Related papers: Fusion systems and localities -- a dictionary
A linking system of difference sets is a collection of mutually related group difference sets, whose advantageous properties have been used to extend classical constructions of systems of linked symmetric designs. The central problems are…
We introduce layer systems for proving generalizations of the modularity of confluence for first-order rewrite systems. Layer systems specify how terms can be divided into layers. We establish structural conditions on those systems that…
A p-local finite group consists of a finite p-group S, together with a pair of categories which encode ``conjugacy'' relations among subgroups of S, and which are modelled on the fusion in a Sylow p-subgroup of a finite group. It contains…
In this paper we revisit two concepts which were originally introduced by Aschbacher and are crucial in the theory of saturated fusion systems: Firstly, we give a new approach to defining the centralizer of a normal subsystem. Secondly, we…
In this paper, we study local systems of locally finite associative algebras over fields of characteristic p\ge0. We describe the perfect local systems and study the relation between them and their corresponding locally finite associative…
This work provides new insights and constructs to the field of computer architecture and systems, and these insights are expected to be useful for the broad software stack. First, this work introduces Functionality Locality: this form of…
Modeling relations between components of 3D objects is essential for many geometry editing tasks. Existing techniques commonly rely on labeled components, which requires substantial annotation effort and limits components to a dictionary of…
This paper introduces {\em fusion subspace clustering}, a novel method to learn low-dimensional structures that approximate large scale yet highly incomplete data. The main idea is to assign each datum to a subspace of its own, and minimize…
We introduce a new form of density functional theory for the {\em ab initio} description of electronic systems in contact with a molecular liquid environment. This theory rigorously joins an electron density-functional for the electrons of…
The definition of the complement of a fuzzy subset is algebraic in nature and when it is used in the context of fuzzy topological spaces it does not share any similarity with the usual property of topological spaces that the complement of…
Many of the conjectures of current interest in the representation theory of finite groups in characteristic $p$ are local-to-global statements, in that they predict consequences for the representations of a finite group $G$ given data about…
The periodic Temperley-Lieb category consists of connectivity diagrams drawn on a ring with $N$ and $N'$ nodes on the outer and inner boundary, respectively. We consider families of modules, namely sequences of modules $\mathsf{M}(N)$ over…
We clarified the connection between measurements and partitions, and discussed the meaning of semiotics for measurements based on functions. The terms of property and relation quantity were defined by our understanding of partitions and…
Combinatorial design theory studies set systems with certain balance and symmetry properties and has applications to computer science and elsewhere. This paper presents a modular approach to formalising designs for the first time using…
The concept of typed topological space is introduced, for which open sets in a topology on a finite set will be assigned types (from lattice). The neighborhood system of a point, the closure and the connectedness can be defined according to…
A partial monoid $P$ is a set with a partial multiplication $\times$ (and total identity $1_P$) which satisfies some associativity axiom. The partial monoid $P$ may be embedded in a free monoid $P^*$ and the product $\star$ is simulated by…
We establish a correspondence between consistent comprehension schemes and complete orthogonal factorisation systems. The comprehensive factorisation of a functor between small categories arises in this way. Similar factorisation systems…
We extend Dwyer's sharp subgroup homology decomposition of the classifying space of a finite group to arbitrary saturated fusion systems and arbitrary Mackey functors.
We show that every fusion system on a p-group S is equal to the fusion system associated to a discrete group G with the property that every p-subgroup of G is conjugate to a subgroup of S.
Coherent structures emerge from the dynamics of many kinds of dissipative, externally driven, nonlinear systems, and continue to provoke new questions that challenge our physical and mathematical understanding. In one specific sub-class of…