Related papers: On non-negative solutions to large systems of rand…
Large systems of linear equations are ubiquitous in science. Quite often, e.g. when considering population dynamics or chemical networks, the solutions must be non-negative. Recently, it has been shown that large systems of random linear…
Complex ecosystems generally consist of a large number of different species utilizing a large number of different resources. Several of their features cannot be captured by models comprising just a few species and resources. Recently,…
This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system…
This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of…
We study linear systems of equations with coefficients in a generic partially ordered ring $R$ and a unique solution, and seek conditions for the solution to be nonnegative, that is, every component of the solution is a quotient of two…
This paper addresses multilinear systems of equations which arise in various applications such as data mining and numerical partial differential equations. When the multilinear system under consideration involves a nonsingular…
Stochastic spectral methods have become a popular technique to quantify the uncertainties of nano-scale devices and circuits. They are much more efficient than Monte Carlo for certain design cases with a small number of random parameters.…
A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…
We present a numerical algorithm for finding real non-negative solutions to polynomial equations. Our methods are based on the expectation maximization and iterative proportional fitting algorithms, which are used in statistics to find…
We study the biodiversity problem for resource competition systems with extinctions and self-limitation effects. Our main result establishes estimates of biodiversity in terms of the fundamental parameters of the model. We also prove the…
Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…
This paper deals with existence of a nontrivial positive solution to systems of equations involving nontrivial nonhomogeneous terms and critical or subcritical nonlinearities. Via a minimization argument we prove existence of a positive…
Binomial data with unknown sizes often appear in biological and medical sciences. The previous methods either use the Poisson approximation or the quasi-likelihood approach. A full likelihood approach is proposed by treating unknown sizes…
Model uncertainties and simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., "unresolved") due to lack in our understanding of these mechanisms or…
A binary fluid mixture in contact with lateral particle reservoirs is considered. By imposing different particle concentrations in these reservoirs, the system can be maintained under controlled non-equilibrium conditions. Previous…
The resolution of linear system with positive integer variables is a basic yet difficult computational problem with many applications. We consider sparse uncorrelated random systems parametrised by the density $c$ and the ratio $\alpha=N/M$…
The goal of this paper is to demonstrate the general modeling and practical simulation of random equations with mixture model parameter random variables. Random equations, understood as stationary (non-dynamical) equations with parameters…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
We give an efficient algorithm for finding sparse approximate solutions to linear systems of equations with nonnegative coefficients. Unlike most known results for sparse recovery, we do not require {\em any} assumption on the matrix other…
The long run behaviour of linear dynamical systems is often studied by looking at eventual properties of matrices and recurrences that underlie the system. A basic problem that lies at the core of many questions in this setting is the…