相关论文: The weighted difference substitutions and Nonnegat…

This book deals with functions allowing to express the dissimilarity (discrepancy) between two data fields or ''divergence functions'' with the aim of applications to linear inverse problems. Most of the divergences found in the litterature…

Weighted sieves are used to detect numbers with at most $S$ prime factors with $S \in \mathbb{N}$ as small as possible. When one studies problems with two variables in somewhat symmetric roles (such as Chen primes, that is primes $p$ such…

Dynamic feature selection (DFS) addresses budget constraints in decision-making by sequentially acquiring features for each instance, making it appealing for resource-limited scenarios. However, existing DFS methods require models…

Associated to any finite metric space are a large number of objects and quantities which provide some degree of structural or geometric information about the space. In this paper we show that in the setting of subsets of weighted Hamming…

Machine learning models can be used to predict physical quantities like homogenized elasticity stiffness tensors, which must always be symmetric positive definite (SPD) based on conservation arguments. Two datasets of homogenized elasticity…

An instance-weighted variant of the support vector machine (SVM) has attracted considerable attention recently since they are useful in various machine learning tasks such as non-stationary data analysis, heteroscedastic data modeling,…

Averaging iterations of Stochastic Gradient Descent (SGD) have achieved empirical success in training deep learning models, such as Stochastic Weight Averaging (SWA), Exponential Moving Average (EMA), and LAtest Weight Averaging (LAWA).…

Given an SFT $\Sigma$ and a finite set $S$ of finite words, let $\Sigma\langle S\rangle$ denote the subshift of $\Sigma$ that avoids $S$. We establish a general criterion under which we can bound the entropy perturbation…

This paper illustrates the richness of the concept of regular sets of time bounds and demonstrates its application to problems of computational complexity. There is a universe of bounds whose regular subsets allow to represent several time…

The power of multiple testing procedures can be increased by using weighted p-values (Genovese, Roeder and Wasserman 2005). We derive the optimal weights and we show that the power is remarkably robust to misspecification of these weights.…

The calculus of finite differences is a solid foundation for the development of operations such as the derivative and the integral for infinite sequences. Here we showed a way to extend it for finite sequences. We could then define…

The literature on Multiple Criteria Decision Analysis (MCDA) proposes several methods in order to sort alternatives evaluated on several attributes into ordered classes. Non Compensatory Sorting models (NCS) assign alternatives to classes…

The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that can not be written in normal form because the derivatives are multiplied by a singular linear operator. The concept of…

In this paper, we consider the inverse problem of determining some coefficients within a coupled nonlinear parabolic system, through boundary observation of its non-negative solutions. In the physical setup, the non-negative solutions…

Positive definite forms $f$ which are sums of squares are constructed to have the additional property that the members of any collection of forms whose squares sum to $f$ must share a nontrivial complex root.

The paper describes known and new results about finite difference calculus on configuration spaces. We describe finite difference geometry on configuration spaces, connect finite difference operators with cannonical commutation relations,…

Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…

Differential algebraic geometry seeks to extend the results of its algebraic counterpart to objects defined by differential equations. Many notions, such as that of a projective algebraic variety, have close differential analogues but their…

In this thesis, we develop various techniques for working with sets in machine learning. Each input or output is not an image or a sequence, but a set: an unordered collection of multiple objects, each object described by a feature vector.…

Determining whether a program terminates is a core challenge in program analysis with direct implications for correctness, verification, and security. We investigate whether transformer architectures can recognise termination patterns…