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The Mathematical Life of Fan Chung

Steve Butler
2020 Notices of the American Mathematical Society  
He gave her a paper in the area of Ramsey theory to read and an appointment to meet a week later. At that appointment she pointed to a result and declared that she could "do a little better."  ...  Her performance attracted the attention of a faculty member who sought her out in hopes of recruiting her as a student.  ...  The author thanks Fan Chung for help in preparing the article, as well as the many years of mentoring and friendship.  ... 
doi:10.1090/noti2036 fatcat:ftxy6cqy25eufouciq6gzrdsde

A remark on charge transfer processes in multi-particle systems [article]

Victor Chulaevsky
2014 arXiv   pre-print
We assess the probability of resonances between sufficiently distant states in a combinatorial graph serving as the configuration space of an N-particle disordered quantum system.  ...  We show that more efficient bounds, obtained so far only for 2-particle systems, extend to any number of particles.  ...  Eigenvalue concentration bound for distant balls 3.1. Bounds for weakly separable balls.Lemma 3.1. Let V : Z × Ω → R be a random field satisfying the condition (RCM).  ... 
arXiv:1005.3387v4 fatcat:uzdnczokh5fvxgcymhyxlx5uta

On Partial Charge Transfer Processes in Multiparticle Systems on Graphs

Victor Chulaevsky
2014 Journal of Operators  
We extend to any number of particles the efficient EVC bounds, obtained earlier for the 2-particle systems.  ...  We assess the probability of resonances between sufficiently distant states of an N-particle disordered quantum system in a combinatorial graph Z.  ...  Nariyuki Minami, Stanislav A.  ... 
doi:10.1155/2014/373754 fatcat:guqd6w7urbg2tlvm5nkf7bb3bi

Graph Clustering Using Early-Stopped Random Walks [chapter]

Małgorzata Lucińska, Sławomir T. Wierzchoń
2016 Lecture Notes in Computer Science  
The computed vectors constitute a local approximation of the leading eigenvectors. The algorithm performance is competitive to the traditional spectral solutions in terms of computational complexity.  ...  We propose a novel approach to clustering, based on random walks.  ...  After choosing a seed vertex A, for each vertex i, we update the probability of being absorbed by this A before the random walker will be captured by other distant vertex.  ... 
doi:10.1007/978-3-319-45378-1_37 fatcat:wpuptlwgtnegpnmes46q7s7g5a

Page 1719 of Mathematical Reviews Vol. , Issue 2004c [page]

2004 Mathematical Reviews  
A. (E-UPB-TL; Barcelona) A general spectral bound for distant vertex subsets. (English summary) Combin. Probab. Comput. 12 (2003), no. 1, 17-26.  ...  vertex on a g-cycle and a pendant vertex of a path on n — g vertices.  ... 

A Survey of Algorithms for Dense Subgraph Discovery [chapter]

Victor E. Lee, Ning Ruan, Ruoming Jin, Charu Aggarwal
2010 Managing and Mining Graph Data  
In this chapter, we present a survey of algorithms for dense subgraph discovery.  ...  For example, the problem of clustering is largely concerned with that of finding a fixed partition in the data, whereas the problem of dense subgraph discovery defines these dense components in a much  ...  Alkemade Algorithm 11 Crochet( 1 , 2 , 1 , 2 , ) 1: for all graph do 2: construct set enumeration tree for all possible vertex subsets of ; 3: ← upper bound diameter of complete -quasi-complete graph  ... 
doi:10.1007/978-1-4419-6045-0_10 dblp:series/ads/LeeRJA10 fatcat:u5vzetjlovetpdcxdwjqihdjnq

Glauber dynamics on nonamenable graphs: boundary conditions and mixing time

Alessandra Bianchi
2008 Electronic Journal of Probability  
We show that for all low enough temperatures, the spectral gap of the dynamics with (+)-boundary condition on a class of nonamenable graphs, is strictly positive uniformly in n.  ...  In addition, we construct a graph in this class, for which the mixing time in the free boundary case is exponentially large in n.  ...  I am grateful to an anonymous referee for very useful comments and suggestions on earlier draft.  ... 
doi:10.1214/ejp.v13-574 fatcat:umxvgs7kkjg25ow7f5f47j5pmi

Efficient uncertainty minimization for fuzzy spectral clustering

Brian S. White, David Shalloway
2009 Physical Review E  
However, traditional spectral clustering partitions items into hard clusters, and the ability to instead generate fuzzy item assignments would be advantageous for the growing class of domains in which  ...  Here we develop a new method for solving the minimization problem, which can handle data sets at least two orders of magnitude larger.  ...  subspaces, and the requirement for a spectral gap.  ... 
doi:10.1103/physreve.80.056705 pmid:20365094 fatcat:beqd6aglvva2ximppjeifrygqm

Glauber dynamics on nonamenable graphs: Boundary conditions and mixing time [article]

Alessandra Bianchi
2008 arXiv   pre-print
We show that for all low enough temperatures, the spectral gap of the dynamics with (+)-boundary condition on a class of nonamenable graphs, is strictly positive uniformly in n.  ...  In addition, we construct a graph in this class, for which the mixing time in the free boundary case is exponentially large in n.  ...  Then, in section 4, we deduce from this property a lower bound for the spectral gap of the dynamics and conclude the proof of our main result.  ... 
arXiv:0712.0489v4 fatcat:xax4qu5tfvc6becmvwocgsmdga

Steiner Point Removal --- Distant Terminals Don't (Really) Bother [article]

Yun Kuen Cheung
2017 arXiv   pre-print
of independent exponential random variables, which allow us to show that it is unlikely for a non-terminal being contracted to a distant terminal.  ...  Given a weighted graph G=(V,E,w) with a set of k terminals T⊂ V, the Steiner Point Removal problem seeks for a minor of the graph with vertex set T, such that the distance between every pair of terminals  ...  This allows us to show that it is unlikely for a non-terminal being contracted to a distant terminal. Further Related Work.  ... 
arXiv:1703.08790v1 fatcat:mpvsenjvbrcsxiiuopy2r4xjqa

Global and Local Uncertainty Principles for Signals on Graphs [article]

Nathanael Perraudin, Benjamin Ricaud, David Shuman, Pierre Vandergheynst
2016 arXiv   pre-print
While previous work has focused on generalizing notions of spreads of a graph signal in the vertex and graph spectral domains, our approach is to generalize the methods of Lieb in order to develop uncertainty  ...  principles that provide limits on the concentration of the analysis coefficients of any graph signal under a dictionary transform whose atoms are jointly localized in the vertex and graph spectral domains  ...  Each bump of the global bound corresponds to a local bound of a given spectral band of node 1. For clarity, we plot only bands g 0 and g 2 for node 1.  ... 
arXiv:1603.03030v1 fatcat:jqstt3b5ljgslifsoy2rlycoay

Global and local uncertainty principles for signals on graphs

Nathanael Perraudin, Benjamin Ricaud, David I Shuman, Pierre Vandergheynst
2018 APSIPA Transactions on Signal and Information Processing  
While previous work has focused on generalizing notions of spreads of graph signals in the vertex and graph spectral domains, our approach generalizes the methods of Lieb in order to develop uncertainty  ...  Accordingly, we suggest new notions of locality, and develop local uncertainty principles that bound the concentration of the analysis coefficients of each atom of a localized graph spectral filter frame  ...  Each bump of the global bound corresponds to a local bound of a given spectral band of node 1. For clarity, we plot only bands g 0 and g 2 for node 1.  ... 
doi:10.1017/atsip.2018.2 fatcat:fvjprrofj5ddfn6gldwprgnozy

Direct Scaling Analysis of Fermionic Multiparticle Correlated Anderson Models with Infinite-Range Interaction

Victor Chulaevsky
2016 Advances in Mathematical Physics  
Combined with a recent eigenvalue concentration bound for multiparticle systems, the new method leads to a simpler proof of the multiparticle dynamical localization with optimal decay bounds in a natural  ...  distance in the multiparticle configuration space, for a large class of strongly mixing random external potentials.  ...  Acknowledgments It is a pleasure to thank Tom Spencer, Boris Shapiro, Abel Klein, and Misha Goldstein for fruitful discussions of the localization techniques, the organizers of the programs "Mathematics  ... 
doi:10.1155/2016/2129682 fatcat:7keofuqj7vd3re2qsoxhcyi6ea

On Laplacian and Normalized Laplacian of a Social Network

2019 VOLUME-8 ISSUE-10, AUGUST 2019, REGULAR ISSUE  
In this paper we have found certain useful bounds involving the eigenvalues of both combinatorial Laplacian and normalized Laplacian and applied the same on a collaboration graph obtained from a social  ...  In the task of structural identification of a network a vital tool is the underlying spectrum associated with the normalized graph Laplacian.  ...  |is bounded above by (𝜂/p) √((p-|X|)|X||Y|(p-|Y|)) for any two subset X,Y of V(G), where Z= E 0 -(d/p)|X||Y|+ d |X ∩Y| -V 0 (X ∩Y).  ... 
doi:10.35940/ijitee.a4217.119119 fatcat:5gx55paz7fes5cgymr7lf67vwe

On graphs with maximum Harary spectral radius [article]

Fei Huang, Xueliang Li, Shujing Wang
2014 arXiv   pre-print
Let G be a simple graph with vertex set V(G) = {v_1 ,v_2 ,... ,v_n}.  ...  In this paper, we characterize graphs with maximum spectral radius of Harary matrix in three classes of simple connected graphs with n vertices: graphs with fixed matching number, bipartite graphs with  ...  Let X 0 be a vertex subset such that n − 2p = o(G − X 0 ) − |X 0 |. For convenience, let |X 0 | = s and o(G − X 0 ) = k. Then n − 2p = k − s. Since 1 ≤ p < ⌊ n 2 ⌋, we know that k − s ≥ 2.  ... 
arXiv:1411.6832v1 fatcat:3etxf22nabcwhkow5egx445dxy
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