![]() ![]() All these forces depend on distances between the respective points, and applying them means moving a point in a direction. A third force, gravity, pulls all vertices towards the center of gravity, in our case the center point of the Poincaré disk. This algorithm works by applying forces to the vertices of the graph: All the vertices repel each other, while edges act as “springs” that pull vertices together. Our algorithm of choice was the already existing “Force Atlas 2” algorithm. As common graph layout tools, such as Gephi, can only layout graphs in Euclidean space, our goal in this semester’s project “Physical Graph Layout in Hyperbolic Space” was to implement an algorithm to layout graphs in hyperbolic space, that is, on the Poincaré disk model. Visual graph layouts are a nice tool to quickly spot symmetries and other structures on graphs. Voronov, “The Swiss-cheese operad”, in Homotopy Invariant Algebraic Structures, Contemporary Mathematics 239 (1999) 365–373.Written by David Li, Anna Roth Introduction Tamari, “Monoïdes préordonnés et chaînes de Malcev”, Doctorat ès-Sciences Mathématiques Thèse de Mathématiques, Université de Paris (1951).Ī. Stasheff, “Homotopy associativity of H-spaces”, Transactions of the American Mathematical Society 108 (1963), 275–292.ĭ. ![]() Ratcliffe, Foundations of hyperbolic manifolds, Springer-Verlag, New York, 1994. Wolfson, “Pseudo-holomorphic maps and bubble trees”, Journal ofGeometric Analysis 3 (1993) 63–98. Kirwan, Geometric Invariant Theory, Springer-Verlag, New York, 1994. Lee, “The associahedron and triangulations of the n-gon”, European Journal of Combinatorics 10 (1989) 551–560.ĭ. Manin, “Gromov-Witten classes, quantum cohomology, and enumerative geometry”, Communications in Mathematical Physics 164 (1994) 525–562.Ĭ. Kontsevich, “Deformation quantization of Poisson manifolds”, Letters in Mathematical Physics 66 (2003) 157–216. Stasheff, “Open-closed homotopy algebra in mathematical physics”, Journal of Mathematical Physics 47 (2006). Hoefel, “OCHA and the Swiss-cheese operad”, Journal ofHomotopy and Related Structures 4 (2009) 123–151. ![]() Manin “Multiple ζ-motives and moduli spaces ¯ℳ 0, n(ℝ)”, Compositio Mathematica 140 (2004) 1–14.Į. MacPherson, “A compactification of configuration spaces”, Annals of Mathematics 139 (1994) 183–225.Ī. Ono, “Lagrangian intersection Floer theory: anomaly and obstruction”, Kyoto Department of Mathematics 00–17. Morava, “Diagonalizing the genome I”, /abs/1009.3224. Vipismakul, “Deformations of bordered surfaces and convex polytopes”, Notices of the American Mathematical Society (2011) 530–541. Devadoss, “Combinatorial equivalence of real moduli spaces”, Notices of the American Mathematical Society (2004) 620–628. Devadoss, “A space of cyclohedra”, Discrete and Computational Geometry 29 (2003), 61–75. Devadoss, “Tessellations of moduli spaces and the mosaic operad”, in Homotopy Invariant Algebraic Structures, Contemporary Mathematics 239 (1999) 91–114. Procesi, “Wonderful models of subspace arrangements”, Selecta Mathematica 1 (1995) 459–494. Devadoss, “Coxeter complexes and graph-associahedra”, Topology and its Applications 153 (2006) 2155–2168.Ĭ. Taubes, “On the self-linking of knots”, Journal of Mathematical Physics 35 (1994) 5247–5287. Singer, “Chern-Simons perturbation theory II”, Journal of Differential Geometry 39 (1994) 173–213. Manapat, “Particle configurations and Coxeter operads”, Journal of Homotopy and Related Structures 4 (2009) 83–109. ![]()
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