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We consider the generalization of Laplace invariants to linear differential systems of arbitrary rank and dimension. We discuss completeness of certain subsets of invariants.
We supply basic tools for the study of the topological order of a multiplet which is an eigenspace of a finite-dimensional normal operator with continuous parameters. We allow intrinsic degeneracies within the multiplet where a well-known…
The notion of random self-decomposability is generalized here. Its relation to self-decomposability, Harris infinite divisibility and its connection with a stationary first order generalized autoregressive model are presented. The notion is…
Compounding submodular monotone (i.e. 2-alternating) set functions on a finite set preserves this property, as shown in 2010. A natural generalization to k-alternating functions was presented in 2018, however hardly readable because of page…
We study the dynamics of the renormalization operator for multimodal maps. In particular, we prove the exponential convergence of this operator for infinitely renormalizable maps with same bounded combinatorial type.
Set-functions appear in many areas of computer science and applied mathematics, such as machine learning, computer vision, operations research or electrical networks. Among these set-functions, submodular functions play an important role,…
Transformer-based models excel in various tasks but their generalization capabilities, especially in arithmetic reasoning, remain incompletely understood. Arithmetic tasks provide a controlled framework to explore these capabilities, yet…
A brief overview is presented of recent developments concerning resummed small-x evolution, based upon the renormalization group equation. The non-singlet and singlet structure functions are discussed for both polarized and unpolarized…
In the last two decades, many algebras of generalized functions have been constructed, particularly the so-called generalized Sobolev algebras. Our goal is to study the latter and some of their main properties. In this framework, we pose…
The bulk macroscopic response of a system of particles or inclusions with field-induced forces is studied. The susceptibilities and transport coefficients in such a system are expressed as averages of a multiple scattering expansion. A…
Non-closedness of subexponentiality by the convolution operation is well-known. We go a step further and show that subexponentiality and non-subexponentiality are generally changeable by the convolution. We also give several conditions, by…
In this paper, some results on vanishing and non-vanishing of generalized local cohomology modules are presented and some relations between those modules and, Ext and ordinary local cohomology modules are studied. Also, several cofiniteness…
A subvariety of a quasi-projective complex variety $X$ is called ``universally irreducible'' if its preimage inside the universal cover of $X$ is irreducible. In this paper we investigate sufficient conditions for universal irreducibility.…
We study the bundles of generalized theta functions constructed from moduli spaces of sheaves over abelian surfaces. In degree 0, the splitting type of these bundles is expressed in terms of indecomposable semihomogeneous factors.…
We present a generalisation of the theory of iterated function systems and associated fractals to the setting of noncommutative geometry. Along the way, we discuss some ideas surrounding locally compact noncommutative metric spaces.
We show that the irreducible components of any moduli space of semistable representations of a special biserial algebra are always isomorphic to products of projective spaces of various dimensions. This is done by showing that irreducible…
Many vision-related tasks benefit from reasoning over multiple modalities to leverage complementary views of data in an attempt to learn robust embedding spaces. Most deep learning-based methods rely on a late fusion technique whereby…
The categories with noninvertible morphisms are studied analogously to the semisupermanifolds with noninvertible transition functions. The concepts of regular n-cycles, obstruction and the regularization procedure are introduced and…
We generalize the notion of an anomaly for a symmetry to a noninvertible symmetry enacted by surface operators using the framework of condensation in 2-categories. Given a multifusion 2-category, potentially with some additional levels of…
The irreducible decomposition of a unitary representation often contains continuous spectrum when restricted to a non-compact subgroup. The author singles out a nice class of branching problems where each irreducible summand occurs…