Related papers: Blending two discrete integrability criteria: sing…
We present a systematic study of the Gambier system, which in the continuous case is given by two Riccati equations in cascade. We derive the condition for its integrability and show that the generic Gambier system contains one free…
Many quantities that characterize network elements are defined in an explicit form and calculated directly from the network structure; examples of include several centrality measures like degree, closeness, or betweenness. However, there…
We study singularity confinement phenomena in examples of delay-differential Painlev\'e equations, which involve shifts and derivatives with respect to a single independent variable. We propose a geometric interpretation of our results in…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
We show that the conditions imposed on a second order linear differential equation with rational coefficients on the complex line by requiring it to have regular singularities with fixed exponents at the points of a finite set $P$ and…
We apply the 'almost good reduction' (AGR) criterion, which has been introduced in our previous (arXiv:1206.4456 and arXiv:1209.0223), to several classes of discrete integrable equations. We verify our conjecture that AGR plays the same…
Dual decomposition provides a tractable framework for designing algorithms for finding the most probable (MAP) configuration in graphical models. However, for many real-world inference problems, the typical decomposition has a large…
We consider an integrability test for ultradiscrete equations based on the singularity confinement analysis for discrete equations. We show how singularity pattern of the test is transformed into that of ultradiscrete equation. The…
The discretization of the density matrix is proposed as a nonlinear positive map for systems with continuous variables. This procedure is used to calculate the entanglement between two modes through different criteria, such as Tsallis…
Many common methods for data analysis rely on linear algebra. We provide new results connecting data analysis error to numerical accuracy, which leads to the first meaningful stopping criterion for two way spectral partitioning. More…
To integer programming problems, computational algebraic approaches using Grobner bases or standard pairs via the discreteness of toric ideals have been studied in recent years. Although these approaches have not given improved time…
We apply the results of singularity analysis to the isotropic cosmological models in general relativity and string theory with a variety of matter terms. For some of these models the standard Painlev\'{e} test is sufficient to demonstrate…
This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete…
This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…
We describe an efficient theoretical criterion, suitable for indistinguishable particles to quantify the quantum correlations of any pure two-fermion state, based on the Slater rank concept. It represents the natural generalization of the…
Recently a strong connection has been shown between the tractability of integer programming (IP) with bounded coefficients on the one side and the structure of its constraint matrix on the other side. To that end, integer linear programming…
We present a new automated method for finding integrable symplectic maps of the plane. These dynamical systems possess a hidden symmetry associated with an existence of conserved quantities, i.e. integrals of motion. The core idea of the…
We study the growth of entanglement entropy in density matrix renormalization group calculations of the real-time quench dynamics of the Anderson impurity model. We find that with appropriate choice of basis, the entropy growth is…
We propose an algorithmic procedure i) to study the ``distance'' between an integrable PDE and any discretization of it, in the small lattice spacing epsilon regime, and, at the same time, ii) to test the (asymptotic) integrability…
Studies of density matrices for random quantum states lead naturally to the fixed trace Laguerre ensemble in random matrix theory. Previous studies have uncovered explicit rational function formulas for moments of purity statistic (trace of…