Related papers: Computing differential subresultants with Maple
We present the G-MAPLE (Generalised Modal Analysis from the Poles of the Laplace Expansion) software that allows decomposing data depending on a single parameter (such as time series data) into a set of exponential functions having complex…
We study differential operators, whose coefficients define noncommutative algebras. As algebra of coefficients, we consider crossed products, corresponding to action of a discrete group on a smooth manifold. We give index formulas for…
We present a method for computing reduced-order models of parameterized partial differential equation solutions. The key analytical tool is the singular value expansion of the parameterized solution, which we approximate with a singular…
Offline Goal-Conditioned Reinforcement Learning (GCRL) is tasked with learning to achieve multiple goals in an environment purely from offline datasets using sparse reward functions. Offline GCRL is pivotal for developing generalist agents…
A pseudodifferential calculus for parameter-dependent operators on smooth manifolds with boundary in the spirit of Boutet de Monvel's algebra is constructed. The calculus contains, in particular, the resolvents of realizations of…
Quadratic fluctuations require an evaluation of ratios of functional determinants of second-order differential operators. We relate these ratios to the Green functions of the operators for Dirichlet, periodic and antiperiodic boundary…
We present an optimized algorithm calculating determinant for multivariate polynomial matrix on GPU. The novel algorithm provides precise determinant for input multivariate polynomial matrix in controllable time. Our approach is based on…
An explicit formula to find symmetry recursion operators for partial differential equations (PDEs) is obtained from new results connecting variational integrating factors and non-variational symmetries. The formula is special case of a…
This papers studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs). It presents a new framework using discrete ODEs as a central tool for computation and provides several implicit characterizations…
Several definitions of differential operators on modules over noncommutative rings are discussed.
We investigate causal computations taking sequences of inputs to sequences of outputs where the $n$th output depends on the first $n$ inputs only. We model these in category theory via a construction taking a Cartesian category $C$ to…
The purpose of this paper is to introduce two new classes of accelerated distributed proximal conjugate gradient algorithms for multi-agent constrained optimization problems; given as minimization of a function decomposed as a sum of M…
Differential operators on Schwartz distributions conventionally are defined as the transpose of differential operators on functions with compact support. They do not exhaust all differential operators. We follow algebraic formalism of…
This paper is a contribution to the search for efficient and high-level mathematical tools to specify and reason about (abstract) programming languages or calculi. Generalising the reduction monads of Ahrens et al., we introduce transition…
In this note, we extend the result of \cite{PoulyG16} about the complexity of solving polynomial differential equations over unbounded domains to work with non-rational input. In order to deal with arbitrary input, we phrase the result in…
We consider one-point commuting difference operators of rank one. The coefficients of these operators depend on a functional parameter, shift operators being included only with positive degrees. We study these operators in the case of…
In this paper, we briefly explain the spectral expansion problem for differential operators defined on the entire real line, generated by a differential expression with periodic, complex-valued coefficients.
Fractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets…
The nature of so-called differential-algebraic operators and their approximations is constitutive for the direct treatment of higher-index differential-algebraic equations. We treat first-order differential-algebraic operators in detail and…
This paper addresses the complex issue of resource-constrained scheduling, an NP-hard problem that spans critical areas including chip design and high-performance computing. Traditional scheduling methods often stumble over scalability and…