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Algebraic Graph Theory
, 2011
"... Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area is the investiga ..."
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Cited by 892 (13 self)
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is the investigation of the relation between properties of a graph and the spectrum of its adjacency matrix. A central topic and important source of tools is the theory of association schemes. An association scheme is, roughly speaking, a collection of graphs on a common vertex set which fit together in a highly
The Determinants of Credit Spread Changes.
 Journal of Finance
, 2001
"... ABSTRACT Using dealer's quotes and transactions prices on straight industrial bonds, we investigate the determinants of credit spread changes. Variables that should in theory determine credit spread changes have rather limited explanatory power. Further, the residuals from this regression are ..."
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Cited by 422 (2 self)
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used. We conclude in Section V. 2 I. Theoretical Determinants of Credit Spread Changes Socalled structural models of default provide an intuitive framework for identifying the determinants of credit spread changes. 4 These models build on the original insights of Black and Scholes (1973), who
EIGENVALUES AND EXPANDERS
 COMBINATORICA
, 1986
"... Linear expanders have numerous applications to theoretical computer science. Here we show that a regular bipartite graph is an expander ifandonly if the second largest eigenvalue of its adjacency matrix is well separated from the first. This result, which has an analytic analogue for Riemannian mani ..."
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Cited by 400 (20 self)
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Linear expanders have numerous applications to theoretical computer science. Here we show that a regular bipartite graph is an expander ifandonly if the second largest eigenvalue of its adjacency matrix is well separated from the first. This result, which has an analytic analogue for Riemannian
Trading Group Theory for Randomness
, 1985
"... In a previous paper [BS] we proved, using the elements of the Clwory of nilyotenf yroupu, that some of the /undamcnla1 computational problems in mat & proup, belong to NP. These problems were also ahown to belong to CONP, assuming an unproven hypofhedi.9 concerning finilc simple Q ’ oup,. The a ..."
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Cited by 353 (9 self)
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,. The aim of this paper is t.o replace most of the (proven and unproven) group theory of IBS] by elementary combinatorial argumenls. The rev & we prove is that relative to a random oracle f3, tbc meutioned matrix group problems belong to (NPncoNP)L! Thr problems we consider arr membership in and order
An Aprioribased Algorithm for Mining Frequent Substructures from Graph Data
, 2000
"... This paper proposes a novel approach named AGM to efficiently mine the association rules among the frequently appearing substructures in a given graph data set. A graph transaction is represented by an adjacency matrix, and the frequent patterns appearing in the matrices are mined through the exte ..."
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Cited by 310 (7 self)
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This paper proposes a novel approach named AGM to efficiently mine the association rules among the frequently appearing substructures in a given graph data set. A graph transaction is represented by an adjacency matrix, and the frequent patterns appearing in the matrices are mined through
A steepest descent method for oscillatory Riemann–Hilbert problems: asymptotics for the MKdV equation
 Ann. of Math
, 1993
"... In this announcement we present a general and new approach to analyzing the asymptotics of oscillatory RiemannHilbert problems. Such problems arise, in particular, in evaluating the longtime behavior of nonlinear wave equations solvable by the inverse scattering method. We will restrict ourselves ..."
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Cited by 303 (27 self)
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for the MKdV equation leads to a RiemannHilbert factorization problem for a 2 × 2 matrix valued function m = m(·; x, t) analytic in C\R, (1) where m+(z) = m−(z)vx,t, z ∈ R, m(z) → I as z → ∞, m±(z) = lim ε↓0 m(z ± iε; x, t), vx,t(z) ≡ e −i(4tz3 +xz)σ3 v(z)e i(4tz 3 +xz)σ3, σ3 =
LexRank: Graphbased lexical centrality as salience in text summarization
 Journal of Artificial Intelligence Research
, 2004
"... We introduce a stochastic graphbased method for computing relative importance of textual units for Natural Language Processing. We test the technique on the problem of Text Summarization (TS). Extractive TS relies on the concept of sentence salience to identify the most important sentences in a doc ..."
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Cited by 266 (9 self)
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representation of sentences. In this model, a connectivity matrix based on intrasentence cosine similarity is used as the adjacency matrix of the graph representation of sentences. Our system, based on LexRank ranked in rst place in more than one task in the recent DUC 2004 evaluation. In this paper we present
A spectral technique for correspondence problems using pairwise constraints
 In International Conference on Computer Vision
, 2005
"... Abstract We present an efficient spectral method for finding consistent correspondences between two sets of features. We build the adjacency matrix M of a graph whose nodes represent the potential correspondences and the weights on the links represent pairwise agreements between potential correspon ..."
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Cited by 251 (10 self)
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Abstract We present an efficient spectral method for finding consistent correspondences between two sets of features. We build the adjacency matrix M of a graph whose nodes represent the potential correspondences and the weights on the links represent pairwise agreements between potential
The adjacency matrix of the graph depicted above is
"... There are several possibilities to represent a graph G = (V,E) in memory. Let the set of nodes be V = {1, 2,..., n} with edges E ⊆ V × V, and let m: = E. ..."
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There are several possibilities to represent a graph G = (V,E) in memory. Let the set of nodes be V = {1, 2,..., n} with edges E ⊆ V × V, and let m: = E.
On Krylov subspace approximations to the matrix exponential operator
 SIAM J. NUMER. ANAL
, 1997
"... Krylov subspace methods for approximating the action of matrix exponentials are analyzed in this paper. We derive error bounds via a functional calculus of Arnoldi and Lanczos methods that reduces the study of Krylov subspace approximations of functions of matrices to that of linear systems of equ ..."
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Cited by 183 (6 self)
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Krylov subspace methods for approximating the action of matrix exponentials are analyzed in this paper. We derive error bounds via a functional calculus of Arnoldi and Lanczos methods that reduces the study of Krylov subspace approximations of functions of matrices to that of linear systems
Results 1  10
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