相关论文: Solution of the Voter Model by Spectral Analysis

This paper is devoted to the error analysis of a time-spectral algorithm for fractional diffusion problems of order $\alpha$ ($0 < \alpha < 1$). The solution regularity in the Sobolev space is revisited, and new regularity results in the…

In this work, the propagation of an ultrasonic pulse in a thin plate is computed solving the differential equations modeling this problem. To solve these equations finite differences are used to discretize the temporal variable, while…

As a stochastic model for quantum mechanics we present a stationary quantum Markov process for the time evolution of the Wigner function on a lattice phase space Z_N x Z_N with N odd. By introducing a phase factor extension to the phase…

We derive spectral width estimates for traces of tempered solutions of a large class of multiplier equations in $\mathbf{R}^n$. The estimates are uniform for solutions up to a given order. In the process, we find a rather explicit…

We develop a model of issue-specific voting behavior. This model can be used to explore lawmakers' personal voting patterns of voting by issue area, providing an exploratory window into how the language of the law is correlated with…

In this paper we address the problem of electing a committee among a set of $m$ candidates and on the basis of the preferences of a set of $n$ voters. We consider the approval voting method in which each voter can approve as many candidates…

The voter model on $\mathbb{Z}^d$ is a particle system that serves as a rough model for changes of opinions among social agents or, alternatively, competition between biological species occupying space. When $d \geq 3$, the set of…

We describe a generalization of the voter model on complex networks that encompasses different sources of degree-related heterogeneity and that is amenable to direct analytical solution by applying the standard methods of heterogeneous…

This article is a direct continuation of [1] where we begun the study of the transfer matrix spectral problem for the cyclic representations of the trigonometric 6-vertex reflection algebra associated to the Bazhanov-Stroganov Lax operator.…

We formulate a spectral graph-partitioning algorithm that uses the two leading eigenvectors of the matrix corresponding to a selected quality function to split a network into three communities in a single step. In so doing, we extend the…

Identifying coherent spatiotemporal patterns generated by complex dynamical systems is a central problem in many science and engineering disciplines. Here, we combine ideas from the theory of operator-valued kernels with delay-embedding…

A fast and accurate numerical method for the solution of scalar and matrix Wiener--Hopf problems is presented. The Wiener--Hopf problems are formulated as Riemann--Hilbert problems on the real line, and a numerical approach developed for…

We introduce a novel spectral element method based on the ultraspherical spectral method and the hierarchical Poincar\'{e}-Steklov scheme for solving second-order linear partial differential equations on polygonal domains with unstructured…

The quality of numerically simulated spectra using real-time evolution methods for strongly correlated systems is affected by both the length of simulation time and the system size, limiting resolution in both frequency and momentum. In…

In this work, we introduce a Variational Multi-Scale (VMS) method for the numerical approximation of parabolic problems, where sub-grid scales are approximated from the eigenpairs of associated elliptic operator. The abstract method is…

This article introduces a novel and computationally fast model to study the association between covariates and power spectra of replicated time series. A random covariate-dependent Cram\'{e}r spectral representation and a semiparametric…

The essential spectral radius of a sub-Markovian process is defined as the infimum of the spectral radiuses of all local perturbations of the process. When the family of rescaled processes satisfies sample path large deviation principle,…

In the past, the Voter Model has been explicitly used to model the impact of propaganda on a dynamic, interconnected population, and certain factors have been identified that influence the behavior of voters when under outside influence.…

The solution of the Lippman-Schwinger (L-S) integral equation is equivalent to the the solution of the Schroedinger equation. A new numerical algorithm for solving the L-S equation is described in simple terms, and its high accuracy is…

Equations arising in General Relativity are usually too complicated to be solved analytically and one has to rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses…