Related papers: Angle-restricted sets and zero-free regions for th…
We study algorithms for approximating the permanent of a random matrix when the entries are slightly biased away from zero. This question is motivated by the goal of understanding the classical complexity of linear optics and \emph{boson…
For a real polynomial $f$ we present explicit zero-free angular sectors in the complex plane, symmetric with respect to the real axis, with angles depending only on the degree of $f$, and vertices expressed in terms of the coefficients of…
The intersection cut paradigm is a powerful framework that facilitates the generation of valid linear inequalities, or cutting planes, for a potentially complex set S. The key ingredients in this construction are a simplicial conic…
We introduce the concept of $b$-suprametric spaces and establish a fixed point result for mappings satisfying a nonlinear contraction in such spaces. The obtained result generalizes a fixed point theorem of Czerwik and a recent result of…
We introduce the class of principal symmetric ideals, which are ideals generated by the orbit of a single polynomial under the action of the symmetric group. Fixing the degree of the generating polynomial, this class of ideals is…
It is known from the work of Shearer (1985) (and also Scott and Sokal (2005)) that the independence polynomial $Z_G(\lambda)$ of a graph $G$ of maximum degree at most $d+1$ does not vanish provided that $\vert{\lambda}\vert \leq…
We introduce symmetric arithmetic circuits, i.e. arithmetic circuits with a natural symmetry restriction. In the context of circuits computing polynomials defined on a matrix of variables, such as the determinant or the permanent, the…
Consider a given space, e.g., the Euclidean plane, and its decomposition into Voronoi regions induced by given sites. It seems intuitively clear that each point in the space belongs to at least one of the regions, i.e., no neutral region…
The mode-locking regions of a dynamical system are the subsets of the parameter space of the system within which there exists an attracting periodic solution. For piecewise-linear continuous maps, these regions have a curious chain…
We study zeros of the partition functions of ferromagnetic 2-state spin systems in terms of the external field, and obtain new zero-free regions of these systems via a refinement of Asano's and Ruelle's contraction method. The strength of…
We introduce a new technique to prove bounds for the spectral radius of a random matrix, based on using Jensen's formula to establish the zerofreeness of the associated characteristic polynomial in a region of the complex plane. Our…
Matrix convexity generalizes convexity to the dimension free setting and has connections to many mathematical and applied pursuits including operator theory, quantum information, noncommutative optimization, and linear control systems. In…
In this paper, a combination of algebraic and topological methods are applied to obtain new and structural results on harmonic rings. Especially, it is shown that if a Gelfand ring $A$ modulo its Jacobson radical is a zero dimensional ring,…
Given a symmetric variety Y defined over the rationals and a non-zero polynomial with integer coefficients, we use techniques from homogeneous dynamics to establish conditions under which the polynomial can be made r-free for a Zariski…
This paper presents algorithms for solving multiobjective integer programming problems. The algorithm uses Barvinok's rational functions of the polytope that defines the feasible region and provides as output the entire set of nondominated…
For a graph $G=(V,E)$, $k\in \mathbb{N}$, and a complex number $w$ the partition function of the univariate Potts model is defined as \[ {\bf Z}(G;k,w):=\sum_{\phi:V\to [k]}\prod_{\substack{uv\in E \\ \phi(u)=\phi(v)}}w, \] where…
Strict positive realness (SPR) is an important concept in absolute stability theory, adaptive control, system identification, etc. This paper characterizes the strictly positive real regions in coefficient space and presents a robust design…
The zero sets of harmonic polynomials play a crucial role in the study of the free boundary regularity problem for harmonic measure. In order to understand the fine structure of these free boundaries a detailed study of the singular points…
In response to a question raised (and answered in the negative) by Terry Tao on his blog as to whether it is possible to rotate a line segment continuously within a set of area zero, we show that there is a set of area zero in the plane…
The aim of this paper is to study the topological properties of algebraic sets with zero divisors. We impose a subbasic topology on the set of proper ideals of a $k$-algebra and this new ``$k$-space'' becomes a generalization of the…