2,516 research outputs found

    Zero Forcing Sets and Bipartite Circulants

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    In this paper we introduce a class of regular bipartite graphs whose biadjacency matrices are circulant matrices and we describe some of their properties. Notably, we compute upper and lower bounds for the zero forcing number for such a graph based only on the parameters that describe its biadjacency matrix. The main results of the paper characterize the bipartite circulant graphs that achieve equality in the lower bound.Comment: 22 pages, 13 figure

    On the t-Term Rank of a Matrix

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    For t a positive integer, the t-term rank of a (0,1)-matrix A is defined to be the largest number of 1s in A with at most one 1 in each column and at most t 1s in each row. Thus the 1-term rank is the ordinary term rank. We generalize some basic results for the term rank to the t-term rank, including a formula for the maximum term rank over a nonempty class of (0,1)-matrices with the the same row sum and column sum vectors. We also show the surprising result that in such a class there exists a matrix which realizes all of the maximum terms ranks between 1 and t.Comment: 18 page

    Cyclic Matching Sequencibility of Graphs

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    We define the cyclic matching sequencibility of a graph to be the largest integer dd such that there exists a cyclic ordering of its edges so that every dd consecutive edges in the cyclic ordering form a matching. We show that the cyclic matching sequencibility of K2mK_{2m} and K2m+1K_{2m+1} equal m‚ąí1m-1

    Spectral arbitrariness for trees fails spectacularly

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    If GG is a graph and m\mathbf{m} is an ordered multiplicity list which is realizable by at least one symmetric matrix with graph GG, what can we say about the eigenvalues of all such realizing matrices for m\mathbf{m}? It has sometimes been tempting to expect, especially in the case that GG is a tree, that any spacing of the multiple eigenvalues should be realizable. In 2004, however, F. Barioli and S. Fallat produced the first counterexample: a tree on 16 vertices and an ordered multiplicity list for which every realizing set of eigenvalues obeys a nontrivial linear constraint. We extend this by giving an infinite family of trees and ordered multiplicity lists whose sets of realizing eigenvalues are very highly constrained, with at most 5 degrees of freedom, regardless of the size of the tree in this family. In particular, we give the first examples of multiplicity lists for a tree which impose nontrivial nonlinear eigenvalue constraints and produce an ordered multiplicity list which is achieved by a unique set of eigenvalues, up to shifting and scaling.Comment: 45 page

    Glueball production in radiative J/psi, Upsilon decays

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    Using a bound-state model of weakly bound gluons for glueballs made of two gluons and a natural generalization of the perturbative QCD formalism for exclusive hadronic processes, we present results for glueball production in radiative J/psi, Upsilon decays into several possible glueball states, including L \not= 0 ones. We perform a detailed phenomenological analysis, presenting results for the more favored experimental candidates and for decay angular distributions.Comment: RevTeX4, 26 pages, 11 eps figure

    Enhanced stability of layered phases in parallel hard-spherocylinders due to the addition of hard spheres

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    There is increasing evidence that entropy can induce microphase separation in binary fluid mixtures interacting through hard particle potentials. One such phase consists of alternating two dimensional liquid-like layers of rods and spheres. We study the transition from a uniform miscible state to this ordered state using computer simulations and compare results to experiments and theory. We conclude that (1) there is stable entropy driven microphase separation in mixtures of parallel rods and spheres, (2) adding spheres smaller then the rod length decreases the total volume fraction needed for the formation of a layered phase, therefore small spheres effectively stabilize the layered phase; the opposite is true for large spheres and (3) the degree of this stabilization increases with increasing rod length.Comment: 11 pages, 9 figures. Submitted to Phys. Rev. E. See related website http://www.elsie.brandeis.ed

    A surveillance system for monitoring, public reporting, and improving minority access to cancer clinical trials

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    The Institute of Medicine (IOM) has recommended that each person with cancer should have access to clinical trials, which have been associated with improving care quality and disparities. With no effective enrollment monitoring system, patterns of trial enrollment remain unclear
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