相关论文: An Algebra of Resource Sharing Machines

We propose a high dimensional generalisation of the standard Klein bottle, going beyond those considered previously. We address the problem of generating continuous scalar fields (distributions) and dynamical systems (flows) on such state…

A scheme for logical computation using non-linear dynamical systems is presented. Examples of discrete-time maps configured as AND, OR, NAND and NOR gates are given. It is seen that the logical operations are flexible in the sense that an…

We present the first steps of interaction spaces theory, a universal mathematical theory of complex systems which is able to embed cellular automata, agent based models, master equation based models, stochastic or deterministic, continuous…

Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…

Influence systems form a large class of multiagent systems designed to model how influence, broadly defined, spreads across a dynamic network. We build a general analytical framework which we then use to prove that, while sometimes chaotic,…

A notion of time is fundamental in the study of dynamical systems. Time arises as a standalone dynamical system and also in solutions or trajectories as a special kind of map between systems. We characterize time by a universal property and…

Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…

We introduce a framework that represents a dynamic program as a family of operators acting on a partially ordered set. We provide an optimality theory based only on order-theoretic assumptions and show how applications across almost all…

We show that all non-relativistic quantum processes, whether open or closed, are either unitary or probabilistic unitary, i.e., probabilistic combination of unitary evolutions. This means that for open quantum systems, its continuous…

This paper presents the basic concepts of a systemic theory of interaction between non-deterministic open dynamics with varying temporalities, which includes three stages: the definition of these dynamics as lax-functors, the notion of…

We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…

To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…

Unlike computation or the numerical analysis of differential equations, simulation does not have a well established conceptual and mathematical foundation. Simulation is an arguable unique union of modeling and computation. However,…

We define a notion of social machine and envisage an algebra that can describe networks of such. To start with, social machines are defined as tuples of input, output, processes, constraints, state, requests and responses; apart from…

The study of neural computation aims to understand the function of a neural system as an information processing machine. Neural systems are undoubtedly complex, necessitating principled and automated tools to abstract away details to…

In this work a collective of interacting stateless automata in a discrete geometric $n$-dimenstional environment is considered as an integral automaton-like computational dynamic object. For such distributed on the environment object…

We use ideas from distributed computing and game theory to study dynamic and decentralized environments in which computational nodes, or decision makers, interact strategically and with limited information. In such environments, which arise…

We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more…

Dynamical systems at the edge of chaos, which have been considered as models of self-organization phenomena, are marked by their ability to perform nontrivial computations. To distinguish them from systems with limited computing power, we…

We consider a dynamic social network model in which agents play repeated games in pairings determined by a stochastically evolving social network. Individual agents begin to interact at random, with the interactions modeled as games. The…