9 citations · 9 across the 14 of their papers we have counts for
15 papers
Layered mixed matrices and reaction networks
Arne Kuhrs, Máté L. Telek, Nicola Vassena
The purpose of this work is twofold. In the first part, we consider layered mixed matrices introduced by Murota, relate them to existing notions in combinatorial commutative algebr…
A note on o-minimal tropicalizations
Lorenzo Baldi, Máté L. Telek
In this note, we provide several equivalent descriptions of the tropicalization of definable sets in a polynomially bounded o-minimal expansion of a real closed field. We show that…
Root bounds of vertical systems using tropical geometry
Elisenda Feliu, Paul Alexander Helminck, Oskar Henriksson +3
Sparse polynomial systems with vertical coefficient dependencies arise naturally when describing the critical points of optimization problems and, when augmented with linear forms,…
Copositivity, discriminants and nonseparable signed supports
Elisenda Feliu, Joan Ferrer, Máté L. Telek
We establish a connection between discriminants and copositivity of sparse Laurent polynomials. More generally, we consider signomials, which are defined on the positive orthant by…
Toric extensions of Pólya's theorem
Lorenzo Baldi, Rainer Sinn, Máté L. Telek +1
The classical version of Pólya's theorem provides a simple method for certifying that a homogeneous polynomial of degree d is strictly copositive, that is, it takes only positive v…
Copositive geometry of Feynman integrals
Bernd Sturmfels, Máté L. Telek
Copositive matrices and copositive polynomials are objects from optimization. We connect these to the geometry of Feynman integrals in physics. The integral is guaranteed to conver…
Binary geometries from pellytopes
Lara Bossinger, Máté L. Telek, Hannah Tillmann-Morris
Binary geometries have recently been introduced in particle physics in connection with stringy integrals. In this work, we study a class of simple polytopes, called \emph{pellytope…
Computing positive tropical varieties and lower bounds on the number of positive roots
Kemal Rose, Máté L. Telek
We present two effective tools for computing the positive tropicalization of algebraic varieties. First, we outline conditions under which the initial ideal can be used to compute…
Connectivity of Parameter Regions of Multistationarity for Multisite Phosphorylation Networks
Nidhi Kaihnsa, Máté L. Telek
The parameter region of multistationarity of a reaction network contains all the parameters for which the associated dynamical system exhibits multiple steady states. Describing th…
Viro's patchworking and the signed reduced A-discriminant
Weixun Deng, J. Maurice Rojas, Máté L. Telek
Computing the isotopy type of a hypersurface, defined as the positive real zero set of a multivariate polynomial, is a challenging problem in real algebraic geometry. We focus on t…
Geometry of the signed support of a multivariate polynomial and Descartes' rule of signs
Máté L. Telek
We investigate the signed support, that is, the set of the exponent vectors and the signs of the coefficients, of a multivariate polynomial . We describe conditions on the signe…
On the Number of Real Zeros of Random Sparse Polynomial Systems
Alperen A. Ergür, Máté L. Telek, Josué Tonelli-Cueto
Consider a random system of random real polynomials in variables, where each has a prescribed set of expon…
Real tropicalization and negative faces of the Newton polytope
Máté L. Telek
In this work, we explore the relation between the tropicalization of a real semi-algebraic set defined in the positive orthant and the combinato…
Topological descriptors of the parameter region of multistationarity: deciding upon connectivity
Máté L. Telek, Elisenda Feliu
Switch-like responses arising from bistability have been linked to cell signaling processes and memory. Revealing the shape and properties of the set of parameters that lead to bis…
On generalizing Descartes' rule of signs to hypersurfaces
Elisenda Feliu, Máté L. Telek
We give partial generalizations of the classical Descartes' rule of signs to multivariate polynomials (with real exponents), in the sense that we provide upper bounds on the number…