883 lines
262 KiB
Plaintext
883 lines
262 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "269c4188",
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"metadata": {},
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"source": [
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"# Exercise sheet\n",
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"\n",
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"Some general remarks about the exercises:\n",
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"* For your convenience functions from the lecture are included below. Feel free to reuse them without copying to the exercise solution box.\n",
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"* 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",
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"* 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",
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"* 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",
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"* 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",
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"* 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",
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"\n",
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"Please fill in your name here:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "220d541e",
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"metadata": {},
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"outputs": [],
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"source": [
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"NAME = \"Kees van Kempen\"\n",
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"NAMES_OF_COLLABORATORS = \"\""
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]
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},
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{
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"cell_type": "markdown",
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"id": "b6944e4c",
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"metadata": {},
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"source": [
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"---"
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]
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},
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"cell_type": "markdown",
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"id": "c53fbab6",
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"source": [
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"**Exercise sheet 8**\n",
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"\n",
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"Code from the lectures:"
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]
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},
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{
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"cell_type": "code",
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"locked": true,
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"task": false
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}
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},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"rng = np.random.default_rng() \n",
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"import matplotlib.pylab as plt\n",
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"%matplotlib inline\n",
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"\n",
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"def fan_triangulation(n):\n",
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" '''Generates a fan-shaped triangulation of even size n.'''\n",
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" return np.array([[(i-3)%(3*n),i+5,i+4,(i+6)%(3*n),i+2,i+1] \n",
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" for i in range(0,3*n,6)],dtype=np.int32).flatten()\n",
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"\n",
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"def is_fpf_involution(adj):\n",
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" '''Test whether adj defines a fixed-point free involution.'''\n",
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" for x, a in enumerate(adj):\n",
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" if a < 0 or a >= len(adj) or x == a or adj[a] != x:\n",
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" return False\n",
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" return True\n",
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"\n",
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"from collections import deque \n",
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"\n",
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"def triangle_neighbours(adj,i):\n",
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" '''Return the indices of the three neighboring triangles.'''\n",
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" return [j//3 for j in adj[3*i:3*i+3]]\n",
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"\n",
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"def connected_components(adj):\n",
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" '''Calculate the number of connected components of the triangulation.'''\n",
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" n = len(adj)//3 # the number of triangles\n",
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" # array storing the component index of each triangle\n",
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" component = np.full(n,-1,dtype=np.int32) \n",
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" index = 0\n",
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" for i in range(n):\n",
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" if component[i] == -1: # new component found, let us explore it\n",
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" component[i] = index\n",
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" queue = deque([i]) # use an exploration queue for breadth-first search\n",
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" while queue:\n",
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" for nbr in triangle_neighbours(adj,queue.pop()):\n",
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" # the neighboring triangle has not been explored yet\n",
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" if component[nbr] == -1: \n",
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" component[nbr] = index\n",
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" queue.appendleft(nbr) # add it to the exploration queue\n",
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" index += 1\n",
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" return index\n",
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"\n",
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"def next_around_triangle(i):\n",
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" '''Return the label of the side following side i in counter-clockwise direction.'''\n",
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" return i - i%3 + (i+1)%3\n",
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"\n",
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"def prev_around_triangle(i):\n",
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" '''Return the label of the side preceding side i in counter-clockwise direction.'''\n",
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" return i - i%3 + (i-1)%3\n",
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"\n",
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"def vertex_list(adj):\n",
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" '''\n",
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" Return the number of vertices and an array `vertex` of the same size \n",
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" as `adj`, such that `vertex[i]` is the index of the vertex at the \n",
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" start (in ccw order) of the side labeled `i`.\n",
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" '''\n",
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" # a side i that have not been visited yet has vertex[i]==-1\n",
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" vertex = np.full(len(adj),-1,dtype=np.int32) \n",
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" vert_index = 0 \n",
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" for i in range(len(adj)):\n",
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" if vertex[i] == -1:\n",
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" side = i\n",
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" while vertex[side] == -1: # find all sides that share the same vertex\n",
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" vertex[side] = vert_index\n",
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" side = next_around_triangle(adj[side])\n",
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" vert_index += 1\n",
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" return vert_index, vertex\n",
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"\n",
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"def number_of_vertices(adj):\n",
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" '''Calculate the number of vertices in the triangulation.'''\n",
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" return vertex_list(adj)[0]\n",
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"\n",
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"def is_sphere_triangulation(adj):\n",
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" '''Test whether adj defines a triangulation of the 2-sphere.'''\n",
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" if not is_fpf_involution(adj) or connected_components(adj) != 1:\n",
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" return False\n",
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" num_vert = number_of_vertices(adj)\n",
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" num_face = len(adj)//3\n",
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" num_edge = len(adj)//2\n",
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" # verify Euler's formula for the sphere\n",
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" return num_vert - num_edge + num_face == 2\n",
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"\n",
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"def flip_edge(adj,i):\n",
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" if adj[i] == next_around_triangle(i) or adj[i] == prev_around_triangle(i):\n",
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" # flipping an edge that is adjacent to the same triangle on both sides makes no sense\n",
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" return False\n",
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" j = prev_around_triangle(i)\n",
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" k = adj[i]\n",
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" l = prev_around_triangle(k)\n",
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" n = adj[l]\n",
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" adj[i] = n # it is important that we first update\n",
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" adj[n] = i # these adjacencies, before determining m,\n",
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" m = adj[j] # to treat the case j == n appropriately\n",
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" adj[k] = m\n",
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" adj[m] = k\n",
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" adj[j] = l\n",
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" adj[l] = j\n",
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" return True\n",
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"\n",
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"def random_flip(adj):\n",
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" random_side = rng.integers(0,len(adj))\n",
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" return flip_edge(adj,random_side)\n",
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"\n",
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"import networkx as nx\n",
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"from mpl_toolkits.mplot3d import Axes3D\n",
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"from mpl_toolkits.mplot3d.art3d import Poly3DCollection\n",
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"\n",
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"def triangulation_edges(triangulation,vertex):\n",
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" '''Return a list of vertex-id pairs corresponding to the edges in the triangulation.'''\n",
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" return [(vertex[i],vertex[j]) for i,j in enumerate(triangulation) if i < j]\n",
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"\n",
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"def triangulation_triangles(triangulation,vertex):\n",
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" '''Return a list of vertex-id triples corresponding to the triangles in the triangulation.'''\n",
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" return [vertex[i:i+3] for i in range(0,len(triangulation),3)]\n",
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"\n",
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"def plot_triangulation_3d(adj):\n",
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" '''Display an attempt at embedding the triangulation in 3d.'''\n",
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" num_vert, vertex = vertex_list(adj)\n",
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" edges = triangulation_edges(adj,vertex)\n",
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" triangles = triangulation_triangles(adj,vertex)\n",
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" # use the networkX 3d graph layout algorithm to find positions for the vertices\n",
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" pos = np.array(list(nx.spring_layout(nx.Graph(edges),dim=3).values()))\n",
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" fig = plt.figure()\n",
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" ax = fig.add_subplot(111, projection='3d')\n",
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" tris = Poly3DCollection(pos[triangles])\n",
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" tris.set_edgecolor('k')\n",
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" ax.add_collection3d(tris)\n",
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" ax.set_xlim3d(np.amin(pos[:,0]),np.amax(pos[:,0]))\n",
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" ax.set_ylim3d(np.amin(pos[:,1]),np.amax(pos[:,1]))\n",
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" ax.set_zlim3d(np.amin(pos[:,2]),np.amax(pos[:,2]))\n",
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" plt.show()\n",
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" \n",
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"def vertex_neighbors_list(adj):\n",
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" '''Return a list `neighbors` such that `neighbors[v]` is a list of neighbors of the vertex v.'''\n",
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" num_vertices, vertex = vertex_list(adj)\n",
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" neighbors = [[] for _ in range(num_vertices)]\n",
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" for i,j in enumerate(adj):\n",
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" neighbors[vertex[i]].append(vertex[j])\n",
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" return neighbors\n",
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"\n",
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"def vertex_distance_profile(adj,max_distance=30):\n",
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" '''Return array `profile` of size `max_distance` such that `profile[r]` is the number\n",
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" of vertices that have distance r to a randomly chosen initial vertex.'''\n",
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" profile = np.zeros((max_distance),dtype=np.int32)\n",
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" neighbors = vertex_neighbors_list(adj)\n",
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" num_vertices = len(neighbors)\n",
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" start = rng.integers(num_vertices) # random starting vertex\n",
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" distance = np.full(num_vertices,-1,dtype=np.int32) # array tracking the known distances (-1 is unknown)\n",
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" queue = deque([start]) # use an exploration queue for the breadth-first search\n",
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" distance[start] = 0\n",
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" profile[0] = 1 # of course there is exactly 1 vertex at distance 0\n",
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" while queue:\n",
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" current = queue.pop()\n",
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" d = distance[current] + 1 # every unexplored neighbour will have this distance\n",
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" if d >= max_distance:\n",
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" break\n",
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" for nbr in neighbors[current]:\n",
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" if distance[nbr] == -1: # this neighboring vertex has not been explored yet\n",
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" distance[nbr] = d\n",
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" profile[d] += 1\n",
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" queue.appendleft(nbr) # add it to the exploration queue\n",
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" return profile\n",
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" \n",
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"def perform_sweeps(adj,t):\n",
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" '''Perform t sweeps of flip moves, where 1 sweep is N moves.'''\n",
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" for _ in range(len(adj)*t//3):\n",
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" random_flip(adj)\n",
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"\n",
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"def batch_estimate(data,observable,k):\n",
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" '''Devide data into k batches and apply the function observable to each.\n",
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" Returns the mean and standard error.'''\n",
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" batches = np.reshape(data,(k,-1))\n",
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" values = np.apply_along_axis(observable, 1, batches)\n",
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" return np.mean(values), np.std(values)/np.sqrt(k-1)"
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]
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"source": [
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"## Estimating Hausdorff dimensions in various 2D quantum gravity models \n",
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"\n",
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"**(100 Points)**\n",
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"\n",
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"In the lecture we considered the model of two-dimensional Dynamical Triangulations of the 2-sphere. The corresponding partition function is\n",
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"$$ Z^{U}_{S^2,N} = \\sum_T 1, \\tag{1}$$\n",
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"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",
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"\n",
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"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",
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"$$ Z = \\int [\\mathcal{D}g_{ab}]\\int [\\mathcal{D}\\phi] e^{-\\frac{1}{\\hbar}(S_E[g_{ab}] + S_m[\\phi,g_{ab}])} = \\int [\\mathcal{D}g_{ab}]e^{-\\frac{1}{\\hbar}S_E[g_{ab}]} Z^*_m[g_{ab}],$$\n",
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"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",
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"$$Z^*_{S^2,N} = \\sum_T Z^*_m[T],$$\n",
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"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",
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"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",
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"\n",
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"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",
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"* $Z^{U}_{S^2,N}$: the standard Dynamical Triangulations with **U**niform distribution (U)\n",
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"* $Z^{W}_{S^2,N}$: triangulations coupled to a matter system called a Schnyder **W**ood (W)\n",
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"* $Z^{S}_{S^2,N}$: triangulations coupled to a matter system called a **S**panning tree (S)\n",
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"* $Z^{B}_{S^2,N}$: triangulations coupled to a matter system called a **B**ipolar orientation (B)\n",
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"\n",
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"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",
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"\n",
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"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."
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]
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"data": {
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"text/plain": [
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"True"
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"import subprocess\n",
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"\n",
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"def generate_random_triangulation(n,model):\n",
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" '''\n",
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" Returns a random triangulation generated by the program `generator` in the form \n",
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" of an array of length 3n storing the adjacency information of the triangle sides.\n",
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" Parameters:\n",
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" n - number of triangles in the triangulation, must be positive and even\n",
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" model - a one-letter string specifying the model from which the triangulation is sampled:\n",
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" 'U': Uniform triangulations\n",
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" 'W': Schnyder-Wood-decorated triangulations\n",
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" 'S': Spanning-tree decorated triangulations\n",
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" 'B': Bipolar-oriented triangulations\n",
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" '''\n",
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" program = \"/vol/cursus/NM042B/bin/generator\"\n",
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" output = subprocess.check_output([program,\"-s{}\".format(n),\"-t{}\".format(model)]).decode('ascii').split('\\n')[:-1]\n",
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" return np.array([int(num) for num in output],dtype=np.int32)\n",
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"\n",
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"adj = generate_random_triangulation(100,'B')\n",
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"is_sphere_triangulation(adj)"
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]
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},
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"source": [
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"Recall that the **distance profile** $\\rho_T(r)$ of a triangulation is defined as \n",
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"$$ \\rho_T(r) = \\frac{1}{V} \\sum_{x=0}^{V-1} \\sum_{y=0}^{V-1} \\mathbf{1}_{\\{d_T(x,y)=r\\}},$$\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 $y$."
|
|
]
|
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},
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"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)**"
|
|
]
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|
},
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{
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"locked": false,
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"points": 20,
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}
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"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",
|
|
"$$\n",
|
|
"\\mathbb{E}[d_T(X,Y)] = \\sum_{r=0}^\\infty r\\, \\mathbb{P}(d_T(X,Y) = r) = \\frac{1}{V}\\sum_{r=0}^\\infty r\\, \\mathbb{E}[ \\rho_T(r) ].\n",
|
|
"$$"
|
|
]
|
|
},
|
|
{
|
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"cell_type": "markdown",
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"id": "29704f5d",
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"metadata": {
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}
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},
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|
"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",
|
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"metadata": {
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"grade": true,
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"points": 15,
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"solution": true,
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|
"task": false
|
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}
|
|
},
|
|
"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",
|
|
"$$\n",
|
|
" \\mathbb{E} \\left[ d_T(X,Y) \\right] \\approx cV^{1/d_H}.\n",
|
|
"$$"
|
|
]
|
|
},
|
|
{
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"cell_type": "markdown",
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}
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},
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|
"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)**"
|
|
]
|
|
},
|
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{
|
|
"cell_type": "code",
|
|
"execution_count": 4,
|
|
"id": "ee683060",
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"metadata": {
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"grade": true,
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"locked": false,
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}
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},
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"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)"
|
|
]
|
|
},
|
|
{
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"cell_type": "code",
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"outputs": [
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|
{
|
|
"data": {
|
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"image/png": 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\n",
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"text/plain": [
|
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"<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",
|
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" \"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": 6,
|
|
"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 864x576 with 4 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"max_distance = 15\n",
|
|
"\n",
|
|
"fig, axs = plt.subplots(2, 2, figsize=(12, 8))\n",
|
|
"axs = axs.ravel()\n",
|
|
"fig.suptitle(r\"Finite-size scaling with Hausdorff dimension $d_H$ for different triangulation models\")\n",
|
|
"\n",
|
|
"for idx_model, model in enumerate(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",
|
|
" \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",
|
|
" ax = axs[idx_model]\n",
|
|
" ax.set_title(f\"{model_names[model]} ({model}) with $d_H = {d_H:.2f}$\")\n",
|
|
" for i, profile in enumerate(mean_profiles):\n",
|
|
" rvals = np.arange(len(profile))\n",
|
|
" ax.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",
|
|
" ax.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",
|
|
" ax.set_xlabel(r\"$x = r/V^{1/d_H}$\")\n",
|
|
" ax.set_ylabel(r\"$V^{1/d_H}\\,\\mathbb{E}[\\frac{1}{V}\\rho_T(r)]$\")\n",
|
|
" ax.set_xlim(0,3)\n",
|
|
" ax.grid(True, which=\"both\", ls=\"-\")\n",
|
|
" ax.legend(sizes, title=\"V\")\n",
|
|
" \n",
|
|
"fig.tight_layout()\n",
|
|
"fig.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
|
|
}
|