length of cells $\mu$ -is set at $\mu=1$ - -i.e. it is factored out of the $\invmat{M}$ matrices. This means that the -parameter $\alpha$ incorporates the value of $\mu$ into the ratio of drag from the substrate to -resistance to deformation of cells. It seems sensible that this should be the -same as the ratio $\Gamma = \mu/\gamma$, where $\gamma$ is the resistance to -change in length (see appendix). This would be nice because the whole model -would then be parameterised only by $\Gamma$. Need to think about this a bit more. -\end{note} - -\section{Adhesion} -Now we want to form a matrix $\mat{G}$ that adds a quadratic energy to the -system to simulate adhesion. Consider adhesion that acts only in the plane of -the cell surface at each contact (tangent plane), such that $E_k = (\Delta -d^{\perp}_k)^2 = \|\Delta \vec{d}^\perp_k\|^2$ where $\Delta \vec{d}^\perp_k$ is -the movement vector in the tangent plane -between contact points on each cell involved in contact $k$. This is a -$3\times1$ vector that is the projection of the total movement into the tangent plane of -the contact. In this case -\begin{equation*} -\mat{G}\invmat{M}\Delta \tilde{\vec{p}} = \Delta \vec{d}^\perp -\end{equation*} -where the matrices and vectors are in block form, with one block per cell or -contact. - -This matrix $\mat{G}$ is closely related to the above described $\mat{B}$ -matrix, which projects the movement of each contact point along its respective contact -normal $\hat{n}_k$. The tangent plane is perpendicular to this normal vector. -For cell $i$ and contact $k$, -\begin{equation*} -\mat{B}_{ik} = -\left[ -\begin{array}{lll} -\hat{n}_k^{\textrm{T}} & -\left(\hat{n}_k\times\vec{z}_{ik}\right)^{\textrm{T}} & -\frac{\left(\hat{n}_k\cdot\hat{a}_i\right)\left(\vec{z}_{ik}\cdot\hat{a}_i\right)}{l_0} \\ -\end{array} -\right] -\end{equation*} -where $\mat{B}_{ik}$ is a $1\times7$ matrix. The matrix blocks $\mat{G}_{ik}$ -are $3\times7$ and given by -\begin{eqnarray*} -\mat{G}_{ik} &=& -\left[ -\begin{array}{lll} -\mat{Q} & \mat{Q}\mat{Z}^\times_{ik} & -\left[\hat{a}_i - \hat{n}_k\left(\hat{n}_k\cdot\hat{a}_i\right)\right] \frac{\left(\vec{z}_{ik}\cdot\hat{a}_i\right)}{l_0} \\ -\end{array} -\right]\\ -&=& -\left[ -\begin{array}{lll} -\mat{Q} & \mat{Q}\mat{Z}^\times_{ik} & -\frac{\left(\vec{z}_{ik}\cdot\hat{a}_i\right)}{l_0} \mat{Q}\hat{a}_i \\ -\end{array} -\right]\\ -&=& -\mat{Q} -\left[ -\begin{array}{lll} -\mat{I} & \mat{Z}^\times_{ik} & -\frac{\left(\vec{z}_{ik}\cdot\hat{a}_i\right)}{l_0} \hat{a}_i \\ -\end{array} -\right] -\end{eqnarray*} -Here $\mat{Q}$ is the $3\times3$ matrix projecting into the tangent plane, so that for any vector -$\vec{u}$ -\begin{equation} -\mat{Q}\vec{u} = \vec{u} - \hat{n}_k\left(\hat{n}_k \cdot \vec{u}\right) -\label{eqn:Q} -\end{equation} -and $\mat{Z}^\times_{ik}$ is the matrix representing the cross product -\begin{equation} -\mat{Z}^\times_{ik} \vec{u} = \vec{z}_{ik} \times \vec{u} -\label{eqn:Z} -\end{equation} -These first two blocks ($\mat{Q}$ and $\mat{Q}\mat{Z}^\times_{ik}$) of $\mat{G}_{ik}$ are $3\times3$ and the third -($\frac{\left(\vec{z}_{ik}\cdot\hat{a}_i\right)}{l_0} \mat{Q}\vec{a}_i$) is -$3\times1$. - -\begin{note} -We could explicitly store the $3\times3$ blocks and apply them as matrix -multiplications. However, it is more efficient to do the computation directly -using equations \ref{eqn:Q} and \ref{eqn:Z}. -\end{note} - -\begin{note} -The result of applying each block $\mat{G}_{ik}$ to the cells impulse $\Delta -\tilde{\vec{p}}_i$ is a $3\times1$ vector. Hence the array storing the result of -$\mat{G}\Delta \tilde{\vec{p}}$ must use \texttt{float4} types. This might seem -counterintuitive since the distances are projected onto a plane, but note that -the tangent plane of each contact is in general different. -\end{note} - -\section{Viscous adhesion} -Because we recompute the closest points for contacts at each time step the above -described adhesion energy will be completely dissipated. This is effectively a -viscous model in which -\begin{equation*} -\vec{F} = C \frac{d\vec{x}}{dt} \approx C \frac{\Delta \vec{x}}{\Delta t} -\end{equation*} -and thus $E \approx \frac{1}{\Delta t}C\|\Delta \vec{x}\|^2$. So that using the -above analyis the energy from viscous adhesion is given by -\begin{equation*} -E = \left(\frac{1}{\Delta t}C \right) \|\mat{G}\invmat{M}\Delta \tilde{\vec{p}}\|^2 -\end{equation*} -for the same viscosity coefficient at each contact. More generally, -\begin{equation*} -E = \left(\frac{1}{\Delta t} \right) -\Delta \tilde{\vec{p}}^\textrm{T}\invmat{M}\mat{G}^\textrm{T}\mat{C}\mat{G}\invmat{M}\Delta \tilde{\vec{p}} -\end{equation*} -where $\mat{C}$ is a diagonal matrix of viscosity coefficients for each contact. -In practice this matrix is best implemented by just scaling each block -$\mat{G}_{ik}$ by the appropriate coefficient. - -\begin{note} -The scaling by $1/\Delta t$ is required to make this purely viscous model physically sensible. -To implement a purely elastic model of contact would require keeping track of -the original point of contact between each pair of cells. -\end{note} - -\section{Implementation in CellModeller4} -The following table describes which functions or OpenCL kernels perform which -calculations and data arrays that contain the results, using the mathematical notation above. - -\begin{table}[H] -\begin{tabular}{c c p{4in}} -\toprule -Function/kernel & Maths & Description\\ -\midrule -\texttt{find\_contacts} & $\vec{d}$, $\hat{\vec{n}}$ & Finds overlapping cells -and computes the overlap distance $d_k$ and surface normal $\hat{\vec{n}}_k$ for -each contact $k$.\\ -\addlinespace -\texttt{rel\_dists} & $\vec{d}$ & Stores the vector of overlap distances, one -element (\texttt{float}) per contact.\\ -\addlinespace -\texttt{compute\_Minvx} & $\invmat{M}$ & Applies the inverse drag matrix to some -given vector of length $n_\mathrm{cells}$ and type \texttt{float8} (only first 7 -elements are used). It does this per cell, by applying its $\invmat{M}_i$ matrix -block.\\ -\bottomrule -\end{tabular} -\end{table} - -% Long maths in appendix for ease of reading -\begin{appendices} -\chapter{Equations of motion} -\label{app:eqmot} -Consider a capsule with main axis $\hat{\vec{a}}$, mass $m$, and length $l$. -When in motion the capsule is associated with linear ($\vec{v}_\textrm{lin}$), -angular ($\vec{w}$), and growth ($v_\textrm{growth}$) velocities (figure -\ref{fig:model}b). -Now consider a point on the -surface of the capsule with position $\vec{r}$ relative to the -capsule's center of mass. The velocity of that point is given by: -\begin{align*} -\vec{v}_{r} -&= -\vec{v}_\textrm{lin} -+ \vec{w} \times \vec{r} -+ \frac{1}{2}\frac{\hat{a}\cdot\vec{r}}{l_0}\hat{a}v_\textrm{growth} \\ -&= -\vec{v}_\textrm{lin} -- \vec{r} \times \vec{w} -+ \frac{1}{2}\frac{\hat{a}\cdot\vec{r}}{l_0}\hat{a}v_\textrm{growth} -\end{align*} -where $l_0$ is the current capsule length. The first term in this expression is -the linear velocity of the whole cell, the second term is the angular component, -and the final term is due to growth. Growth is assumed to occur by extension of -all parts of the cell wall along the axis, meaning that any point on the cell is -moving away from the centre of mass at a rate proportional to its distance from -the centre. The maximum velocity due to growth then occurs at the tips of the cell -which are each moving away from the centre of mass at rate -$\frac{1}{2}v_\textrm{growth}$ along the cell axis $\hat{\vec{a}}$. - -Each point on the cell surface experiences viscous drag from the growth substrate due -to its motion. The viscous drag force on a differential length $dr$ of the -capsule is approximately given by: \[d\vec{F} = -\mu dr \vec{v}_r\] where $\mu$ -is a drag coefficient per unit length. To understand the motion of the capsule -shape, initially at rest, after the application of a generalised impulse -$\Delta\tilde{\vec{p}}$, which can be divided into linear, angular and growth -components $\left(\begin{array}{lll}\deltap & \deltaL & -\deltag\end{array}\right)^T$, we must find the net force on the capsule due to -viscous drag at each point on its surface. Given this force, Newton's laws can -be applied to find the change in generalised position. - -\section{Linear impulse $\deltap$} -Approximating the forces on the differential length element at the average -position, so that position $\vec{r}=r\hat{a}$ lies on the axis of the cell: - -\begin{align*} -d\vec{F} &= -\mu dr \vec{v}_r\\ -d\vec{F} &= -\mu dr -\left( -\vec{v}_\textrm{lin} -- \vec{r} \times \vec{w} -+ \frac{1}{2}\frac{\hat{a}\cdot\vec{r}}{l_0}\hat{a}v_\textrm{growth} -\right) -\\ -d\vec{F} &= -\mu dr -\left( -\vec{v}_\textrm{lin} -- r\hat{a} \times \vec{w} -+ \frac{1}{2}\frac{r}{l_0}\hat{a}v_\textrm{growth} -\right) -\\ -\end{align*} - -The total force on the capsule is given by the integral over the length of -the capsule from $-\frac{l_0}{2}$ to $+\frac{l_0}{2}$. The -second two terms in the expression for velocity are odd in $r$ and -so will cancel when integrated so the total force on -the capsule is: -\begin{align*} -\vec{F} &= -\mu \vec{v}_\textrm{lin} \int_{-\frac{l_0}{2}}^{+\frac{l_0}{2}} dr \\ -&= -\mu \vec{v}_\textrm{lin} l_0 \\ -\end{align*} -And following Newton's laws: -\begin{align*} -m \frac{d\vec{v}_\textrm{lin}}{dt} &= -\mu l_0 \vec{v}_\textrm{lin}\\ -\vec{v}_\textrm{lin} &= v_0\exp{(-\frac{\mu l_0}{m}t)} \\ -&= \frac{\deltap}{m}\exp{(-\frac{\mu l_0}{m}t)} \\ -\end{align*} - -The change in position of the centre of mass of the capsule $\vec{x}$ due to -linear impulse $\deltap$, and thus the change in position of any point on the -cell is then found as: -\begin{align*} -\frac{d\vec{x}}{dt} &= \frac{\deltap}{m}\exp{(-\frac{\mu l_0}{m}t)} \\ -%x &= -\frac{m\deltap}{m\mu l}\exp{(-\frac{\mu l}{m}t)} + C \\ -\Delta \vec{x} &= \frac{\deltap}{\mu l_0}\left(1-\exp{(-\frac{\mu l_0}{m}t)}\right) \\ -\end{align*} -In the case of a bacterium, inertial effects are very small compared to drag -forces~\cite{Purcell:1977} meaning $m/\mu \approx 0$, so that the -exponential term is nearly zero and so: -\begin{equation} -\Delta \vec{x} \approx \frac{\deltap}{\mu l_0} -\label{eqn:deltax} -\end{equation} - -\section{Angular impulse $\Delta\vec{L}$} -Now consider the rotational motion of the cell. The torque applied at a -differential section of the cell at position $\vec{r}=r\hat{\vec{a}}$ is: -\begin{align*} -d\vec{\tau} &= \vec{r} \times d\vec{F} \\ -&= \vec{r} \times -\mu dr \vec{v}_r \\ -&= \vec{r} \times -\mu dr \left( -\vec{v}_\textrm{linear} -- r\hat{a} \times \vec{w} -+ \frac{1}{2}\frac{r}{l_0}\hat{a}v_\textrm{growth} -\right) \\ -\end{align*} - -The drag force due to linear velocity makes no total -contribution to torque (the contributions on the two sides of the -capsule's center of mass cancel) and neither does drag force due to -growth velocity (it is parallel to $\vec{r}$). Note that the triple product: -\begin{align*} -\vec{r}\times(\vec{w}\times\vec{r}) &= \vec{w}(\vec{r}\cdot\vec{r}) - \vec{r}(\vec{r}\cdot\vec{w}) \\ -&= \vec{w}r^2 - \vec{r}(\vec{r}\cdot\vec{w}) -\end{align*} -and so: -\begin{align*} -d\tau &= -\mu \left( \vec{w}r^2 - r\hat{a}(r\hat{a}\cdot\vec{w}) \right) dr \\ - &= -\mu \left( \vec{w} - \hat{a}(\hat{a}\cdot\vec{w}) \right) r^2 dr \\ -\tau &= -\mu \left( \vec{w} - \hat{a}(\hat{a}\cdot\vec{w}) \right) \int_{-\frac{l_0}{2}}^{\frac{l_0}{2}}r^2dr \\ -&=-\frac{1}{12}\mu l_0^3 \left( \vec{w} - \hat{a}(\hat{a}\cdot\vec{w}) \right) = \mat{I}\frac{d\vec{w}}{dt} \\ -\end{align*} - -The expression $\vec{w} - \hat{a}(\hat{a}\cdot\vec{w})$ represents a projection of the vector $\vec{w}$ onto the -plane perpendicular to the axis $\hat{a}$, and can be written as $\mat{P}\vec{w}$ where $\mat{P}$ is the -appropriate projection matrix: - -\begin{align*} -\tau &=-\frac{1}{12}\mu l_0^3 \mat{P}\vec{w} = I\frac{d\vec{w}}{dt} \\ -\vec{w} &= \vec{w}_0 \exp{\left( -\frac{\mu l_0^3 \mat{P}t}{12 I} \right)} \\ -\end{align*} - -For a projection matrix $\mat{P}$, an exponential of the form $\exp{(k\mat{P})}$, where $k$ is a scalar, is: -\[\exp{(k\mat{P})} = \mat{P}\exp{(k)} + \left(\mat{I}-\mat{P}\right)\] - so: -\[\vec{w} = \mat{P} \vec{w}_0 \exp{\left( -\frac{\mu l_0^3 t}{12 I} \right)} + \left(\mat{I}-\mat{P}\right) \vec{w}_0\] - - -In which the second term $\left(\mat{I}-\mat{P}\right) \vec{w}_0$ is the angular velocity about the cell axis $\hat{a}$. -Approximating the capsule as a `slender rod' with no rotational inertia about its axis -the second term can be ignored, and: - -\begin{align*} -%\frac{dw}{w} &= -\frac{\mu l^3}{12I}dt \\ -%\log{w} &= -\frac{\mu l^3}{12I}t + C \\ -\vec{w} &= \mat{P} \vec{w}_0\exp{(-\frac{\mu l_0^3}{12I}t)} \\ -&= \frac{\mat{P} \deltaL}{I}\exp{(-\frac{\mu l_0^3}{12I}t)} = \frac{d\vec{\theta}}{dt} \\ -%\Delta \theta &= -\frac{12I \mat{P} \deltaL}{I\mu l_0^3}\exp{(-\frac{\mu l_0^3}{12I}t)} + C \\ -%&= \frac{12 \mat{P} \deltaL}{\mu l_0^3}\left(1-\exp{(-\frac{\mu l_0^3}{12I}t)}\right) \\ -\end{align*} - -Making the same approximation for negligible inertia as above $I/\mu \approx -0$ gives: - -\begin{equation} -\Delta \vec{\theta} \approx \frac{12 \mat{P} \deltaL}{\mu l_0^3} -\label{eqn:deltatheta} -\end{equation} - -So, the effect of a rotational impulse is projected onto the plane of the cell axis - that is, it only causes rotation -about the other two axes. - -\section{Growth impulse $\Delta g$} -A growth impulse tends to elongate the cell, and is resisted by compressive forces along the axis of the capsule due to drag: - -\begin{align*} - F_c &= \mu \frac{1}{2} \left[ \int_{0}^{\frac{l_0}{2}}{\frac{r}{l_0}v_\textrm{growth}} dr - - \int_{-\frac{l_0}{2}}^{0}{\frac{r}{l_0}v_\textrm{growth}} dr \right] \\ - &= \frac{\mu}{2} v_\textrm{growth} \left[ \int_{0}^{\frac{l_0}{2}}{\frac{r}{l_0}} dr - - \int_{-\frac{l_0}{2}}^{0}{\frac{r}{l_0}} dr \right] \\ - &= \frac{\mu l_0}{8} v_\textrm{growth} -\end{align*} - -%Here we have written the same drag coefficient $\mu$. We incorporate forces from the cells growth, -% and resulting resistance to length change, as a drag term. Thus rewriting: -This is the drag due to interaction with the substrate. In order to -model the cell's resistance to change in length due to its own structural and -mechanical properties, I incorporate an additional -drag term: -\begin{align*} - F_c = \left( \frac{\mu l_0}{8} + \gamma \right) v_\textrm{growth} -\end{align*} -where $\gamma$ describes cell growth drag. Following the same -reasoning as above, integrating and neglecting inertial effects, and assuming -that $\Delta l << l$ so that $l_0$ can be taken as constant, the effect of -growth impulse $\delta g$ on cell length is: -\begin{align*} - \Delta l \approx \frac{8 \Delta g}{\mu l_0 + 8 \gamma} -\end{align*} -where $\Delta g$ is the applied growth impulse. Assuming that the resistance of -the cell to deformation dominates viscous drag from the substrate, then -this can be reduced to: -\begin{equation} - \Delta l \approx \frac{\Delta g}{\gamma} - \label{eqn:deltal} -\end{equation} - -\section{Motion due to generalised impulse} -%We have shown above that the change in the capsule generalised position vector -Combining the results for each component of motion from equations -\ref{eqn:deltax}, \ref{eqn:deltatheta} and \ref{eqn:deltal}, the change in generalised -position $\tilde{\vec{x}} = \left(\begin{array}{lll}\vec{x} & \vec{\theta} & l -\end{array}\right)^T$ after the application of a general impulse $\Delta\tilde{\vec{p}} = -\left(\begin{array}{lll} \deltap & \deltaL & \deltag\end{array}\right)^T$ -can be written in block matrix form as: -\begin{align} -\Delta \tilde{\vec{ x}} &= -\left[ -\begin{array}{l} -\frac{\deltap}{\mu l_0} \\ -\frac{12\mat{P}\deltaL}{\mu l_0^3} \\ -\frac{\deltag}{\gamma} \\ -\end{array} -\right] \\ -&= -\left[ -\begin{array}{lll} -\textrm{diag}(\frac{1}{\mu l_0}) & 0 & 0 \\ -0 & \frac{12\mat{P}}{\mu l_0^3} & 0 \\ -0 & 0 & \frac{1}{\gamma} \\ -\end{array} -\right] -\left[ -\begin{array}{l} -\deltap \\ \deltaL \\ \deltag -\end{array} -\right]%\\ -%&= -%\mat{M}^{-1}\deltap -\label{eqn:motion} -\end{align} - - -\end{document} diff --git a/Doc/modules.pdf b/Doc/modules.pdf deleted file mode 100644 index 0340d954..00000000 Binary files a/Doc/modules.pdf and /dev/null differ diff --git a/Doc/modules.png b/Doc/modules.png deleted file mode 100644 index 9fcbb22e..00000000 Binary files a/Doc/modules.png and /dev/null differ diff --git a/DoxygenConfig b/DoxygenConfig deleted file mode 100644 index 86b2c5fe..00000000 --- a/DoxygenConfig +++ /dev/null @@ -1,2366 +0,0 @@ -# Doxyfile 1.8.9.1 - -# This file describes the settings to be used by the documentation system -# doxygen (www.doxygen.org) for a project. -# -# All text after a double hash (##) is considered a comment and is placed in -# front of the TAG it is preceding. -# -# All text after a single hash (#) is considered a comment and will be ignored. -# The format is: -# TAG = value [value, ...] -# For lists, items can also be appended using: -# TAG += value [value, ...] -# Values that contain spaces should be placed between quotes (\" \"). - -#--------------------------------------------------------------------------- -# Project related configuration options -#--------------------------------------------------------------------------- - -# This tag specifies the encoding used for all characters in the config file -# that follow. The default is UTF-8 which is also the encoding used for all text -# before the first occurrence of this tag. Doxygen uses libiconv (or the iconv -# built into libc) for the transcoding. See http://www.gnu.org/software/libiconv -# for the list of possible encodings. -# The default value is: UTF-8. - -DOXYFILE_ENCODING = UTF-8 - -# The PROJECT_NAME tag is a single word (or a sequence of words surrounded by -# double-quotes, unless you are using Doxywizard) that should identify the -# project for which the documentation is generated. This name is used in the -# title of most generated pages and in a few other places. -# The default value is: My Project. - -PROJECT_NAME = Cellmodeller - -# The PROJECT_NUMBER tag can be used to enter a project or revision number. This -# could be handy for archiving the generated documentation or if some version -# control system is used. - -PROJECT_NUMBER = - -# Using the PROJECT_BRIEF tag one can provide an optional one line description -# for a project that appears at the top of each page and should give viewer a -# quick idea about the purpose of the project. Keep the description short. - -PROJECT_BRIEF = - -# With the PROJECT_LOGO tag one can specify a logo or an icon that is included -# in the documentation. The maximum height of the logo should not exceed 55 -# pixels and the maximum width should not exceed 200 pixels. Doxygen will copy -# the logo to the output directory. - -PROJECT_LOGO = - -# The OUTPUT_DIRECTORY tag is used to specify the (relative or absolute) path -# into which the generated documentation will be written. If a relative path is -# entered, it will be relative to the location where doxygen was started. If -# left blank the current directory will be used. - -OUTPUT_DIRECTORY = - -# If the CREATE_SUBDIRS tag is set to YES then doxygen will create 4096 sub- -# directories (in 2 levels) under the output directory of each output format and -# will distribute the generated files over these directories. Enabling this -# option can be useful when feeding doxygen a huge amount of source files, where -# putting all generated files in the same directory would otherwise causes -# performance problems for the file system. -# The default value is: NO. - -CREATE_SUBDIRS = NO - -# If the ALLOW_UNICODE_NAMES tag is set to YES, doxygen will allow non-ASCII -# characters to appear in the names of generated files. If set to NO, non-ASCII -# characters will be escaped, for example _xE3_x81_x84 will be used for Unicode -# U+3044. -# The default value is: NO. - -ALLOW_UNICODE_NAMES = NO - -# The OUTPUT_LANGUAGE tag is used to specify the language in which all -# documentation generated by doxygen is written. Doxygen will use this -# information to generate all constant output in the proper language. -# Possible values are: Afrikaans, Arabic, Armenian, Brazilian, Catalan, Chinese, -# Chinese-Traditional, Croatian, Czech, Danish, Dutch, English (United States), -# Esperanto, Farsi (Persian), Finnish, French, German, Greek, Hungarian, -# Indonesian, Italian, Japanese, Japanese-en (Japanese with English messages), -# Korean, Korean-en (Korean with English messages), Latvian, Lithuanian, -# Macedonian, Norwegian, Persian (Farsi), Polish, Portuguese, Romanian, Russian, -# Serbian, Serbian-Cyrillic, Slovak, Slovene, Spanish, Swedish, Turkish, -# Ukrainian and Vietnamese. -# The default value is: English. - -OUTPUT_LANGUAGE = English - -# If the BRIEF_MEMBER_DESC tag is set to YES, doxygen will include brief member -# descriptions after the members that are listed in the file and class -# documentation (similar to Javadoc). Set to NO to disable this. -# The default value is: YES. - -BRIEF_MEMBER_DESC = YES - -# If the REPEAT_BRIEF tag is set to YES, doxygen will prepend the brief -# description of a member or function before the detailed description -# -# Note: If both HIDE_UNDOC_MEMBERS and BRIEF_MEMBER_DESC are set to NO, the -# brief descriptions will be completely suppressed. -# The default value is: YES. - -REPEAT_BRIEF = YES - -# This tag implements a quasi-intelligent brief description abbreviator that is -# used to form the text in various listings. Each string in this list, if found -# as the leading text of the brief description, will be stripped from the text -# and the result, after processing the whole list, is used as the annotated -# text. Otherwise, the brief description is used as-is. If left blank, the -# following values are used ($name is automatically replaced with the name of -# the entity):The $name class, The $name widget, The $name file, is, provides, -# specifies, contains, represents, a, an and the. - -ABBREVIATE_BRIEF = - -# If the ALWAYS_DETAILED_SEC and REPEAT_BRIEF tags are both set to YES then -# doxygen will generate a detailed section even if there is only a brief -# description. -# The default value is: NO. - -ALWAYS_DETAILED_SEC = NO - -# If the INLINE_INHERITED_MEMB tag is set to YES, doxygen will show all -# inherited members of a class in the documentation of that class as if those -# members were ordinary class members. Constructors, destructors and assignment -# operators of the base classes will not be shown. -# The default value is: NO. - -INLINE_INHERITED_MEMB = NO - -# If the FULL_PATH_NAMES tag is set to YES, doxygen will prepend the full path -# before files name in the file list and in the header files. If set to NO the -# shortest path that makes the file name unique will be used -# The default value is: YES. - -FULL_PATH_NAMES = YES - -# The STRIP_FROM_PATH tag can be used to strip a user-defined part of the path. -# Stripping is only done if one of the specified strings matches the left-hand -# part of the path. The tag can be used to show relative paths in the file list. -# If left blank the directory from which doxygen is run is used as the path to -# strip. -# -# Note that you can specify absolute paths here, but also relative paths, which -# will be relative from the directory where doxygen is started. -# This tag requires that the tag FULL_PATH_NAMES is set to YES. - -STRIP_FROM_PATH = - -# The STRIP_FROM_INC_PATH tag can be used to strip a user-defined part of the -# path mentioned in the documentation of a class, which tells the reader which -# header file to include in order to use a class. If left blank only the name of -# the header file containing the class definition is used. Otherwise one should -# specify the list of include paths that are normally passed to the compiler -# using the -I flag. - -STRIP_FROM_INC_PATH = - -# If the SHORT_NAMES tag is set to YES, doxygen will generate much shorter (but -# less readable) file names. This can be useful is your file systems doesn't -# support long names like on DOS, Mac, or CD-ROM. -# The default value is: NO. - -SHORT_NAMES = NO - -# If the JAVADOC_AUTOBRIEF tag is set to YES then doxygen will interpret the -# first line (until the first dot) of a Javadoc-style comment as the brief -# description. If set to NO, the Javadoc-style will behave just like regular Qt- -# style comments (thus requiring an explicit @brief command for a brief -# description.) -# The default value is: NO. - -JAVADOC_AUTOBRIEF = NO - -# If the QT_AUTOBRIEF tag is set to YES then doxygen will interpret the first -# line (until the first dot) of a Qt-style comment as the brief description. If -# set to NO, the Qt-style will behave just like regular Qt-style comments (thus -# requiring an explicit \brief command for a brief description.) -# The default value is: NO. - -QT_AUTOBRIEF = NO - -# The MULTILINE_CPP_IS_BRIEF tag can be set to YES to make doxygen treat a -# multi-line C++ special comment block (i.e. a block of //! or /// comments) as -# a brief description. This used to be the default behavior. The new default is -# to treat a multi-line C++ comment block as a detailed description. Set this -# tag to YES if you prefer the old behavior instead. -# -# Note that setting this tag to YES also means that rational rose comments are -# not recognized any more. -# The default value is: NO. - -MULTILINE_CPP_IS_BRIEF = NO - -# If the INHERIT_DOCS tag is set to YES then an undocumented member inherits the -# documentation from any documented member that it re-implements. -# The default value is: YES. - -INHERIT_DOCS = YES - -# If the SEPARATE_MEMBER_PAGES tag is set to YES then doxygen will produce a new -# page for each member. If set to NO, the documentation of a member will be part -# of the file/class/namespace that contains it. -# The default value is: NO. - -SEPARATE_MEMBER_PAGES = NO - -# The TAB_SIZE tag can be used to set the number of spaces in a tab. Doxygen -# uses this value to replace tabs by spaces in code fragments. -# Minimum value: 1, maximum value: 16, default value: 4. - -TAB_SIZE = 4 - -# This tag can be used to specify a number of aliases that act as commands in -# the documentation. An alias has the form: -# name=value -# For example adding -# "sideeffect=@par Side Effects:\n" -# will allow you to put the command \sideeffect (or @sideeffect) in the -# documentation, which will result in a user-defined paragraph with heading -# "Side Effects:". You can put \n's in the value part of an alias to insert -# newlines. - -ALIASES = - -# This tag can be used to specify a number of word-keyword mappings (TCL only). -# A mapping has the form "name=value". For example adding "class=itcl::class" -# will allow you to use the command class in the itcl::class meaning. - -TCL_SUBST = - -# Set the OPTIMIZE_OUTPUT_FOR_C tag to YES if your project consists of C sources -# only. Doxygen will then generate output that is more tailored for C. For -# instance, some of the names that are used will be different. The list of all -# members will be omitted, etc. -# The default value is: NO. - -OPTIMIZE_OUTPUT_FOR_C = NO - -# Set the OPTIMIZE_OUTPUT_JAVA tag to YES if your project consists of Java or -# Python sources only. Doxygen will then generate output that is more tailored -# for that language. For instance, namespaces will be presented as packages, -# qualified scopes will look different, etc. -# The default value is: NO. - -OPTIMIZE_OUTPUT_JAVA = NO - -# Set the OPTIMIZE_FOR_FORTRAN tag to YES if your project consists of Fortran -# sources. Doxygen will then generate output that is tailored for Fortran. -# The default value is: NO. - -OPTIMIZE_FOR_FORTRAN = NO - -# Set the OPTIMIZE_OUTPUT_VHDL tag to YES if your project consists of VHDL -# sources. Doxygen will then generate output that is tailored for VHDL. -# The default value is: NO. - -OPTIMIZE_OUTPUT_VHDL = NO - -# Doxygen selects the parser to use depending on the extension of the files it -# parses. With this tag you can assign which parser to use for a given -# extension. Doxygen has a built-in mapping, but you can override or extend it -# using this tag. The format is ext=language, where ext is a file extension, and -# language is one of the parsers supported by doxygen: IDL, Java, Javascript, -# C#, C, C++, D, PHP, Objective-C, Python, Fortran (fixed format Fortran: -# FortranFixed, free formatted Fortran: FortranFree, unknown formatted Fortran: -# Fortran. In the later case the parser tries to guess whether the code is fixed -# or free formatted code, this is the default for Fortran type files), VHDL. For -# instance to make doxygen treat .inc files as Fortran files (default is PHP), -# and .f files as C (default is Fortran), use: inc=Fortran f=C. -# -# Note: For files without extension you can use no_extension as a placeholder. -# -# Note that for custom extensions you also need to set FILE_PATTERNS otherwise -# the files are not read by doxygen. - -EXTENSION_MAPPING = - -# If the MARKDOWN_SUPPORT tag is enabled then doxygen pre-processes all comments -# according to the Markdown format, which allows for more readable -# documentation. See http://daringfireball.net/projects/markdown/ for details. -# The output of markdown processing is further processed by doxygen, so you can -# mix doxygen, HTML, and XML commands with Markdown formatting. Disable only in -# case of backward compatibilities issues. -# The default value is: YES. - -MARKDOWN_SUPPORT = YES - -# When enabled doxygen tries to link words that correspond to documented -# classes, or namespaces to their corresponding documentation. Such a link can -# be prevented in individual cases by putting a % sign in front of the word or -# globally by setting AUTOLINK_SUPPORT to NO. -# The default value is: YES. - -AUTOLINK_SUPPORT = YES - -# If you use STL classes (i.e. std::string, std::vector, etc.) but do not want -# to include (a tag file for) the STL sources as input, then you should set this -# tag to YES in order to let doxygen match functions declarations and -# definitions whose arguments contain STL classes (e.g. func(std::string); -# versus func(std::string) {}). This also make the inheritance and collaboration -# diagrams that involve STL classes more complete and accurate. -# The default value is: NO. - -BUILTIN_STL_SUPPORT = NO - -# If you use Microsoft's C++/CLI language, you should set this option to YES to -# enable parsing support. -# The default value is: NO. - -CPP_CLI_SUPPORT = NO - -# Set the SIP_SUPPORT tag to YES if your project consists of sip (see: -# http://www.riverbankcomputing.co.uk/software/sip/intro) sources only. Doxygen -# will parse them like normal C++ but will assume all classes use public instead -# of private inheritance when no explicit protection keyword is present. -# The default value is: NO. - -SIP_SUPPORT = NO - -# For Microsoft's IDL there are propget and propput attributes to indicate -# getter and setter methods for a property. Setting this option to YES will make -# doxygen to replace the get and set methods by a property in the documentation. -# This will only work if the methods are indeed getting or setting a simple -# type. If this is not the case, or you want to show the methods anyway, you -# should set this option to NO. -# The default value is: YES. - -IDL_PROPERTY_SUPPORT = YES - -# If member grouping is used in the documentation and the DISTRIBUTE_GROUP_DOC -# tag is set to YES then doxygen will reuse the documentation of the first -# member in the group (if any) for the other members of the group. By default -# all members of a group must be documented explicitly. -# The default value is: NO. - -DISTRIBUTE_GROUP_DOC = NO - -# Set the SUBGROUPING tag to YES to allow class member groups of the same type -# (for instance a group of public functions) to be put as a subgroup of that -# type (e.g. under the Public Functions section). Set it to NO to prevent -# subgrouping. Alternatively, this can be done per class using the -# \nosubgrouping command. -# The default value is: YES. - -SUBGROUPING = YES - -# When the INLINE_GROUPED_CLASSES tag is set to YES, classes, structs and unions -# are shown inside the group in which they are included (e.g. using \ingroup) -# instead of on a separate page (for HTML and Man pages) or section (for LaTeX -# and RTF). -# -# Note that this feature does not work in combination with -# SEPARATE_MEMBER_PAGES. -# The default value is: NO. - -INLINE_GROUPED_CLASSES = NO - -# When the INLINE_SIMPLE_STRUCTS tag is set to YES, structs, classes, and unions -# with only public data fields or simple typedef fields will be shown inline in -# the documentation of the scope in which they are defined (i.e. file, -# namespace, or group documentation), provided this scope is documented. If set -# to NO, structs, classes, and unions are shown on a separate page (for HTML and -# Man pages) or section (for LaTeX and RTF). -# The default value is: NO. - -INLINE_SIMPLE_STRUCTS = NO - -# When TYPEDEF_HIDES_STRUCT tag is enabled, a typedef of a struct, union, or -# enum is documented as struct, union, or enum with the name of the typedef. So -# typedef struct TypeS {} TypeT, will appear in the documentation as a struct -# with name TypeT. When disabled the typedef will appear as a member of a file, -# namespace, or class. And the struct will be named TypeS. This can typically be -# useful for C code in case the coding convention dictates that all compound -# types are typedef'ed and only the typedef is referenced, never the tag name. -# The default value is: NO. - -TYPEDEF_HIDES_STRUCT = NO - -# The size of the symbol lookup cache can be set using LOOKUP_CACHE_SIZE. This -# cache is used to resolve symbols given their name and scope. Since this can be -# an expensive process and often the same symbol appears multiple times in the -# code, doxygen keeps a cache of pre-resolved symbols. If the cache is too small -# doxygen will become slower. If the cache is too large, memory is wasted. The -# cache size is given by this formula: 2^(16+LOOKUP_CACHE_SIZE). The valid range -# is 0..9, the default is 0, corresponding to a cache size of 2^16=65536 -# symbols. At the end of a run doxygen will report the cache usage and suggest -# the optimal cache size from a speed point of view. -# Minimum value: 0, maximum value: 9, default value: 0. - -LOOKUP_CACHE_SIZE = 0 - -#--------------------------------------------------------------------------- -# Build related configuration options -#--------------------------------------------------------------------------- - -# If the EXTRACT_ALL tag is set to YES, doxygen will assume all entities in -# documentation are documented, even if no documentation was available. Private -# class members and static file members will be hidden unless the -# EXTRACT_PRIVATE respectively EXTRACT_STATIC tags are set to YES. -# Note: This will also disable the warnings about undocumented members that are -# normally produced when WARNINGS is set to YES. -# The default value is: NO. - -EXTRACT_ALL = YES - -# If the EXTRACT_PRIVATE tag is set to YES, all private members of a class will -# be included in the documentation. -# The default value is: NO. - -EXTRACT_PRIVATE = NO - -# If the EXTRACT_PACKAGE tag is set to YES, all members with package or internal -# scope will be included in the documentation. -# The default value is: NO. - -EXTRACT_PACKAGE = NO - -# If the EXTRACT_STATIC tag is set to YES, all static members of a file will be -# included in the documentation. -# The default value is: NO. - -EXTRACT_STATIC = NO - -# If the EXTRACT_LOCAL_CLASSES tag is set to YES, classes (and structs) defined -# locally in source files will be included in the documentation. If set to NO, -# only classes defined in header files are included. Does not have any effect -# for Java sources. -# The default value is: YES. - -EXTRACT_LOCAL_CLASSES = YES - -# This flag is only useful for Objective-C code. If set to YES, local methods, -# which are defined in the implementation section but not in the interface are -# included in the documentation. If set to NO, only methods in the interface are -# included. -# The default value is: NO. - -EXTRACT_LOCAL_METHODS = NO - -# If this flag is set to YES, the members of anonymous namespaces will be -# extracted and appear in the documentation as a namespace called -# 'anonymous_namespace{file}', where file will be replaced with the base name of -# the file that contains the anonymous namespace. By default anonymous namespace -# are hidden. -# The default value is: NO. - -EXTRACT_ANON_NSPACES = NO - -# If the HIDE_UNDOC_MEMBERS tag is set to YES, doxygen will hide all -# undocumented members inside documented classes or files. If set to NO these -# members will be included in the various overviews, but no documentation -# section is generated. This option has no effect if EXTRACT_ALL is enabled. -# The default value is: NO. - -HIDE_UNDOC_MEMBERS = NO - -# If the HIDE_UNDOC_CLASSES tag is set to YES, doxygen will hide all -# undocumented classes that are normally visible in the class hierarchy. If set -# to NO, these classes will be included in the various overviews. This option -# has no effect if EXTRACT_ALL is enabled. -# The default value is: NO. - -HIDE_UNDOC_CLASSES = NO - -# If the HIDE_FRIEND_COMPOUNDS tag is set to YES, doxygen will hide all friend -# (class|struct|union) declarations. If set to NO, these declarations will be -# included in the documentation. -# The default value is: NO. - -HIDE_FRIEND_COMPOUNDS = NO - -# If the HIDE_IN_BODY_DOCS tag is set to YES, doxygen will hide any -# documentation blocks found inside the body of a function. If set to NO, these -# blocks will be appended to the function's detailed documentation block. -# The default value is: NO. - -HIDE_IN_BODY_DOCS = NO - -# The INTERNAL_DOCS tag determines if documentation that is typed after a -# \internal command is included. If the tag is set to NO then the documentation -# will be excluded. Set it to YES to include the internal documentation. -# The default value is: NO. - -INTERNAL_DOCS = NO - -# If the CASE_SENSE_NAMES tag is set to NO then doxygen will only generate file -# names in lower-case letters. If set to YES, upper-case letters are also -# allowed. This is useful if you have classes or files whose names only differ -# in case and if your file system supports case sensitive file names. Windows -# and Mac users are advised to set this option to NO. -# The default value is: system dependent. - -CASE_SENSE_NAMES = NO - -# If the HIDE_SCOPE_NAMES tag is set to NO then doxygen will show members with -# their full class and namespace scopes in the documentation. If set to YES, the -# scope will be hidden. -# The default value is: NO. - -HIDE_SCOPE_NAMES = NO - -# If the HIDE_COMPOUND_REFERENCE tag is set to NO (default) then doxygen will -# append additional text to a page's title, such as Class Reference. If set to -# YES the compound reference will be hidden. -# The default value is: NO. - -HIDE_COMPOUND_REFERENCE= NO - -# If the SHOW_INCLUDE_FILES tag is set to YES then doxygen will put a list of -# the files that are included by a file in the documentation of that file. -# The default value is: YES. - -SHOW_INCLUDE_FILES = YES - -# If the SHOW_GROUPED_MEMB_INC tag is set to YES then Doxygen will add for each -# grouped member an include statement to the documentation, telling the reader -# which file to include in order to use the member. -# The default value is: NO. - -SHOW_GROUPED_MEMB_INC = NO - -# If the FORCE_LOCAL_INCLUDES tag is set to YES then doxygen will list include -# files with double quotes in the documentation rather than with sharp brackets. -# The default value is: NO. - -FORCE_LOCAL_INCLUDES = NO - -# If the INLINE_INFO tag is set to YES then a tag [inline] is inserted in the -# documentation for inline members. -# The default value is: YES. - -INLINE_INFO = YES - -# If the SORT_MEMBER_DOCS tag is set to YES then doxygen will sort the -# (detailed) documentation of file and class members alphabetically by member -# name. If set to NO, the members will appear in declaration order. -# The default value is: YES. - -SORT_MEMBER_DOCS = YES - -# If the SORT_BRIEF_DOCS tag is set to YES then doxygen will sort the brief -# descriptions of file, namespace and class members alphabetically by member -# name. If set to NO, the members will appear in declaration order. Note that -# this will also influence the order of the classes in the class list. -# The default value is: NO. - -SORT_BRIEF_DOCS = NO - -# If the SORT_MEMBERS_CTORS_1ST tag is set to YES then doxygen will sort the -# (brief and detailed) documentation of class members so that constructors and -# destructors are listed first. If set to NO the constructors will appear in the -# respective orders defined by SORT_BRIEF_DOCS and SORT_MEMBER_DOCS. -# Note: If SORT_BRIEF_DOCS is set to NO this option is ignored for sorting brief -# member documentation. -# Note: If SORT_MEMBER_DOCS is set to NO this option is ignored for sorting -# detailed member documentation. -# The default value is: NO. - -SORT_MEMBERS_CTORS_1ST = NO - -# If the SORT_GROUP_NAMES tag is set to YES then doxygen will sort the hierarchy -# of group names into alphabetical order. If set to NO the group names will -# appear in their defined order. -# The default value is: NO. - -SORT_GROUP_NAMES = NO - -# If the SORT_BY_SCOPE_NAME tag is set to YES, the class list will be sorted by -# fully-qualified names, including namespaces. If set to NO, the class list will -# be sorted only by class name, not including the namespace part. -# Note: This option is not very useful if HIDE_SCOPE_NAMES is set to YES. -# Note: This option applies only to the class list, not to the alphabetical -# list. -# The default value is: NO. - -SORT_BY_SCOPE_NAME = NO - -# If the STRICT_PROTO_MATCHING option is enabled and doxygen fails to do proper -# type resolution of all parameters of a function it will reject a match between -# the prototype and the implementation of a member function even if there is -# only one candidate or it is obvious which candidate to choose by doing a -# simple string match. By disabling STRICT_PROTO_MATCHING doxygen will still -# accept a match between prototype and implementation in such cases. -# The default value is: NO. - -STRICT_PROTO_MATCHING = NO - -# The GENERATE_TODOLIST tag can be used to enable (YES) or disable (NO) the todo -# list. This list is created by putting \todo commands in the documentation. -# The default value is: YES. - -GENERATE_TODOLIST = YES - -# The GENERATE_TESTLIST tag can be used to enable (YES) or disable (NO) the test -# list. This list is created by putting \test commands in the documentation. -# The default value is: YES. - -GENERATE_TESTLIST = YES - -# The GENERATE_BUGLIST tag can be used to enable (YES) or disable (NO) the bug -# list. This list is created by putting \bug commands in the documentation. -# The default value is: YES. - -GENERATE_BUGLIST = YES - -# The GENERATE_DEPRECATEDLIST tag can be used to enable (YES) or disable (NO) -# the deprecated list. This list is created by putting \deprecated commands in -# the documentation. -# The default value is: YES. - -GENERATE_DEPRECATEDLIST= YES - -# The ENABLED_SECTIONS tag can be used to enable conditional documentation -# sections, marked by \if ... \endif and \cond -# ... \endcond blocks. - -ENABLED_SECTIONS = - -# The MAX_INITIALIZER_LINES tag determines the maximum number of lines that the -# initial value of a variable or macro / define can have for it to appear in the -# documentation. If the initializer consists of more lines than specified here -# it will be hidden. Use a value of 0 to hide initializers completely. The -# appearance of the value of individual variables and macros / defines can be -# controlled using \showinitializer or \hideinitializer command in the -# documentation regardless of this setting. -# Minimum value: 0, maximum value: 10000, default value: 30. - -MAX_INITIALIZER_LINES = 30 - -# Set the SHOW_USED_FILES tag to NO to disable the list of files generated at -# the bottom of the documentation of classes and structs. If set to YES, the -# list will mention the files that were used to generate the documentation. -# The default value is: YES. - -SHOW_USED_FILES = YES - -# Set the SHOW_FILES tag to NO to disable the generation of the Files page. This -# will remove the Files entry from the Quick Index and from the Folder Tree View -# (if specified). -# The default value is: YES. - -SHOW_FILES = YES - -# Set the SHOW_NAMESPACES tag to NO to disable the generation of the Namespaces -# page. This will remove the Namespaces entry from the Quick Index and from the -# Folder Tree View (if specified). -# The default value is: YES. - -SHOW_NAMESPACES = YES - -# The FILE_VERSION_FILTER tag can be used to specify a program or script that -# doxygen should invoke to get the current version for each file (typically from -# the version control system). Doxygen will invoke the program by executing (via -# popen()) the command command input-file, where command is the value of the -# FILE_VERSION_FILTER tag, and input-file is the name of an input file provided -# by doxygen. Whatever the program writes to standard output is used as the file -# version. For an example see the documentation. - -FILE_VERSION_FILTER = - -# The LAYOUT_FILE tag can be used to specify a layout file which will be parsed -# by doxygen. The layout file controls the global structure of the generated -# output files in an output format independent way. To create the layout file -# that represents doxygen's defaults, run doxygen with the -l option. You can -# optionally specify a file name after the option, if omitted DoxygenLayout.xml -# will be used as the name of the layout file. -# -# Note that if you run doxygen from a directory containing a file called -# DoxygenLayout.xml, doxygen will parse it automatically even if the LAYOUT_FILE -# tag is left empty. - -LAYOUT_FILE = - -# The CITE_BIB_FILES tag can be used to specify one or more bib files containing -# the reference definitions. This must be a list of .bib files. The .bib -# extension is automatically appended if omitted. This requires the bibtex tool -# to be installed. See also http://en.wikipedia.org/wiki/BibTeX for more info. -# For LaTeX the style of the bibliography can be controlled using -# LATEX_BIB_STYLE. To use this feature you need bibtex and perl available in the -# search path. See also \cite for info how to create references. - -CITE_BIB_FILES = - -#--------------------------------------------------------------------------- -# Configuration options related to warning and progress messages -#--------------------------------------------------------------------------- - -# The QUIET tag can be used to turn on/off the messages that are generated to -# standard output by doxygen. If QUIET is set to YES this implies that the -# messages are off. -# The default value is: NO. - -QUIET = NO - -# The WARNINGS tag can be used to turn on/off the warning messages that are -# generated to standard error (stderr) by doxygen. If WARNINGS is set to YES -# this implies that the warnings are on. -# -# Tip: Turn warnings on while writing the documentation. -# The default value is: YES. - -WARNINGS = YES - -# If the WARN_IF_UNDOCUMENTED tag is set to YES then doxygen will generate -# warnings for undocumented members. If EXTRACT_ALL is set to YES then this flag -# will automatically be disabled. -# The default value is: YES. - -WARN_IF_UNDOCUMENTED = YES - -# If the WARN_IF_DOC_ERROR tag is set to YES, doxygen will generate warnings for -# potential errors in the documentation, such as not documenting some parameters -# in a documented function, or documenting parameters that don't exist or using -# markup commands wrongly. -# The default value is: YES. - -WARN_IF_DOC_ERROR = YES - -# This WARN_NO_PARAMDOC option can be enabled to get warnings for functions that -# are documented, but have no documentation for their parameters or return -# value. If set to NO, doxygen will only warn about wrong or incomplete -# parameter documentation, but not about the absence of documentation. -# The default value is: NO. - -WARN_NO_PARAMDOC = NO - -# The WARN_FORMAT tag determines the format of the warning messages that doxygen -# can produce. The string should contain the $file, $line, and $text tags, which -# will be replaced by the file and line number from which the warning originated -# and the warning text. Optionally the format may contain $version, which will -# be replaced by the version of the file (if it could be obtained via -# FILE_VERSION_FILTER) -# The default value is: $file:$line: $text. - -WARN_FORMAT = "$file:$line: $text" - -# The WARN_LOGFILE tag can be used to specify a file to which warning and error -# messages should be written. If left blank the output is written to standard -# error (stderr). - -WARN_LOGFILE = - -#--------------------------------------------------------------------------- -# Configuration options related to the input files -#--------------------------------------------------------------------------- - -# The INPUT tag is used to specify the files and/or directories that contain -# documented source files. You may enter file names like myfile.cpp or -# directories like /usr/src/myproject. Separate the files or directories with -# spaces. -# Note: If this tag is empty the current directory is searched. - -INPUT = - -# This tag can be used to specify the character encoding of the source files -# that doxygen parses. Internally doxygen uses the UTF-8 encoding. Doxygen uses -# libiconv (or the iconv built into libc) for the transcoding. See the libiconv -# documentation (see: http://www.gnu.org/software/libiconv) for the list of -# possible encodings. -# The default value is: UTF-8. - -INPUT_ENCODING = UTF-8 - -# If the value of the INPUT tag contains directories, you can use the -# FILE_PATTERNS tag to specify one or more wildcard patterns (like *.cpp and -# *.h) to filter out the source-files in the directories. If left blank the -# following patterns are tested:*.c, *.cc, *.cxx, *.cpp, *.c++, *.java, *.ii, -# *.ixx, *.ipp, *.i++, *.inl, *.idl, *.ddl, *.odl, *.h, *.hh, *.hxx, *.hpp, -# *.h++, *.cs, *.d, *.php, *.php4, *.php5, *.phtml, *.inc, *.m, *.markdown, -# *.md, *.mm, *.dox, *.py, *.f90, *.f, *.for, *.tcl, *.vhd, *.vhdl, *.ucf, -# *.qsf, *.as and *.js. - -FILE_PATTERNS = - -# The RECURSIVE tag can be used to specify whether or not subdirectories should -# be searched for input files as well. -# The default value is: NO. - -RECURSIVE = YES - -# The EXCLUDE tag can be used to specify files and/or directories that should be -# excluded from the INPUT source files. This way you can easily exclude a -# subdirectory from a directory tree whose root is specified with the INPUT tag. -# -# Note that relative paths are relative to the directory from which doxygen is -# run. - -EXCLUDE = - -# The EXCLUDE_SYMLINKS tag can be used to select whether or not files or -# directories that are symbolic links (a Unix file system feature) are excluded -# from the input. -# The default value is: NO. - -EXCLUDE_SYMLINKS = NO - -# If the value of the INPUT tag contains directories, you can use the -# EXCLUDE_PATTERNS tag to specify one or more wildcard patterns to exclude -# certain files from those directories. -# -# Note that the wildcards are matched against the file with absolute path, so to -# exclude all test directories for example use the pattern */test/* - -EXCLUDE_PATTERNS = - -# The EXCLUDE_SYMBOLS tag can be used to specify one or more symbol names -# (namespaces, classes, functions, etc.) that should be excluded from the -# output. The symbol name can be a fully qualified name, a word, or if the -# wildcard * is used, a substring. Examples: ANamespace, AClass, -# AClass::ANamespace, ANamespace::*Test -# -# Note that the wildcards are matched against the file with absolute path, so to -# exclude all test directories use the pattern */test/* - -EXCLUDE_SYMBOLS = - -# The EXAMPLE_PATH tag can be used to specify one or more files or directories -# that contain example code fragments that are included (see the \include -# command). - -EXAMPLE_PATH = - -# If the value of the EXAMPLE_PATH tag contains directories, you can use the -# EXAMPLE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp and -# *.h) to filter out the source-files in the directories. If left blank all -# files are included. - -EXAMPLE_PATTERNS = - -# If the EXAMPLE_RECURSIVE tag is set to YES then subdirectories will be -# searched for input files to be used with the \include or \dontinclude commands -# irrespective of the value of the RECURSIVE tag. -# The default value is: NO. - -EXAMPLE_RECURSIVE = NO - -# The IMAGE_PATH tag can be used to specify one or more files or directories -# that contain images that are to be included in the documentation (see the -# \image command). - -IMAGE_PATH = - -# The INPUT_FILTER tag can be used to specify a program that doxygen should -# invoke to filter for each input file. Doxygen will invoke the filter program -# by executing (via popen()) the command: -# -# -# -# where is the value of the INPUT_FILTER tag, and is the -# name of an input file. Doxygen will then use the output that the filter -# program writes to standard output. If FILTER_PATTERNS is specified, this tag -# will be ignored. -# -# Note that the filter must not add or remove lines; it is applied before the -# code is scanned, but not when the output code is generated. If lines are added -# or removed, the anchors will not be placed correctly. - -INPUT_FILTER = - -# The FILTER_PATTERNS tag can be used to specify filters on a per file pattern -# basis. Doxygen will compare the file name with each pattern and apply the -# filter if there is a match. The filters are a list of the form: pattern=filter -# (like *.cpp=my_cpp_filter). See INPUT_FILTER for further information on how -# filters are used. If the FILTER_PATTERNS tag is empty or if none of the -# patterns match the file name, INPUT_FILTER is applied. - -FILTER_PATTERNS = - -# If the FILTER_SOURCE_FILES tag is set to YES, the input filter (if set using -# INPUT_FILTER) will also be used to filter the input files that are used for -# producing the source files to browse (i.e. when SOURCE_BROWSER is set to YES). -# The default value is: NO. - -FILTER_SOURCE_FILES = NO - -# The FILTER_SOURCE_PATTERNS tag can be used to specify source filters per file -# pattern. A pattern will override the setting for FILTER_PATTERN (if any) and -# it is also possible to disable source filtering for a specific pattern using -# *.ext= (so without naming a filter). -# This tag requires that the tag FILTER_SOURCE_FILES is set to YES. - -FILTER_SOURCE_PATTERNS = - -# If the USE_MDFILE_AS_MAINPAGE tag refers to the name of a markdown file that -# is part of the input, its contents will be placed on the main page -# (index.html). This can be useful if you have a project on for instance GitHub -# and want to reuse the introduction page also for the doxygen output. - -USE_MDFILE_AS_MAINPAGE = - -#--------------------------------------------------------------------------- -# Configuration options related to source browsing -#--------------------------------------------------------------------------- - -# If the SOURCE_BROWSER tag is set to YES then a list of source files will be -# generated. Documented entities will be cross-referenced with these sources. -# -# Note: To get rid of all source code in the generated output, make sure that -# also VERBATIM_HEADERS is set to NO. -# The default value is: NO. - -SOURCE_BROWSER = YES - -# Setting the INLINE_SOURCES tag to YES will include the body of functions, -# classes and enums directly into the documentation. -# The default value is: NO. - -INLINE_SOURCES = YES - -# Setting the STRIP_CODE_COMMENTS tag to YES will instruct doxygen to hide any -# special comment blocks from generated source code fragments. Normal C, C++ and -# Fortran comments will always remain visible. -# The default value is: YES. - -STRIP_CODE_COMMENTS = YES - -# If the REFERENCED_BY_RELATION tag is set to YES then for each documented -# function all documented functions referencing it will be listed. -# The default value is: NO. - -REFERENCED_BY_RELATION = NO - -# If the REFERENCES_RELATION tag is set to YES then for each documented function -# all documented entities called/used by that function will be listed. -# The default value is: NO. - -REFERENCES_RELATION = NO - -# If the REFERENCES_LINK_SOURCE tag is set to YES and SOURCE_BROWSER tag is set -# to YES then the hyperlinks from functions in REFERENCES_RELATION and -# REFERENCED_BY_RELATION lists will link to the source code. Otherwise they will -# link to the documentation. -# The default value is: YES. - -REFERENCES_LINK_SOURCE = YES - -# If SOURCE_TOOLTIPS is enabled (the default) then hovering a hyperlink in the -# source code will show a tooltip with additional information such as prototype, -# brief description and links to the definition and documentation. Since this -# will make the HTML file larger and loading of large files a bit slower, you -# can opt to disable this feature. -# The default value is: YES. -# This tag requires that the tag SOURCE_BROWSER is set to YES. - -SOURCE_TOOLTIPS = YES - -# If the USE_HTAGS tag is set to YES then the references to source code will -# point to the HTML generated by the htags(1) tool instead of doxygen built-in -# source browser. The htags tool is part of GNU's global source tagging system -# (see http://www.gnu.org/software/global/global.html). You will need version -# 4.8.6 or higher. -# -# To use it do the following: -# - Install the latest version of global -# - Enable SOURCE_BROWSER and USE_HTAGS in the config file -# - Make sure the INPUT points to the root of the source tree -# - Run doxygen as normal -# -# Doxygen will invoke htags (and that will in turn invoke gtags), so these -# tools must be available from the command line (i.e. in the search path). -# -# The result: instead of the source browser generated by doxygen, the links to -# source code will now point to the output of htags. -# The default value is: NO. -# This tag requires that the tag SOURCE_BROWSER is set to YES. - -USE_HTAGS = NO - -# If the VERBATIM_HEADERS tag is set the YES then doxygen will generate a -# verbatim copy of the header file for each class for which an include is -# specified. Set to NO to disable this. -# See also: Section \class. -# The default value is: YES. - -VERBATIM_HEADERS = YES - -#--------------------------------------------------------------------------- -# Configuration options related to the alphabetical class index -#--------------------------------------------------------------------------- - -# If the ALPHABETICAL_INDEX tag is set to YES, an alphabetical index of all -# compounds will be generated. Enable this if the project contains a lot of -# classes, structs, unions or interfaces. -# The default value is: YES. - -ALPHABETICAL_INDEX = YES - -# The COLS_IN_ALPHA_INDEX tag can be used to specify the number of columns in -# which the alphabetical index list will be split. -# Minimum value: 1, maximum value: 20, default value: 5. -# This tag requires that the tag ALPHABETICAL_INDEX is set to YES. - -COLS_IN_ALPHA_INDEX = 5 - -# In case all classes in a project start with a common prefix, all classes will -# be put under the same header in the alphabetical index. The IGNORE_PREFIX tag -# can be used to specify a prefix (or a list of prefixes) that should be ignored -# while generating the index headers. -# This tag requires that the tag ALPHABETICAL_INDEX is set to YES. - -IGNORE_PREFIX = - -#--------------------------------------------------------------------------- -# Configuration options related to the HTML output -#--------------------------------------------------------------------------- - -# If the GENERATE_HTML tag is set to YES, doxygen will generate HTML output -# The default value is: YES. - -GENERATE_HTML = YES - -# The HTML_OUTPUT tag is used to specify where the HTML docs will be put. If a -# relative path is entered the value of OUTPUT_DIRECTORY will be put in front of -# it. -# The default directory is: html. -# This tag requires that the tag GENERATE_HTML is set to YES. - -HTML_OUTPUT = html - -# The HTML_FILE_EXTENSION tag can be used to specify the file extension for each -# generated HTML page (for example: .htm, .php, .asp). -# The default value is: .html. -# This tag requires that the tag GENERATE_HTML is set to YES. - -HTML_FILE_EXTENSION = .html - -# The HTML_HEADER tag can be used to specify a user-defined HTML header file for -# each generated HTML page. If the tag is left blank doxygen will generate a -# standard header. -# -# To get valid HTML the header file that includes any scripts and style sheets -# that doxygen needs, which is dependent on the configuration options used (e.g. -# the setting GENERATE_TREEVIEW). It is highly recommended to start with a -# default header using -# doxygen -w html new_header.html new_footer.html new_stylesheet.css -# YourConfigFile -# and then modify the file new_header.html. See also section "Doxygen usage" -# for information on how to generate the default header that doxygen normally -# uses. -# Note: The header is subject to change so you typically have to regenerate the -# default header when upgrading to a newer version of doxygen. For a description -# of the possible markers and block names see the documentation. -# This tag requires that the tag GENERATE_HTML is set to YES. - -HTML_HEADER = - -# The HTML_FOOTER tag can be used to specify a user-defined HTML footer for each -# generated HTML page. If the tag is left blank doxygen will generate a standard -# footer. See HTML_HEADER for more information on how to generate a default -# footer and what special commands can be used inside the footer. See also -# section "Doxygen usage" for information on how to generate the default footer -# that doxygen normally uses. -# This tag requires that the tag GENERATE_HTML is set to YES. - -HTML_FOOTER = - -# The HTML_STYLESHEET tag can be used to specify a user-defined cascading style -# sheet that is used by each HTML page. It can be used to fine-tune the look of -# the HTML output. If left blank doxygen will generate a default style sheet. -# See also section "Doxygen usage" for information on how to generate the style -# sheet that doxygen normally uses. -# Note: It is recommended to use HTML_EXTRA_STYLESHEET instead of this tag, as -# it is more robust and this tag (HTML_STYLESHEET) will in the future become -# obsolete. -# This tag requires that the tag GENERATE_HTML is set to YES. - -HTML_STYLESHEET = - -# The HTML_EXTRA_STYLESHEET tag can be used to specify additional user-defined -# cascading style sheets that are included after the standard style sheets -# created by doxygen. Using this option one can overrule certain style aspects. -# This is preferred over using HTML_STYLESHEET since it does not replace the -# standard style sheet and is therefore more robust against future updates. -# Doxygen will copy the style sheet files to the output directory. -# Note: The order of the extra style sheet files is of importance (e.g. the last -# style sheet in the list overrules the setting of the previous ones in the -# list). For an example see the documentation. -# This tag requires that the tag GENERATE_HTML is set to YES. - -HTML_EXTRA_STYLESHEET = - -# The HTML_EXTRA_FILES tag can be used to specify one or more extra images or -# other source files which should be copied to the HTML output directory. Note -# that these files will be copied to the base HTML output directory. Use the -# $relpath^ marker in the HTML_HEADER and/or HTML_FOOTER files to load these -# files. In the HTML_STYLESHEET file, use the file name only. Also note that the -# files will be copied as-is; there are no commands or markers available. -# This tag requires that the tag GENERATE_HTML is set to YES. - -HTML_EXTRA_FILES = - -# The HTML_COLORSTYLE_HUE tag controls the color of the HTML output. Doxygen -# will adjust the colors in the style sheet and background images according to -# this color. Hue is specified as an angle on a colorwheel, see -# http://en.wikipedia.org/wiki/Hue for more information. For instance the value -# 0 represents red, 60 is yellow, 120 is green, 180 is cyan, 240 is blue, 300 -# purple, and 360 is red again. -# Minimum value: 0, maximum value: 359, default value: 220. -# This tag requires that the tag GENERATE_HTML is set to YES. - -HTML_COLORSTYLE_HUE = 220 - -# The HTML_COLORSTYLE_SAT tag controls the purity (or saturation) of the colors -# in the HTML output. For a value of 0 the output will use grayscales only. A -# value of 255 will produce the most vivid colors. -# Minimum value: 0, maximum value: 255, default value: 100. -# This tag requires that the tag GENERATE_HTML is set to YES. - -HTML_COLORSTYLE_SAT = 100 - -# The HTML_COLORSTYLE_GAMMA tag controls the gamma correction applied to the -# luminance component of the colors in the HTML output. Values below 100 -# gradually make the output lighter, whereas values above 100 make the output -# darker. The value divided by 100 is the actual gamma applied, so 80 represents -# a gamma of 0.8, The value 220 represents a gamma of 2.2, and 100 does not -# change the gamma. -# Minimum value: 40, maximum value: 240, default value: 80. -# This tag requires that the tag GENERATE_HTML is set to YES. - -HTML_COLORSTYLE_GAMMA = 80 - -# If the HTML_TIMESTAMP tag is set to YES then the footer of each generated HTML -# page will contain the date and time when the page was generated. Setting this -# to NO can help when comparing the output of multiple runs. -# The default value is: YES. -# This tag requires that the tag GENERATE_HTML is set to YES. - -HTML_TIMESTAMP = YES - -# If the HTML_DYNAMIC_SECTIONS tag is set to YES then the generated HTML -# documentation will contain sections that can be hidden and shown after the -# page has loaded. -# The default value is: NO. -# This tag requires that the tag GENERATE_HTML is set to YES. - -HTML_DYNAMIC_SECTIONS = NO - -# With HTML_INDEX_NUM_ENTRIES one can control the preferred number of entries -# shown in the various tree structured indices initially; the user can expand -# and collapse entries dynamically later on. Doxygen will expand the tree to -# such a level that at most the specified number of entries are visible (unless -# a fully collapsed tree already exceeds this amount). So setting the number of -# entries 1 will produce a full collapsed tree by default. 0 is a special value -# representing an infinite number of entries and will result in a full expanded -# tree by default. -# Minimum value: 0, maximum value: 9999, default value: 100. -# This tag requires that the tag GENERATE_HTML is set to YES. - -HTML_INDEX_NUM_ENTRIES = 100 - -# If the GENERATE_DOCSET tag is set to YES, additional index files will be -# generated that can be used as input for Apple's Xcode 3 integrated development -# environment (see: http://developer.apple.com/tools/xcode/), introduced with -# OSX 10.5 (Leopard). To create a documentation set, doxygen will generate a -# Makefile in the HTML output directory. Running make will produce the docset in -# that directory and running make install will install the docset in -# ~/Library/Developer/Shared/Documentation/DocSets so that Xcode will find it at -# startup. See http://developer.apple.com/tools/creatingdocsetswithdoxygen.html -# for more information. -# The default value is: NO. -# This tag requires that the tag GENERATE_HTML is set to YES. - -GENERATE_DOCSET = NO - -# This tag determines the name of the docset feed. A documentation feed provides -# an umbrella under which multiple documentation sets from a single provider -# (such as a company or product suite) can be grouped. -# The default value is: Doxygen generated docs. -# This tag requires that the tag GENERATE_DOCSET is set to YES. - -DOCSET_FEEDNAME = "Doxygen generated docs" - -# This tag specifies a string that should uniquely identify the documentation -# set bundle. This should be a reverse domain-name style string, e.g. -# com.mycompany.MyDocSet. Doxygen will append .docset to the name. -# The default value is: org.doxygen.Project. -# This tag requires that the tag GENERATE_DOCSET is set to YES. - -DOCSET_BUNDLE_ID = org.doxygen.Project - -# The DOCSET_PUBLISHER_ID tag specifies a string that should uniquely identify -# the documentation publisher. This should be a reverse domain-name style -# string, e.g. com.mycompany.MyDocSet.documentation. -# The default value is: org.doxygen.Publisher. -# This tag requires that the tag GENERATE_DOCSET is set to YES. - -DOCSET_PUBLISHER_ID = org.doxygen.Publisher - -# The DOCSET_PUBLISHER_NAME tag identifies the documentation publisher. -# The default value is: Publisher. -# This tag requires that the tag GENERATE_DOCSET is set to YES. - -DOCSET_PUBLISHER_NAME = Publisher - -# If the GENERATE_HTMLHELP tag is set to YES then doxygen generates three -# additional HTML index files: index.hhp, index.hhc, and index.hhk. The -# index.hhp is a project file that can be read by Microsoft's HTML Help Workshop -# (see: http://www.microsoft.com/en-us/download/details.aspx?id=21138) on -# Windows. -# -# The HTML Help Workshop contains a compiler that can convert all HTML output -# generated by doxygen into a single compiled HTML file (.chm). Compiled HTML -# files are now used as the Windows 98 help format, and will replace the old -# Windows help format (.hlp) on all Windows platforms in the future. Compressed -# HTML files also contain an index, a table of contents, and you can search for -# words in the documentation. The HTML workshop also contains a viewer for -# compressed HTML files. -# The default value is: NO. -# This tag requires that the tag GENERATE_HTML is set to YES. - -GENERATE_HTMLHELP = NO - -# The CHM_FILE tag can be used to specify the file name of the resulting .chm -# file. You can add a path in front of the file if the result should not be -# written to the html output directory. -# This tag requires that the tag GENERATE_HTMLHELP is set to YES. - -CHM_FILE = - -# The HHC_LOCATION tag can be used to specify the location (absolute path -# including file name) of the HTML help compiler (hhc.exe). If non-empty, -# doxygen will try to run the HTML help compiler on the generated index.hhp. -# The file has to be specified with full path. -# This tag requires that the tag GENERATE_HTMLHELP is set to YES. - -HHC_LOCATION = - -# The GENERATE_CHI flag controls if a separate .chi index file is generated -# (YES) or that it should be included in the master .chm file (NO). -# The default value is: NO. -# This tag requires that the tag GENERATE_HTMLHELP is set to YES. - -GENERATE_CHI = NO - -# The CHM_INDEX_ENCODING is used to encode HtmlHelp index (hhk), content (hhc) -# and project file content. -# This tag requires that the tag GENERATE_HTMLHELP is set to YES. - -CHM_INDEX_ENCODING = - -# The BINARY_TOC flag controls whether a binary table of contents is generated -# (YES) or a normal table of contents (NO) in the .chm file. Furthermore it -# enables the Previous and Next buttons. -# The default value is: NO. -# This tag requires that the tag GENERATE_HTMLHELP is set to YES. - -BINARY_TOC = NO - -# The TOC_EXPAND flag can be set to YES to add extra items for group members to -# the table of contents of the HTML help documentation and to the tree view. -# The default value is: NO. -# This tag requires that the tag GENERATE_HTMLHELP is set to YES. - -TOC_EXPAND = NO - -# If the GENERATE_QHP tag is set to YES and both QHP_NAMESPACE and -# QHP_VIRTUAL_FOLDER are set, an additional index file will be generated that -# can be used as input for Qt's qhelpgenerator to generate a Qt Compressed Help -# (.qch) of the generated HTML documentation. -# The default value is: NO. -# This tag requires that the tag GENERATE_HTML is set to YES. - -GENERATE_QHP = NO - -# If the QHG_LOCATION tag is specified, the QCH_FILE tag can be used to specify -# the file name of the resulting .qch file. The path specified is relative to -# the HTML output folder. -# This tag requires that the tag GENERATE_QHP is set to YES. - -QCH_FILE = - -# The QHP_NAMESPACE tag specifies the namespace to use when generating Qt Help -# Project output. For more information please see Qt Help Project / Namespace -# (see: http://qt-project.org/doc/qt-4.8/qthelpproject.html#namespace). -# The default value is: org.doxygen.Project. -# This tag requires that the tag GENERATE_QHP is set to YES. - -QHP_NAMESPACE = org.doxygen.Project - -# The QHP_VIRTUAL_FOLDER tag specifies the namespace to use when generating Qt -# Help Project output. For more information please see Qt Help Project / Virtual -# Folders (see: http://qt-project.org/doc/qt-4.8/qthelpproject.html#virtual- -# folders). -# The default value is: doc. -# This tag requires that the tag GENERATE_QHP is set to YES. - -QHP_VIRTUAL_FOLDER = doc - -# If the QHP_CUST_FILTER_NAME tag is set, it specifies the name of a custom -# filter to add. For more information please see Qt Help Project / Custom -# Filters (see: http://qt-project.org/doc/qt-4.8/qthelpproject.html#custom- -# filters). -# This tag requires that the tag GENERATE_QHP is set to YES. - -QHP_CUST_FILTER_NAME = - -# The QHP_CUST_FILTER_ATTRS tag specifies the list of the attributes of the -# custom filter to add. For more information please see Qt Help Project / Custom -# Filters (see: http://qt-project.org/doc/qt-4.8/qthelpproject.html#custom- -# filters). -# This tag requires that the tag GENERATE_QHP is set to YES. - -QHP_CUST_FILTER_ATTRS = - -# The QHP_SECT_FILTER_ATTRS tag specifies the list of the attributes this -# project's filter section matches. Qt Help Project / Filter Attributes (see: -# http://qt-project.org/doc/qt-4.8/qthelpproject.html#filter-attributes). -# This tag requires that the tag GENERATE_QHP is set to YES. - -QHP_SECT_FILTER_ATTRS = - -# The QHG_LOCATION tag can be used to specify the location of Qt's -# qhelpgenerator. If non-empty doxygen will try to run qhelpgenerator on the -# generated .qhp file. -# This tag requires that the tag GENERATE_QHP is set to YES. - -QHG_LOCATION = - -# If the GENERATE_ECLIPSEHELP tag is set to YES, additional index files will be -# generated, together with the HTML files, they form an Eclipse help plugin. To -# install this plugin and make it available under the help contents menu in -# Eclipse, the contents of the directory containing the HTML and XML files needs -# to be copied into the plugins directory of eclipse. The name of the directory -# within the plugins directory should be the same as the ECLIPSE_DOC_ID value. -# After copying Eclipse needs to be restarted before the help appears. -# The default value is: NO. -# This tag requires that the tag GENERATE_HTML is set to YES. - -GENERATE_ECLIPSEHELP = NO - -# A unique identifier for the Eclipse help plugin. When installing the plugin -# the directory name containing the HTML and XML files should also have this -# name. Each documentation set should have its own identifier. -# The default value is: org.doxygen.Project. -# This tag requires that the tag GENERATE_ECLIPSEHELP is set to YES. - -ECLIPSE_DOC_ID = org.doxygen.Project - -# If you want full control over the layout of the generated HTML pages it might -# be necessary to disable the index and replace it with your own. The -# DISABLE_INDEX tag can be used to turn on/off the condensed index (tabs) at top -# of each HTML page. A value of NO enables the index and the value YES disables -# it. Since the tabs in the index contain the same information as the navigation -# tree, you can set this option to YES if you also set GENERATE_TREEVIEW to YES. -# The default value is: NO. -# This tag requires that the tag GENERATE_HTML is set to YES. - -DISABLE_INDEX = NO - -# The GENERATE_TREEVIEW tag is used to specify whether a tree-like index -# structure should be generated to display hierarchical information. If the tag -# value is set to YES, a side panel will be generated containing a tree-like -# index structure (just like the one that is generated for HTML Help). For this -# to work a browser that supports JavaScript, DHTML, CSS and frames is required -# (i.e. any modern browser). Windows users are probably better off using the -# HTML help feature. Via custom style sheets (see HTML_EXTRA_STYLESHEET) one can -# further fine-tune the look of the index. As an example, the default style -# sheet generated by doxygen has an example that shows how to put an image at -# the root of the tree instead of the PROJECT_NAME. Since the tree basically has -# the same information as the tab index, you could consider setting -# DISABLE_INDEX to YES when enabling this option. -# The default value is: NO. -# This tag requires that the tag GENERATE_HTML is set to YES. - -GENERATE_TREEVIEW = YES - -# The ENUM_VALUES_PER_LINE tag can be used to set the number of enum values that -# doxygen will group on one line in the generated HTML documentation. -# -# Note that a value of 0 will completely suppress the enum values from appearing -# in the overview section. -# Minimum value: 0, maximum value: 20, default value: 4. -# This tag requires that the tag GENERATE_HTML is set to YES. - -ENUM_VALUES_PER_LINE = 4 - -# If the treeview is enabled (see GENERATE_TREEVIEW) then this tag can be used -# to set the initial width (in pixels) of the frame in which the tree is shown. -# Minimum value: 0, maximum value: 1500, default value: 250. -# This tag requires that the tag GENERATE_HTML is set to YES. - -TREEVIEW_WIDTH = 250 - -# If the EXT_LINKS_IN_WINDOW option is set to YES, doxygen will open links to -# external symbols imported via tag files in a separate window. -# The default value is: NO. -# This tag requires that the tag GENERATE_HTML is set to YES. - -EXT_LINKS_IN_WINDOW = NO - -# Use this tag to change the font size of LaTeX formulas included as images in -# the HTML documentation. When you change the font size after a successful -# doxygen run you need to manually remove any form_*.png images from the HTML -# output directory to force them to be regenerated. -# Minimum value: 8, maximum value: 50, default value: 10. -# This tag requires that the tag GENERATE_HTML is set to YES. - -FORMULA_FONTSIZE = 10 - -# Use the FORMULA_TRANPARENT tag to determine whether or not the images -# generated for formulas are transparent PNGs. Transparent PNGs are not -# supported properly for IE 6.0, but are supported on all modern browsers. -# -# Note that when changing this option you need to delete any form_*.png files in -# the HTML output directory before the changes have effect. -# The default value is: YES. -# This tag requires that the tag GENERATE_HTML is set to YES. - -FORMULA_TRANSPARENT = YES - -# Enable the USE_MATHJAX option to render LaTeX formulas using MathJax (see -# http://www.mathjax.org) which uses client side Javascript for the rendering -# instead of using pre-rendered bitmaps. Use this if you do not have LaTeX -# installed or if you want to formulas look prettier in the HTML output. When -# enabled you may also need to install MathJax separately and configure the path -# to it using the MATHJAX_RELPATH option. -# The default value is: NO. -# This tag requires that the tag GENERATE_HTML is set to YES. - -USE_MATHJAX = NO - -# When MathJax is enabled you can set the default output format to be used for -# the MathJax output. See the MathJax site (see: -# http://docs.mathjax.org/en/latest/output.html) for more details. -# Possible values are: HTML-CSS (which is slower, but has the best -# compatibility), NativeMML (i.e. MathML) and SVG. -# The default value is: HTML-CSS. -# This tag requires that the tag USE_MATHJAX is set to YES. - -MATHJAX_FORMAT = HTML-CSS - -# When MathJax is enabled you need to specify the location relative to the HTML -# output directory using the MATHJAX_RELPATH option. The destination directory -# should contain the MathJax.js script. For instance, if the mathjax directory -# is located at the same level as the HTML output directory, then -# MATHJAX_RELPATH should be ../mathjax. The default value points to the MathJax -# Content Delivery Network so you can quickly see the result without installing -# MathJax. However, it is strongly recommended to install a local copy of -# MathJax from http://www.mathjax.org before deployment. -# The default value is: http://cdn.mathjax.org/mathjax/latest. -# This tag requires that the tag USE_MATHJAX is set to YES. - -MATHJAX_RELPATH = http://cdn.mathjax.org/mathjax/latest - -# The MATHJAX_EXTENSIONS tag can be used to specify one or more MathJax -# extension names that should be enabled during MathJax rendering. For example -# MATHJAX_EXTENSIONS = TeX/AMSmath TeX/AMSsymbols -# This tag requires that the tag USE_MATHJAX is set to YES. - -MATHJAX_EXTENSIONS = - -# The MATHJAX_CODEFILE tag can be used to specify a file with javascript pieces -# of code that will be used on startup of the MathJax code. See the MathJax site -# (see: http://docs.mathjax.org/en/latest/output.html) for more details. For an -# example see the documentation. -# This tag requires that the tag USE_MATHJAX is set to YES. - -MATHJAX_CODEFILE = - -# When the SEARCHENGINE tag is enabled doxygen will generate a search box for -# the HTML output. The underlying search engine uses javascript and DHTML and -# should work on any modern browser. Note that when using HTML help -# (GENERATE_HTMLHELP), Qt help (GENERATE_QHP), or docsets (GENERATE_DOCSET) -# there is already a search function so this one should typically be disabled. -# For large projects the javascript based search engine can be slow, then -# enabling SERVER_BASED_SEARCH may provide a better solution. It is possible to -# search using the keyboard; to jump to the search box use + S -# (what the is depends on the OS and browser, but it is typically -# , /