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The Mathematical Life of Fan Chung

2020
*
Notices of the American Mathematical Society
*

He gave her

doi:10.1090/noti2036
fatcat:ftxy6cqy25eufouciq6gzrdsde
*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. ...##
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A remark on charge transfer processes in multi-particle systems
[article]

2014
*
arXiv
*
pre-print

We assess the probability of resonances between sufficiently

arXiv:1005.3387v4
fatcat:uzdnczokh5fvxgcymhyxlx5uta
*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). ...##
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On Partial Charge Transfer Processes in Multiparticle Systems on Graphs

2014
*
Journal of Operators
*

We extend to any number of particles the efficient EVC

doi:10.1155/2014/373754
fatcat:guqd6w7urbg2tlvm5nkf7bb3bi
*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*. ...##
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Graph Clustering Using Early-Stopped Random Walks
[chapter]

2016
*
Lecture Notes in Computer Science
*

The computed vectors constitute

doi:10.1007/978-3-319-45378-1_37
fatcat:wpuptlwgtnegpnmes46q7s7g5a
*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*. ...##
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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. ...

##
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A Survey of Algorithms for Dense Subgraph Discovery
[chapter]

2010
*
Managing and Mining Graph Data
*

In this chapter, we present

doi:10.1007/978-1-4419-6045-0_10
dblp:series/ads/LeeRJA10
fatcat:u5vzetjlovetpdcxdwjqihdjnq
*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 ...##
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Glauber dynamics on nonamenable graphs: boundary conditions and mixing time

2008
*
Electronic Journal of Probability
*

We show that

doi:10.1214/ejp.v13-574
fatcat:umxvgs7kkjg25ow7f5f47j5pmi
*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. ...##
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Efficient uncertainty minimization for fuzzy spectral clustering

2009
*
Physical Review E
*

However, traditional

doi:10.1103/physreve.80.056705
pmid:20365094
fatcat:beqd6aglvva2ximppjeifrygqm
*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. ...##
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Glauber dynamics on nonamenable graphs: Boundary conditions and mixing time
[article]

2008
*
arXiv
*
pre-print

We show that

arXiv:0712.0489v4
fatcat:xax4qu5tfvc6becmvwocgsmdga
*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. ...##
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Steiner Point Removal --- Distant Terminals Don't (Really) Bother
[article]

2017
*
arXiv
*
pre-print

of independent exponential random variables, which allow us to show that it is unlikely

arXiv:1703.08790v1
fatcat:mpvsenjvbrcsxiiuopy2r4xjqa
*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. ...##
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Global and Local Uncertainty Principles for Signals on Graphs
[article]

2016
*
arXiv
*
pre-print

While previous work has focused on

arXiv:1603.03030v1
fatcat:jqstt3b5ljgslifsoy2rlycoay
*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. ...##
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Global and local uncertainty principles for signals on graphs

2018
*
APSIPA Transactions on Signal and Information Processing
*

While previous work has focused on

doi:10.1017/atsip.2018.2
fatcat:fvjprrofj5ddfn6gldwprgnozy
*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. ...##
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Direct Scaling Analysis of Fermionic Multiparticle Correlated Anderson Models with Infinite-Range Interaction

2016
*
Advances in Mathematical Physics
*

Combined with

doi:10.1155/2016/2129682
fatcat:7keofuqj7vd3re2qsoxhcyi6ea
*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 ...##
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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

doi:10.35940/ijitee.a4217.119119
fatcat:5gx55paz7fes5cgymr7lf67vwe
*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). ...##
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On graphs with maximum Harary spectral radius
[article]

2014
*
arXiv
*
pre-print

Let G be

arXiv:1411.6832v1
fatcat:3etxf22nabcwhkow5egx445dxy
*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. ...
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