Related papers: Fusion Action Systems
A complex system is a system composed of many interacting parts, often called agents, which displays collective behavior that does not follow trivially from the behaviors of the individual parts. Examples include condensed matter systems,…
While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…
An algebraic formalism for the study of interacting particle systems is developed. Particle processes are described in terms of the category theory. The problem for the unique description of these processes is discussed. Categories relevant…
Dividing the world into subsystems is an important component of the scientific method. The choice of subsystems, however, is not defined a priori. Typically, it is dictated by experimental capabilities, which may be different for different…
Reaction systems are a formal model that has been introduced to investigate the interactive behaviors of biochemical reactions. Based on the formal framework of reaction systems, we propose new computing models called reaction automata that…
We determine the fusion rules of the equivariantization of a fusion category $\mathcal{C}$ under the action of a finite group $G$ in terms of the fusion rules of $\mathcal{C}$ and group-theoretical data associated to the group action. As an…
Multi-agent approach has become popular in computer science and technology. However, the conventional models of multi-agent and multicomponent systems implicitly or explicitly assume existence of absolute time or even do not include time in…
We propose a model for deterministic distributed function computation by a network of identical and anonymous nodes, with bounded computation and storage capabilities that do not scale with the network size. Our goal is to characterize the…
For a prime $p$, fusion systems over discrete $p$-toral groups are categories that model and generalize the $p$-local structure of Lie groups and certain other infinite groups in the same way that fusion systems over finite $p$-groups model…
Building upon the findings presented in the first three papers of this series, we formulate an effective field theory for interacting collective states. These states consist of a large number of interconnected neurons and are distinguished…
These are introductory notes on some aspects of concentration of measure in the presence of an acting group and its links to Ramsey theory.
We address the problem of fusing array operations based on criteria such as shape compatibility, data reusability, and communication. We formulate the problem as a graph partition problem that is general enough to handle loop fusion,…
This paper generalizes the basic notions of additive and multiplicative combinatorics to the setting of group actions: if $G$ is a group acting on a set $X$, and we have subsets $A\subseteq G$ and $Y\subseteq X$ such that the set of pairs…
In this work, we introduce the notion of a partial action of a group on a strict monoidal category. We propose, in the context of Monoidal categories, new constructions analogous to those existing for partial group actions over an algebra…
This research presents the idea of activity fusion into existing Pose Estimation architectures to enhance their predictive ability. This is motivated by the rise in higher level concepts found in modern machine learning architectures, and…
In this paper, we review multi-agent collective behavior algorithms in the literature and classify them according to their underlying mathematical structure. For each mathematical technique, we identify the multi-agent coordination tasks it…
This paper presents a technique which exploits the occurrence of certain events as observed by different sensors, to detect and classify objects. This technique explores the extent of dependence between features being observed by the…
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…
Intelligent autonomous systems are part of a system of systems that interact with other agents to accomplish tasks in complex environments. However, intelligent autonomous systems integrated system of systems add additional layers of…
The term active matter describes diverse systems, spanning macroscopic (e.g. shoals of fish and flocks of birds) to microscopic scales (e.g. migrating cells, motile bacteria and gels formed through the interaction of nanoscale molecular…