[PDF] Top 20 On eigenvalue inequalities of a matrix whose graph is bipartite

... We consider the set of real zero diagonal symmetric matrices whose underlying graph, if not told otherwise, is bipartite. Then we establish relations between the eigenvalues of such matrices and ... See full document

... 2 ) −e(G) , (1.1) where e(G) is the number of the edges of G. Most of the random graphs studies are devoted to the cases where p N → 0 as N → ∞. Intersection of these two branches of the theory of graphs includes the ... See full document

... the graph K(G, u j1 , u j2 ), the number of incoming and outgoing edges are the same, while c i1 has two more outgoing edges than incoming and c i2 has two more incom- ing edges than ...simple graph of K ... See full document

... connected, and a ij = 0 otherwise). The spectrum of the graph is the set of n eigenvalues of the adjacency matrix. The model of a random graph, introduced by P. Erdos (see, e.g., [7] and references ... See full document

... N i denotes the set of its neighbours. A clique means a complete subgraph. The clique number of G is the size of a maximal clique in G and is denoted by cl (G). By K p we denote the complete graph on p vertices. ... See full document

... Hermitian matrix, and properties of and decomposition algorithms for parahermitian matrices. The parahermitian EVD problem is then mapped to the unit circle, i.e. |z| = 1 , in Section III where we look at the ... See full document

... HAO TANG ET AL.: BIPARTITE GRAPH REASONING GANS Figure 6: (left) Qualitative comparisons of ablation study on Market-1501. (right) Visual- ization of the learned attention masks and intermediate results. ... See full document

... Both examples discussed before illustrate scenarios in which mismatches and improper hit type classifications may increase, if the size of the target video clip is not carefully chosen. Thus, the size of the target video ... See full document

... constrained graph layout has involved projection of simple two-variable linear equality and inequality constraints in the context of majorization or gradient-projection based ... See full document

... In this paper we introduced the semi-bipartite graph for the visual analysis of microarray experiments using the Gene Ontology. Among the proposed lay- out algorithms, sub-hierarchy barycenter, partition ... See full document

... Expression microarrays [2] have been widely used to measure gene expression level —the activity level of genes—in biological experiments. A typical microar- ray experiment involves comparing the gene expression levels of ... See full document

... (10) Combining Eqs. (9) and (10) we get the result (8). Theorem 3.2. Let G be any graph with n vertices and let ∆ be the absolute value of the determinant of the eccentricity sum matrix ES(G). Then ... See full document

... ordinary eigenvalue problem for a given matrix is defined, as well as the terms of eigenvalues, eigenvectors and characteristic poly- nomial of ...generalized eigenvalue problem for matrix ... See full document

... Clearly, C(n,0) = 1 for all n, and by the results of [33], see also [22, 25, 1], one can take C(2,k) = 2k + 1 for k > 1. To our knowledge, the question above is open even for convex domains, where we have a positive ... See full document

... related matrix parameters, such as the norm of the monic orthogonal polynomials, the coefficients of the three term recurrence relation or the coefficients of the linear relation between the polynomials and their ... See full document

... b Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 24-107, Cambridge, MA 02139, USA Abstract This paper presents new algorithms for use in the ... See full document

... complete graph is a collection of graphs such that every two of them share exactly one edge and every edge of the complete graph belongs to exactly two of the ...the graph to be covered twice is the ... See full document

... fixed matrix, the problem of column subset selection requests a column subma- trix that has favorable spectral ...selection whose algorithmic implications have not been ...each matrix with normalized ... See full document

... covariance matrix or its inverse, called the precision matrix, is an important and sometimes inevitable task in data ...random matrix theory researches (see Bai and Silverstein (2010), for example), ... See full document

... [ ] a b , and the labellings [ 0, 1 − ] of the lower vertices [ ] c d , are sequences. The goal of this paper is to find new sequence in order to generate wrapped Δ -labellings as cluttered orderings for the complete ... See full document