Related papers: Bounds on the permanent and some applications
Let A be an n by n doubly substochastic matrix and denote {\sigma}(A) the sum of all elements of A. In this paper we give the upper bound of the permanent of (I-A) with respect to n and {\sigma}(A).
A determinantal approximation is obtained for the permanent of a doubly stochastic matrix. For moderate-deviation matrix sequences, the asymptotic relative error is of order $O(n^{-1})$.
The monomer-dimer model is fundamental in statistical mechanics. However, it is $#P$-complete in computation, even for two dimensional problems. A formulation in matrix permanent for the partition function of the monomer-dimer model is…
We define two new families of polynomials that generalize permanents and prove upper and lower bounds on their determinantal complexities comparable to the known bounds for permanents. One of these families is obtained by replacing…
In this paper we present a new bound obtained with the probabilistic method for the solution of the Set Covering problem with unit costs. The bound is valid for problems of fixed dimension, thus extending previous similar asymptotic…
We explore singular second-order boundary value problems with mixed boundary conditions on a general time scale. Using the lower and upper solutions method combined with the Brouwer fixed point theorem we demonstrate the existence of a…
Sinkhorn's alternative minimization algorithm applied to a positive $n\times n$ matrix converges to a doubly stochastic matrix. If the algorithm, applied to a $2\times 2$ matrix, converges in a finite number of iterations, then it converges…
We derive here the Friedland-Tverberg inequality for positive hyperbolic polynomials. This inequality is applied to give lower bounds for the number of matchings in $r$-regular bipartite graphs. It is shown that some of these bounds are…
How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational…
There are many ways of establishing upper bounds on fluctuations of random variables, but there is no systematic approach for lower bounds. As a result, lower bounds are unknown in many important problems. This paper introduces a general…
We formulate conjectures regarding the maximum value and maximizing matrices of the permanent and of diagonal products on the set of stochastic matrices with bounded rank. We formulate equivalent conjectures on upper bounds for these…
Using duality in optimization theory we formulate a dual approach to the S-matrix bootstrap that provides rigorous bounds to 2D QFT observables as a consequence of unitarity, crossing symmetry and analyticity of the scattering matrix. We…
We develop here the method for obtaining approximate stability boundaries in the space of parameters for systems with parametric excitation. The monodromy (Floquet) matrix of linearized system is found by averaging method. For system with 2…
A general framework for determining fundamental bounds in nanophotonics is introduced in this paper. The theory is based on convex optimization of dual problems constructed from operators generated by electromagnetic integral equations. The…
We use an old elementary arithmetic argument to find new upper and lower bounds for Sylvester's denumerant function. These bounds are tight enough to get the asymptotic behavior of the denumerant.
We study the validity of the so-called Smoluchowski-Kramers approximation for a two dimensional system of stochastic partial differential equations, subject to a constant magnetic field. As the small mass limit does not yield to the…
We consider boundary value problems for stochastic differential equations of second order with a small parameter. For this case we prove a special existence and unicity theorem for strong solutions. The asymptotic behavior of these…
When an eigenvector of a semi-bounded operator is positive, we show that a remarkably simple argument allows to obtain upper and lower bounds for its associated eigenvalue. This theorem is a substantial generalization of Barta-like…
Computing the permanent of a non-negative matrix is a computationally challenging, \#P-complete problem with wide-ranging applications. We introduce a novel permanental analogue of Schur's determinant formula, leveraging a newly defined…
This paper investigates the existence of positive solutions for regular discrete second-order single-variable boundary value problems with mixed boundary conditions, including a nonhomogeneous Dirichlet boundary condition, of the form:…