Related papers: Non Total-Unimodularity Neutralized Simplicial Com…

Stabilizing an unknown dynamical system is one of the central problems in control theory. In this paper, we study the sample complexity of the learn-to-stabilize problem in Linear Time-Invariant (LTI) systems on a single trajectory. Current…

In the paper, we propose solving optimization problems (OPs) and understanding the Newton method from the optimal control view. We propose a new optimization algorithm based on the optimal control problem (OCP). The algorithm features…

We develop a homotopy-based framework for computing Karush-Kuhn-Tucker (KKT) points of multiobjective optimization problems. The proposed homotopy map continuously deforms an easily solvable system into the KKT conditions associated with…

This paper presents "oriented pivoting systems" as an abstract framework for complementary pivoting. It gives a unified simple proof that the endpoints of complementary pivoting paths have opposite sign. A special case are the Nash…

Using the Mathematica program we calculate numerically the difference of the diagonal matrix elements of the time dependent effective Hamiltonian for the neutral K meson complex. We consider the exactly solvable neutral K meson model based…

In a $k$-critical bifiltration, every simplex enters along a staircase with at most $k$ steps. Examples with $k>1$ include degree-Rips bifiltrations and models of the multicover bifiltration. We consider the problem of converting a…

Topology optimization of frame structures under free-vibration eigenvalue constraints constitutes a challenging nonconvex polynomial optimization problem with disconnected feasible sets. In this article, we first formulate it as a…

We reveal a complexity chasm, separating the trinomial and tetranomial cases, for solving univariate sparse polynomial equations over certain local fields. First, for any fixed field $K\in\{\mathbb{Q}_2,\mathbb{Q}_3,\mathbb{Q}_5,\ldots\}$,…

We propose a general solution approach for min-max-robust counterparts of combinatorial optimization problems with uncertain linear objectives. We focus on the discrete scenario case, but our approach can be extended to other types of…

${ NP}$-complete problem "Hamiltonian cycle"\ for graph $G=(V,E)$ is extended to the "Hamiltonian Complement of the Graph"\ problem of finding the minimal cardinality set $H$ containing additional edges so that graph $G=(V,E\cup H)$ is…

We show that, for a complete simplicial toric variety $X$, we can determine its homotopy $\KH$-theory entirely in terms of the torus pieces of open sets forming an open cover of $X$. We then construct conditions under which, given two…

This paper considers the class of deterministic continuous-time optimal control problems (OCPs) with piecewise-affine (PWA) vector field, polynomial Lagrangian and semialgebraic input and state constraints. The OCP is first relaxed as an…

We introduce a new algorithm for the structural analysis of finite abstract simplicial complexes based on local homology. Through an iterative and top-down procedure, our algorithm computes a stratification $\pi$ of the poset $P$ of…

For open radial sets $\Omega\subset \mathbb{R}^N$, $N\geq 2$ we consider the nonlinear problem \[ (P)\quad Iu=f(|x|,u) \quad\text{in $\Omega$,}\quad u\equiv 0\quad \text{on $\mathbb{R}^N\setminus \Omega$ and }\lim_{|x|\to\infty} u(x)=0, \]…

Let $X$ and $Y$ be finite simplicial sets (e.g. finite simplicial complexes), both equipped with a free simplicial action of a finite group $G$. Assuming that $Y$ is $d$-connected and $\dim X\le 2d$, for some $d\geq 1$, we provide an…

Ordered matchings, defined as graphs with linearly ordered vertices, where each vertex is connected to exactly one edge, play a crucial role in the area of ordered graphs and their homomorphisms. Therefore, we consider related problems from…

We prove that a maximal totally complex submanifold $N^{2n}$ of the quaternionic projective space $\mathbb{H}\mathbb{P}^n$ ($n\geq 2$) is a parallel submanifold, provided one of the following conditions is satisfied: (1) $N$ is the orbit of…

Let $H$ be a $k$-graph on $n$ vertices, with minimum codegree at least $n/k + cn$ for some fixed $c > 0$. In this paper we construct a polynomial-time algorithm which finds either a perfect matching in $H$ or a certificate that none exists.…

Integer Linear Programming (ILP) can be seen as the archetypical problem for NP-complete optimization problems, and a wide range of problems in artificial intelligence are solved in practice via a translation to ILP. Despite its huge range…

A decision problem is called parameterized if its input is a pair of strings. One of these strings is referred to as a parameter. The problem: given a propositional logic program P and a non-negative integer k, decide whether P has a stable…