Related papers: Artin approximation property and the General Neron…

We study metric Diophantine approximation in local fields of positive characteristic. Specifically, we study the problem of improving Dirichlet's theorem in Diophantine approximation and prove very general results in this context.

In this paper, we study numerical approximations of the ground states in finite temperature density functional theory. We formulate the problem with respect to the density matrices and justify the convergence of the finite dimensional…

Artin glueings provide a way to reconstruct a frame from a closed sublocale and its open complement. We show that Artin glueings can be described as the weakly Schreier split extensions in the category of frames with finite-meet preserving…

Recent work in Information Retrieval (IR) using Deep Learning models has yielded state of the art results on a variety of IR tasks. Deep neural networks (DNN) are capable of learning ideal representations of data during the training…

In this paper, we obtained some global approximation results for general Gamma type operators.

I formulate a deformation of the dimensional-regularization technique that is useful for theories where the common dimensional regularization does not apply. The Dirac algebra is not dimensionally continued, to avoid inconsistencies with…

In this paper we develop a new machinery to study the capacity of artificial neural networks (ANNs) to approximate high-dimensional functions without suffering from the curse of dimensionality. Specifically, we introduce a concept which we…

Several general properties, concerning reduction algebras - rings of definition and algorithmic efficiency of the set of ordering relations - are discussed. For the reduction algebras, related to the diagonal embedding of the Lie algebra…

In this paper, we introduce a generalised diagonal dimension. We explain why the generalised diagonal dimension extends the notion of diagonal dimension defined by Li, Liao, and Winter, and under which conditions these dimensions coincide.…

We develop the notion of deformation of a morphism in a left-proper model category. As an application we provide a geometric/homotopic description of deformations of commutative (non-positively) graded differential algebras over a local…

This thesis presents a local-to-global perspective on graph neural networks (GNN), the leading architecture to process graph-structured data. After categorizing GNN into local Message Passing Neural Networks (MPNN) and global Graph…

The inhomogeneous Groshev type theory for dual Diophantine approximation on manifolds is developed. In particular, the notion of nice manifolds is introduced and the divergence part of the theory is established for all such manifolds. Our…

The successful fabrication of single layer graphene has greatly stimulated the progress of the research on graphene. In this article, focusing on the basic electronic and transport properties of graphene nanoribbons (GNRs), we review the…

We present an algorithmic embedded desingularization of arithmetic surfaces bearing in mind implementability. Our algorithm is based on work by Cossart-Jannsen-Saito, though our variant uses a refinement of the order instead of the…

We characterize some variations of pseudoskeleton (also called CUR) decompositions for matrices and tensors over arbitrary fields. These characterizations extend previous results to arbitrary fields and to decompositions which use…

We explicitly construct an embedding of a right-angled Artin group into a classical pure braid group. Using this we obtain a number of corollaries describing embeddings of arbitrary Artin groups into right-angled Artin groups and linearly…

Different formalisms for unintegrated parton densities are discussed, and some results and applications are presented.

We study the existence and uniqueness of solutions of a nonlinear integro-differential problem which we reformulate introducing the notion of the decreasing rearrangement of the solution. A dimensional reduction of the problem is obtained…

These notes form the next episode in a series of articles dedicated to a detailed proof of a cohomological index formula for transversally elliptic pseudo-differential operators and applications. The first two chapters are already available…

We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…