Related papers: Networks of open systems
Real-world networks typically exhibit several aspects, or layers, of interactions among their nodes. By permuting the role of the nodes and the layers, we establish a new criterion to construct the dual of a network. This approach allows to…
The practice of scientific research is often thought of as individuals and small teams striving for disciplinary advances. Yet as a whole, this endeavor more closely resembles a complex system of natural computation, in which information is…
Representing various networked data as multiplex networks, networks of networks and other multilayer networks can reveal completely new types of structures in these system. We introduce a general and principled graphlet framework for…
Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
Heteroclinic structures organize global features of dynamical systems. We analyze whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more…
We present a general framework that enables one to model high-order interaction among entangled dynamical systems, via hypergraphs. Several relevant processes can be ideally traced back to the proposed scheme. We shall here solely elaborate…
In the course of the growth of the Internet and due to increasing availability of data, over the last two decades, the field of network science has established itself as an own area of research. With quantitative scientists from computer…
In a Networked Dynamical System (NDS), each node is a system whose dynamics are coupled with the dynamics of neighboring nodes. The global dynamics naturally builds on this network of couplings and it is often excited by a noise input with…
We introduce and investigate the concept of Stratified Algebra, a new algebraic framework equipped with a layer-based structure on a vector space. We formalize a set of axioms governing intra-layer and inter-layer interactions, study their…
Some of the basic properties of any dynamical system can be summarized by a graph. The dynamical systems in our theory run from maps like the logistic map to ordinary differential equations to dissipative partial differential equations. Our…
Many different classification tasks need to manage structured data, which are usually modeled as graphs. Moreover, these graphs can be dynamic, meaning that the vertices/edges of each graph may change during time. Our goal is to jointly…
Until recently, artificial neural networks were typically designed with a fixed network structure. Here, I argue that network structure is highly relevant to function, and therefore neural networks should be livewired (Eagleman 2020):…
The algebraic analysis of social systems, or algebraic social network analysis, refers to a collection of methods designed to extract information about the structure of a social system represented as a directed graph. Central among these…
Many natural systems are organized as networks, in which the nodes (be they cells, individuals or populations) interact in a time-dependent fashion. The dynamic behavior of these networks depends on how these nodes are connected, which can…
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…
The vertices of an interval graph represent intervals over a real line where overlapping intervals denote that their corresponding vertices are adjacent. This implies that the vertices are measurable by a metric and there exists a linear…
Revealing physical interactions in complex systems from observed collective dynamics constitutes a fundamental inverse problem in science. Current reconstruction methods require access to a system's model or dynamical data at a level of…
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…
Modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and function of complex systems. Generally speaking,…