相关论文: A Simple Mathematical Model of Politics (II)
A new approach to solving eigenvalue optimization problems for large structured matrices is proposed and studied. The class of optimization problems considered is related to computing structured pseudospectra and their extremal points, and…
A map of a set to itself admits a representation by a graph with vertices being the elements of the set and an edge between every vertex and its image. Communities defined as the maximal connected components are uni-cyclic. The…
An efficient algorithm for computing eigenvectors of a matrix of integers by exact computation is proposed. The components of calculated eigenvectors are expressed as polynomials in the eigenvalue to which the eigenvector is associated, as…
Matrix functions play an important role in applied mathematics. In network analysis, in particular, the exponential of the adjacency matrix associated with a network provides valuable information about connectivity, as well as about the…
Community structure analysis is a powerful tool for complex networks, which can simplify their functional analysis considerably. Recently, many approaches were proposed to community structure detection, but few works were focused on the…
We consider a class of rotationally invariant unitary random matrix ensembles where the eigenvalue density falls off as an inverse power law. Under a new scaling appropriate for such power law densities (different from the scaling required…
Euclidean random matrices arise in a wide range of physical systems where interactions are determined by spatial configurations, including disordered media and cooperative phenomena in atomic ensembles. Unlike classical random matrix…
Many real-world networks exhibit a high degeneracy at few eigenvalues. We show that a simple transformation of the network's adjacency matrix provides an understanding of the origins of occurrence of high multiplicities in the networks…
Families form the basis of society, and anthropologists have characterised various family systems. This study developed a multi-level evolutionary model of pre-industrial agricultural societies to simulate the evolution of family systems…
In the unidimensional unfolding model, given m objects in general position there arise 1+m(m-1)/2 rankings. The set of rankings is called the ranking pattern of the m given objects. By changing these m objects, we can generate various…
We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…
Emergence of hierarchies is investigated by Monte Carlo simulation in a timid society where all individuals are pacifist. The self-organiztion of hierarchies is shown to occur in two steps as the population is increased, i.e. there are…
For a given graph, $G$, let $A$ be the adjacency matrix, $D$ is the diagonal matrix of degrees, $L' = D - A$ is the combinatorial Laplacian, and $L = D^{-1/2}L'D^{-1/2}$ is the normalized Laplacian. Recently, the eigenvectors corresponding…
We consider the reduced density matrix $\rho_{A}^{(m)}$ of a bipartite system $AB$ of dimensionality $mn$ in a Gaussian ensemble of random, complex pure states of the composite system. For a given dimensionality $m$ of the subsystem $A$,…
Search engines like Google have become major information gatekeepers that use artificial intelligence (AI) to determine who and what voters find when searching for political information. This article proposes and tests a framework of…
We construct families of prime ideals in polynomial rings for which the number of associated primes of the second power (or higher powers) is exponential in the number of variables in the ring. We give a lower bound on the Ananyan-Hochster…
This note deals with a simultaneous approximation of several matrices by a finite family of diagonalizable matrices satisfying an additional condition for the spectrum of a matrix product. That is the simplicity of all eigenvalues.
In this paper we are concerned to find the eigenvalues and eigenvectors of a real symetric matrix by applying a new numerical method similar to Jacobi method. Our approch consists to use a new orthogonal matrix. The computation of the…
Many networks of interest in the sciences, including a variety of social and biological networks, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community structure has attracted…
The eigenvalue problem plays a central role in linear algebra and its applications in control and optimization methods. In particular, many matrix decompositions rely upon computation of eigenvalue-eigenvector pairs, such as diagonal or…