English
Related papers

Related papers: Involutive Division Technique: Some Generalization…

200 papers

Integration-by-parts reductions play a central role in perturbative QFT calculations. They allow the set of Feynman integrals contributing to a given observable to be reduced to a small set of basis integrals, and they moreover facilitate…

High Energy Physics - Theory · Physics 2016-07-08 Kasper J. Larsen , Yang Zhang

Developed by Buchberger for commutative polynomial rings, Groebner Bases are frequently applied to solve algorithmic problems, such as the congruence problem for ideals. Until now, these ideas have been transmitted to different in part…

Rings and Algebras · Mathematics 2009-03-31 Birgit Reinert

We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based…

Exactly Solvable and Integrable Systems · Physics 2012-07-17 Iosif Krasil'shchik , Alexander Verbovetsky , Raffaele Vitolo

In this paper, we propose an inertial forward backward splitting algorithm to compute a zero of the sum of two monotone operators, with one of the two operators being co-coercive. The algorithm is inspired by the accelerated gradient method…

Computer Vision and Pattern Recognition · Computer Science 2014-09-15 Dirk A. Lorenz , Thomas Pock

A non-unital algebra in a closed monoidal category is called self-induced if the multiplication induces an isomorphism between A\otimes_A A and A. For such an algebra, we define smoothening and roughening functors that retract the category…

Rings and Algebras · Mathematics 2015-10-23 Ralf Meyer

Most exact algorithms for general partially observable Markov decision processes (POMDPs) use a form of dynamic programming in which a piecewise-linear and convex representation of one value function is transformed into another. We examine…

Artificial Intelligence · Computer Science 2013-02-08 Anthony R. Cassandra , Michael L. Littman , Nevin Lianwen Zhang

A recently-established necessary condition for polynomials that preserve the class of entrywise nonnegative matrices of a fixed order is shown to be necessary and sufficient for the class of nonnegative monomial matrices. Along the way, we…

Rings and Algebras · Mathematics 2024-01-04 Benjamin J. Clark , Pietro Paparella

A categorical point of view about minimization in subrecursive classes is presented by extending the concept of Symmetric Monoidal Comprehension to that of Distributive Minimization Comprehension. This is achieved by endowing the former…

Category Theory · Mathematics 2017-03-29 Joaquín Díaz Boils

Factoring ideals in integral domains is a central topic in multiplicative ideal theory. In the present paper we study monoids of ideals and consider factorizations of ideals into multiplicatively irreducible ideals. The focus is on the…

Commutative Algebra · Mathematics 2017-10-02 Alfred Geroldinger , Andreas Reinhart

The approximation properties of the finite element method can often be substantially improved by choosing smooth high-order basis functions. It is extremely difficult to devise such basis functions for partitions consisting of arbitrarily…

Numerical Analysis · Mathematics 2021-01-18 Eky Febrianto , Michael Ortiz , Fehmi Cirak

We investigate a notion of inverse for neutrices inspired by Van den Berg and Koudjeti's decomposition of a neutrix as the product of a real number and an idempotent neutrix. We end up with an algebraic structure that can be characterized…

Logic · Mathematics 2023-09-06 Bruno Dinis , Emanuele Bottazzi

Multimodal normal incestual systems are investigated in terms of multiple categories. The different sorted composition of operators are exhibited as 2-cells in multiple categories built up from 2-categories giving rise to different axioms.…

Category Theory · Mathematics 2015-08-11 Joaquín Díaz Boils

We compute the nonlinearity of Boolean functions with Groebner basis techniques, providing two algorithms: one over the binary field and the other over the rationals. We also estimate their complexity. Then we show how to improve our…

Information Theory · Computer Science 2014-04-11 E. Bellini , I. Simonetti , M. Sala

We consider N-fold 4-block decomposable integer programs, which simultaneously generalize N-fold integer programs and two-stage stochastic integer programs with N scenarios. In previous work [R. Hemmecke, M. Koeppe, R. Weismantel, A…

Optimization and Control · Mathematics 2017-01-03 Raymond Hemmecke , Matthias Köppe , Robert Weismantel

There exist initial segments of both the Dyment lattice and the Dyment-Muchnik lattice that yield Brouwer algebras modeling exactly the intuitionistic propositional calculus. For the Dyment-Muchnik lattice, this result is obtained by…

While several classes of integer linear optimization problems are known to be solvable in polynomial time, far fewer tractability results exist for integer nonlinear optimization. In this work, we narrow this gap by identifying a broad…

Optimization and Control · Mathematics 2026-02-09 Alberto Del Pia

There are several efficient methods to solve linear interval polynomial systems in the context of interval computations, however, the general case of interval polynomial systems is not yet covered as well. In this paper we introduce a new…

Symbolic Computation · Computer Science 2015-06-09 Sajjad Rahmany , Abdolali Basiri , Benyamin M. -Alizadeh

In this paper, we describe improved algorithms to compute Janet and Pommaret bases. To this end, based on the method proposed by Moller et al., we present a more efficient variant of Gerdt's algorithm (than the algorithm presented by…

Symbolic Computation · Computer Science 2017-05-10 Bentolhoda Binaei , Amir Hashemi , Werner M. Seiler

For a general one-sided nonautonomous dynamics defined by a sequence of linear operators, we consider the notion of a polynomial dichotomy with respect to a sequence of norms and we characterize it completely in terms of the admissibility…

Dynamical Systems · Mathematics 2019-06-04 Davor Dragicevic

Through introducing a new iterative formula for divided differnce using Neville's and Aitken's algorithms,we study new iterative methods for interpolation,numerical differentiation and numerical integration formulas with arbitrary order of…

Numerical Analysis · Mathematics 2009-09-29 Ramesh Kumar Muthumalai