相关论文: Minimal characteristic bisets for fusion systems

In the present paper we study tensor C*-categories with non-simple unit realised as C*-dynamical systems (F,G,\beta) with a compact (non-Abelian) group G and fixed point algebra A := F^G. We consider C*-dynamical systems with minimal…

Convolutional neural networks and supervised learning have achieved remarkable success in various fields but are limited by the need for large annotated datasets. Few-shot learning (FSL) addresses this limitation by enabling models to…

The pointed fusion system of a block is a structure consisting of the fusions and relative multiplicities between the local pointed groups associated with a maximal Brauer pair. We show that the pointed fusion system is preserved by…

The idea of reduction of couplings consists in searching for renormalization group invariant relations between parameters of a renormalizable theory that hold to all orders of perturbation theory. Based on the principle of the reduction of…

Let $(X, f)$ be a topological dynamical system and $\mathcal {F}$ be a Furstenberg family (a collection of subsets of $\mathbb{N}$ with hereditary upward property). A point $x\in X$ is called an $\mathcal {F}$-transitive point if for every…

We characterize the fundamental group of a locally finite graph G with ends combinatorially, as a group of infinite words. Our characterization gives rise to a canonical embedding of this group in the inverse limit of the (free) fundamental…

A group $G$ is said to satisfy the finitely generated intersection property (f.g.i.p.) if the intersection of any two finitely generated subgroups of $G$ is again finitely generated. The aim of this article is to understand when the…

Flat band (FB) systems provide ideal playgrounds for studying correlation physics, whereas multi-orbital characteristics in real materials are distinguished from most simple FB models. Here, we propose a systematic and versatile framework…

A model M of cardinality lambda is said to have the small index property if for every G subseteq Aut(M) such that [Aut(M):G] <= lambda there is an A subseteq M with |A|< lambda such that Aut_A(M) subseteq G. We show that if M^* is a…

The study of band connectivity is a fundamental problem in condensed matter physics. Here, we develop a new method for analyzing band connectivity, which completely solves the outstanding questions of the reducibility and decomposition of…

Confined quantum systems involving $N$ identical interacting particles are to be found in many areas of physics, including condensed matter, atomic and chemical physics. A beyond-mean-field perturbation method that is applicable, in…

The fuzzy quantification model FA has been identified as one of the best behaved quantification models in several revisions of the field of fuzzy quantification. This model is, to our knowledge, the unique one fulfilling the strict…

Given a block of a finite group, any source algebra has a basis invariant under the multiplicative actions of the defect group. Is such a basis a characteristic biset of the block fusion system? If the basis can be chosen to consist…

Cross-device Federated Learning (FL) faces significant challenges where low-end clients that could potentially make unique contributions are excluded from training large models due to their resource bottlenecks. Recent research efforts have…

This article contains a basic introduction to the local study of finite groups, including a brief perspective on the theory of fusion systems and $p$-local finite groups. -- Este art\'iculo contiene una introducci\'on b\'asica al estudio…

A novel Thomas-Fermi (TF) approach to inhomogeneous superfluid Fermi-systems is presented and shown that it works well also in cases where the Local Density Approximation (LDA) breaks down. The novelty lies in the fact that the…

In this paper, we focus attention on extending the topological conjugacy of adding machine maps and minimal systems to iterated function systems. We provide necessary and sufficient conditions for an iterated function system to be…

Given an (infinite) relational structure $\mathbb S$, we say that a finite structure $\mathbb C$ is a minimal finite factor of $\mathbb S$ if for every finite structure $\mathbb A$ there is a homomorphism $\mathbb S\to \mathbb A$ if and…

Cylindrical Algebraic Decomposition (CAD) algorithms typically produce a decomposition adapted to a finite family of semi-algebraic sets $\mathcal{F}$ (i.e. every member of $\mathcal{F}$ is a union of cells). Different algorithms may…

System F, the polymorphic lambda calculus, features the principle of impredicativity: polymorphic types may be (explicitly) instantiated at other types, enabling many powerful idioms such as Church encoding and data abstraction.…