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The ergodicity landscape of quantum theories

Wen Wei Ho, Đorđe Radičević
2018 International Journal of Modern Physics A  
We also provide an operator-based discussion of quantum chaos and propose criteria to distinguish bases that can usefully diagnose ergodicity.  ...  As a special case, we study the SYK model and report on the transition from maximal to partial ergodicity as the disorder strength is decreased.  ...  A similar story exists for metric graphs, where random matrix theory is accessed through counting graph cycles of a given length [68] .  ... 
doi:10.1142/s0217751x18300041 fatcat:7722hqun2fb6vhbxnajxuuvjny

Dynamical properties of profinite actions

MIKLÓS ABÉRT, GÁBOR ELEK
2011 Ergodic Theory and Dynamical Systems  
That this is not true for families of subgroups in general leads to the question of Lubotzky and Zuk: for families of subgroups, is property (τ ) inherited by the lattice of subgroups generated by the  ...  We show that two strongly ergodic profinite actions of a group are weakly equivalent if and only if they are isomorphic.  ...  Strong ergodicity and spectral gap for finite index subgroups This section analyzes what happens to the strong ergodicity and spectral gap properties for a general measure-preserving action when restricting  ... 
doi:10.1017/s0143385711000654 fatcat:drgqf7tbyban5itak3qfnz276e

Recent results of quantum ergodicity on graphs and further investigation

Nalini Anantharaman, Mostafa Sabri
2019 Annales de la Faculté des Sciences de Toulouse  
de Strasbourg, and by Institut Universitaire de France.  ...  Acknowledgements This material is based upon work supported by the Agence Nationale de la Recherche under grant No.ANR-13-BS01-0007-01, by the Labex IRMIA and the Institute of Advance Study of Université  ...  Quantum ergodicity is a result of spatial delocalization for the eigenfunctions of the adjacency matrix (and more generally, discrete Schrödinger operators) on a large graph.  ... 
doi:10.5802/afst.1609 fatcat:poxiyyrasvfjxgyrrge73wacne

Causal and non-causal filtering for network reconstruction

Donatello Materassi, Murti V. Salapaka
2011 Proceedings of the 2011 American Control Conference  
children) in the graph.  ...  In particular, it is proven that the method determines a link to be present only between the kins of a node where kins of a node consist of parents, children and co-parents (other parents of all of its  ...  In [12] a similar strategy, where the correlation metric is replaced by a metric based on the coherence function, is numerically shown to provide an exact reconstruction for tree topologies.  ... 
doi:10.1109/acc.2011.5991173 fatcat:p535av2ci5hctj7igxcwjjqezq

Obtaining Measure Concentration from Markov Contraction [article]

Leonid Kontorovich
2012 arXiv   pre-print
Our technique consists of expressing probabilities as matrix products and applying Markov contraction to these expressions; thus it is fairly general and holds the potential to yield further results in  ...  As an alternative to coupling, we use the elementary Markov contraction lemma to obtain simple, useful, and apparently novel concentration results for various Markov-type processes.  ...  Acknowledgments Many thanks to Gideon Schechtman for hosting and guidance at the Weizmann Institute, and to Elchanan Mossel and Cosma Shalizi for helpful comments on the manuscript.  ... 
arXiv:0711.0987v2 fatcat:eyriin5igfctdjioo7blnhyeee

On the Problem of Reconstructing an Unknown Topology via Locality Properties of the Wiener Filter

Donatello Materassi, Murti V. Salapaka
2012 IEEE Transactions on Automatic Control  
His research interests include nonlinear dynamics, system identification, and classical control theory with applications to atomic force microscopy, single molecule force spectroscopy, biophysics, statistical  ...  mechanics, and quantitative finance.  ...  Definition 3 (Children and Parents): Given a graph and a node , the children of are defined as and the parents of as .  ... 
doi:10.1109/tac.2012.2183170 fatcat:idxh6w4hyfepvitjn6c4uqq7w4

Survey: Information flow on trees [article]

Elchanan Mossel
2004 arXiv   pre-print
In this paper, we survey developments and challenges related to this problem.  ...  For which T and M does the configuration obtained at level n of T typically contain significant information on the root variable?  ...  I want to thank him for many fruitful conversations about the problem.  ... 
arXiv:math/0406446v1 fatcat:c4ntnojm2rhqrfikxrz3kkaqcm

Survey: Information flow on trees [chapter]

Elchanan Mossel
2004 DIMACS Series in Discrete Mathematics and Theoretical Computer Science  
In this paper, we survey developments and challenges related to this problem.  ...  For which T and M does the configuration obtained at level n of T typically contain significant information on the root variable?  ...  I want to thank him for many fruitful conversations about the problem.  ... 
doi:10.1090/dimacs/063/12 dblp:conf/dimacs/Mossel01 fatcat:hngd3fec65dhfhh73rpk3znu3m

Introduction to Teichmüller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards [article]

Giovanni Forni, Carlos Matheus
2013 arXiv   pre-print
We sketch two applications of the ergodic properties of the Teichmüller flow and Kontsevich-Zorich cocycle, with respect to Masur-Veech measures, to the unique ergodicity, deviation of ergodic averages  ...  , Geometry and Number Theory" (from 4 to 16 July, 2011).  ...  shorter and shorter (so that they wrap around the surface less and less), thus making it reasonably easier to analyze.  ... 
arXiv:1311.2758v1 fatcat:cpfkei7kinbnvffcu3gzoixb64

Some topics in the dynamics of group actions on rooted trees

R. I. Grigorchuk
2011 Proceedings of the Steklov Institute of Mathematics  
The concepts of asymptotic expander and asymptotic Ramanujan graph are introduced, and examples of such graphs are given.  ...  It presents a review of some results obtained during the last decade in problems related to the dynamics of branch and self-similar groups on the boundary of a spherically homogeneous rooted tree and to  ...  ACKNOWLEDGMENTS In conclusion, I would like to express my deep gratitude to my colleagues and students for the long fruitful joint research, for the useful discussions that took place during the two years  ... 
doi:10.1134/s0081543811040067 fatcat:ntspoyasofbcffubrj5cw33bdm

Detecting Communities under Differential Privacy [article]

Hiep H. Nguyen, Abdessamad Imine, Michael Rusinowitch
2016 arXiv   pre-print
We analyze the major challenges behind the problem and propose several schemes to tackle them from two perspectives: input perturbation and algorithm perturbation.  ...  We choose Louvain method as the back-end community detection for input perturbation schemes and propose the method LouvainDP which runs Louvain algorithm on a noisy super-graph.  ...  Community Detection in Graphs There is a vast literature on community detection in graphs. For a recent comprehensive survey, we refer to [13] .  ... 
arXiv:1607.02060v1 fatcat:nsvxlgvbj5ffhfr5fqqpuz5q6e

Universal Graph Compression: Stochastic Block Models [article]

Alankrita Bhatt, Ziao Wang, Chi Wang, Lele Wang
2021 arXiv   pre-print
, and Lempel-Ziv compressor for two-dimensional data) take 2.4 to 27 times the space needed by the proposed scheme.  ...  The key ideas in establishing universality for stochastic block models include: 1) block decomposition of the adjacency matrix of the graph; 2) generalization of the Krichevsky-Trofimov probability assignment  ...  She is grateful to Young-Han Kim and Ofer Shayevitz for their interest and encouragement in this result. C. Wang would like to thank Richard Peng for his suggestion in writing.  ... 
arXiv:2006.02643v2 fatcat:kb27g2dorvhvzboxiz6pjnj2xi

Some Fundamental Theorems in Mathematics [article]

Oliver Knill
2022 arXiv   pre-print
An expository hitchhikers guide to some theorems in mathematics.  ...  For a literature source, see [363] . For more general number theory literature, see [333, 119] .  ...  For literature, see [351] .  ... 
arXiv:1807.08416v4 fatcat:lw7lbsxyznfrnaozilxapihmdy

HAMDA: Hybrid Approach for MiRNA-Disease Association prediction

Xing Chen, Ya-Wei Niu, Guang-Hui Wang, Gui-Ying Yan
2017 Journal of Biomedical Informatics  
In this study, we developed a computational model of Hybrid Approach for MiRNA-Disease Association prediction (HAMDA), which involved the hybrid graph-based recommendation algorithm, to reveal novel miRNA-disease  ...  for predicting potential associations between disease and miRNA.  ...  for diseases and miRNAs, into a heterogeneous graph to infer the potential association between a miRNA and a disease by summarizing all paths with the length equal to three in the graph.  ... 
doi:10.1016/j.jbi.2017.10.014 pmid:29097278 fatcat:xghdummklfda7fxk3nll4bdbyi

Generating Nearly Sorted Sequences – The use of measures of disorder

Vladimir Estivill-Castro
2004 Electronical Notes in Theoretical Computer Science  
We show here that definitions that allow equivalence to an operational formulation allow for the construction of an algorithm for pseudo-random generation of nearly sorted sequences.  ...  benchmarks datasets to compare such algorithms.  ...  Section 2 presents right invariant metrics and measures of disorder appearing in the literature.  ... 
doi:10.1016/j.entcs.2003.12.006 fatcat:h2fyvsv22jcg7e6gky2zjkfndm
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