Related papers: Polytime reductions of AF-algebraic problems
Integrable delay analogues of the two-dimensional Toda lattice equation are presented and their muti-soliton solutions are constructed by applying the delay reduction to the Gram determinant solution.
We contribute to the classification of finite dimensional algebras under stable equivalence of Morita type. More precisely we give a classification of the class of Erdmann's algebras of dihedral, semi-dihedral and quaternion type and obtain…
In this note we discuss Morita equivalence classes of arbitrary finitely presented algebras
Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equations. We apply this principle by finding some \emph{affine…
We discuss factorization of the hypergeometric-type difference equations on the uniform lattices and show how one can construct a dynamical algebra, which corresponds to each of these equations. Some examples are exhibited, in particular,…
This paper investigates the equivalence reduction for several classes of multivariate polynomial matrices and their Smith forms, establishing some criteria for such reduction. In particular, we employ algebra isomorphisms as a key tool to…
Satisfiability of Boolean circuits is among the most known and important problems in theoretical computer science. This problem is NP-complete in general but becomes polynomial time when restricted either to monotone gates or linear gates.…
The aim of this article is to give a method to construct bimodule resolutions of associative algebras, generalizing Bardzell's well-known resolution of monomial algebras. We stress that this method leads to concrete computations, providing…
The diverse world of machine learning applications has given rise to a plethora of algorithms and optimization methods, finely tuned to the specific regression or classification task at hand. We reduce the complexity of algorithm design for…
Optimization algorithms such as projected Newton's method, FISTA, mirror descent, and its variants enjoy near-optimal regret bounds and convergence rates, but suffer from a computational bottleneck of computing ``projections'' in…
In this paper we propose a general methodology for solving a broad class of continuous, multifacility location problems, in any dimension and with $\ell_\tau$-norms proposing two different methodologies: 1) by a new second order cone mixed…
In this article, a posteriori error analysis of the elliptic obstacle problem is addressed using hybrid high-order methods. The method involve cell unknowns represented by degree-$r$ polynomials and face unknowns represented by degree-$s$…
Revisiting the results by Winternitz [Symmetry in physics, CRM Proc. Lecture Notes 34, American Mathematical Society, Providence, RI, 2004, pp. 215-227], we thoroughly refine his classification of Lie subalgebras of the real order-three…
Matrix functions are a central topic of linear algebra, and problems requiring their numerical approximation appear increasingly often in scientific computing. We review various limited-memory methods for the approximation of the action of…
When a group acts on a set, it naturally partitions it into orbits, giving rise to orbit problems. These are natural algorithmic problems, as symmetries are central in numerous questions and structures in physics, mathematics, computer…
A problem list in singularity theory. Most of these problems are related with the algorithmic enumeration of possible topological types of non-discriminant Morsifications of real function singularities, and/or with the Picard--Lefschetz…
We consider multicriteria problems of evaluating absolute ratings (scores, priorities, weights) of given alternatives for making decisions, which are compared in pairs under several criteria. Given matrices of pairwise comparisons of…
In this paper, we develop a numerical algorithm for an inverse problem on determining fractional orders of time derivatives simultaneously in a coupled subdiffusion system. Following the theoretical uniqueness, we reformulate the order…
We systematically study the completion of choice problems in the Weihrauch lattice. Choice problems play a pivotal role in Weihrauch complexity. For one, they can be used as landmarks that characterize important equivalences classes in the…
In this survey, we address the worst-case, average-case, and generic-case time complexity of the word problem and some other algorithmic problems in several classes of groups and show that it is often the case that the average-case…