相关论文: Desingularization algorithms I. Role of exceptiona…
Over the last decade, implementations of several desingularization algorithms have appeared in various contexts. These differ as widely in their methods and in their practical efficiency as they differ in the situations in which they may be…
Conventional ways to solve optimization problems on low-rank matrix sets which appear in great number of applications ignore its underlying structure of an algebraic variety and existence of singular points. This leads to appearance of…
The philosophy of the article is that the desingularization invariant together with natural geometric information can be used to compute local normal forms of singularities. The idea is used in two related problems: (1) We give a proof of…
Randomization is a fundamental tool used in many theoretical and practical areas of computer science. We study here the role of randomization in the area of submodular function maximization. In this area most algorithms are randomized, and…
This article is an exposition of an elementary constructive proof of canonical resolution of singularities in characteristic zero, presented in detail in Invent. Math. 128 (1997), 207-302. We define a new local invariant and get an…
In this paper we construct a combinatorial algorithm of resolution of singularities for binomial ideals, over a field of arbitrary characteristic. This algorithm is applied to any binomial ideal. This means ideals generated by binomial…
We prove that the algorithm for desingularization of algebraic varieties in characteristic zero of the first two authors is functorial with respect to regular morphisms. For this purpose, we show that, in characteristic zero, a regular…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
The huge amount of available data nowadays is a challenge for kernel-based machine learning algorithms like SVMs with respect to runtime and storage capacities. Local approaches might help to relieve these issues and to improve statistical…
These are introductional notes to resolution of singularities and Log principalization of ideals over fields of characteristic zero. We refer to `A simplified proof of desingularization and applications', A. Bravo, S. Encinas and O.…
This article contains an elementary constructive proof of resolution of singularities in characteristic zero. Our proof applies in particular to schemes of finite type and to analytic spaces (so we recover the great theorems of Hironaka).…
The purpose of this article is to delve into the properties of invariants. The properties, explained in [2], reveal new ways to develop algorithms that allow us to test the primality of a number. In this article, some of these are shown,…
In characteristic zero, we construct relative principalization of ideals for logarithmically regular morphisms of logarithmic schemes, and use it to construct logarithmically regular desingularization of morphisms. These constructions are…
Recent decades have provided a host of examples and applications motivating the study of nonlocal differential operators. We discuss a class of such operators acting on bounded domains, focusing on those with integrable kernels having…
We show that a general miraculous cancellation formula, the divisibility of certain characteristic numbers and some other topologiclal results are con- sequences of the modular invariance of elliptic operators on loop spaces. Previously we…
A theoretical framework is presented for a (copula-based) notion of dissimilarity between continuous random vectors and its main properties are studied. The proposed dissimilarity assigns the smallest value to a pair of random vectors that…
We present a new class of exponential integrators for ordinary differential equations. They are locally exact, i.e., they preserve the linearization of the original system at every point. Their construction consists in modifying existing…
A well-known theorem factors a scalar coefficient differential operator given a linearly independent set of functions in its kernel. The goal of this paper is to generalize this useful result to other types of operators. In place of the…
A number of machine learning tasks entail a high degree of invariance: the data distribution does not change if we act on the data with a certain group of transformations. For instance, labels of images are invariant under translations of…
We attempt to better understand randomization in local distributed graph algorithms by exploring how randomness is used and what we can gain from it: - We first ask the question of how much randomness is needed to obtain efficient…