相关论文: Higher dimensional hypercategories

This is the first of two papers aimed at economically capturing the collider phenomenology of warped extra dimensions with bulk Standard Model fields, where the hierarchy problem is solved non-supersymmetrically. This scenario is related…

We study in detail the relationship between strong subadditivity for a boundary field theory and energy conditions for its bulk dual in 2+1 dimensions. We provide a discussion of known facts and new results organized from the simplest case…

Equality saturation, a technique for program optimisation and reasoning, has gained attention due to the resurgence of equality graphs (e-graphs). E-graphs represent equivalence classes of terms under rewrite rules, enabling simultaneous…

Tannaka Duality describes the relationship between algebraic objects in a given category and their representations; an important case is that of Hopf algebras and their categories of representations; these have strong monoidal forgetful…

This thesis is devoted to the proof of a theorem showing the existence of a closed model category structure for weakly enriched categories. It requires first of all the definitions of weakly enriched categories and equivalences of weakly…

The notion of pseudocategory, as considered in [11], is extended from the context of a 2-category to the more general one of a sesquicategory, which is considered as a category equipped with a 2-cell structure. Some particular examples of…

This paper presents a finding that leveraging the hierarchical structures among labels for relationships and objects can substantially improve the performance of scene graph generation systems. The focus of this work is to create an…

We discuss the cohomology of superforms and integral forms from a new perspective based on a recently proposed Hodge dual operator. We show how the superspace constraints (a.k.a. rheonomic parametrisation) are translated from the space of…

We generalize the concept of stack one dimension higher, introducing a notion of 2-stack suitable for a trihomomorphism from a 2-category equipped with a bitopology into the tricategory of bicategories. Moreover, we give a characterization…

We give a simple algebraic description of opetopes in terms of chain complexes, and we show how this description is related to combinatorial descriptions in terms of treelike structures. More generally, we show that the chain complexes…

Graph representation learning has made major strides over the past decade. However, in many relational domains, the input data are not suited for simple graph representations as the relationships between entities go beyond pairwise…

Multilayer networks have permeated all the sciences as a powerful mathematical abstraction for interdependent heterogenous complex systems such as multimodal brain connectomes, transportation, ecological systems, and scientific…

Let (W, S) be a Coxeter system. A W-graph is an encoding of a representation of the corresponding Iwahori-Hecke algebra. Especially important examples include the W-graph corresponding to the action of the Iwahori-Hecke algebra on the…

Leveraging hypergraph structures to model advanced processes has gained much attention over the last few years in many areas, ranging from protein-interaction in computational biology to image retrieval using machine learning. Hypergraph…

Title: From favorable atomic configurations to supershell structures: a new interpretation of conductance histograms Authors: A. Hasmy (IVIC), E. Medina (IVIC), P.A. Serena (CSIC,IVIC) Comments: 7 pages, 3 figures, cond-mat.anwar.10825…

Graph generation techniques are increasingly being adopted for drug discovery. Previous graph generation approaches have utilized relatively small molecular building blocks such as atoms or simple cycles, limiting their effectiveness to…

Our understanding of the dynamics of complex networked systems has increased significantly in the last two decades. However, most of our knowledge is built upon assuming pairwise relations among the system's components. This is often an…

We provide a new approach to categorical graph and hypergraph theory by using categorical syntax and semantics. For each monoid $M$ and action on a set $X$, there is an associated presheaf topos of $(X,M)$-graphs where each object can be…

We introduce the notion of a higher covering diagram in a base $\infty$-category $\mathcal{C}$. The theory of higher covering diagrams in $\mathcal{C}$ will be shown to recover various descent conditions known from the $\infty$-categorical…

In this thesis, we develop the theory of bifibrations of polycategories. We start by studying how to express certain categorical structures as universal properties by generalising the shape of morphism. We call this phenomenon…