Towards a Spectral Theory for Simplicial Complexes

Towards a Spectral Theory for Simplicial Complexes

[1]  J. W. Alexander,et al.  The Combinatorial Theory of Complexes , 1930 .

[2]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[3]  The Hodge laplacian on manifolds with boundary , 2003 .

[4]  A. Sokal,et al.  Bounds on the ² spectrum for Markov chains and Markov processes: a generalization of Cheeger’s inequality , 1988 .

[5]  Magnus Egerstedt,et al.  Control Using Higher Order Laplacians in Network Topologies , 2006 .

[6]  B. Eckmann Harmonische Funktionen und Randwertaufgaben in einem Komplex , 1944 .

[7]  M. Fiedler Algebraic connectivity of graphs , 1973 .

[8]  Ronald Rosenfeld,et al.  Semi-supervised learning with graphs , 2005 .

[9]  Matthew Kahle,et al.  Coboundary expanders , 2010, 1012.5316.

[10]  N. Alon,et al.  il , , lsoperimetric Inequalities for Graphs , and Superconcentrators , 1985 .

[11]  J. Cheeger A lower bound for the smallest eigenvalue of the Laplacian , 1969 .

[12]  R. Meshulam,et al.  Homological connectivity of random k-dimensional complexes , 2009, Random Struct. Algorithms.

[13]  László Lovász,et al.  Random Walks on Graphs: A Survey , 1993 .

[14]  Sergey Fomin,et al.  Cluster algebras and triangulated surfaces. Part I: Cluster complexes , 2006 .

[15]  F. Chung Random walks and local cuts in graphs , 2007 .

[16]  Jianbo Shi,et al.  A Random Walks View of Spectral Segmentation , 2001, AISTATS.

[17]  L. Asz Random Walks on Graphs: a Survey , 2022 .

[18]  Bernhard Schölkopf,et al.  Learning from Labeled and Unlabeled Data Using Random Walks , 2004, DAGM-Symposium.

[19]  James R. Lee,et al.  Multiway Spectral Partitioning and Higher-Order Cheeger Inequalities , 2011, JACM.

[20]  Tamal K. Dey,et al.  Optimal homologous cycles, total unimodularity, and linear programming , 2010, STOC '10.

[21]  Tommi S. Jaakkola,et al.  Partially labeled classification with Markov random walks , 2001, NIPS.

[22]  Alexander Lubotzky,et al.  Ramanujan complexes and high dimensional expanders , 2012, 1301.1028.

[23]  Anna Gundert,et al.  On laplacians of random complexes , 2012, SoCG '12.

[24]  Kevin Françoisse,et al.  Semi-supervised Classification from Discriminative Random Walks , 2008, ECML/PKDD.

[25]  Nathan Linial,et al.  Homological Connectivity Of Random 2-Complexes , 2006, Comb..

[26]  J. Dodziuk Difference equations, isoperimetric inequality and transience of certain random walks , 1984 .

[27]  N. Linial,et al.  Expander Graphs and their Applications , 2006 .

[28]  Bojan Mohar,et al.  Isoperimetric numbers of graphs , 1989, J. Comb. Theory, Ser. B.