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The problem of stabilizing an unstable plant over a noisy communication link is an increasingly important one that arises in problems of distributed control and networked control systems. Although the work of Schulman and Sahai over the…

We prove a multiple recurrence result for arbitrary measure-preserving transformations along polynomials in two variables of the form $m+p_i(n)$, with rationally independent $p_i$'s with zero constant term. This is in contrast to the single…

Consider in R^2 the semi-planes N={y>0} and S={y<0}$ having as common boundary the straight line D={y=0}$. In N and S are defined polynomial vector fields X and Y, respectively, leading to a discontinuous piecewise polynomial vector field…

We prove a general representation stability result for polynomial coefficient systems which lets us prove representation stability and secondary homological stability for many families of groups with polynomial coefficients. This gives two…

We prove a sharp degree bound for polynomials constant on a hyperplane with a fixed number of distinct monomials for dimensions 2 and 3. We study the connection with monomial CR maps of hyperquadrics and prove similar bounds in this setup…

High-order ARX models can be used to approximate a quite general class of linear systems in a parametric model structure, and well-established methods can then be used to retrieve the true plant and noise models from the ARX polynomials.…

This work aims to accelerate the convergence of proximal gradient methods used to solve regularized linear inverse problems. This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal…

Estimation of covariance matrices or their inverses plays a central role in many statistical methods. For these methods to work reliably, estimated matrices must not only be invertible but also well-conditioned. In this paper we present an…

The motivation of this work is to construct an analog of compactified moduli of abelian varieties and toric pairs in the case of non-commutative algebraic group G. We introduce a class of "stable reductive varieties" which contain connected…

The Sanathanan-Koerner iteration developed in 1963 is classical approach for rational approximation. This approach multiplies both sides of the approximation by the denominator polynomial yielding a linear problem and then introduces a…

We develop a multigraded variant of Castelnuovo-Mumford regularity. Motivated by toric geometry, we work with modules over a polynomial ring graded by a finitely generated abelian group. As in the standard graded case, our definition of…

Let $k$ be a field. Then Gaussian elimination over $k$ and the Euclidean division algorithm for the univariate polynomial ring $k[x]$ allow us to write any matrix in $SL_n(k)$ or $SL_n(k[x])$, $n\geq 2$, as a product of elementary matrices.…

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 theory of persistence, which arises from topological data analysis, has been intensively studied in the one-parameter case both theoretically and in its applications. However, its extension to the multi-parameter case raises numerous…

We prove that a random labeled (unlabeled) tree is balanced. We also prove that random labeled and unlabeled trees are strongly $k$-balanced for any $k\geq 3$.

Ouroboros functions have shown some interesting properties when subjected to conventional operations. The aim of this paper is to continue our investigation and prove some additional properties of these functions. Using algebraic methods,…

Y. Miyashita gave characterizations of a separable polynomial and a Hirata separable polynomial in skew polynomial rings. In the previous paper, the author and S. Ikehata gave direct and elementary proofs of Miyashita's theorems in skew…

Extending the thoroughly studied theory of group stability, we study Ulam stability type problems for associative and Lie algebras; namely, we investigate obstacles to rank-approximation of almost solutions by exact solutions for systems of…

Multi-label classification is a common challenge in various machine learning applications, where a single data instance can be associated with multiple classes simultaneously. The current paper proposes a novel tree-based method for…

We generalize the recent work of S. Fomin and G. Mikhalkin on polynomial formulas for Severi degrees. The degree of the Severi variety of plane curves of degree d and delta nodes is given by a polynomial in d, provided delta is fixed and d…