Related papers: Graphical criteria for positive solutions to linea…
High-dimensional covariates often admit linear factor structure. To effectively screen correlated covariates in high-dimension, we propose a conditional variable screening test based on non-parametric regression using neural networks due to…
We survey the problem of deciding the stability or stabilizability of uncertain linear systems whose region of uncertainty is a polytope. This natural setting has applications in many fields of applied science, from Control Theory to…
The condition number of solutions to full rank linear least-squares problem are shown to be given by an optimization problem that involves nuclear norms of rank 2 matrices. The condition number is with respect to the least-squares…
A nonautonomous periodic chemostat model with delays modelling $n$ species in competition is considered. Sufficient conditions on the coefficients and consumption functions for the species are given, for both the extinction of the species…
We introduce a unifying and generalizing framework for complex and detailed balanced steady states in chemical reaction network theory. To this end, we generalize the graph commonly used to represent a reaction network. Specifically, we…
We develop a new tool, namely polynomial and linear algebraic methods, for studying systems of word equations. We illustrate its usefulness by giving essentially simpler proofs of several hard problems. At the same time we prove extensions…
Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization problems, well-known to be challenging due to…
The characterization of quantum critical phenomena is pivotal for the understanding and harnessing of quantum many-body physics. However, their complexity makes the inference of such fundamental processes difficult. Thus, efficient and…
In this paper, we prove several theorems on systems of polynomials with at least one positive real zero based on the theory of conceive polynomials. These theorems provide sufficient conditions for systems of multivariate polynomials…
It is common in stability analysis to linearize a system and investigate the spectrum of the Jacobian matrix. This approach faces the challenge of determining the matrix spectrum when the coefficients depend on parameters or when the…
The dual phosphorylation network provides an essential component of intracellular signaling, affecting the expression of phenotypes and cell metabolism. For particular choices of kinetic parameters, this system exhibits multistationarity, a…
We report conditions on a switching signal that guarantee that solutions of a switched linear systems converge asymptotically to zero. These conditions are apply to continuous, discrete-time and hybrid switched linear systems, both those…
In this paper we study the multiplicity of positive solutions for nonlinear elliptic equations on $\R^N$. The number of solutions is greater or equal than the number of disjoint intervals on which the nonlinear term is negative.…
This paper investigates the existence of solutions for a class of nonlinear higher-order dynamic equations subject to mixed boundary conditions. We consider boundary value problems in which the nonlinear reaction functions satisfy…
Motivated by quantum thermodynamics we first investigate the notion of strict positivity, that is, linear maps which map positive definite states to something positive definite again. We show that strict positivity is decided by the action…
A linear map between matrix spaces is positive if it maps positive semidefinite matrices to positive semidefinite ones, and is called completely positive if all its ampliations are positive. In this article quantitative bounds on the…
We are concerned with the tensor equation with an M-tensor or Z-tensor, which we call the M- tensor equation or Z-tensor equation respectively. We derive a necessary and sufficient condition for a Z (or M)-tensor equation to have…
In this paper, we study the existence of multiple positive solutions for a class of fractional Schr\"{o}dinger-Poisson systems involving sign-changing potential and critical nonlinearities on an unbounded domain. With the help of Nehari…
We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases…
We investigate the signed support, that is, the set of the exponent vectors and the signs of the coefficients, of a multivariate polynomial $f$. We describe conditions on the signed support ensuring that the semi-algebraic set, denoted as…