Related papers: Cartesian Linearly Distributive Categories: Revisi…

Morphisms between (formal) contexts are certain pairs of maps, one between objects and one between attributes of the contexts in question. We study several classes of such morphisms and the connections between them. Among other things, we…

We present an unbiased theory of symmetric multicategories, where sequences are replaced by families. To be effective, this approach requires an explicit consideration of indexing and reindexing of objects and arrows, handled by the double…

Cobordism categories are known to be compact closed. They can therefore be used to define non-degenerate models of multiplicative linear logic by combining the Int construction with double glueing. In this work we detail such construction…

Novel Categories Discovery (NCD) aims to cluster novel data based on the class semantics of known classes using the open-world partial class space annotated dataset. As an alternative to the traditional pseudo-labeling-based approaches, we…

We examine a variant of hypergraphs that we call interfaced linear hypergraphs, with the aim of creating a sound and complete graphical language for symmetric traced monoidal categories (STMCs) suitable for graph rewriting. In particular,…

LDPC codes based on multiple-edge protographs potentially have larger minimum distances compared to their counterparts, single-edge protographs. However, considering different features of their Tanner graph, such as short cycles, girth and…

This paper is concerned with linear superposition systems in which all components of the superimposed signal are coded with an identical binary low-density parity-check (LDPC) code.

Cameron-Liebler sets were originally defined as collections of lines (`line classes') in $\mathrm{PG}(3,q)$ sharing certain properties with line classes of symmetric tactical decompositions. While there are many equivalent…

fc-multicategories are a very general kind of two-dimensional structure, encompassing bicategories, monoidal categories, double categories and ordinary multicategories. We define them and explain how they provide a natural setting for two…

It is known that different categorial grammars have surface representation in a fragment of first order multiplicative linear logic (MLL1). We show that the fragment of interest is equivalent to the recently introduced extended tensor type…

A braided monoidal category may be considered a $3$-category with one object and one $1$-morphism. In this paper, we show that, more generally, $3$-categories with one object and $1$-morphisms given by elements of a group $G$ correspond to…

For classical discrete system under constant composition, typically reffered to as substitutional alloys, correspondence between interatomic many-body interactions and structure in thermodynamic equilibrium exhibit profound, complicated…

We define for each $n \geq 1$ a symmetric monoidal $(\infty, n+1)$-category $n\mathrm{Pr}^L$ whose objects we call presentable $(\infty,n)$-categories, generalizing the usual theory of presentable $(\infty,1)$-categories. We show that each…

Semantic segmentation has made significant progress in recent years thanks to deep neural networks, but the common objective of generating a single segmentation output that accurately matches the image's content may not be suitable for…

In this paper, we study a new class of high-rate spatially coupled LDPC (SC-LDPC) codes based on the convolutional self-orthogonal codes (CSOCs) first introduced by Massey. The SC-LDPC codes are constructed by treating the irregular graph…

A double category of relations is essentially a cartesian equipment with strong, discrete and functorial tabulators and for which certain local products satisfy a Frobenius Law. A double category of relations is equivalent to a double…

Link prediction tasks focus on predicting possible future connections. Most existing researches measure the likelihood of links by different similarity scores on node pairs and predict links between nodes. However, the similarity-based…

The "linear dual" of a cocomplete linear category $\mathcal C$ is the category of all cocontinuous linear functors $\mathcal C \to \mathrm{Vect}$. We study the questions of when a cocomplete linear category is reflexive (equivalent to its…

Recent advances have shown that sequential fine-tuning (SeqFT) of pre-trained vision transformers (ViTs), followed by classifier refinement using approximate distributions of class features, can be an effective strategy for…

Additive codes have attracted considerable attention for their potential to outperform linear codes. However, distinguishing strictly additive codes from those that are equivalent to linear codes remains a fundamental challenge. To resolve…