Related papers: On the existence of global saturation for spectral…

Asking which sets are fixed-parameter tractable for a given parameterization constitutes much of the current research in parameterized complexity theory. This approach faces some of the core difficulties in complexity theory. By focussing…

We present an approach to the verification of systems for whose description some elements - constants or functions - are underspecified and can be regarded as parameters, and, in particular, describe a method for automatically generating…

Let $\alpha\in[0,1)$, and let $G$ be a graph of even order $n$ with $n\geq f(\alpha)$, where $f(\alpha)=10$ for $0\leq \alpha\leq1/2$, $f(\alpha)=14$ for $1/2<\alpha\leq 2/3$ and $f(\alpha)=5/(1-\alpha)$ for $2/3<\alpha<1$. In this paper,…

We consider a class of discretionary stopping problems within the $G$-framework. We first establish the well-definedness of the stopping problem under the $G$-expectation, by showing the quasi-continuity of the stopped process. We then…

In this article we study optimal control problems for systems that are affine in one part of the control variable. Finitely many equality and inequality constraints on the initial and final values of the state are considered. We investigate…

Beginning with a historical account of the spectral classification, its refinement through additional criteria is presented. The line strengths and ratios used in two dimensional classifications of each spectral class are described. A…

This article defines a complement of a function and conditions for existence of such a complement function and presents few algorithms to construct a complement.

The widely used nuclear norm heuristic for rank minimization problems introduces a regularization parameter which is difficult to tune. We have recently proposed a method to approximate the regularization path, i.e., the optimal solution as…

Motivated by the control of invasive biological populations, we consider a class of optimization problems for moving sets $t\mapsto \Omega(t)\subset\mathbb{R}^2$. Given an initial set $\Omega_0$, the goal is to minimize the area of the…

We establish a regularity result for optimal sets of the isoperimetric problem with double density under mild ($\alpha$-)H\"older regularity assumptions on the density functions. Our main Theorem improves some previous results and allows to…

Submodular function maximization has found a wealth of new applications in machine learning models during the past years. The related supermodular maximization models (submodular minimization) also offer an abundance of applications, but…

This is an exposition of facts about p-local spectra, p-complete spectra and modules over the p-complete sphere spectrum, including homological criteria for finiteness. Most things are well-known to the experts, with a couple of potential…

In this contribution we revisit regular model checking, a powerful framework that has been successfully applied for the verification of infinite-state systems, especially parameterized systems (concurrent systems with an arbitrary number of…

Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for…

The criteria for determining graph isomorphism are crucial for solving graph isomorphism problems. The necessary condition is that two isomorphic graphs possess invariants, but their function can only be used to filtrate and subdivide…

Let $C \subseteq \P^d$ denote the rational normal curve of order $d$. Its homogeneous defining ideal $I_C \subseteq \QQ[a_0,...,a_d]$ admits an $SL_2$-stable filtration $J_2 \subseteq J_4 \subseteq ... \subseteq I_C$ by sub-ideals such that…

We establish the global $C^{1, \alpha}$-regularity for functions in solution classes, whenever ellipticity constants are sufficiently close. As an application, we derive the global regularity result concerning the parabolic normalized…

Satisfiability is a classic problem in computational complexity theory, in which one wishes to determine whether an assignment of values to a collection of Boolean variables exists in which all of a collection of clauses composed of logical…

Generalising the concept of a complete permutation polynomial over a finite field, we define completness to level $k$ for $k\ge1$ in fields of odd characteristic. We construct two families of polynomials that satisfy the condition of high…

In this paper we study possibilities of using hierarchical reasoning, symbol elimination and model generation for the verification of parametric systems, where the parameters can be constants or functions. Our goal is to automatically…