8 pages matching separation histograms PSH in this book
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3-manifold of constant arises in simulations average number Clifford translation comparable catalogues computer-aided simulations connected space constant curvature cosmic images cosmic objects covering group covering isometries covering manifold cubic manifold T4 distance correlations dodecahedron EPSH corresponding exp(s exp(si expected number extract the topological Figure FÍSICA flat manifolds FP and Ba fs(si give rise hyperbolic geometry hyperbolic manifolds images per catalogue isometry g mean pair separation MPSH procedure MPSH technique multiply connected manifold multiply connected RW multiply connected universe multiply-connectedness non-translational isometries number of images number of pairs number of seeds observable images observed universe Ba obtaining extracting obtaining the topological p(si pair separation histogram polyhedron quotient manifolds Rio de Janeiro Robertson-Walker role of non-translational separation histograms PSH signature of multiply spacetimes specific isometry spike spectrum spikes in PSH's statistical fluctuations statistical noises suitable approach tetrahedron theoretical results topological signature arises topological signature ps(si topological spikes uniform distribution universe with radius