910 lines
271 KiB
Plaintext
910 lines
271 KiB
Plaintext
{
|
|
"cells": [
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "269c4188",
|
|
"metadata": {},
|
|
"source": [
|
|
"# Exercise sheet\n",
|
|
"\n",
|
|
"Some general remarks about the exercises:\n",
|
|
"* For your convenience functions from the lecture are included below. Feel free to reuse them without copying to the exercise solution box.\n",
|
|
"* For each part of the exercise a solution box has been added, but you may insert additional boxes. Do not hesitate to add Markdown boxes for textual or LaTeX answers (via `Cell > Cell Type > Markdown`). But make sure to replace any part that says `YOUR CODE HERE` or `YOUR ANSWER HERE` and remove the `raise NotImplementedError()`.\n",
|
|
"* Please make your code readable by humans (and not just by the Python interpreter): choose informative function and variable names and use consistent formatting. Feel free to check the [PEP 8 Style Guide for Python](https://www.python.org/dev/peps/pep-0008/) for the widely adopted coding conventions or [this guide for explanation](https://realpython.com/python-pep8/).\n",
|
|
"* Make sure that the full notebook runs without errors before submitting your work. This you can do by selecting `Kernel > Restart & Run All` in the jupyter menu.\n",
|
|
"* For some exercises test cases have been provided in a separate cell in the form of `assert` statements. When run, a successful test will give no output, whereas a failed test will display an error message.\n",
|
|
"* Each sheet has 100 points worth of exercises. Note that only the grades of sheets number 2, 4, 6, 8 count towards the course examination. Submitting sheets 1, 3, 5, 7 & 9 is voluntary and their grades are just for feedback.\n",
|
|
"\n",
|
|
"Please fill in your name here:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 1,
|
|
"id": "220d541e",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"NAME = \"Kees van Kempen\"\n",
|
|
"NAMES_OF_COLLABORATORS = \"\""
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "b6944e4c",
|
|
"metadata": {},
|
|
"source": [
|
|
"---"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "c53fbab6",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "da0f2845f08ee29eb0450f8eff343e98",
|
|
"grade": false,
|
|
"grade_id": "cell-3cb26b1434512d8d",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"**Exercise sheet 8**\n",
|
|
"\n",
|
|
"Code from the lectures:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 2,
|
|
"id": "5e4391a6",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "1814f5ba5f2d71b14a4c534cfe3ad7ff",
|
|
"grade": false,
|
|
"grade_id": "cell-40c62687f6a2c579",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"import numpy as np\n",
|
|
"rng = np.random.default_rng() \n",
|
|
"import matplotlib.pylab as plt\n",
|
|
"%matplotlib inline\n",
|
|
"\n",
|
|
"def fan_triangulation(n):\n",
|
|
" '''Generates a fan-shaped triangulation of even size n.'''\n",
|
|
" return np.array([[(i-3)%(3*n),i+5,i+4,(i+6)%(3*n),i+2,i+1] \n",
|
|
" for i in range(0,3*n,6)],dtype=np.int32).flatten()\n",
|
|
"\n",
|
|
"def is_fpf_involution(adj):\n",
|
|
" '''Test whether adj defines a fixed-point free involution.'''\n",
|
|
" for x, a in enumerate(adj):\n",
|
|
" if a < 0 or a >= len(adj) or x == a or adj[a] != x:\n",
|
|
" return False\n",
|
|
" return True\n",
|
|
"\n",
|
|
"from collections import deque \n",
|
|
"\n",
|
|
"def triangle_neighbours(adj,i):\n",
|
|
" '''Return the indices of the three neighboring triangles.'''\n",
|
|
" return [j//3 for j in adj[3*i:3*i+3]]\n",
|
|
"\n",
|
|
"def connected_components(adj):\n",
|
|
" '''Calculate the number of connected components of the triangulation.'''\n",
|
|
" n = len(adj)//3 # the number of triangles\n",
|
|
" # array storing the component index of each triangle\n",
|
|
" component = np.full(n,-1,dtype=np.int32) \n",
|
|
" index = 0\n",
|
|
" for i in range(n):\n",
|
|
" if component[i] == -1: # new component found, let us explore it\n",
|
|
" component[i] = index\n",
|
|
" queue = deque([i]) # use an exploration queue for breadth-first search\n",
|
|
" while queue:\n",
|
|
" for nbr in triangle_neighbours(adj,queue.pop()):\n",
|
|
" # the neighboring triangle has not been explored yet\n",
|
|
" if component[nbr] == -1: \n",
|
|
" component[nbr] = index\n",
|
|
" queue.appendleft(nbr) # add it to the exploration queue\n",
|
|
" index += 1\n",
|
|
" return index\n",
|
|
"\n",
|
|
"def next_around_triangle(i):\n",
|
|
" '''Return the label of the side following side i in counter-clockwise direction.'''\n",
|
|
" return i - i%3 + (i+1)%3\n",
|
|
"\n",
|
|
"def prev_around_triangle(i):\n",
|
|
" '''Return the label of the side preceding side i in counter-clockwise direction.'''\n",
|
|
" return i - i%3 + (i-1)%3\n",
|
|
"\n",
|
|
"def vertex_list(adj):\n",
|
|
" '''\n",
|
|
" Return the number of vertices and an array `vertex` of the same size \n",
|
|
" as `adj`, such that `vertex[i]` is the index of the vertex at the \n",
|
|
" start (in ccw order) of the side labeled `i`.\n",
|
|
" '''\n",
|
|
" # a side i that have not been visited yet has vertex[i]==-1\n",
|
|
" vertex = np.full(len(adj),-1,dtype=np.int32) \n",
|
|
" vert_index = 0 \n",
|
|
" for i in range(len(adj)):\n",
|
|
" if vertex[i] == -1:\n",
|
|
" side = i\n",
|
|
" while vertex[side] == -1: # find all sides that share the same vertex\n",
|
|
" vertex[side] = vert_index\n",
|
|
" side = next_around_triangle(adj[side])\n",
|
|
" vert_index += 1\n",
|
|
" return vert_index, vertex\n",
|
|
"\n",
|
|
"def number_of_vertices(adj):\n",
|
|
" '''Calculate the number of vertices in the triangulation.'''\n",
|
|
" return vertex_list(adj)[0]\n",
|
|
"\n",
|
|
"def is_sphere_triangulation(adj):\n",
|
|
" '''Test whether adj defines a triangulation of the 2-sphere.'''\n",
|
|
" if not is_fpf_involution(adj) or connected_components(adj) != 1:\n",
|
|
" return False\n",
|
|
" num_vert = number_of_vertices(adj)\n",
|
|
" num_face = len(adj)//3\n",
|
|
" num_edge = len(adj)//2\n",
|
|
" # verify Euler's formula for the sphere\n",
|
|
" return num_vert - num_edge + num_face == 2\n",
|
|
"\n",
|
|
"def flip_edge(adj,i):\n",
|
|
" if adj[i] == next_around_triangle(i) or adj[i] == prev_around_triangle(i):\n",
|
|
" # flipping an edge that is adjacent to the same triangle on both sides makes no sense\n",
|
|
" return False\n",
|
|
" j = prev_around_triangle(i)\n",
|
|
" k = adj[i]\n",
|
|
" l = prev_around_triangle(k)\n",
|
|
" n = adj[l]\n",
|
|
" adj[i] = n # it is important that we first update\n",
|
|
" adj[n] = i # these adjacencies, before determining m,\n",
|
|
" m = adj[j] # to treat the case j == n appropriately\n",
|
|
" adj[k] = m\n",
|
|
" adj[m] = k\n",
|
|
" adj[j] = l\n",
|
|
" adj[l] = j\n",
|
|
" return True\n",
|
|
"\n",
|
|
"def random_flip(adj):\n",
|
|
" random_side = rng.integers(0,len(adj))\n",
|
|
" return flip_edge(adj,random_side)\n",
|
|
"\n",
|
|
"import networkx as nx\n",
|
|
"from mpl_toolkits.mplot3d import Axes3D\n",
|
|
"from mpl_toolkits.mplot3d.art3d import Poly3DCollection\n",
|
|
"\n",
|
|
"def triangulation_edges(triangulation,vertex):\n",
|
|
" '''Return a list of vertex-id pairs corresponding to the edges in the triangulation.'''\n",
|
|
" return [(vertex[i],vertex[j]) for i,j in enumerate(triangulation) if i < j]\n",
|
|
"\n",
|
|
"def triangulation_triangles(triangulation,vertex):\n",
|
|
" '''Return a list of vertex-id triples corresponding to the triangles in the triangulation.'''\n",
|
|
" return [vertex[i:i+3] for i in range(0,len(triangulation),3)]\n",
|
|
"\n",
|
|
"def plot_triangulation_3d(adj):\n",
|
|
" '''Display an attempt at embedding the triangulation in 3d.'''\n",
|
|
" num_vert, vertex = vertex_list(adj)\n",
|
|
" edges = triangulation_edges(adj,vertex)\n",
|
|
" triangles = triangulation_triangles(adj,vertex)\n",
|
|
" # use the networkX 3d graph layout algorithm to find positions for the vertices\n",
|
|
" pos = np.array(list(nx.spring_layout(nx.Graph(edges),dim=3).values()))\n",
|
|
" fig = plt.figure()\n",
|
|
" ax = fig.add_subplot(111, projection='3d')\n",
|
|
" tris = Poly3DCollection(pos[triangles])\n",
|
|
" tris.set_edgecolor('k')\n",
|
|
" ax.add_collection3d(tris)\n",
|
|
" ax.set_xlim3d(np.amin(pos[:,0]),np.amax(pos[:,0]))\n",
|
|
" ax.set_ylim3d(np.amin(pos[:,1]),np.amax(pos[:,1]))\n",
|
|
" ax.set_zlim3d(np.amin(pos[:,2]),np.amax(pos[:,2]))\n",
|
|
" plt.show()\n",
|
|
" \n",
|
|
"def vertex_neighbors_list(adj):\n",
|
|
" '''Return a list `neighbors` such that `neighbors[v]` is a list of neighbors of the vertex v.'''\n",
|
|
" num_vertices, vertex = vertex_list(adj)\n",
|
|
" neighbors = [[] for _ in range(num_vertices)]\n",
|
|
" for i,j in enumerate(adj):\n",
|
|
" neighbors[vertex[i]].append(vertex[j])\n",
|
|
" return neighbors\n",
|
|
"\n",
|
|
"def vertex_distance_profile(adj,max_distance=30):\n",
|
|
" '''Return array `profile` of size `max_distance` such that `profile[r]` is the number\n",
|
|
" of vertices that have distance r to a randomly chosen initial vertex.'''\n",
|
|
" profile = np.zeros((max_distance),dtype=np.int32)\n",
|
|
" neighbors = vertex_neighbors_list(adj)\n",
|
|
" num_vertices = len(neighbors)\n",
|
|
" start = rng.integers(num_vertices) # random starting vertex\n",
|
|
" distance = np.full(num_vertices,-1,dtype=np.int32) # array tracking the known distances (-1 is unknown)\n",
|
|
" queue = deque([start]) # use an exploration queue for the breadth-first search\n",
|
|
" distance[start] = 0\n",
|
|
" profile[0] = 1 # of course there is exactly 1 vertex at distance 0\n",
|
|
" while queue:\n",
|
|
" current = queue.pop()\n",
|
|
" d = distance[current] + 1 # every unexplored neighbour will have this distance\n",
|
|
" if d >= max_distance:\n",
|
|
" break\n",
|
|
" for nbr in neighbors[current]:\n",
|
|
" if distance[nbr] == -1: # this neighboring vertex has not been explored yet\n",
|
|
" distance[nbr] = d\n",
|
|
" profile[d] += 1\n",
|
|
" queue.appendleft(nbr) # add it to the exploration queue\n",
|
|
" return profile\n",
|
|
" \n",
|
|
"def perform_sweeps(adj,t):\n",
|
|
" '''Perform t sweeps of flip moves, where 1 sweep is N moves.'''\n",
|
|
" for _ in range(len(adj)*t//3):\n",
|
|
" random_flip(adj)\n",
|
|
"\n",
|
|
"def batch_estimate(data,observable,k):\n",
|
|
" '''Devide data into k batches and apply the function observable to each.\n",
|
|
" Returns the mean and standard error.'''\n",
|
|
" batches = np.reshape(data,(k,-1))\n",
|
|
" values = np.apply_along_axis(observable, 1, batches)\n",
|
|
" return np.mean(values), np.std(values)/np.sqrt(k-1)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "bed55184",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "8c9a6c198119d4649dd87308e8933611",
|
|
"grade": false,
|
|
"grade_id": "cell-5f5adc7840fea9ad",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"## Estimating Hausdorff dimensions in various 2D quantum gravity models \n",
|
|
"\n",
|
|
"**(100 Points)**\n",
|
|
"\n",
|
|
"In the lecture we considered the model of two-dimensional Dynamical Triangulations of the 2-sphere. The corresponding partition function is\n",
|
|
"$$ Z^{U}_{S^2,N} = \\sum_T 1, \\tag{1}$$\n",
|
|
"where the sum is over all triangulations of size $N$ with the topology of $S^2$, each of which is represented as an adjacency list $\\operatorname{adj}: \\{0,\\ldots,3N-1\\} \\to \\{0,\\ldots,3N-1\\}$. To emphasize that we are dealing with the **uniform** probability distribution on such triangulations, we have added the label $^U$. It is a lattice model of two-dimensional Euclidean quantum gravity with no coupled matter.\n",
|
|
"\n",
|
|
"One can also consider two-dimensional quantum gravity coupled to matter fields (e.g. a scalar field) supported on the geometry. Formally the corresponding path integral in the continuum reads\n",
|
|
"$$ Z = \\int [\\mathcal{D}g_{ab}]\\int [\\mathcal{D}\\phi] e^{-\\frac{1}{\\hbar}(S_E[g_{ab}] + S_m[\\phi,g_{ab}])} = \\int [\\mathcal{D}g_{ab}]e^{-\\frac{1}{\\hbar}S_E[g_{ab}]} Z^*_m[g_{ab}],$$\n",
|
|
"where $S_m[\\phi,g_{ab}]$ and $Z_m[g_{ab}]$ are the matter action and path integral of the field $\\phi$ on the geometry described by $g_{ab}$. The natural analogue in Dynamical Triangulations is\n",
|
|
"$$Z^*_{S^2,N} = \\sum_T Z^*_m[T],$$\n",
|
|
"where the sum is over the same triangulations as in (1) but now the summand $Z^*_m[T]$ is the lattice partition function of a matter system supported on the triangulation $T$, which generically depends in a non-trivial way on $T$. For instance, the matter system could be an Ising model in which the spin are supported on the triangles of $T$ and $Z^{\\text{Ising}}_m[T]$ would be the corresponding Ising partition function.\n",
|
|
"In other words, when Dynamical Triangulations are coupled to matter the uniform distribution $\\pi^U(T) = 1/Z^U_{S^2,N}$ is changed into a non-uniform distribution $\\pi^*(T) = Z^*_m[T] / Z^*_{S^2,N}$. This can have significant effect on the critical exponents of the random triangulation as $N\\to\\infty$, like the Hausdorff dimension. \n",
|
|
"\n",
|
|
"The goal of this exercise is to estimate the **Hausdorff dimension** of random triangulations in four different models and to conclude based on this that they belong to four different universality classes (i.e. that if they possess well-defined continuum limits that they are described by four different EQFTs): \n",
|
|
"* $Z^{U}_{S^2,N}$: the standard Dynamical Triangulations with **U**niform distribution (U)\n",
|
|
"* $Z^{W}_{S^2,N}$: triangulations coupled to a matter system called a Schnyder **W**ood (W)\n",
|
|
"* $Z^{S}_{S^2,N}$: triangulations coupled to a matter system called a **S**panning tree (S)\n",
|
|
"* $Z^{B}_{S^2,N}$: triangulations coupled to a matter system called a **B**ipolar orientation (B)\n",
|
|
"\n",
|
|
"What these matter systems precisely represent will not be important. We have provided for you a **black box generator** that samples from the corresponding four distributions $\\pi^U(T)$, $\\pi^W(T)$, $\\pi^S(T)$, $\\pi^B(T)$. It does so in an efficient manner (linear time in $N$) using direct Monte Carlo sampling algorithms and therefore returns independent samples with exactly the desired distribution $\\pi^*(T)$ (within numerical precision).\n",
|
|
"\n",
|
|
"The black box generator is provided by the executable program `generator` provided to you on the science server. It can be called directly from this notebook with the following function `generate_random_triangulation`, that takes the desired size $N$ and model (`'U'`,`'W'`, `'S'`, `'B'`) and returns a single random triangulation in the usual form of an adjacency list."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 3,
|
|
"id": "bcc7acba",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "7d6abad00aa217998ca44ecc5e89f423",
|
|
"grade": false,
|
|
"grade_id": "cell-266ff66f880583d7",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"True"
|
|
]
|
|
},
|
|
"execution_count": 3,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"import subprocess\n",
|
|
"\n",
|
|
"def generate_random_triangulation(n,model):\n",
|
|
" '''\n",
|
|
" Returns a random triangulation generated by the program `generator` in the form \n",
|
|
" of an array of length 3n storing the adjacency information of the triangle sides.\n",
|
|
" Parameters:\n",
|
|
" n - number of triangles in the triangulation, must be positive and even\n",
|
|
" model - a one-letter string specifying the model from which the triangulation is sampled:\n",
|
|
" 'U': Uniform triangulations\n",
|
|
" 'W': Schnyder-Wood-decorated triangulations\n",
|
|
" 'S': Spanning-tree decorated triangulations\n",
|
|
" 'B': Bipolar-oriented triangulations\n",
|
|
" '''\n",
|
|
" program = \"/vol/cursus/NM042B/bin/generator\"\n",
|
|
" output = subprocess.check_output([program,\"-s{}\".format(n),\"-t{}\".format(model)]).decode('ascii').split('\\n')[:-1]\n",
|
|
" return np.array([int(num) for num in output],dtype=np.int32)\n",
|
|
"\n",
|
|
"adj = generate_random_triangulation(100,'B')\n",
|
|
"is_sphere_triangulation(adj)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "4518f51f",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "37e92f3a59f2d5c6d117868d04d8f0d4",
|
|
"grade": false,
|
|
"grade_id": "cell-6aacf5fa6d8c4eb9",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"Recall that the **distance profile** $\\rho_T(r)$ of a triangulation is defined as \n",
|
|
"$$ \\rho_T(r) = \\frac{1}{V} \\sum_{x=0}^{V-1} \\sum_{y=0}^{V-1} \\mathbf{1}_{\\{d_T(x,y)=r\\}},$$\n",
|
|
"where $V = (N+4)/2$ is the number of vertices and $d_T(x,y)$ is the graph distance between the vertices with label $x$ and $y$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "d59143f0",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "afcdbf86f64bd17b8ac9b4f9ec422206",
|
|
"grade": false,
|
|
"grade_id": "cell-8e6d6fcefb5ab644",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"**(a)** Let $T$ be a random triangulation of size $N$ and $X$, $Y$ two independent numbers chosen uniformly from $0,\\ldots,V-1$, corresponding to two random vertices in $T$. Explain with a calculation that $\\frac{1}{V}\\mathbb{E}[ \\rho_T(r) ] = \\mathbb{P}(d_T(X,Y) = r)$ and that the expected distance between $X$ and $Y$ is related to the distance profile via\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\mathbb{E}[d_T(X,Y)] = \\frac{1}{V}\\sum_{r=0}^\\infty r\\, \\mathbb{E}[ \\rho_T(r) ]. \\tag{2}\n",
|
|
"$$\n",
|
|
"\n",
|
|
"**(20 pts)**"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "dd1b43bf",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "74963ed3d7cbd9eaa06be2e66a8f939e",
|
|
"grade": true,
|
|
"grade_id": "cell-f86454063d193cd6",
|
|
"locked": false,
|
|
"points": 20,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"**To proof**\n",
|
|
"\n",
|
|
"$\\frac{1}{V}\\mathbb{E}[ \\rho_T(r) ] = \\mathbb{P}(d_T(X,Y) = r)$\n",
|
|
"\n",
|
|
"**Proof**\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\frac{1}{V} \\mathbb{E}\\left[ \\rho_T(r)\\right]\n",
|
|
" = \\frac{1}{V} \\mathbb{E} \\left[\\frac{1}{V} \\sum_{x=0}^{V-1}\\sum_{y=0}^{V-1} \\mathbf{1}_{\\{d_T(x,y)=r\\}} \\right]\n",
|
|
" = \\frac{1}{V^2} \\mathbb{E} \\left[ \\sum_{x=0}^{V-1}\\sum_{y=0}^{V-1} \\mathbf{1}_{\\{d_T(x,y)=r\\}} \\right]\n",
|
|
" = \\frac{1}{V^2} \\sum_{x=0}^{V-1}\\sum_{y=0}^{V-1} \\mathbb{E} \\left[ \\mathbf{1}_{\\{d_T(x,y)=r\\}} \\right]\n",
|
|
"$$\n",
|
|
"\n",
|
|
"The order of summation is changed, as the sum of expectation values is equal to the expectation value of the sum.\n",
|
|
"The latter expectation value of the indicator function is exactly equal to the chance $\\mathbb{P}(d_T(x,y)=r)$ for given $x, y$.\n",
|
|
"For the uniformly distributed $X, Y$, we find $\\mathbb{P}(X = x) = \\frac{1}{V} = \\mathbb{P}(Y = y)$.\n",
|
|
"This allows us to write the right hand side as follows.\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\frac{1}{V} \\mathbb{E}\\left[ \\rho_T(r)\\right]\n",
|
|
" = \\frac{1}{V^2} \\sum_{x=0}^{V-1}\\sum_{y=0}^{V-1} \\mathbb{P}(d_T(x,y)=r)\n",
|
|
" = \\sum_{x=0}^{V-1}\\sum_{y=0}^{V-1} \\mathbb{P}(X = x) \\mathbb{P}(Y = y) \\mathbb{P}(d_T(x,y)=r)\n",
|
|
" = \\mathbb{P}(d_T(X,Y)=r),\n",
|
|
"$$\n",
|
|
"\n",
|
|
"which is what we sought.\n",
|
|
"\n",
|
|
"Using this result, it is just a matter of writing out the definition of an expectation value to get to the result.\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\mathbb{E}[d_T(X,Y)] = \\sum_{r=0}^\\infty r\\, \\mathbb{P}(d_T(X,Y) = r) = \\frac{1}{V}\\sum_{r=0}^\\infty r\\, \\mathbb{E}[ \\rho_T(r) ].\n",
|
|
"$$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "29704f5d",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "e2cc0493d54bcf087ce14bcb2e8a8d2f",
|
|
"grade": false,
|
|
"grade_id": "cell-aafca9797e5cfee4",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"**(b)** We will work under the assumption that \n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\mathbb{E}[\\rho_T(r)] \\approx V^{1-1/d_H} f(r V^{-1/d_H})\n",
|
|
"$$ \n",
|
|
"\n",
|
|
"for a positive real number $d_H$ called the **Hausdorff dimension** and a continuous function $f$ that are both independent of $N$ but do depend on the model. Show that \n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\mathbb{E}[d_T(X,Y)] \\approx c\\,V^{1/d_H}, \\qquad c = \\int_0^\\infty \\mathrm{d}x\\,x\\,f(x). \\tag{3}\n",
|
|
"$$\n",
|
|
"\n",
|
|
"_Hint:_ Approximate the summation by an integral. **(15 pts)**"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "0c062ba6",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "2db525e8acbc2412c1c5948052526a15",
|
|
"grade": true,
|
|
"grade_id": "cell-bcf3b38d64a4408d",
|
|
"locked": false,
|
|
"points": 15,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"**To proof**\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\mathbb{E}[d_T(X,Y)] \\approx c\\,V^{1/d_H}, \\qquad c = \\int_0^\\infty \\mathrm{d}x\\,x\\,f(x)\n",
|
|
"$$\n",
|
|
"\n",
|
|
"**Proof**\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\mathbb{E} \\left[ d_T(X,Y) \\right]\n",
|
|
" = \\frac{1}{V} \\sum_{r=0}^\\infty r\\, \\mathbb{E} \\left[ \\rho_T(r) \\right]\n",
|
|
" = \\frac{1}{V} \\sum_{r=0}^\\infty rV^{1-1/d_H}f(rV^{-1/d_H})\n",
|
|
" = \\frac{1}{V} \\sum_{r=0}^\\infty xV^{1/d_H} \\cdot V^{1-1/d_H}f(x)\n",
|
|
" = \\sum_{r=0}^\\infty xf(x),\n",
|
|
"$$\n",
|
|
"where the first equality sign is due to (2), the second due to the given assumption, the third using $x = rV^{-1/d_H}$.\n",
|
|
"\n",
|
|
"Now we approximate the summation by an integral.\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\sum_{r=0}^\\infty xf(x)\n",
|
|
" \\approx \\int_{r=0}^\\infty xf(x)dr\n",
|
|
" = V^{1/d_H} \\int_{x=0}^\\infty xf(x)dx\n",
|
|
" = cV^{1/d_H},\n",
|
|
"$$\n",
|
|
"using $\\frac{dr}{dx} = V^{1/d_H}$ for substitution.\n",
|
|
"This yields the desired approximation\n",
|
|
"$$\n",
|
|
" \\mathbb{E} \\left[ d_T(X,Y) \\right] \\approx cV^{1/d_H}.\n",
|
|
"$$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "eba53e6d",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "ba14acd8cc24c2dfea35f3b8106cdfc8",
|
|
"grade": false,
|
|
"grade_id": "cell-fcab32195688a5c5",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"**(c)** For each of the four models estimate $\\mathbb{E}[d_T(X,Y)]$ with errors for $N = 2^7, 2^8, \\ldots, 2^{12}$ using (2) and based on $100$ samples each. Store your data in the file `qgdimension.hdf5`. Make an estimate of $d_H$ (with errors) for each of the models by fitting the parameters $c$ and $d_H$ of the ansatz (3). For each model, plot the data together with the fit in a log-log plot. **(40 pts)**"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 7,
|
|
"id": "ee683060",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "c3664034dec3a350f7fe0533fe2454cb",
|
|
"grade": true,
|
|
"grade_id": "cell-01f5fde55f35f2dc",
|
|
"locked": false,
|
|
"points": 15,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"models = ['U','W','S','B']\n",
|
|
"sizes = [2**k for k in range(7,13)]\n",
|
|
"num_vertices = (np.array(sizes)+4)/2\n",
|
|
"measurements = 100\n",
|
|
"\n",
|
|
"# data gathering and storing in qgdimension.hdf5\n",
|
|
"import h5py\n",
|
|
"\n",
|
|
"max_distance = 30\n",
|
|
"def expected_distance(V, adj, max_distance=30):\n",
|
|
" '''\n",
|
|
" Calculates the expectation value of the distance profile given the amount\n",
|
|
" of vertices V, an array of adjacencies for a triangulation sample,\n",
|
|
" and max_distance as upper limit for the summation for the expectation value.\n",
|
|
" '''\n",
|
|
" return 1/V*vertex_distance_profile(adj,max_distance)@np.arange(max_distance)\n",
|
|
"\n",
|
|
"with h5py.File(\"qgdimension.hdf5\", \"a\") as f:\n",
|
|
" if not \"num-vertices\" in f:\n",
|
|
" f.create_dataset(\"num-vertices\",data=num_vertices)\n",
|
|
" \n",
|
|
" for model in models:\n",
|
|
" models_key = f\"expectation-graph-distance-{model}\"\n",
|
|
" if not models_key in f:\n",
|
|
" graph_distance_expectations = np.zeros((len(num_vertices), measurements))\n",
|
|
" for idx_N, N in enumerate(num_vertices):\n",
|
|
" V = (N + 4)/2\n",
|
|
" for idx_measurement in range(measurements):\n",
|
|
" adj = generate_random_triangulation(N, model)\n",
|
|
" expectation = expected_distance(V, adj, max_distance)\n",
|
|
" graph_distance_expectations[idx_N][idx_measurement] = expectation\n",
|
|
"\n",
|
|
" f.create_dataset(models_key,data=graph_distance_expectations)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 8,
|
|
"id": "351f7a01",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "000725107fe51acebc0bc68eef8c1c9c",
|
|
"grade": true,
|
|
"grade_id": "cell-9e8f666073e1e2df",
|
|
"locked": false,
|
|
"points": 25,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": "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\n",
|
|
"text/plain": [
|
|
"<Figure size 864x576 with 4 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Fitting and plotting\n",
|
|
"from matplotlib import pyplot as plt\n",
|
|
"from scipy.optimize import curve_fit\n",
|
|
"\n",
|
|
"# Define a dictionary of model names for the plot titles.\n",
|
|
"model_names = {\"U\": \"Uniform triangulations\",\n",
|
|
" \"W\": \"Schnyder-Wood-decorated triangulations\",\n",
|
|
" \"S\": \"Spanning-tree decorated triangulations\",\n",
|
|
" \"B\": \"Bipolar-oriented triangulations\"}\n",
|
|
"\n",
|
|
"d_H_list = {}\n",
|
|
"\n",
|
|
"with h5py.File(\"qgdimension.hdf5\", \"r\") as f:\n",
|
|
" num_vertices = np.array(f[\"num-vertices\"])\n",
|
|
" expectations = {model: np.array(f[f\"expectation-graph-distance-{model}\"]) for model in models}\n",
|
|
" \n",
|
|
" fig, axs = plt.subplots(2, 2, figsize=(12, 8))\n",
|
|
" axs = axs.ravel()\n",
|
|
" fig.suptitle(r\"Graph distance expectation Monte Carlo simulations and Hausdorff dimension $d_H$ fits using $\\mathbb{E}[d_T(X,Y)] \\approx c\\,V^{1/d_H}$ for different triangulation models\")\n",
|
|
" \n",
|
|
" for idx_model, model in enumerate(models):\n",
|
|
" # Calculate mean and standard deviation of the expectations.\n",
|
|
" # TODO: Look at whether I store the right data and do the right calculations.\n",
|
|
" mu = np.mean(expectations[model], 1)\n",
|
|
" sigma = np.std(expectations[model], 1)/np.sqrt(len(expectations[model]) - 1)\n",
|
|
"\n",
|
|
" fitfunc = lambda V, c, d_H: c*V**(1/d_H)\n",
|
|
" popt, pcov = curve_fit(fitfunc, num_vertices, mu, sigma=sigma)\n",
|
|
" d_H_list[model] = popt[1]\n",
|
|
" num_vertices_fit = np.linspace(np.min(num_vertices)/2, np.max(num_vertices)*2, 1000)\n",
|
|
"\n",
|
|
" ax = axs[idx_model]\n",
|
|
" ax.set_title(f\"{model_names[model]} ({model})\")\n",
|
|
" ax.errorbar(num_vertices, mu, sigma, label=\"Monte Carlo\",\n",
|
|
" fmt='.', markersize=10, capsize=4)\n",
|
|
" ax.plot(num_vertices_fit, fitfunc(num_vertices_fit, *popt),\n",
|
|
" label=r\"fit: $c = {:.2f}$, $d_H = {:.2f}$\".format(*popt))\n",
|
|
" ax.set_xlabel(r\"$V$\")\n",
|
|
" ax.set_ylabel(r\"$\\mathbb{E}[d_T(X,Y)]$\")\n",
|
|
" ax.set_yscale(\"log\")\n",
|
|
" ax.set_xscale(\"log\")\n",
|
|
" ax.grid(True, which=\"both\", ls=\"-\")\n",
|
|
" ax.legend()\n",
|
|
" \n",
|
|
" fig.tight_layout()\n",
|
|
" fig.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "b505b3cf",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "be7888d11d6b9ca0f2666739857578cb",
|
|
"grade": false,
|
|
"grade_id": "cell-032c7f8d6147d9f9",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"**(d)** Produce a *collapse* plot for each of the four models as follows: plot \n",
|
|
"$$V^{1/d_H}\\,\\mathbb{E}[\\frac{1}{V}\\rho_T(r)] \\quad\\text{ as function of } x = r / V^{1/d_H},$$ \n",
|
|
"where for $d_H$ you take the estimate obtained in the previous exercise. Show errors in the mean distance profiles via shaded regions (just like in the lecture). Verify that the curves collapse reasonably well. **(25 pts)**"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 11,
|
|
"id": "988bfe95",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "7b7eceb7923231bc3710d4e3036265b6",
|
|
"grade": true,
|
|
"grade_id": "cell-faf328e7505cf6a2",
|
|
"locked": false,
|
|
"points": 25,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": "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\n",
|
|
"text/plain": [
|
|
"<Figure size 432x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"data": {
|
|
"image/png": "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\n",
|
|
"text/plain": [
|
|
"<Figure size 432x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"data": {
|
|
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAZIAAAEdCAYAAAAmZOH3AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAABzFklEQVR4nO3dd3xcV5nw8d8zvWhGvcuy3C33XhLHcbrTSQESEiAkEMIuu4SyEHhhYWEp2V3qBggBAgSyCYT0npDESezYSdy7bFmS1XsZTW/n/WPGjqLItmRZHks6389n7Jl7z9z73Hs188w5595zRSmFpmmapp0sQ6oD0DRN00Y3nUg0TdO0YdGJRNM0TRsWnUg0TdO0YdGJRNM0TRsWnUg0TdO0YdGJRNM0TRsWnUg0TdO0YdGJBBCRPSKy5lSXHY7TtZ7hEJEaEbmwz+uUxnyi9fePd7QQkT+KyH+e5HtniMg2EekVkX891rTBrj/Vx3ggpzMmEfl3EbnndKxrNBlXiST5RRIQEW+fR5FSarZSat1gltG/7Eh9OQ0lpjNFqmPuu/7hHpeB3i8it4jI+mGGebp9FVinlHIppX5xnGmDkupjPJDTHNMsYNdILVxE/iIiTSLiEZEDIvLp45T9vIhsFpGQiPxxgPnefo+YiPzvSMQ9rhJJ0pVKqbQ+j8ZUB6RpI0FETMBEYE+/WQNN0wZnNrBzBJf/Q6BMKeUGrgL+U0QWH6NsI/CfwP0Dzez7PQfkAwHgkRGIeVwmkg8YoImmRkS+IiI7RaRHRP4qIrb+ZUXkz0Ap8HQy439VRIpE5FERaROR6hM1HYjI10SkIdnMUCEiFwywno/2+2UREpF1yXmDXt9x1jVBRB5LLqOjb9VdRO4SkUPJ9+wVkWsGsx+Ptw+T8xf1aV55JDn/A803IvIpEXm6z+tKEflbn9d1IrKg7/oHOi59FrngWDEN1Yn2jYgoEZna53XfJqIBj0Vy3kIR2Zqc91eg734rF5F1ItItiSadq/qtsya57J1ABDgPuCe5H6aLyKv9pw2wXcdb/0CflX9L7lOfiPxeRPJF5Pnk+/8hIpnJssf9Wz3e38wJ9lffv7tj7p8T/U0OsB8MIvJ1EakVkUYRuQGYCuw+1nuGSym1RykVOvIy+ZhyjLKPKaWeADoGsejrgVbgzVMR50DBjJsHUANceKLpydfvAEVAFrAPuOM4ZS9MPjcAW4B/ByzAZKAKuOQY8cwA6oCi5OsyYMoJYnUn4/nsUNZ3rHUBRmAH8FPASeJLY1Wf9304uR8MwEcBH1A4iH1xvH1oAQ4DXwDMwLVAGPjPAeKeDHQn11+YfF9Dn3ldgOEY67+w37KOGdNg/laAW4D1g9k3yfkKmNrn9R9J/II83nE/sm++mNw315NICP+ZfF0JfCNZ7nygF5jRL+7twATADqwDPt1vOz4wrc+8Y67/OMd8E4lfvMUkvqy2AgsBK/Aq8G0G8bd6rONzvP3VN6YT7Z+hHP9k+e8AG0jU4NKTz6uG8H3zDIm/3YEezxznfb8C/CT+frYCaSdYz38CfzxBmVeB75zsd+eJHuOxRvJE8tdKt4g8cZxyv1BKNSqlOoGngQWDWPZSIFcp9V2lVFgpVQX8FrjhGOVjJD5ss0TErJSqUUodOtbCRcQA/B+J9u3fDHF9x1rXMhIfrH9TSvmUUkGl1NF+AKXUI8n9EFdK/RU4mHzPYBxrH64ATMn5EaXUYyQ+4B+Q3Kbe5HvPBV4EGkRkZvL1m0qp+CDjOV5MA+n7t9JN4gPeN7aT3TfHO+4rSHwh/iy5b/4OvNtnXhrwo+TxfpXEl9WNA2xjnVIqMIhY+jve+o/lf5VSLUqpBhK/eN9WSm1TiV/Wj5NIKoP9Wx3o+Az2czKY/TOo4y8iucBXgE8opQ4rpXqAZ0k2ayVr0bP7lN8qiabEo5RSVyilMo7xuOJYO1Mp9U+ACzgHeAwIHavsYIhIKYnPyp+Gs5zjGY+J5EN9DuaHjlOuuc9zP4k/0BOZCBT1+/L5Bolfa4jITfJe89TzSqlK4E4Sv3xaReRhESk6zvK/T+IP7EiTwHHX19dx1jUBOKyUig60QhH5hIhs77P8OUDOIPYFHHsfFpGoVfS9h0HdcZbzOrAGWJ18vo7EB+Pc5OuhGMpx7fu3kgH8U9+ZJ7tvTnDcB9o3h/vMq+uXOA+TqAn0dbx9eSLHW/+xtPR5HhjgdRqD/1v9wPEZwudkMPtnsMf/AmBfv4SVz3sd7TNJ1H4QESMQO9Zn6GQopWLJH3QlwOeGubhPkKhJVw8/soGNx0RyqvX/Mqzu98vDpZS6DEAp9aB6rwPs0uS0/1NKrSLxQVPA3QOtJNk+eyNwvVIqMpj1fSDQgddVB5T2/zWVXOdEEr8aPw9kJ79MdwMylB00gCagWET6LmfCccofSSTnJJ+/zokTyYjeaGeQ+8YPOPq8Ljga3LGP+0D7pjT5fyMwIVkz7TuvoV94w9n2461/OIb0t9rfID8ng90/g5FDopkOABExAx8CdoqIBTCp9/oyJpFMKn0l+4n6nzl19IfkIOMwcYw+kiH4BCNYGwGdSE6FFhLtvZBonvEkOwbtImIUkTkisnSgN0rifP7zRcQKBEn8eosNUG4h8L8kfiG39Zk16PUdZ13vkPjy+JGIOEXEJiJnJ9/mJPGhbUsu41MkfnUP18bkuj8vIiYRuZrjNwm9TqKD2K6UqifRfLIWyAa2HeM9fY/LSBjMvtkOfCx5XNaSSHwnOu4bgSjwr8l9cy3v7Zu3SfTDfFVEzJK4duJK4OFTuF3HW/9wDOmz0ddgPyec2v1TAaySxAkK6cCvSSSlXUA5kCuJTv11JJrvPtABr5S6VL3/DNG+j0sH2M48EblBRNKS++cSEj8eXx0owOTxsZHo5zQmP7umfmXOIlEjG5GztY7QiWT4fgh8M1lV/yKJP9wFQDXQDvyOREfdQKzAj5LlmoE8EtX9/q4GMoH1/ZrGYkNY34Dr6rOMqUAtUE+i4xil1F7gxyS+XFqAuSQ6HIdFKRUm0cF+G4mOx5tJtGUP2BaslDoAeEmecaKU8pDoqN2QjH8gR4+LiHxluDEPENNg9s0XSOzbbuAm4Ink9GMe9z775hYSJxJ8lEQ7+ZF5VwGXJt/7KxJt+PtP4XYdc/3DXO5Q/lb7G9Tn5FTuH6XUyyQS0GYSfURtJJLYQRI/GH6tlFqjlFoD/I1Tczq1ItGMVU9i3/8PcKdS6kk4WsPpu93fJJFU7yLxGQokp/X1SeAxpVTvKYjvmOT9TaGalhoi8jZwr1LqD6mORdOOR0R+CGxVSj2SfP0I8PVkX864pGskWkqIyLkiUpCsnn8SmAe8kOq4NG0Q+l+UOJVEDXnc+kAHq6adJjNINAmkAYdInETQlNqQNO3ElFJX9Xu9MFWxnCl005amaZo2LLppS9M0TRsWnUg0TdO0YRmTfSQ5OTmqrKws1WFomqaNGlu2bGlXSuWezHvHZCIpKytj8+bNqQ5D0zRt1BCREw2Fc0y6aUvTNE0bFp1INE3TtGHRiUTTNE0bljHZR6JpmjZYkUiE+vp6gsFgqkM5LWw2GyUlJZjN5lO2TJ1INE0b1+rr63G5XJSVlfH+0fPHHqUUHR0d1NfXM2nSpFO2XN20pWnauBYMBsnOzh7zSQRARMjOzj7ltS+dSDRNG/fGQxI5YiS2VScS7aSEgwFi0VN2Z1FNGxfWrFnDiy+++L5pP/vZz/inf/qnY7xjdNCJRBuSeCxGT2sLXY0N+Lo6Ux2Opo0qN954Iw8//P4bNj788MPceOONKYro1NCJRBs0v6eH9rrDBL2Jm60Fej1EwgPe1FDTtAFcf/31PPPMM4RCic9NTU0NjY2NrFq1KsWRDU9KE4mI3C8irSLygfsd9yu3VERiInL96YpNe08kHKKzsZ7e9jZUPP6+ed7OjhRFpWmjT3Z2NsuWLeOFFxL3cHv44Yf56Ec/Our7aFJdI/kjsPZ4BUTECNwNvHi8ctqpp+Jxejva6ayvI3KMszzCfj/hgP80R6Zpo1ff5q2x0KwFKU4kSqk3gBM1tP8L8CjQOvIRaUcEvV7a62vx93QPOF8pRTxZO+nt0LUSTRusD33oQ7zyyits3bqVQCDAokWLUh3SsJ3RFySKSDFwDXA+sPQEZW8HbgcoLS0d+eDGKBWP093aTNg/cC0jFo1StfUddr/2Mo6MTC7+zOeJhkMEvL3Y01ynOVpNG33S0tJYs2YNt95665iojUDqm7ZO5GfA15RSsRMVVErdp5RaopRakpt7UkPqa4Cvp3vAJBKPxTj47kae+skPePvxvyEGI201VVRtSwzX7+3sQN+2WdMG58Ybb2THjh3ccMMNqQ7llDijayTAEuDhZEdUDnCZiESVUk+kNKoxKh6PfaApKx6LUbXtXXa/+jLerg6yS0pZdvX1FE2byQu//hnbX3yG0jnzMQP+nm6cGZkpiV3TRpNrrrlmTP3wOqMTiVLq6GAwIvJH4BmdREaOr7vr6FlZ8ViM6u2b2fXqy3g728kqnsCaq66lcOpMjCYjAEuuvJYXf/0z9qz7BwsuuRxfdxd2txuDwZjKzdA07TRLaSIRkYeANUCOiNQD3wbMAEqpe1MY2rgTj8Xw9/QQj8Wo2bGFXa++RG9HO5lFJaz5xKcpnjmboDeCpyOIzWnG5jCTW1pG2YLF7F3/GlOXriAtKxtfVxeu7JxUb46maadRShOJUmrQPU1KqVtGMJRxz9fdBUrx+l/up2H/HjILizn347dRUj4HESEcjBLwhgEI9IYJ+aPY0ywsXHsldXt2sfX5p1h906fw93TjSE/HaDp1Q1RrmnZmO6ObtrTTIxaN4vf00FJ9iIb9e5h7wSXMO/8SxJA4FyMaieHrfv8V7PFYHF9PEKPZSvnZa9i97iVaqirJnzwVb2cH6XkFqdgUTdNS4Ew/a0s7DXzdnaAUu155AZvLzexzLziaROKxON6u0NGOQYPRhN2VSUZBKVani1gkRnH5CuzuDN59+jHi8ThBr5dIaHzcJEjTNJ1Ixr1YNELA46G1+hDNhw4ye/X5mMwWIHHRoa87TDymsNiddDRYqdwaQwxOjCYTDncWYjBiMFmYcdYldDc3snf9emKxuL5IUdPGEZ1IxjlvZ2JggZ2vvIgtzcW05WcdnRfyxzHZXGQWTsDXY2PHq03U7Ozghft2c/DdFpQCqzIQbW6moGwmmUUT2bvuRTrqu/C09RD0elO1WZo2qtx6663k5eUxZ86co9P+7d/+jZkzZzJv3jyuueYauru7gcStgT/5yU8yd+5cysvL+eEPf5iiqN+jE8k4Fg2HCXp7aa2povnQAWYlayNWZxp2Vy52dyEOdyZ+T4xNT1aRnmfn4ttmkV3sZPs/6njldzvpbQhgFCNxr5dZqy8jHPBT+c5rBLxh6vfXE/RFUr2ZmnbGu+WWW44O5HjERRddxO7du9m5cyfTp08/mjAeeeQRQqEQu3btYsuWLfzmN7+hpqYmBVG/RyeScczXnaiN7PjH81icTgoWzCVsihNzWOnyBAlGg3gDfjY8dhCAZVdOwI6XpUtNLFmZRigY581XPFRVWgl7/LizCiiZtZDq7RvxdbcTCQVpr2sdUxdeadpIWL16NVlZWe+bdvHFF2MyJc6HWrFiBfX19UDiDoc+n49oNEogEMBiseB2u097zH3ps7bGqUg4RNDrpbWmipZDB5l43tl0xXsIGSw01vpRsUQfSc0/fHhaw0w9Bzqbd9B5JClkQvkqofGgmdpqRWO9lfzpDWTNX0TTwd3se/MFllx5M77uLoLeHOwua2o3WNMG4T+e3sPeRs8pXeasIjffvnL2sJZx//3389GPfhRI3NPkySefpLCwEL/fz09/+tMPJKHTTddIxilfsm9k1ysvYnY4yF84F6PVSthr5MjIZq1bfXQeDFM0PUy6yw/9ahYGs6JkVphZMxuwWKM07EmjfrOTnPIltFbvp722kngsiqet53RvnqaNGd///vcxmUzcdNNNALzzzjsYjUYaGxuprq7mxz/+MVVVVSmNUddIxqFIKEjI76PtcDVNlRVMPO9sjBYzKCfxsAJ/gN5KL/XvGMjIj1EwJXFvdoNRYbJAOJC4CY94PNiee5b0rVvJnjSZqos/S9MhB/6OxZise9j7xnOs+tg/09vZRfaEbExmPXSKdmYbbs3hVPvTn/7EM888wyuvvHL05lf/93//x9q1azGbzeTl5XH22WezefNmJk+enLI4dY1kHDpyV8Odr7yAJVkbUVEzyhOBxhbChzupeseAzaEomxdGBBCwuRRWh8KRFsG6fh2u//4vzDt2EJ0yBXN1FcWmWqYsbsVdLIhpNd7OVvZv2EQkFMTXE0jtRmvaKPPCCy9w991389RTT+FwOI5OLy0t5dVXX02cnu/zsWnTJmbOnJnCSHUiGXfCwQDhQCBRGzlYQfHyxYAJ1eKDtk7igQiHtlqIx2HK4hDG5EgnNmccoxHYexDT936G7alniU+ZhPfLX8H3qVuJOxxY163DmW6nsLyb0vMmYLJOoGb7azRWduNp69Kd7pp2DDfeeCMrV66koqKCkpISfv/73/P5z3+e3t5eLrroIhYsWMAdd9wBwD//8z/j9XqZM2cOS5cu5VOf+hTz5s1Lafy6aWucea828iIWh5OcubOI9sSxxwWloHaPBX+PkSmLQtjSEl/8ZpvC7O1Cfv8ssmUXKjeL+L/eQmjuZDqCPTR5a8hZVsbU1/fwbMNfCWS6uSz7SqatXc2+J/+PAxtfpbQ8j5A/is2px+DStP4eeuihD0y77bbbBiyblpbGI488MtIhDYlOJONIyO8nEgzSVltD08H9TD//fCJBI9Zk53p7nYmOehMFUyLY8wM0x3rwRNvJeu1dJv5jDwp464JcnlthppW/46t6bxgU9zzFr9ZD6fq9/PIyxVTfFGZkz8FdMAdP8w46my4hs9CHzZmRkm3XNG3k6EQyjni7ErWRXa+8gNXhxDV1OvG4gd2BXRxq7aB0zwW0Zx7iL3m/w9vtZ9HBOLf8I05BN2yaITx2URqSYyfL5GaaaRLZpgyyTelkm9xkm9KRs9axesNmnlnt4jXjBmao2eTPm4mneRcH391NXlkhGQUu3emuaWOMTiTjRCQYJBoK0V5bQ+OB/cy68GJicSGuwvyl4xmu2nMnAauHqpnrON87lfNerKP4QBvB/Aza//ViFsydxzLDAM1SZhMU5kFzO1x2Lrz5Dp/ekc23zq6mPlhHcfEEjGY37Yd3EvSuJOiNkJapE4mmjSU6kYwTIb8PSPSNWB1OsmbPwuuPsbNnG2sO3Iwz5qJ8kZeL3s7E+vo6MJuIf+RyLBecRZbpGH8m7jTIzwGjEbLSIRyGJXOZ/m4F2UusvBZ8k4/bbyZj4gw6KjdTv7+V9Pw8nBnWo6cyapo2+umztsaJkN9Pe91hGg/sY+aqcwmEolhMZtr22insncLU9Eryf3M3tldfIbpwPur7X4FLVsMAScQbjkFBHhTlJ5IIQLoLTEbU2nORQIjP7C9gW2g3HlMn2XMmA4qaHTsJ9PYS8kdP78ZrmjaidCIZB2LRCNFwKHGmlt1B0cKFxGLQcMDDhMaFmMzbKX385yi7Hf8//xOGz34UMgYYu0dBR0xoycql22J7/zwRyEiHshJU+VQWbGjBFjPwuncdjpwcLM5cetv30NPSi79H36tE08aSlCYSEblfRFpFZPcx5t8kIjuTj7dEZP7pjnEsSNRGamms2MusZUvwdtSgvFHatztpcB9g+Y4niRaX4L3zTszzJiID/FUoBS1mO13ZuSizmS5fmHg8Mc9isJBlzaK4pJyJ6ZNIu+pKDD1ePnWohDd7thA0B8icPhUVa6Z6ZwO+bg/RSOz07gRNO4PV1dVx3nnnUV5ezuzZs/n5z38OwHe+8x2Ki4tZsGABCxYs4Lnnnjv6np07d7Jy5Upmz57N3LlzCQZT9wMt1X0kfwTuAR44xvxq4FylVJeIXArcByw/TbGNGSG/j92vvYTF7mDKnKlUd3XRXWmHuA1lfwFrayv+665JXHRo+mAWiRmMNDvcBJI3vDKJCbvRiZUMJmVkYza+1wkfyQ6TuXgZvtJizl7fxb3TorzZs45zp59Ny7aNNFbsIHDuVILebN3prmlJJpOJH//4xyxatIje3l4WL17MRRddBMAXv/hFvvKVr7yvfDQa5eabb+bPf/4z8+fPp6OjA7M5dddopbRGopR6A+g8zvy3lFJdyZebgJLTEtgYouJxvF2dNFTsZerCRfhiYQwmO611FurTK7hoRw9xmxVmF2EO1kFvEwS6IRICBRGHg6aMfAyObHJs+ZQ4J1HqmkquvZBw2A68PxkYs7MxGc1Yr1iLuaWTG+sm8JpnI8puxJ5dQsS/j8bKHvyeACqur3TXNIDCwkIWLVoEgMvlory8nIaGhmOWf+mll5g3bx7z5ycaabKzszEaU/fDLNU1kqG4DXg+1UGMNqGAn8aKvah4nJIppXj8IYJtaaiQjaa8dyk40Epk+QKsruSXejSMIRrBZgphzCvCY8lkgjmbmMUFhsSfSyQWx2RIDMDV4glSkvneOEAGiwWj203OOedR/7fHuPitAA9OCPB2cBOzyqdRv/41anZWM2l+IaFAmr7SXTuzPH8XNO86tcssmAuX/mjQxWtqati2bRvLly9nw4YN3HPPPTzwwAMsWbKEH//4x2RmZnLgwAFEhEsuuYS2tjZuuOEGvvrVr57auIdgVHS2i8h5JBLJ145T5nYR2Swim9va2k5fcGe4sN9P/d49WB1O3Jk2wgYzrVVmgiYfq2vqkHgcwznl2E0Wsixuimw5TMqaSM7kWYQNbqwRP2ZvHbbOvVi7DrLrYBU3/34TD75dC0C3P0KwX3+HKScHs9mGZe2F2KububStiFd9b5FWUgxipLtpN13N3QR6w6nYJZp2xvJ6vVx33XX87Gc/w+1287nPfY5Dhw6xfft2CgsL+fKXvwwkmrbWr1/Pgw8+yPr163n88cd55ZVXUhb3GV8jEZF5wO+AS5VSHccqp5S6j0QfCkuWLNFtJkmBXg+NFXspmTmTnkAIiVroaXNwMO91PvdsF/FppbiKCsi3ZQJgykzH53TT7g3Rfye+Ue3h7k0BFPDo1joumRClIDub5i4oy0s/Ws5gt2NwOsi6aC3NTzzLtW8Lz1/Zy47oTnJLyvDUV1C3t4e8iX5c2TZ9pbt25hhCzeFUi0QiXHfdddx0001ce+21AOTn5x+d/5nPfIYrrrgCgJKSEs4991xycnIAuOyyy9i6dSsXXHDB6Q+cM7xGIiKlwGPAx5VSB1Idz2gTCQZprjpIOBigZFIpPgW+fR5EGUgPbMPiDcCq2bhNDsRowlJSiMfhom2AJPLUwTDffyvAjCwj917ixGSA+99tw+ytJdK4E1/jXuhthkjizBFTTg52ZzrGC1eTvruW5T05vBraQObUKaAC1O09SKC3l0Cvvqe7pimluO222ygvL+dLX/rS0elNTU1Hnz/++OPMmTMHgEsuuYSdO3fi9/uJRqO8/vrrzJo167THfURKayQi8hCwBsgRkXrg24AZQCl1L/DvQDbwq+SV0FGl1JLURDv6hPw+6vfuxmA0kpGXTqCrisraAlqcNVy19SDGNCN5rgrSOowYpy+jLRynN/z+ZiqlFA/sDvGXPWFWFJn45ll2rCbhhnIrf9wVYkdLlPn5Jjo7u3ASAl8b5JZjdLkwWC1kXHYFHc+9ws2bHfzLBbUcTu/AYLYS8u2l8eB83Lk5pGVYEYO+0l0bvzZs2MCf//xn5s6dy4IFCwD4wQ9+wEMPPcT27dsREcrKyvjNb34DQGZmJl/60pdYunQpIsJll13G5ZdfnrL4U5pIlFI3nmD+p4FPn6Zwxpygz0f9vj0UTJpMQART1SE80WU0ZT1EVr0B12JFVtsmpHU97LuPPKON9PRJhNKnEMqYjN89hZ8ezOWpKrhkkpkvLrVhTH7hXz/DwnOHwty7Pcg9FzkJRuP0BqO4bICnATInYszJwR0K0bl6OXmvbWT6ygzWGTZybdl8OisPUru3i0nz/YQCdt3pro1rq1atGvB+PZdddtkx33PzzTdz8803j2RYg3bG95FoJycWjdLZUIu3s53yJQvwRyJ4mwqIGkIsq96PMhrovOIT2LJLCIofCTRg7a7E1nMId90rGKqfAeC/lYmvuktxWaYSqplCKGMKIXcZVpONT8+38YONAV6uibB2soV2X4g0qwkJdII9E2NGBtHWVtxXXEHPq29x244svrayGn/RUjgYpaO2gu7WEpwZLp1ING0U04lkjAr5fdTvSwwY4M7LxNi6n22BFVRnbePWDd2ouVMwuzLoDBuJFc9AZCa9pYmOOl84xm9er8LYVcXNhXXMNRzG1rSJ9MMvAaAwEHaVcEP6ZMQ9gXd2TmRNwWxsDhfdgQiZDjP01CO5MzFlZZEZmYxn2XzKNu6hYJGD1507WOVwEQvv4/CuReRMKCAaielOd00bpXQiGaMSiWQPWYWFRC0WwpW9xJUdh3cT5lCU0IpZxIJGbFnO943E2xWM843XA1R35/OV5RPJLrPQCKAUpkAbtp4qsoKHibZUYG/fxWfC6/gMwEsQdhQQzppO7Jx/wejKBW8Lxqw8DG1tOK+8HN+mbdy+byLfXVDNmtLziOyvpq6indnn9hLoteHK0olE00YjnUjGIBWP42lro622htkrlxEO+2nomEaPrYWLttURy8+iOy+HQoMtMRR8UpM3zl3rfHQGFN89x86yoj7NTSIoZz4ZxROxmo2Eg1FqPEGMoW6e2LiPeHsln0yrJ7vpbSJvhDFe/iPwtiD2DIyZmWROn4N3znRmbWjANdfMjrxGpu9XhDwVNOyfgDM9Q3e6a9oodUaf/qudnHAwQMP+3aAU7vwcbHWHaI3MpNW2kYKWIN7FM3EYHYjDjiSHia/sivGFf/joDcPd5znen0QAk0EozrRjTzY/uWwmbGYjMWsGK5Yt57fqav6NL9Ax8yasDZuIVr8FKOipx5Sdjclgwn7FpRg8Pm47WMKmtAOYM9KJR/dTs7ebaDiih5fXtFFKJ5IxKJQ8W8vhcqGcaXQdtqKIMffQZuIWM4G5U3AaHZCeGCp+R0uUL7/qw2SAn17gYFbO+yuqZqOB4kw71n4DOua5rAiQ6zDwkZkW1tVG2eC+jJCrFN76BURDEPYikV6M6elkLliKmljM8g0dGOLQVBghHmmms66d7pYuAl59pbumjUY6kYxB/p5umg7up2BSGcrbQ3XvPOrdu1m2txvfwtmo3BmonBlE8meyrs3N198IkOMw85O1+ZRmpYGYgUQTk9WUSCIW4wf/VKwmA257ouby4XIrOXbh1zuitMy7A5OvmejWBxMFPQ2YMtxYTTbMl1+MsbWTmw9P4I3CQwDEwvs5uL2ZSChGNKyHl9fGp7KysqPXkSxZkrhc7pFHHmH27NkYDAY2b958tOzLL7/M4sWLmTt3LosXL+bVV19NVdiA7iMZcyKhII0H9xMNh3Hn5yA1bYTis7B7NmKKKXrPXkGaJQOVXcALB/38al090/Jc/PsVs3DbzYT6LMtujFOUacZEDGJRiEcgFkn+H4VYmOw08Aaj2E1w6zwr//V2kGe8M7m55FxcOx+CGRdDegmGcEdi2JRV59Ly96e4YKOPP94YIpRtxe7ZR+OBFUQuCBLwWnSnuzZuvfbaa0eHPQGYM2cOjz32GJ/97GffVy4nJ4enn36aoqIidu/ezSWXXHLc0YJHmq6RjDEhn4+GfXswmc2Q5qalJZeguYvzt+0nOLGIWFERNpODvx7s5Z7XKllYmsl/fmjO0ZrFEU6rkUn5GZhsaWBLB2c2uAogYwJkTYbc6VAwB2PxQjImLSSUMY1z5k1jeo6V+3eGqJ95K3GDiej6XyTuihXsxuSy4rCkYVx7PtbDLVzVVMyOolbikR4i3hYO7asn6Ivo4eU1Lam8vJwZM2Z8YPrChQspKioCYPbs2QSDQUKh0AfKnS66RjLGJK5m3012SQnB1g6agktod7xETk+E9suWYDE4+G1VlGcq6zhvRi7/ev40TP2ardx2ExMyHRgGeQZVlttJZzBOIGzntnNn8LVHd/JQtZN/nXkzubt/C4fXQ9k5GGNdGCxmMs6/gI7Hn+PqdxR3XN7D0j0ZxGP7OLyrkJkLFaFAVF+gqKXE3e/czf7O/ad0mTOzZvK1ZcccuPwoEeHiiy9GRPjsZz/L7bffPqjlP/rooyxcuBCr1TrcUE+arpGMIbFolNaaQ/g9PRgzspBmBRgor9xE1GmnZ/Y8flth4plKDx9aUMydF07/QBLJcJgpzRp8EjmiKMMOwKxCN+dMyeRv+8McLLiMkLuM+Ib/hUgAYmGMtijutGzkwnNw7atjeXcOjXlB4uEKehqitLd1EA7os7e08WfDhg1s3bqV559/nl/+8pe88cYbJ3zPnj17+NrXvnZ0DK5U0TWSMSTk91G9K3FTHoPTTWvdBDocFZx3oI3O1cv5VaWbvd1RPnVWGdcu+uDNJrPSLBQnE8JQOSwmMhxmuv0Rbjl7CpuqN/P7XVEmzLuDCevvQm19EFn+aYzGEFEMuC9ZS89zr3LDFgt3L+ykuNlKPFJHxVYHufk5KKXed6Gkpp0Og6k5jJQjTVV5eXlcc801vPPOO6xevfqY5evr67nmmmt44IEHmDJlyukKc0C6RjKGNLV2UbdvN86cPGyeKL5YDvaejSDwP1nnsb/HwBfOKhkwieS5rSedRI4oSLdhMECe28aHFhTxyuEI26Ucz4TzYdfD0F2LCJhMQdKzC5DVy8ndUYfbaiVsVojspW1/CF/ITzioz97Sxg+fz0dvb+/R5y+99NLRIeMH0t3dzeWXX84Pf/hDzj777NMV5jHpRDJGNHT6OFxdi6+1EVt2NtHONGIGH+ds28GWonL2GLL5+gIXFy6c+IH3FqTbyHfbhh2D2Wggz5VYzvVLSsm0G/n11iBts24hbrQS35DoeDc6TZjCPhyXXQoCn9zmorrAS9hXSdgXo7qiiZBP36dEGz9aWlpYtWoV8+fPZ9myZVx++eWsXbuWxx9/nJKSEjZu3Mjll1/OJZdcAsA999xDZWUl3/ve91iwYAELFiygtbU1ZfHrpq1RTilFXWeA9k4P3VWJTkKLLZ3W1ql0m98i3R/m2UVn87V5sHxGIfRrLirOtJPltJyyeHLSLHT5w4CJj6+YxC9eq+SVVhcfKr+ZvJ2/gerXkclrMJpDZBVOwLdsARO37ML/kXSoiyHUU7/DwtRZXlzZNt28pY0LkydPZseOHR+Yfs0113DNNdd8YPo3v/lNvvnNb56O0AZF10hGMaUUVe0+egIRogEfXVX7sTjTsPgcxDEzs/ItmlyZXHR+IQuyXZCeefS9IlCa5TilSSSxXDna8X5+eT5Tsm38bkeQ1gmXEkyfgnrrHoj4MaWnYQp0YrvsYiQc4dKWDKKGOFHzPnrr47R1dxDRzVuaNiroRDKK+cIx/KHEl23I001P7SHsWTl4PEUEzLXMra4nvmwOE91WrO5sMCdOqRWBidkO0h0jc4ptmtVEut2M0SDctnoarX7F3w/EaJt/B+Jvhy0PIGYTRosis3QiatIE5u3ooi07gt97EBWHxoPd9PR6RyQ+TdNOLZ1IRjFPINGPEAuH6K4+gIrHaGACgUge1p63iJoMqLMW4DClQUYWAAYDTMpx4rKN7HUaBek2RGBucTpnTcrg4X0hGuwz6Jl4MWrXI9BVgykrA1vIg+ncszC1dlBgScMSiKJMbXQdDNHS1T7gXeM0TTuz6EQyinmCiUQSDfrpPLSPuNFCPFyMkjArdm7GN2sycXcWDnsWOJ0YDcLknDSc1pHvGrOYDOS5EhdI3bJqCtE4/GFniI5ZnyRussP6n2GwmDHaTGQsmYuyWljemEga3cZ36G2I0ePx4PX7RzxWTdOGJ6WJRETuF5FWEdl9jPkiIr8QkUoR2Skii053jGeqQDhGJJr44g16e2mu3E+lbSIFkSyCbCMtGCB41mKsRgfGrGzMJmFyrhO75fSNY5XrsmIxGShMt3PVvCJeqo6w35dG+6xPQtN2OPQqxsx0XEaQZfPJ3nOIiNOAP1iBikN3TYSWzvbTFq+maScn1TWSPwJrjzP/UmBa8nE78OvTENOocKQ2Eg6HeeAfOzBFAuQ58ogrG9MOvUVPYTrhiZNwmN1YsjKZnJOG7TTfylZEKEhPnA78kaWluG1Gfr0tSM/EiwhlTkNt+hVGs8Jgs+JauQCJRCkROxk9irC5m87KEN2eXt28pWlnuJQmEqXUG0DncYpcDTygEjYBGSJSeHqiO7N5AhGCkRj/+ew+vDUVKBEmSyFxQwvTaiuJLpmPmJ1k5BYwpSAdiyk1hzrdbibNZsJpNXHTijJ2tcVY36Bomfc58HfClj9izHCRWTYBVZTHhLo2jEposLxOb12EUCBCj683JbFr2uly6623kpeX976LEDs7O7nooouYNm0aF110EV1dXcDghpC/6qqrjntB46mW6hrJiRQDdX1e1yenfYCI3C4im0Vkc1tb22kJLlVC0RjBSJxfvHqQ7Y29LIwdxubKwh8pxdqziZDNSGDRPDLtLiZNnfCB8bROt8Jkx/vFswqYmGXjvu1Bet3T6J20FrX7UYyRVoxGE7az5pNT24TBaCAaOYSKC901YTq7e1Iav6aNtFtuuYUXXnjhfdN+9KMfccEFF3Dw4EEuuOACfvSjHwHvDSG/a9cu/vSnP/Hxj3/8fe977LHHSEtL43Q60xPJQFejDdjOoZS6Tym1RCm1JDc3d4TDSi1PIIovFGXjoQ6uKIhg8HZiNpUAMRbt2UT3vMlY3BlMLynFnOZMdbjYzEZy0qyJ04FXTaHZp3j8QJi28k+gLGnIWz/HmOYge+USxGwiJy7kd4PP3E3HwQBdvZ5Ub4KmjajVq1eTlZX1vmlPPvkkn/zkJwH45Cc/yRNPPAEcfwh5r9fLT37yk9N+seKZfmV7PTChz+sSoDFFsZwxPMEI79Z0Eo0rZoUP4wdQMyG2F2fQQ2TVleRm5+DIK0h1qEfluax0+cMsLM1k6cQM/m9PNxdPSiOt/Bbyt/8CY8c7WJyzMMydSkFdM61F2dQ63sJRt5agL4zH58XtPL2/srTxp/kHPyC079QOI28tn0nBN74x5Pe1tLRQWJhoyS8sLBxwCJT+Q8h/61vf4stf/jIOh2N4QQ/RmV4jeQr4RPLsrRVAj1KqKdVBpVIkFscfirHhUDtZdhPGxgpMNhdRiik9vIXmyZm4p0wi3Z6FMT091eEeZTAIhcmO91tXTSYUgz/tCuGZeCGR7HIM236PgQgZq1eQ25mogZhjdUjcQFd1kI7u7hRGr2lnnv5DyG/fvp3KysoBh1QZaSmtkYjIQ8AaIEdE6oFvA2YApdS9wHPAZUAl4Ac+lZpIzxy9wSiBcIyth7u5sMRE7746HO7pxAlT1rCL4E2rMFhduPOKEcOZ9Tshw2GhwxemJNPB5fMKeWZnE1dNs2Cb+1lKXv8S5rqncM+4lo5MN+mRKHgUPms3hyu8FM9JP0bvmKadOidTcxgp+fn5NDU1UVhYSFNTE3l5eUfnDTSE/MaNG9myZQtlZWVEo1FaW1tZs2YN69atG/FYU33W1o1KqUKllFkpVaKU+r1S6t5kEiF5ttY/K6WmKKXmKqU2pzLeM4EnEGHz4U7CsThzYnWgFErNxObbg88ZwbFgLmnWdMzZOSdeWAoUZ9gRgRuXTsRpMXLvtiCB9Cn4p1yOVD2PwVuHbfl88to90OOnIX078UY7fl8IX0BfnKiNH1dddRV/+tOfAPjTn/7E1VdfDRx7CPnPfe5zNDY2UlNTw/r165k+ffppSSIwhEQiIlmDeGSMYKzjXiyu8IaivHWog3SbCXvzAcRoJm6YxNSaLXgWTwG7m/SsAgyWUzsY46liMxvJdFpIs5n42PKJbGuJsakxSvP0m8DqxnLoQTJXLibXFwDAQT2GuJHOmiAd+uwtbYy68cYbWblyJRUVFZSUlPD73/+eu+66i5dffplp06bx8ssvc9dddwFn3hDyMLSmrcbk43jjehuB0mFFpB2TNxglGImx+XAn55Sm0fNmJVZ7IUiY7I7dxBZdg9WWgTP3zL7UpsBto8cfYe3sAp7d2chvtodYstZJ55xbyd78E5x5u0mfVIw1EiOvO4DP3EN9hZ/SuZmUFp7Z26ZpJ+Ohhx4acPorr7zygWmDGUK+rKyM3bsHHDBkRAylaWufUmqyUmrSsR5Ax0gFqkFPIMLW2m6CkTgLTW3EQkEU07D4duJ3g2niRFxp2Rjd7lSHelxGQ+KKd5PRwG3nTKahN87TlWE6i88jmjcHS/WjuJbOIdfjQ9q9HM7cQbTBitcbIBAIpjp8TdP6GUoiWXmKymgnQSlFbyjCW5XtuGwm3C37EjOM05las4XorEkYrG4y8kZHhTDLacFuMbBkYhaLJqTz591hesLJK96jPnLSdpKrFDGlsBoPY4gb6a4J0dHTnerQNU3rZ9CJRCn1vp+CIuIUEePxyminjjcUJRSJ805NJ0tLXPTUHMBszUYZ4uS17yN9/hwcjmws2dmpDnXQjtwA69ZVk/FHFQ/sDuFPm0ho2lXY2t6ieGoeEleUtnrxmz3UV3TR5dEXJ2ramWYone0GEfmYiDwrIq3AfqBJRPaIyH+LyLSRC1PrCUTYXteNPxxjSXqYYFcHGKZiCO4gahWYOZWMnGLEdKZfY/oeh8VEhsPMxGwna2cX8ExlhMM9MZqmfwys6Uwo3EeWL4ClPUB11k7C9UZ6e/0EQ+FUh65pWh9Dadp6DZgCfB0oUEpNUErlAecAm4AficjNIxCjRuL6kbcOteO0GMltSXSiiWk606s3E585EbMzG1fe6LvQoiDdhsEAH1s+EbvZwG+2B4maHHhmfwoHDRRaFAHAYKnCEDfRXROiq0efvaVpZ5KhJJILge8DVyil4kcmKqU6lVKPKqWuA/56qgPUwBeKEgzH2FTVyZLSdLqr92Mw2omaLRS1HsSyYCbujEIMztSPqzVUZqOBPJeNdLuZG5ZN5N2mGO80RmgtOY+Iezqz8g4DMOtwJ36zh8b9nXTqRKJpZ5Sh9JFEkgnkwuOVOSVRae/jCUbY2dCDNxRlSZ4Jb3M9YpoMke0gCpk7m/TcklSHedJy0ixYzQYun1tIUbqV32wPEUXomHkrxQVdOMMRbG1hqrN2Emgw0uPxEQlHUx22pp0ydXV1nHfeeZSXlzN79mx+/vOfA8ceSv6I2tpa0tLS+J//+Z+j0x566CHmzp3LvHnzWLt2Le3tI39zuJO5sn2biHxbRM6s8TfGME8gcRGi3WyktOsA8WgUg2kq02u2oKaU4Mguxpo5ejrZ+xMRijLsmI0Gbl01mVpPnGcPRfDkTMebt5pSUxc9JgNmqcQQN9FT7dNnb2ljislk4sc//jH79u1j06ZN/PKXv2Tv3r3HHEr+iC9+8YtceumlR19Ho1G+8IUv8Nprr7Fz507mzZvHPffcM+Lxn0wymADcADSKyJMi8j0R+fApjktLCkZiBMIxNlV1sLg0nZ5DewADYbuLSfVVyPzpuNPzz9gr2QcrzWoi3W5mWVkW84rT+dOuEF7MtBReydQiL3GDgUUHmwmYemna16nP3tLGlMLCQhYtStxJ3OVyUV5eTkNDwzGHkgd44oknmDx5MrNnzz46TSmFUgqfz4dSCo/Hc3TI+ZE05FN8lFIfARARKzAbmAssBx45taFpkBhba29jDz2BCMuLnfRsrMZgKiEc24WgkEULcGWNjau9C9JteIIRPn3OZO786zYe3BPittJc3DNXY2o8jL0jRM3kHdiaVtDd1UM0EsN0mm8frI1tb/7tAO113lO6zJwJaZzzkemDLl9TU8O2bdtYvnz5MYeS9/l83H333bz88svva9Yym838+te/Zu7cuTidTqZNm8Yvf/nLU7o9AxnK6b/vGxpFKRVSSm1VSv1JKfWVgcpow+cJRthwqAOLycCUUCNhXy8G82Sm1G4hXpxLeul0jBlnznDxw2ExGchzWZmU4+Si8nyeOBCm2eSm3T6XIluINrudTP9eJG6iu7KbTo/udNfGFq/Xy3XXXcfPfvYz3McZoeLb3/42X/ziFz9wJ8RIJMKvf/1rtm3bRmNjI/PmzeOHP/zhSIc9pBrJayLyKPCkUqr2yEQRsQCrgE+SOEX4j6c0wnEsHI3jC8XYeKiDxaWZeA+8BkDIkUF51WG49GzcrlwMyZvajAW5Litd/gg3rZjIGwfb+O3OMF8rcpE1dSa1e2tZsfcg+6Z4aa0Qupb1kJeddeKFatogDaXmcKpFIhGuu+46brrpJq699lrg2EPJv/322/z973/nq1/9Kt3d3RgMBmw2G8uXLwc4OrT8Rz7ykQ/0q4yEofSRrAViwEMi0igie0WkCjgI3Aj8VCn1xxGIcdzyBCPsb+6l0x9meUka3bVViCGToOEABsC6dOmo7mQfiEhiHK5Mh4WPLCllY0OU3SoTe95kAOI+C41pO+htsdLV1kosFj/BEjXtzKeU4rbbbqO8vJwvfelLR6cfayj5N998k5qaGmpqarjzzjv5xje+wec//3mKi4vZu3cvbW1tALz88suUl5ePePxDGiJFKfUrpdTZwEQSpwHfq5SaqJT6jFJq+0gFOV55AomxtUwGYZapB29HCwbzZEobthDPSMM9c/4ZdRfEUyXdbsZlM3HV/CLy3VZ+f9CEwebA5bTT5nZQ2rYNiZvo2t9JT09vqsPVtGHbsGEDf/7zn3n11VePDg3/3HPPHXMo+WMpKiri29/+NqtXr2bevHls376db5yGm3Wd1HgayetFGkWk7NSGox0RjcXxhaK8VdXBotJMgpXbUSpO2OFm0dYmDGctxp2WNaaatfoqzLDhDUX51FmT+NEL+3ktK4ep+YXUev2cvauC9cu8tFcpOro6yMoae8lUG19WrVqFUmrAeQMNJd/Xd77znfe9vuOOO7jjjjtOVWiDMtxrQdaKyH0icoeILE2eyaWdAr3BKAdavLT1hlg+0U1n9UHAQpe9HnNUYV+2HGN6RqrDHDFWk5GcNCtnTclmdqGbhxucOLLyQASvwUGvaQc9bXY6G+uI6+YtTUup4SaSF4Gvkbin+vnA/UN5s4isFZEKEakUkQ/U2UQkXUSeFpEdycEhx8092z3BCG8dasdoEObbw/Q01WEwT6S4eStxmxn3giUY08/s+44MV57Litlk4NPnTMYThheZgtlspi3TwZS6rYnmrYpOenpP7emamqYNzUklkuRIwCZgk1KqSyn1D6XU3Uqpm4awDCPwS+BSYBZwo4jM6lfsn4G9Sqn5wBrgx8mzxMa0eFwl+kcOdTC/JJ14/T6ikQBRp5tlFW0YZk/H4c7CYLOlOtQRZTAIhek2pualcf7MPJ7rdGHLyqXNncb8fRWEjD7aa4XOtoZUh6pp49qQE4mIfB5oAQ4DXxKRT5/kupcBlUqpKqVUGHgYuLpfGQW4ktenpAGdwJgfZKk3FKWqzUdTT5CVZVl0VFQA0JzWhsuvsC5dMqabtfrKcFhwWI3ctHwiMSVUOycRQfDarcSiO+jpcNBVU42KD9y+rGnayDuZGsmXgblKqWISpwSfLSLfOYnlFAN1fV7XJ6f1dQ9QTuJe8buAL/QdeXisOlIbMQgsckXpqq9BjPnkdO5AGYS0JcvGfLNWX8UZdvLcVhZPcPOyTAcRWgvdlFdthZiJ9oO9+DzdqQ5T08atk0kkXqAVQCnVBNwGXHsSyxnoKvj+PysvAbYDRcAC4B4RGfAbVERuF5HNIrL5yDnUo5FSit5glA2H2plTnI65o5aAvwPlSGfpwS6YVoYrr2TMN2v1ZTMbyXRaWDunkPa4DXFl05yezqT6CqLio6PJSnv9oVSHqWnj1skkkl8Dj4jI1OTrUsB/EsupJzEA5BElJGoefX0KeEwlVALVwMyBFqaUuk8ptUQptSQ3N/ckwjkz+MIxqtt91HcFWDExk/Z9iXuzN2Z0U9yusCxZhGmcNGv1VeC2sXxKLll2I5XOyfijcXwOA1b/Dro7HXRWV8MxTp/UtNEgFouxcOFCrrjiCuDYQ8iHw2E+9alPMXfuXObPn8+6deuOLiMcDnP77bczffp0Zs6cyaOPPnpaYh9yIlFK/Qp4EPidiHSSOGOrQkQ+PMTb7b4LTBORSckO9BuAp/qVqQUuABCRfGAGUDXUmEcTTyDChsp2BFiaCR3VlSAOrL69AKQtXY7R7UptkClgNCSueD9/aiYbDYmr3FunFlFeuQ1iJlprIvg7m1IcpaadvJ///Ofvuwr9WEPI//a3vwVg165dvPzyy3z5y18mHk+0+H//+98nLy+PAwcOsHfvXs4999zTEvtJnbWllHpMKbUGyAMWAa8CZwG/GcIyosDnSZxCvA/4m1JqT/KalCNX03wPOEtEdgGvAF9TSo38XVpS6Mhpv+WFbtK87fR6WjHYM1h8yEOsKA/XpKkY7PZUh5kSmQ4zl8wpoNucQdSaRpMrnZzOChQButvsdFTtT3WImnZS6uvrefbZZ/n0p987d+lYQ8jv3buXCy64AIC8vDwyMjLYvHkzAPfffz9f//rXATAYDOTk5JyW+E/qyvY+QkopI7AT+NNQ36yUeg54rt+0e/s8bwQuHmaMo0YgHKOmzU9Nh5/bVpTSuf8tlArTmhXg4k0K0xULsGSM30EKTUYDM0pymFdgp7K7jHLPHrrzzbi799FlLqezvoEJCwJgHp+JVhu+1/54H62HT22jR97EyZx3y+3HLXPnnXfyX//1X/T2vjfkz7GGkJ8/fz5PPvkkN9xwA3V1dWzZsoW6ujqmT08MOPmtb32LdevWMWXKFO655x7y8/NP6fYMZLgXJAocHQFYG6YjtRGA5blG2g5WAAb88QoMChxLl2I8ztDS40Gm08JF0zLYbytDxRVtM6ZT0rSLeMROR4si2FKT6hA1bUieeeYZ8vLyWLx48aDK33rrrZSUlLBkyRLuvPNOzjrrLEwmE9FolPr6es4++2y2bt3KypUr+cpXvjLC0ScMt0ZypHfzMRG5TynVv49DG4Ijp/3OyHeRFe5hb1cbBms6C6sqiaU7SZ8zf9w2ax3hspk5e3o+979dQqzVRKfNRn5gL6g4njYjHdUHKC6aDgZ9wytt6E5UcxgJGzZs4KmnnuK5554jGAzi8Xi4+eabjzmEvMlk4qc//enR95911llMmzaN7OxsHA4H11xzDQAf/vCH+f3vf39atuFkLkj82gCTrwZKReRBEUndgP6jWCgao6bDT2WblxVlGXgOVBGLddGdFWVhlcK0cD727LxUh3lGKMzJ4JwyFzW2CfR09tI8w4HbU0NXm9DT1oXyjuluNG2M+eEPf0h9fT01NTU8/PDDnH/++fzlL3855hDyfr8fn88HJIaJN5lMzJo1CxHhyiuvPHoW1yuvvMKsWf0HCxkZJ6yRiMjf+r4kcT3H3X3LKKViJK7xeBD4hoiElVL/71QGOtZ5AlE2Jpu1VuYZaVqXOO231VyFNQL2JYvHfbPWEVluB+dPy+A3Wycypb2aYPlsst/aRXX61XR1HSLccAire+TbhTVtJN1111185CMf4fe//z2lpaU88kjibuatra1ccsklGAwGiouL+fOf/3z0PXfffTcf//jHufPOO8nNzeUPf/jDaYl1ME1bHqXU0VMJROTX/QuIyBXAHBJXoVuB4CmLcJzwBCNsqOxgSq6T/JiPAx0dGIw2ZtT1ErOYSF+6fNw3ax1hMRmYXpyNrWQatK8jFIjSnXYIuJpQQxedDXUUTvaCNe2Ey9K0M8maNWtYs2YNANnZ2QMOIV9WVkZFctik/iZOnMgbb7wxkiEOaDBNW9/v97pvTePI1emZwPPAbUqpG5RSt5yC2MaNaCxObYefipZeVk7KxFtZQyTSRCDTwLJKMMydiTO//+gx41tedgarpufRYsmlvd1Hyyw71mAnbQ1WenoDxNpqT7wQTdNOiRMmEqVUNYCIbE2+7uwzz5D8/89KqR3AOyMU55jmCUZ561AHAGcXmGjdux+IUu9qItOrsC/WzVr9ZaU7WT4hjSZXGXh7SM+ahM2/i041nVBXPdGmWoiN+fE9Ne2MMJSztspFZOdx5gugb1V3EhJna7UzMcvBBFOQN9q7QIwUtnaiRHCvPBuDw5HqMM8oIkJ+Tjq5U2YgHe8S7VA05x8kPXIu0d01eCZMIcfTgmTqmpymjbShJJIBx7jqJ3aygYxXsbiirtPP3kYPNy4pJl69j0CoBZVmZ+mBOPGpE3GVTT3xgsahvOxMzpo7mb1b7Hg7gvSWQ+buEI3NBWT0dpPRVI1ZJxJtEJRSJO5WMfYd65a+wzHo03+VUoeBs5VSh4/zqD/lEY5x3mCUjVUdKODsQiOtuysg7qEps5eJrYmztUzpuqI3EJc7jUm5DnoyJ2HpaaVM5RNR+2mxzMdQ9Saxzg5UoDvVYWpnOJvNRkdHx4h8wZ5plFJ0dHRgO8Wjhw/1gsQ1wP8BiMh5SqnXks8XKaW2ntLIxonE2VrtFGfYmWTx83ZTYogEky9xq5a0s3Sz1rGICDkZbgqmzcSwcS++LjcNRZXMaJ1PcGsz/nk+zC2HMZZlpDpU7QxWUlJCfX09o/n2E0Nhs9koKSk5pcscaiLpW/e7EXgt+fwO4PRfEjrKKaWo6/Kzq6GH6xcUYG/aQXegF7E6WVQVJVKQRcbs+akO84yWk5XOogWz2LLxCZo6AsRn+qAVDvfMIb11N2kZGRhLZoLJmupQtTOU2Wxm0qRJqQ5jVBvqle0mEVmYfN43qYyPxsVTzBuKsvFQB3EF55SY6NxVQTzaRGeWYnatwrZoEeZxeO+RobCnpZGbkUYoawLO7iYKYzl4TYdpc89DNv6DmD9AvFsPL69pI2moiSQOOEXkRkBE5BMiUsgH72yoDYInGGVDZQf5bivTrF4O1QUBhT9ehTEOaStXYnA6Ux3mGc1gNJKd6aJo2kyyIl20eiZSlV+Bx12GZ0+IiL+dWGONvumVpo2goSaSbwGTSVyA+BaJm0wtAoZyQystqaHLz876bs6elEFm89s0+wCDhfI6PxGXnYzlZ6c6xFEhI93NtDmzAWht7cXo6gIx0KAWEt72HLGebpS/8wRL0TTtZA0pkSilGpVSDyilfqWUuh/oApzAnhGJbgzzhxPNWtG44pwJJnr37iMSqSeQaWdRlcI8fy627NNzU5rRzupwkl9UgErLIre3DpNk4jf10J47h9DGPahIiHjL4VSHqWlj1rDuR6KU2qOU+ptS6vOnKqDxwhNIXM2ek2ZlnqWdyloBFaLb2ogjBM6VK3Sz1iCZLBbS0+zkT5tJSbCB2t7Z1Gftoz17Fj01FmK1G4m2NkEkkOpQNW1MGu6NrbST1OwJsLW2i7PL3GQ2rqfG6wKEwpY2YmYjmavPT3WIo4rT5aJkxiyMKk5vazdhVztKbHSlTce37lXiwSDxjoZUh6lpY9KQEomIfFFELhERfbnwMAQjMTYc7CASU5wzwUz80Fb8oXZiaW6WVsZQs6fhKDy153mPdVaHgwlTpyJmKxN9tXRb3EQlQsvE+fTuCkBvPbHmwxDXgy9o2qk21BrJ74ArgCtF5FvDXbmIrBWRChGpFJG7jlFmjYhsF5E9IvL6cNd5JvAEI2w41E6Ww8xS22Eq6x2oeAfd7l5yPeBatgJjmm7WGgqzzY7b5SBr0lSmBA9zsGs2TemVNGbPI+wzEdzwNLEej77plaaNgKEmkmlAjVLqXqXU94azYhExAr8ELgVmATeKyKx+ZTKAXwFXKaVmAx8ezjrPFC2eEFsOd7GyzE1m7Wsc6C0CwNZTixLIuPDCFEc4+ogIVoeD4hmzsUX9SI+P7vRmJJ5JIKuQ3neqUREfseaaVIeqaWPOoBKJiNyUvIVuOuBPNnENdMvdoVgGVCqlqpRSYeBhErfs7etjwGNKqVoApVTrMNeZcpFYnA0H2wlF46wuNmKq3kBHIAwWJwurQoQnFeKaPJjxMbX+LA4nk2bPBoSpwcPUWxLjCR2etQpfo5n4vleItbdCyJvaQDVtjBlsjaSNRM3gu8DFQL5S6u7jv+WEioG6Pq/rk9P6mg5kisg6EdkiIp841sJE5HYR2Swim8/kMXMSQ8Z34LaZONu8l9r2HOLROrwZwtTmRLOWwanH1joZVocDV3o67sISyiOH2d81lQ5HA4fdM0CE3nWbiIdCxNvrTrwwTdMGbVCJRCn1EvC2Uuoc4BPAqbiH6UDDqvS//NgELAYuBy4BvpWsGQ0U431KqSVKqSW5ubmnILyR0e4N8W5NJyvLXGTVvcre3hlAjEi4GoD0Cy8eN8NZn2oGgxGzzU7RjFk4e1sxhww0p9dj8ucTm15Cz4E4tO0h2lynb3qlaafQUPpI3CKyGAiRuAhxuOqBCX1elwCNA5R5QSnlU0q1A28Ao3YUw1hcsb6ynUAkxuoisBx+nQa/FcTEnMO9BPPSSZ+/ONVhjmo2p5NJc+YAsDB+mCqTAQMG9s2+kHjEgP+154n1elGelhRHqmljx2D7SBYDXwbOBu4FXjwF634XmCYik0TEAtwAPNWvzJPAOSJiEhEHsBzYdwrWnRK9wQgbDnaQZjVxPu/Q2ptHOFRLxO1k7mGFfeUKTGmnorI3flkcTrKKSrCmuZkTq+eAv4SAyUuN5GLMsdCzrR0V7CDWVJ3qUDVtzBhsjWQ28N/ARBJf7v2/8IdMKRUFPk8iKe0D/qaU2iMid4jIHcky+4AXgJ0k7gf/O6XU7uGuO1XavSHerulgRWkaWQ2vsse/GJSXiGrCoCBz7aW6WWuYTGYzJouFopmzsLfXYo07aUivwdSdT3DpIkLdZqLvPke0qxOCPakOV9PGhMH2kTyglPoC8DWgl0RfxS+Gu3Kl1HNKqelKqSlKqe8np92rlLq3T5n/VkrNUkrNUUr9bLjrTJV4XLGhsgNfKMb5hUEs9Rup8iXG0ppW24Yvz0Xm4hUpjnJssDqdTJq7gHgkzLnmwxwwh7DE7FSULkEs4Fm/GxUKENPjb2naKTHUQRujSqlXlVJfV0r960gFNRZ5w1E2VLZjNxu5MPomvaF0fP5mlN3F3MNRLCuWYna5Ux3mmGB1OCmYOh1rmpsZ3koORXOJSYzqHgOGBaX01hqJV71FrLUBouFUh6tpo95JjbV1Cq4hGXc6vCE2VnWwvNRJZsNr7I+eh4o1oQy9GID8yz6km7VOEYvNjtFkYvKCxcSbDpNvdNCUVovqyaFnxbmgwPvqOmI+P6pH3/RK04ZrsJ3tf+vzeAT49AjHNaYopdh4qIPeYJS1uV2YWnawr3ciAMWNDfTkO8lcsjzFUY4tVoeTyYuWQjzOOVRyyNpLWiCbBkM65sluevYGoKeWqL7plaYN22BrJB6l1EeSjw8D/xjJoMYaXzjGmwfbsZoMXBh5lUjcSpenE4xW5tUEUcsXYEnTzVqnktXpJLOwiPSCIvI6Kqk2JM6GO9AVJXTOcmJBI8HXnybW1anH39K0YRpsIvm+iPQdt+P/jUQwY1WXL8zGqg6WFjvIrH+VKvPlxCKHEbNgBCZcMSaGEDujWO2J0QGmLFpKpK2V6RYzXbY2gt3p9E6cgTHdSM87taiwj2jDoRRHq2mj22DP2qoGnhOR+0WkVCml71s6BG9Xd9Dtj3BNVg3GnsPs9swGFSK3rY6OAjs5S85KdYhjjhgMWB1OyuYvAhEWhA9SZeshw1NEpd8LK2YSaDcT3f4SsdYmVFCPv6VpJ2sone0zgW3A6yLyMxE5c8chOYMEwjFer2jDYhTOD79KXCw0tXsAA/Nregktm4PN4Up1mGOSzeXC4U6nYOp0zA2VtBkyMSoTW3u9BJYvQ0zQ+/q7qFiMaF1lqsPVtFFr0IlEKRVWSv0vUE5i6JK3ReS7IqK/BY+jO5Bs1iqykd7wOo3uq4kEqzGYbZjjirIrPprqEMcsq8OJwWhkysKlxLxeZqS1EzSEiHa6aFKCaU4eniqFathJrPkwKqJPBda0kzHk03+VUkGl1P8Ac4EgsFVEvnLKIxsj3qnupN0b5kb3TgzBLvb4lqHinWT1tNJSYKVw6TmpDnHMEhHsLjcTZs/FaLEwsfcgNZYIpV0z+Uf0EOHzVqFiQu9Lz6NiUaINVakOWdNGpSEnEhEpE5G1JE4BLiVxpfsPTnVgY0EoGmNdRRsmg3BO6DWUxUVNQy8Asw930rN0Og67PltrJNndbkwWKxPnzCdaX0M0DexRFxXeLroyc7FOcdC9zUOss5FYQzUqqkcF1rShGnQiEZGdItIJPAHcAmQArwKf5NQMKz/m9PgjbKhsZ2UBuJs20p13OX5PFQajDWc4wsQrPpLqEMc8o8mMxW5n8qKlxMNhJtoOEkeR21nG+uBhIpedQzwi9D71GCriJ9pYm+qQNW3UGUqN5BogWym1QCl1g1LqP5RSf1NK7Ure4VDrZ0ttF629IT6RtgmJhdgbWkM8Wo/b76W+wMzUZRelOsRxwe5OJ3/SVOzudNI6DtJqjlPWuYBX2YO/aBKOKWZ6NjcR6+km1lilayWaNkRD6Ww/pJS+BHiworE4r+5rxSCw0v86ylVExaFOIEZ5bTPtSybhtOlmrdPB6nBiNJuZvHAJoaYGVEY32YF8Ir1mtvtaiF+8GBUDz5OPo4I9RJvqUx2ypo0qJzXWlnZiPYFEs9b5+T6c7TsITLiEntY9GAx2Mvwh8i69So+tdZqICDaXi0kLl4JS5Jv2EUYxp/lcXlT78U1aiGtyHM/bh4h2e4jVH9S1Ek0bAp1IRsiOum4ae4J80rYeQbEnsIp4pI6MYITDhQYWrvxQqkMcV+yudDLyC8gqKoHmKprdUaa0L6Qy1EiN34vhvFmouMLz9HOokIdoox5iXtMGSyeSERCPK17e14KgWOpbB3mz2LunHlDMqq6hYeEEMuyZqQ5zXDGZ3+t0D3e2k5HdiEkZmdm2nOdiFXimrCB9cpDeTXuIdnYTqzugayWaNkg6kYyA3mCUDZUdXJnTjK33MOGyS+hs3IXJmI47GCL94osxiN71p5vdlU7Z/EWIGMjyVdJsjjG76Xzeie6jUyzYzi4FFaf72VcSZ3Dp60o0bVD0t9kI2NXQTW2nn49b30AZTOz2LSIeaSEjqKgsFFas1IM0poLV6cTuTqdo+kxC9VWE80O4wy7yusp4IXSI7skryZjix7txO5G2TmK1B1CRSKrD1rQzXkoTiYisFZEKEakUkbuOU26piMRE5PrTGd/JUErx4t4WDMRZ4H0TJixn9+b9AJRXVVK9IJdCV2GKoxyfRAS7282kRUuI+HqZ6DyMTxTzmi/mtfAueu1FOFcWIRKn5+kXUbEQ0Xo9BpemnUjKEomIGIFfApcCs4AbRWTWMcrdDbx4eiM8Od5QlA0H27kxswJzqJPgxMvoqN+FyZSPK9iL5fw1mAymVIc5btld6ZSUz8FstWFuPUxzRoyS7snE/MKb8WZapq8lY6of77t7iLS0E6uvRIX1ZVKadjyprJEsAyqVUlXJCxofBq4eoNy/AI8CraczuJO1t8lDVbuPG81voCxOtjZNJB7tIjsQ5kARrFx+bapDHNdMZjN2Vzqlcxfgq6skq8SPAua1XsCLwZ2EHDk4zluAGOJ0P/E0KhYmWncg1WFr2hktlYmkGKjr87o+Oe0oESkmcUX9vSdamIjcLiKbRWRzW1vbKQ10KF7c3YyDIOW+TahJ57H3nW2AkdkHdnFgXhbl2eUpi01LcLjTmbxwCbFImNJQLXXWONOal1EbbGCv9NI2+TwyZ0bwbTtEuKGZWMMhVCiY6rA17YyVykQy0NV4/a+c/xnwNaVU7EQLU0rdp5RaopRakpubmlul+MNR1le280n3NoyxEN1FV+Fp2Y3ZnIMtGmLClR/BYrSkJDbtPVank/zJU3FmZBJqPES8BGwxC9M7l/KsbxdBkxn7JRdgMMXpefRRVDxK9PD+VIetaWesVCaSemBCn9clQGO/MkuAh0WkBrge+JWIfOi0RHcSDjR7OdDi5cOmN1BpBWzcYQTlJ6e7heoJFtas0PceOROICI70DCYtXIKnvop5ZUKnIc7cpovZ5ttDm13ROWEpmXON+PY2Eao5TKy5BhX0pzp0TTsjpTKRvAtME5FJImIBbgCe6ltAKTVJKVWmlCoD/g78k1LqidMe6SC9sKeJPLqY5N9FfOpaanZtATEz91AVsbMXkWnTFyGeKewuN5MWLgGlsLdW05KtyPZmk+Ur4hnvPvxEcVxxPQZzHM/fH0HFY0Rr96U6bE07I6UskSilosDnSZyNtQ/4m1Jqj4jcISJ3pCqukxWMxHj9QDu3pm1CiFObdgVBTwVitmNSitkfuR2r0ZrqMLUkk8VCzoQysktK6TqwhYlz0omgWNJyJW90byGQbqE3dwqZi9PxVXYTqthDrKkWFdD3dte0/lJ6HYlS6jml1HSl1BSl1PeT0+5VSn2gc10pdYtS6u+nP8rBOdTmZX+Thw8Z3kDlzuSdt5qAMCUtNXRNzqF4xqJUh6j1Y3e7mbxoKb62JhZkW6iyxylpnU4sHOeVcD0eFSTt6o9jtMTpefRxlIoTPbw31WFr2hlHX9l+CsTjiud3NTNDaikIHyY0+SqaK7eiDFbm1HaRc/FlujZyBrI505iyZDmf+um95JVNwDzZikkZWNRxCS80rSecmUbAlUXGyhL8tUHCOzYQa2lA+XtSHbqmnVF0IjkFmjxB3jjQxiccb6HEyB7faqKhamKmKAgUXXtDqkPUBiAiuLJzsaW5yM9xcM7cIpqMcaY2rqQt1MJWUy+9hHFedTNGm6L7iRcSZ3DV6FqJpvWlE8kw9QQiVLf52NvYxRWshwnL2LFxFxBjZkMdMnMaaaWTUh2mdgwOdzoAWWlWinPctOUIaUE7U7wLePrwOnw56cTtTjLWzMLfpAhveoZYWzOqtyPFkWvamUMnkmGIxOI0dAV4dX8Ly2UP7lgnXUXX09O8i4jZwrTGAFlrL0t1mNpxmCwWzFYbFpOBzGw75XNzCYhiYdNlVHj2UJtmptcQwXnZ9Zic0PXcRuJhH9HD+gwuTTtCJ5JhqOv0s6/JwwMbD/PptLdQZgfv1k4hHq3DIF5EhKyrr0l1mNoJGE2Jsc9y020sm5LHAXuMrI483OFsnjr0Ip6CPAxmK+kXrSTQZiT8xsPEOtpQPaNi1B5NG3E6kZykVk+Qhq4AP3x+H8WOGKtjbxOfdAEHNr8DwNL6Hqxz52AuyE9xpNpgue0mnG4LrmkuBFjVcT2bWjbQ6XLis5pIu/ASTC4jXa/sR/maidbuB9V/MAZNG390IjkJ/nCUxu4Ad7+wH08gyk/LD2CMBalyfISIt4KgzURBk4f0tWtTHao2BCJCTpaNc2cXUm2KU9Awg3gszovVL+EpLkJMJtIvP59gp5nwq38h1tmB6mlOddialnI6kQxRLK6o7fRz/4Yadjd6+Pz5U5nR+jzKmc+GXWFUrJVcQwwMgvuKK1IdrjZE2WlWinLT6MwzYYkYWe69nJcOv0y31UTUnU3aOaswZ1jpWN8CHXuJVO6C+AmHgtO0MU0nkiFq7A7w0p4WntrRyFXzi7i4KISjdQv+sqvpOrQXBSyp9WCfvwBzXl6qw9WGyGY24s6wMH9uHj0SZ0rDWXijHp479DqeoiLEZCX9qksJdZsJ/eP/iPX26GHmtXFPJ5Ih6PSF2XK4i3teq2ROkZtPnVVGSe0TiIrzhm8VKlRB3G3H3tCKSzdrjVo5bhvLJmez3xknrdvBlPBc1tW/yB5vLyqvFOeKRZhz0ujYEsLQ8AbRwxXE/b5Uh61pKaMTySAFIzH2N3n4wXP7cNtMfHXtTPLSbaQdfBKVO5O925pR8R5mW9LAYMB9xeWpDlk7Sel2M063hezpGURRLG27kpZgPbvbd7Hf4kaZnWRcfRmhHjPBdU+jwr1EDu5A6Y53bZzSiWQQlFIc7vDxXy9W0OkL8/VLy5mY7aDItx/aD7A78yqMXXUoESbtr8W+cCHm7OxUh62dJKNByEq3saY8nwpzDFd9Hm6VzYbGl2mNemlylGBbNAdzQSZt28wYDjxJvKuZaFN9qkPXtJTQiWQQmnqC3PdGFdvruvncminMn5DBhEwHsv0vIAaeP5xPLFxBZlER0tCI+9JLUx2yNkxZTgsT8tPwFFgxxoVV3ddxoHcn9d5qutwZtMTSyPzYdUT8Jtqe2AK+JqK1FcT9+p4l2vijE8kJeIIRntzeyKNbG7h0TgFXzCuiLNuBAQV7n6KtaDnGyk5QAeabnIlmrcv11eyjndNqwukyc+HiQtqMcZyVMzAoE281vEIvfvxZE/EUTiD98tX01trwP/lHCPYQrjmEisdTHb6mnVY6kRxHJBZn/cF2fv7KAWYWuLjj3ClMzHZgMhqg8mXwtfJAcCni344lMxf3O9twLFmMKVPfwGosyEqzMqc0k9J5OWRHTeQ2X8TWrrdo9TUSz8rGb8sjePY52Kdk0Lq+l/DON1BdjUSb9bUl2viiE8lx7G/y8L1n9mI3G/n6pTOZmpeGzWxMzNz+f/gsDnz74qi4hxUTpxJrbtbXjowhmQ4zljQT0+bmIDYD5zaeh4rHeHT3q/QSIJ5TTMjsIn7jJzDZoe2Bl4h1NRNtqSfW25vq8DXttNGJ5BiaPQH+4+m9tPaGuOvSchaUZuK0JsZkIuyHgy/y56wVpHXVYHJm43riaazTppJx3XWpDVw7ZUxGAxlOK9Y0C2WrCskKW1la+1H2Btfxlw1VqMxMos48os50HNetIuJXdNz3O5S3jUhjIyoaTfUmaNppoRPJAPzhKD9/+SCbD3fxmXMmc0F5Hul283sFdj9KKBqg6mA+Kt7DPIMD1dtL/r//O2I0pi5w7ZTLcJoxO01kTHThmmxjQfMy8kIu/lG3if959QCRvGKitmx8M84la5kN/4F2PM8+i/J2EWlsTHX4mnZapDSRiMhaEakQkUoRuWuA+TeJyM7k4y0RmT/SMcXiir++W8dD79Zxwcw8Pr6ilJy0fnc33Pkwf88sJK+pB4M5m/z160i/5hqcS5eOdHjaaea2mbE7TRhMBiauLMZoFS489Any8zfyxoFOvvnKITy5k1EmO/4Lb8BVEqDrydcI7nyXmMdDtKsr1ZugaSMuZYlERIzAL4FLgVnAjSIyq1+xauBcpdQ84HvAfSMd16ZDHfzXCxVMzUvjrktnUpzpeH+B3hbChzeysWUOEutlsteIKTeX/K99daRD01Jkck4a7gwrZpuZ3BUZZPjzmd5YzsVzWtjf5OdLr1RT55pIxDEBx9pyzM4obff+iVhrPdHmZuLhcKo3QdNGVCprJMuASqVUlVIqDDwMXN23gFLqLaXUkZ90m4CSkQyortPP1x7bidkofPfq2UzJTftgoe0P8qzDRslhQYw5TKl4l/y77sLodo9kaFoKWUwGyssyyM6wkT8pF8tEWNRwEdHQbj6zwkWnN8qX32xnNxl0ll5N4Tl+Yl4frf/7K+KhMJH6hlRvgqaNqFQmkmKgrs/r+uS0Y7kNeH6kggmEo3z10Z00dgf45hWzWFaWhcEg7y8UDRHb+TDP+adijgTI97txn3MW6fq6kTFPRJg6OYMJ2S4Kl2cTs0Yo27OYg+FH+NwaGyLw9a3wms+Nb+YlFCzsJrTvIJ1/fZC430+0rS3Vm6BpIyaViUQGmDbgYEUich6JRPK1Yy5M5HYR2Swim9uG+KFVSvHfL1aw8VAHt62azNULihLXivQVCcK7v+MlXx1lh7IQYw7T2qoo/I/vDGld2uhlNBooKkljzoRiclekke0vgv0Onmj5ETed5yHXbeSHB9L5bXQV9llppE2O0/vE0/Ru20aktZV4IJDqTdC0EZHKRFIPTOjzugT4wGkuIjIP+B1wtVKq41gLU0rdp5RaopRakpubO6RAHt/WwB821HDu9FzuvHAqVlO/M68iQXjjv1EvfZPHw6XYQlFcagpTbrsWc2HhkNaljW4Wm4ncXBfz5hfhnGxiUePFODzpPFj9I5YtfIfpRUZ+W5fPH4zXUrywBWOmnY6f/5xASxuRhgZ91bs2JqUykbwLTBORSSJiAW4AnupbQERKgceAjyulRuSmD3sbe/jWk7spy3Fy9/XzcFrN7y8Q9sPz/wZv/g+vlcxlwoE8xJDNFBUi65ZbRiIk7QznzLCSn5HD1DVpmO0Grqi6g2mWubzc+Ai24j+wbFqAu7tWs8M6i+KVTRAK0vyTnxLo6SXa0pLq8DXtlEtZIlFKRYHPAy8C+4C/KaX2iMgdInJHsti/A9nAr0Rku4hsPpUxeAJh/unBrQjCzz46nwK37f0FAj3w91th6wOoGZfxSEcujpDCKTNYetcNiEFfhjNeZee7yc/MoWxNGnGPcEXbp7ki72ZqfZUctv2Ys+bs5SuBW7C6QthWuZDKAzT++f/wtbQR8+p7l2hjiymVK1dKPQc812/avX2efxr49Aitmy88vJ3DHX5+8tH5zJ/Qb3ys3hb42yegbhMsuZXXp13M5Gf+iBicnFVmw7VgzkiEpY0SRqOBiSVF2Ix2eqoO0rY3yNKJq5k0dTqP1v+OXf4HmDxnMffvv4Db8l5m29yVOF94hoYpUykxmXGXT9cXr2pjxrj9Sf2zfxzktYo2bl89mWsW9juruLMaHrgK6t+BNXfB2h/x8p+fxxD1URJyMOubn0tN0NoZxWI3kZXlZuXamVgdRro3hSkzlnB7+dc5p2At1dGt/HlaC+9a3MSndeLLy0X+cB/1FVV4DtedeAWaNkqMy0Ty2v5W/vfVg5wzLYevrZ3x/plNO+CPlyeSyRU/hdVf5bUdW8k+1I1RObnonz6K0WFPTeDaGceRbiEtw8rSyyYR6IwR2Kkosji5vOzD3DLjS8SNMe4ozmB3bgOPLVhENBolft//Ul/VQG/bMc8d0bRRZdwlkroOP194eBsTMh3c87FFGPr2c1S/AX+6CkK98OE/wuJbiERh62/fRMU7mZ3mJvPC81IWu3bmERHcuXaKZ2QycW42DVu8mJqdTHA5mJc7l8/P+Q6z0qbz06xM6ma9xE8WXYrp8GECf/0D1bsP4GlpT/UmaNqwjatEEozEuO2Bd4nGFfd9Ykm/gRgfhwc/DGYbfPxxmJm4yPCpBzYinr1YowbO/a8fpihy7UxmNBpwZ9tZcOEErE4z+1/uIDdWxJScLCZk5nDj1Du4xbmQCquwZ/ULPDWzHOebG+h+60Uqd+2hu7pWnxasjWrjJpEopfjKIzs40OLlfz48nxkFrvdmvn0fPHobZJTCp16EkiUAVO9qp/6t3ahYOwsWL8KSk5Oi6LUzncVuIiPPyZJLJ+JpC7DvtRbyVBHluaUUFRQwZ9K1/DqQzuRokIeuOsCBPCeuh5+gveIdKg5W0L3/oB6TSxu1xk0iuX9DNc/sbOKOcydz2dzkRYRKwSvfTVwnUrIEbn0JssoACHjDvHz/DuL+DVjjcVZ+9ZupC14bFZwZFkpnZ1M2N5v9G5uo29+JyWtnTvZ0ppbNIjzrRv7Y0sUtvV5+fl2QoDlMwS//SOixh9hVuYv2PXuI9fSkejM0bchSevrv6fJ2VQc/eG4/50zL4auXzExMjMfgqX+B7Q/CzCvg+vvBlBguXinFy3/Yg7/jTeKqi8XXXo/RNC52lTYMIoI7x87CS0pprvbw9pNVnHXdVLIiTspyp5I5R7HXYuX6XY9xdtdWfnBLNle+CivXbcS/9wD7PnIZxYGVTCibjqWwCJGBRhHStDOPKDXg8Faj2pIlS9TmzYlrF5t7glz2izdxWo08+6/n4LaZIRKAv348cd/1ZbfD2ruhT6f7E0+to/bxXUT8L+JKM/GZ3z2uP9TaoIUCUQ5tbeGtRw8RCcWYd34J05bmk5FjRzwVVHbV0F21k4J9f+eX9m46G+zc/gK4Agr/2QswXn8lpRPLyZ4yC7FYUr052jghIluUUktO5r1j+md2KBrj9j9vJhCO8fDtKxJJxN8Jf7kOGrfBRd+Fs79wtHy7v53/euVnFDw9CeV/iYxQhE/84W86iWhDYrWbKJ2VTVqmjc3P1rD95TqaD/Ww7IrJZOeXUp7voN3qZm9aCTceeoeK3Ff4xmeE61+D89ZvI7DvILUfu5Lu3lbyp87HlZWf6k3StOMa030k335yDzvre/jxR+YxPd8F3bXwuwugZTdc97ujSSSu4jy470Guevxq7K/moXqfxx6O8qEv/T/MDscJ1qJpH+TMsJKR5+DsD09l4cWltNb28uLvdnNwezeeeCHZxUtZOfssTIsvIWfGv/JttZjes2L85MNCb9SL7X8fov6XP6fireeoqdxKKBpK9SZp2jGN2RrJQ+/U8vC7dcnO9SJo3gV/vibRrHXzYzDpHAD2tu/lOxu/w77OfVzacgPpzVswxEKcN3kW2atXp3grtNHqSH+JzWlmxnIjuaUu3n6qivWPVNJ0qIdFa8vILprM/IwJNGQdYH9mOvNbl5LjfZe9165H7bBx3ttVdO7/MZuuWk7xqqsonjWfidkTMBr00CramWVM9pHMmrdQRa78PssnZfOnW5dhrHkDHv4YWNIS14jkz8IX8fHTLT/lkQOPkGZO47O5d9Lxx9eJRw6zsqWH5U8+jTE9PdWboo0BSin8njC9HUF2ravnwDstuLJtrLx2ChNnZ2OxmQgE/Ryo2UN72yGe3eJhZsdLZIfeJftNB/ld8M48G71XXMi0uVdRVjKFiRl52Mxj9neglgLD6SMZk4nEWTxdLfzXe3nmX1aRcegpePyzkDUZPv44yl3MizUvcve7d9MeaOfKyVfypXlf4a9f/jnB3i3MaujirLu+QfoVl6d6M7QxJhaJ09sZpG5fB+88U0M4EGXumhIWXVyKI91KPK5o7OqlraWaF3dWs/dgIx8OPIr7UDXZO630OOHhizPIWXkFS6aupcRdRHF6Fhl28wdvxKZpQ6QTST+2omlq6+YtzKp5AF76fzBhBXzsr9RFevnupu+yqWkTU9Kn8J2zvsPsWD4Pf/u3tPa8Q2EPnDunnKL//i/dwa6NmKAvQkeDl3eerqbxYDf5ZW5WfXQa+WVuRIQuX5iGTi/ib6W18SB1ezaz+ODjRN4NYu00sqFceGBNDnnZl3LJlPNZWDSRHKeLDIcZt838wVtEa9og6ETSz9RZ81TlT66ATb+E8qsIX/1Lfrf/L/xu1+8wG8z804J/4npZQtfv/8C7e9qoSu8kzZTDzXd9CefcuakOXxsH4nGFtyvI3vWNbH+5DqPZwMprpzDnnGIgMZxPW2+IQDhCtLedaFMF5opncb78Et7dRvwW4YHzDWyclEkofD7zM1ezaspEFpVmU5BuI8NhJs1q0j+ItEHTiaSfJVNy1OaPR2DZ7Wyc/yG+9/b3qeut48IJF/BlLiL85yeoqlHUlCyjJ/IiJouLz/zyHhyutFSHro0zkXCMhoouNjxaSXezn7Ovn8qCC0vfVyYai+MPRwn0tOKv2o28fj/xZ7YR6jAREzhQDNvL7LyTuZxD5guZXZjH0snZLJ+UzawiNxkOMw6L7k/Rjk8nkn6WFBnVcw99j/9Wnbxw+EUm2Iv4j+AlpD3+LtX+IupLziVsNBL1P4zBGObmH/2UrMKiVIetjWPeriBbXjjMwotKcecc5zYFShH3deDfv5nAU/9LfM8uWputmDoSiaLHIewqLuStjBVszZmHIzeLpZNyWDEli9VTc8l1W7Ga9Flf2gfpRNLP5OkFKu/bZRgCIe5qWcKE17uosc2luWAFMTGRPyFIwPMaHQ2VfPhb36dk5uxUh6xpKKWG1BSlAt2oms3EN92DqniD3Z1uDrW7mVAdwR2AOFCTb2dzUSGbc2dSmb6Q2cVlrJqax4Xl+cwscOlOeu0onUj6cZXa1f9euYrpezKoyzmbtuzZEK/HldlEoKcCX3cHYjCw9nN3Mmv1+akOV9OGJ9QL1eth/Y+h/l32mc3s9joIN9nIrDMysREMCnxW2DPRyM6SDLbkTyGQMZvFBbP50NwFrJlWgMWsayrj2ahNJCKyFvg5YAR+p5T6Ub/5kpx/GeAHblFKbT3Rcme4stXXr/ghHnscYoeIx2qIRQIYzWZK5yxg2rKVTF60FGdG5okWpWmjR9gHVW9AewV4Goh7Goj3NOFvb6Kmzo+nyYy93ozDl6j1dDugLR060gW/00zEnUZaQTF5U5aSMf18SC9BDAYMIhgkcZGlMfm/iGA0CAIYRRADGAQMCGIQDCIICmPijRgQDAYQIbE8EstRJAbhhsRwdyaDAaMIRqMk/je899BG1qhMJCJiBA4AFwH1wLvAjUqpvX3KXAb8C4lEshz4uVJq+YmWPSE7T9154Uoghi3NxZTFy5iydAVlcxdittlGYnM07cwUi0I8CrEIeJuJtVYS3P4OPe9uo7OhCV+XD/HEcPQqjPH3f1n3OhR+lxB0muhx2mh3ptHkzKDV6abT7iZkcBBRVqJxG1FlJazshGO2xP9YCWMmfpxRmAQwGBJJyiCCxWjAYko++j23mgxYzUYsJgM2sxHbkf/NBuwWIzaTEbvFiN1sxGFJPrcYcZpN2CzGo2VtJiPW5P/6NOn3G62DNi4DKpVSVQAi8jBwNbC3T5mrgQdUItttEpEMESlUSjUdb8EGQ5zFl1/J1KUrKJpRjkEPKaGNV0ZT4mG2gc2FMWcazlmX4vwY9D29RMViBKr2sXn907RVbyfU0oDq6sXaEyGrK8qsGi+muBdoPvqeL37GSEPOwF/GdqXIVAprXGEFLAqsCixKSNZHko9kNUUZUGJAKUEQOPL7VoEoUHGIBiEK+I9UY4b5G1gkUaMiGQnAVZ3Z2JURkWSEyT6rIznnyHsS8yXxf9/niULJGldiwX3nHV3nGMthqUwkxUBdn9f1JGodJypTDHwgkYjI7cDtAKWlpaz5xKdPabCaNpaJ0Yhj2hxWT5vzvulKKXpCPQTCPoL1VYQO7SZS30CsuY3/t7yckDFKMBogFA0QjAYIRoOEYkFCsTChWIhgLEwoHiEYjxCKRwipKHEVRyUf7z2PooijlCJO4kQBlXzEJfGa5PQjz2PH3Br1/hyj+s89tkXmbtLj/cqpPv8l/1Gq3/Sj++v9b1IMXG6sSWUiGSgn99/XgymTmKjUfcB9kLgfyfBC0zQNEr+gM2wZZNgyYFYxzDon1SFpI+U7J19NSuW5f/XAhD6vS4DGkyijaZqmpVAqE8m7wDQRmSQiFuAG4Kl+ZZ4CPiEJK4CeE/WPaJqmaadXypq2lFJREfk88CKJ03/vV0rtEZE7kvPvBZ4jccZWJYnTfz+Vqng1TdO0gaV0AB6l1HMkkkXfaff2ea6Afz7dcWmapmmDp8dH0DRN04ZFJxJN0zRtWHQi0TRN04ZFJxJN0zRtWMbk6L8i0gtUpDqOEZIDtKc6iBGkt29009s3es1QSrlO5o1j9bZpFSc7+NiZTkQ2j9VtA719o53evtFLRDaf7Ht105amaZo2LDqRaJqmacMyVhPJfakOYASN5W0DvX2jnd6+0eukt21MdrZrmqZpp89YrZFomqZpp4lOJJqmadqwjNpEIiJrRaRCRCpF5K4B5ouI/CI5f6eILEpFnCdrENu3RkR6RGR78vHvqYjzZIjI/SLSKiK7jzF/tB+7E23faD52E0TkNRHZJyJ7ROQLA5QZtcdvkNs3mo+fTUTeEZEdye37jwHKDP34KaVG3YPEsPOHgMmABdgBzOpX5jLgeRJ3WVwBvJ3quE/x9q0Bnkl1rCe5fauBRcDuY8wftcdukNs3mo9dIbAo+dwFHBhjn73BbN9oPn4CpCWfm4G3gRXDPX6jtUayDKhUSlUppcLAw8DV/cpcDTygEjYBGSJSeLoDPUmD2b5RSyn1BtB5nCKj+dgNZvtGLaVUk1Jqa/J5L7APKO5XbNQev0Fu36iVPCbe5Etz8tH/jKshH7/RmkiKgbo+r+v54MEeTJkz1WBjX5msoj4vIrNPT2inxWg+doM16o+diJQBC0n8qu1rTBy/42wfjOLjJyJGEdkOtAIvK6WGffxG6xApA92lvn9WHUyZM9VgYt8KTFRKeUXkMuAJYNpIB3aajOZjNxij/tiJSBrwKHCnUsrTf/YAbxlVx+8E2zeqj59SKgYsEJEM4HERmaOU6tufN+TjN1prJPXAhD6vS4DGkyhzpjph7Eopz5EqqkrcadIsIjmnL8QRNZqP3QmN9mMnImYSX7IPKqUeG6DIqD5+J9q+0X78jlBKdQPrgLX9Zg35+I3WRPIuME1EJomIBbgBeKpfmaeATyTPQFgB9Cilmk53oCfphNsnIgUiIsnny0gcy47THunIGM3H7oRG87FLxv17YJ9S6ifHKDZqj99gtm+UH7/cZE0EEbEDFwL7+xUb8vEblU1bSqmoiHweeJHEGU73K6X2iMgdyfn3krgX/GVAJeAHPpWqeIdqkNt3PfA5EYkCAeAGlTzl4kwnIg+ROPMlR0TqgW+T6PQb9ccOBrV9o/bYAWcDHwd2JdvZAb4BlMKYOH6D2b7RfPwKgT+JiJFEAvybUuqZ4X536iFSNE3TtGEZrU1bmqZp2hlCJxJN0zRtWHQi0TRN04ZFJxJN0zRtWHQi0TRN04ZFJxJN0zRtWHQi0bQzjIhMFpHfi8jf+03/pIgs7fP6EhH5+OmPUNPeTycSTTuNROQ3InKuiOzqN90qItUiMis56vNtA7x9MbBTRO4RkR8AXyUxCoKmpZROJJp2GiSvJAZYDqwHJohI38/f7cDrSqm9x3i/GYgCdwB/Ukp9A7ACxSKyWETcIvKlkdsCTTs2nUg0rR9J3CHvouTz/xSRX5zkch4RkZ+IyGvA10WkHDiQHH21FihLlrMDXwa+c5zFrQbeJDGs+S4RcQHtwEzgPOAHJO6doWmn3agca0vTRti3ge+KSB6JL+6r+s4UkTdJ3D2vv68opf7R5/VcEoP/nZd835eAF5Lz9pFIAlXAPwNPKaVqkuWyge8DC0Xk60qpHwIXAf8J2IB7SYyBdACwKaX+R0Q+Bwx4a19NG2k6kWhaP0qpN5Kju34JWJOsQfSdf86JliEiNiAL+G6fyZfw3gB4+4AZIvIGiUSyos/yO0g0YfWVlhy6/KHk48h6vp58mqeUqkPTUkAP2qhp/YjIXBL3o2hXSp01wPwT1khEZDHwHaXUlcnXDuA1pdTy5OuPAueTaOKyK6W+OSIbo2mnga6RaFofkrg39YMk7lv9CxG5RCn1Yt8yg6mRkGjW2tnn9XnAa31e7wPuInE/iEXDClrTUkx3tmtaUrLW8BjwZaXUPuB7HL8D/Hj6J5JLea9/BKAiWeY+pVTPSa5D084IumlL004DEdkKLFdKRVIdi6adajqRaJqmacOim7Y0TdO0YdGJRNM0TRsWnUg0TdO0YdGJRNM0TRsWnUg0TdO0YdGJRNM0TRsWnUg0TdO0YdGJRNM0TRsWnUg0TdO0Yfn/2kIYGAuDvHgAAAAASUVORK5CYII=\n",
|
|
"text/plain": [
|
|
"<Figure size 432x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"data": {
|
|
"image/png": "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\n",
|
|
"text/plain": [
|
|
"<Figure size 432x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"max_distance = 15\n",
|
|
"\n",
|
|
"for model in models:\n",
|
|
" d_H = d_H_list[model]\n",
|
|
" \n",
|
|
" with h5py.File(\"qgdimension.hdf5\", \"a\") as f:\n",
|
|
" mean_profiles_key = f\"mean-profiles-{model}\"\n",
|
|
" profiles_key = f\"profiles-{model}\"\n",
|
|
" if not mean_profiles_key in f or not profiles_key in f:\n",
|
|
" # Recalculate the profiles as the data stored in the previous exercise is insufficient.\n",
|
|
" mean_profiles = []\n",
|
|
" for size in sizes:\n",
|
|
" profiles = []\n",
|
|
" for _ in range(measurements):\n",
|
|
" adj = generate_random_triangulation(size, model)\n",
|
|
" profiles.append(vertex_distance_profile(adj,max_distance))\n",
|
|
" mean_profiles.append([batch_estimate(data,np.mean,20) for data in np.transpose(profiles)])\n",
|
|
"\n",
|
|
" f.create_dataset(mean_profiles_key,data=mean_profiles)\n",
|
|
" f.create_dataset(profiles_key,data=profiles)\n",
|
|
" \n",
|
|
" else:\n",
|
|
" mean_profiles = np.array(f[mean_profiles_key])\n",
|
|
" profiles = np.array(f[profiles_key])\n",
|
|
"\n",
|
|
" # Plot the collapse plots.\n",
|
|
" for i, profile in enumerate(mean_profiles):\n",
|
|
" rvals = np.arange(len(profile))\n",
|
|
" plt.plot(rvals/num_vertices[i]**(1/d_H),\n",
|
|
" [y[0]*num_vertices[i]**(1/d_H - 1) for y in profile])\n",
|
|
" for i, profile in enumerate(mean_profiles):\n",
|
|
" plt.fill_between(np.arange(len(profile))/num_vertices[i]**(1/d_H),\n",
|
|
" [(y[0]-y[1])*num_vertices[i]**(1/d_H - 1) for y in profile],\n",
|
|
" [(y[0]+y[1])*num_vertices[i]**(1/d_H - 1) for y in profile],\n",
|
|
" alpha=0.2)\n",
|
|
" plt.legend(sizes, title=\"V\")\n",
|
|
" plt.xlabel(r\"$x = r/V^{1/d_H}$\")\n",
|
|
" plt.ylabel(r\"$V^{1/d_H}\\,\\mathbb{E}[\\frac{1}{V}\\rho_T(r)]$\")\n",
|
|
" plt.xlim(0,3)\n",
|
|
" plt.title(f\"Finite-size scaling with Hausdorff dimension $d_H = {d_H:.2f}$\")\n",
|
|
" plt.show()\n",
|
|
"\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "d8f25787",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "7f19410ed936f838773ee891b059d1a3",
|
|
"grade": false,
|
|
"grade_id": "cell-65ae9c46ece5b657",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"**(e) Bonus exercise:** Make more robust estimates of $d_H$ by optimizing the quality of the collapse. You could do this (for each model separately) by taking $\\hat{f}(r) = \\mathbb{E}[\\rho_T(r)] / V_0$, where the right-hand side is the mean distance profile for the largest system size with $V_0 = (2^{12} + 4)/2$ vertices. Then according to our assumption, for another size $V \\leq V_0$ we expect $\\mathbb{E}[\\rho_T(r)] / V \\approx k \\hat{f}(kr)$, where $k \\geq 1$ is a scale factor that should be $k\\approx (V_0/V)^{1/d_H}$. Making sure to interpolate the function $\\hat{f}(r)$ (using [`scipy.interpolate.interp1d`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.interp1d.html#scipy.interpolate.interp1d)), this scale factor can be determined by fitting the curve $k \\hat{f}(kr)$ to the data $\\mathbb{E}[\\rho_T(r)] / V$. Then $d_H$ can be estimated by fitting $k$ versus $V$. **(20 bonus points, but note that maximum grade is 10)**"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "ed4424ce",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "199ffddc14c77d4174b92a61368cd5c9",
|
|
"grade": true,
|
|
"grade_id": "cell-e24b0602e4e8257d",
|
|
"locked": false,
|
|
"points": 20,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# YOUR CODE HERE\n",
|
|
"raise NotImplementedError()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "c9e50c10",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.9.12"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|