Related papers: Valuation theoretic and model theoretic aspects of…

Machine learning models rely on various assumptions to attain high accuracy. One of the preliminary assumptions of these models is the independent and identical distribution, which suggests that the train and test data are sampled from the…

The biduality and reflexivity theorems are known to hold for projective varieties defined over fields of characteristic zero, and to fail in positive characteristic. In this article, we construct a notion of reflexivity and biduality in…

The present paper deals with the perturbation analysis of set-valued inclusion problems, a problem format whose relevance has recently emerged in such contexts as robust and vector optimization as well as in vector equilibrium theory. The…

The increasing complexity of AI systems has made understanding their behavior critical. Numerous interpretability methods have been developed to attribute model behavior to three key aspects: input features, training data, and internal…

Learning-to-rank (LTR) is a class of supervised learning techniques that apply to ranking problems dealing with a large number of features. The popularity and widespread application of LTR models in prioritizing information in a variety of…

Using the character expansion method, we generalize several well-known integrals over the unitary group to the case where general complex matrices appear in the integrand. These integrals are of interest in the theory of random matrices and…

We present a scaling theory for the effect of thermal fluctuations on the characteristics of the depinning transition, and also in the closely related directed percolation model. Thermal effects act as a sort of external field that produces…

In this work we classify the at-point regularities of set-valued mappings into two categories and then we analyze their relationship through several implications and examples. After this theoretical tour, we use the subregularity properties…

This paper presents several independence results concerning the topos-valid and the intuitionistic (generalized) predicative theories of locales. In particular, certain consequences of the consistency of a general form of Troelstra's…

We present a fully relativistic model for localized probes in quantum field theory. Furthermore, we show that it is possible to obtain particle detector models from localized quantum field theories that interact with a free quantum field.…

We extend to Gaussian distributions a result providing smoothed analysis estimates for condition numbers given as relativized distances to illposedness. We also introduce a notion of local analysis meant to capture the behavior of these…

In this paper, local monomialization theorems are proven for analytic morphisms of complex and real analytic spaces. This gives the generalization of the local monomialization theorem for morphisms of algebraic varieties over a field of…

Spatial symmetries of the densities appearing in the nuclear Density Functional Theory are discussed. General forms of the local densities are derived by using methods of construction of isotropic tensor fields. The spherical and axial…

We study the behaviour of differential forms in a manifold having at least one of their maximal isotropic local distributions endowed with the special algebraic property of being decomposable. We show that they can be represented as the sum…

This is an expository paper on the subject of the title. It assumes basic scheme theory, commutative and homological algebra.

We show that the local and deterministic mode of description is not only in conflict with the quantum theory, but also with relativity. We argue that elementary relativistic properties of spacetime lead to the emergence of a…

In this paper we present a characterization for the defect of a simple algebraic extensions of valued fields. This characterization generalizes the known result for the henselian case, namely that the defect is the product of the relative…

Pseudo-variograms appear naturally in the context of multivariate Brown-Resnick processes, and are a useful tool for analysis and prediction of multivariate random fields. We give a necessary and sufficient criterion for a matrix-valued…

Refection Positivity is a central theme at the crossroads of Lie group representations, euclidean and abstract harmonic analysis, constructive quantum field theory, and stochastic processes. This book provides the first presentation of the…

This paper investigates two feature-scoring criteria that make use of estimated class probabilities: one method proposed by \citet{shen} and a complementary approach proposed below. We develop a theoretical framework to analyze each…