Related papers: A new criterion for integral modular categorificat…

In this paper we will give a categorical proof of the Radon-Nikodym theorem. We will do this by describing the trivial version of the result on finite probability spaces as a natural isomorphism. We then proceed to Kan extend this…

Cluster algebras are categorified by cluster categories, and $g$-vectors are categorified by the classic index with respect to cluster tilting subcategories. However, the recently introduced completed discrete cluster categories of Dynkin…

We study exponential sums whose coefficients are completely multiplicative and belong to the complex unit disc. Our main result shows that such a sum has substantial cancellation unless the coefficient function is essentially a Dirichlet…

This article describes an approach to designing a distributed and modular neural classifier. This approach introduces a new hierarchical clustering that enables one to determine reliable regions in the representation space by exploiting…

The algorithmic Markov condition states that the most likely causal direction between two random variables X and Y can be identified as that direction with the lowest Kolmogorov complexity. Due to the halting problem, however, this notion…

Modular data is an important topic of study in rational conformal field theory. A modular datum defines finite dimensional representations of the modular group $\mbox{SL}_2(\mathbf{Z})$. For every Fourier matrix in a modular datum there…

While many approaches exist in the literature to learn low-dimensional representations for data collections in multiple modalities, the generalizability of multi-modal nonlinear embeddings to previously unseen data is a rather overlooked…

Classification and invariants, with respect to basis changes, of finite dimensional algebras are considered. An invariant open, dense (in the Zariscki topology) subset of the space of structural constants is defined. The algebras with…

In this paper, we establish general categorical frameworks that extend Loewy's classification scheme for finite-dimensional real irreducible representations of groups and Borel--Tits' criterion for the existence of rational forms of…

This work proposes and evaluates a novel approach to determine interesting categorical attributes for lists of entities. Once identified, such categories are of immense value to allow constraining (filtering) a current view of a user to…

In this article, we develop and investigate a new classifier based on features extracted using spatial depth. Our construction is based on fitting a generalized additive model to the posterior probabilities of the different competing…

We prove that up to scaling there are only finitely many integral lattices L of signature (2,n) with n>20 or n=17 such that the modular variety defined by the orthogonal group of L is not of general type. In particular, when n>107, every…

The paper proposes a vector generalization of the basic concepts of the theory of complex variable: the concept of modulus and argument of complex number. The author introduces some generalizations of the notion of holomorphic functions and…

The information in an individual finite object (like a binary string) is commonly measured by its Kolmogorov complexity. One can divide that information into two parts: the information accounting for the useful regularity present in the…

Let k be an algebraically closed field of characteristic p>0 and let G be a symplectic or general linear group over k. We consider induced modules for G under the assumption that p is bigger than the greatest hook length in the partitions…

In this lecture note, we discuss a fundamental concept, referred to as the {\it characteristic rank}, which suggests a general framework for characterizing the basic properties of various low-dimensional models used in signal processing.…

Modular categories are important algebraic structures in a variety of subjects in mathematics and physics. We provide an explicit, motivated and elementary definition of a modular category over a field of characteristic 0 as an equivalence…

Khovanov and Sazdanovic recently introduced symmetric monoidal categories parameterized by rational functions and given by quotients of categories of two-dimensional cobordisms. These categories generalize Deligne's interpolation categories…

In order to prove new existence results in Brill-Noether theory for rank-2 vector bundles with fixed special determinant, we develop foundational definitions and results for limit linear series of higher-rank vector bundles. These include…

The ability to detect out-of-distribution (OOD) inputs is critical to guarantee the reliability of classification models deployed in an open environment. A fundamental challenge in OOD detection is that a discriminative classifier is…