Related papers: Open sub-categorical dynamics in interaction

Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this…

We propose a precise definition of a continuous time dynamical system made up of interacting open subsystems. The interconnections of subsystems are coded by directed graphs. We prove that the appropriate maps of graphs called graph…

If Economics is understood as the study of the interactions among intentional agents, being rationality the main source of intentional behavior, the mathematical tools that it requires must be extended to capture systemic effects. Here we…

Relational structures are emerging as ubiquitous mathematical machinery in the semantics of open systems of various kinds. Cartesian bicategories are a well-known categorical algebra of relations that has proved especially useful in recent…

We present a unified field-theoretic framework for the dynamics of activity and connectivity in interacting neuronal systems. Building upon previous works, where a field approach to activity--connectivity dynamics, formation of collective…

We consider a monopolistic seller in a market that may be segmented. The surplus of each consumer in a segment depends on the price that the seller optimally charges, which depends on the set of consumers in the segment. We study which…

Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way. Several open dynamical systems can be…

In this article, we study finite dynamical systems defined over graphs, where the functions are applied asynchronously. Our goal is to quantify and understand stability of the dynamics with respect to the update sequence, and to relate this…

Our aim is to detect mechanistic interaction between the effects of two causal factors on a binary response, as an aid to identifying situations where the effects are mediated by a common mechanism. We propose a formalization of mechanistic…

In this technical note we consider a class of multi-agent network systems that we refer to as Open Multi-Agent Systems (OMAS): in these multi-agent systems, an indefinite number of agents may join or leave the network at any time. Focusing…

Interactions among living organisms, from bacteria colonies to human societies, are inherently more complex than interactions among particles and nonliving matter. Group interactions are a particularly important and widespread class,…

The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential…

A theorem is derived which (i) provides a new class of subfactors which may be interpreted as generalized asymptotic subfactors, and which (ii) ensures the existence of two-dimensional local quantum field theories associated with certain…

Recently, sub-indices and sub-factors of groups with connections to number theory, additive combinatorics, and factorization of groups have been introduced and studied. Since all group subsets are considered in the theory and there are many…

The birth and decline of disciplines are critical to science and society. However, no quantitative model to date allows us to validate competing theories of whether the emergence of scientific disciplines drives or follows the formation of…

The relationship between microsystems and macrosystems is considered in the context of quantum field formulation of statistical mechanics: it is argued that problems on foundations of quantum mechanics can be solved relying on this…

I review few conceptual steps in analytic description of topological interactions, which constitute the basis of a new interdisciplinary branch in mathematical physics, "Statistical Topology", emerged at the edge of topology and statistical…

Characterization of classes of switching signals that ensure stability of switched systems occupies a significant portion of the switched systems literature. This article collects a multitude of stabilizing switching signals under an…

In this paper, we first review some basic concepts associated with a model for social interaction previously proposed by us. Each agent is seen as an array of variables that can be found in different states. The agents are then allowed to…

We review mechanisms of dynamical supersymmetry breaking. Several observations that narrow the search for possible models of dynamical supersymmetry breaking are summarized. These observations include the necessary and sufficient conditions…