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In [21] it was asked if equality on the reals is sharp as a lower bound for the complexity of topological isomorphism between oligomorphic groups. We prove that under the assumption of weak elimination of imaginaries this is indeed the…
The purpose of this paper is to study resolutions of locally analytic representations of a $p$-adic reductive group $G$. Given a locally analytic representation $V$ of $G$, we modify the Schneider-Stuhler complex (originally defined for…
In a previous paper, the first and third authors gave an explicit realization of the geometric Langlands correspondence for hypergeometric sheaves, considered as $\textrm{GL}_n$-local systems. Certain hypergeometric local systems admit a…
Latin squares have been historically used in order to create statistical designs in which, starting from a small number of experiments, it can be obtained a large experimental space. In this sense, the optimization of the selection of Latin…
Recommendation algorithm plays an important role in recommendation system (RS), which predicts users' interests and preferences for some given items based on their known information. Recently, a recommendation algorithm based on the graph…
In this paper we study the rotation and spatial inversion symmetry of regular tetrahedron. We obtain the representation matrix, multiplication table,the order of all group elements, all possible combinations of generator elements, the…
Generalized Pythagoras trees were developed for visualizing hierarchical data, producing organic, fractal-like representations. However, the drawback of the original layout algorithm is visual overlap of tree branches. To avoid such…
A model of representations of a Lie algebra is a representation which a direct sum of all irreducible finite dimensional representations taken with multiplicity $1$. In the paper an explicit construction of a model of representation for all…
In this paper we consider some classical varieties of linear algebras over the field which has characteristic 0. For every considered variety we take a category of the finite generated free algebras of this variety. And for every this…
Computing the autotopism group of a partial Latin rectangle can be performed in a variety of ways. This pilot study has two aims: (a) to compare these methods experimentally, and (b) to identify the design goals one should have in mind for…
We study the classic matrix cross approximation based on the maximal volume submatrices. Our main results consist of an improvement of the classic estimate for matrix cross approximation and a greedy approach for finding the maximal volume…
We provide an algorithm for computing an effective basis of homology of elliptic surfaces over the complex projective line on which integration of periods can be carried out. This allows the heuristic recovery of several algebraic…
In the $(G,H)$-isomorphism game, a verifier interacts with two non-communicating players (called provers) by privately sending each of them a random vertex from either $G$ or $H$, whose aim is to convince the verifier that two graphs $G$…
Copying an element from a photo and pasting it into a painting is a challenging task. Applying photo compositing techniques in this context yields subpar results that look like a collage --- and existing painterly stylization algorithms,…
Large Language Models (LLMs) excel in understanding and generating text but struggle with providing professional literary criticism for works with profound thoughts and complex narratives. This paper proposes GLASS (Greimas Literary…
We construct spherical subgroups in infinite-dimensional classical groups $G$ (usually they are not symmetric and their finite-dimensional analogs are not spherical). We present a structure of a semigroup on double cosets $L\setminus G/L$…
Symmetry plays a central role in accelerating symbolic computation involving polynomials. This chapter surveys recent developments and foundational methods that leverage the inherent symmetries of polynomial systems to reduce complexity,…
This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…
This paper studies the concept of algorithmic equiresolution of a family of embedded varieties or ideals, which means a simultaneous resolution of such a family compatible with a given (suitable) algorithm of resolution in characteristic…
A new robust algorithm for the numerical computation of biarcs, i.e. $G^1$ curves composed of two arcs of circle, is presented. Many algorithms exist but are based on geometric constructions, which must consider many geometrical…