相关论文: A simple uniform approach to complexes arising fro…

In this article we apply ideas from homotopy theory to the study of singular foliations. We verify that a technical lemma remains valid for left semi-model categories. When applied to the category of $L_\infty$-algebroids thanks to the work…

The matching complex of a simple graph $G$ is a simplicial complex consisting of the matchings on $G$. Jeli\'c Milutinovi\'c et al. studied the matching complexes of the polygonal line tilings, and they gave a lower bound for the…

This paper is a continuation of our previous work in which we defined the notion of a polytope complex and its $K$-theory. In this paper we produce formulas for the delooping of a simplicial polytope complex and the cofiber of a morphism of…

This is a survey. The main subject of this survey is the homotopical or homological nature of certain structures which appear in classical problems about groups, Lie rings and group rings. It is well known that the (generalized) dimension…

We introduce a method to reduce the study of the topology of a simplicial complex to that of a simpler one. We give some applications of this method to complexes arising from graphs. As a consequence, we answer some questions raised in…

Tree-based ensembles such as the Random Forest are modern classics among statistical learning methods. In particular, they are used for predicting univariate responses. In case of multiple outputs the question arises whether we separately…

We compute the continuous bounded cohomology of the full automorphism groups of regular trees in all positive degrees, with coefficients arising from any irreducible continuous unitary representations. To the author's knowledge, this seems…

One of the most challenging and frequently arising problems in many areas of science is to find solutions of a system of multivariate nonlinear equations. There are several numerical methods that can find many (or all if the system is small…

The classifying space of a crossed complex generalises the construction of Eilenberg-Mac Lane spaces. We show how the theory of fibrations of crossed complexes allows the analysis of homotopy classes of maps from a free crossed complex to…

Fields exhibit a variety of topological properties, like different topological charges, when field space in the continuum is composed by more than one topological sector. Lattice treatments usually encounter difficulties describing those…

The dual complex of a singularity is defined, up-to homotopy, using resolutions of singularities. In many cases, for instance for isolated singularities, we identify and study a "minimal" representative of the homotopy class that is well…

Symmetric edge polytopes are a recent and well-studied family of centrally symmetric polytopes arising from graphs. In this paper, we introduce a generalization of this family to arbitrary simplicial complexes. We show how topological…

We propose a procedure to build a decision tree which approximates the performance of complex machine learning models. This single approximation tree can be used to interpret and simplify the predicting pattern of random forests (RFs) and…

We consider a certain class of simplicial complexes which includes the independence complexes of forests. We show that if a simplicial complex $K$ belongs to this class, then the polyhedral join $\mathcal{Z}^*_{K}(\underline{X}, \emptyset)$…

This is an introductory textbook to univalent mathematics and homotopy type theory, a mathematical foundation that takes advantage of the structural nature of mathematical definitions and constructions. It is common in mathematical practice…

We construct an effective algorithmic method to compute the homological monodromy of a complex polynomial which is tame. As an application we show the existence of conjugated polynomials in a number field which are not topologically…

This article studies a large, general class of orthogonal polytopes which we may call "generic orthotopes". These objects emerged from a desire to represent a Coxeter complex by an orthogonal polytope that is particularly nice with respect…

Let $M$ be a closed, oriented, simply connected 6-manifold. After localization away from 2, we give a homotopy decomposition of $\Sigma M$ in terms of spheres, Moore spaces and other recognizable spaces. As applications we calculate…

The goal of this paper is to study the path-following method for univariate polynomials. We propose to study the complexity and condition properties when the Newton method is applied as a correction operator. Then we study the geodesics and…

Multilinear systems of equations arise in various applications, such as numerical partial differential equations, data mining, and tensor complementarity problems. In this paper, we propose a homotopy method for finding the unique positive…