Related papers: Asynchronous Networks: Modularization of Dynamics …

We study the synchronization of coupled dynamical systems on a variety of networks. The dynamics is governed by a local nonlinear map or flow for each node of the network and couplings connecting different nodes via the links of the…

This work connects models for virus spread on networks with their equivalent neural network representations. Based on this connection, we propose a new neural network architecture, called Transmission Neural Networks (TransNNs) where…

We introduce Network Automata, a framework which couples the topological evolution of a network to its structure. It is useful for dealing with networks in which the topology evolves according to some specified microscopic rules and,…

The mechanisms by which modularity emerges in complex networks are not well understood but recent reports have suggested that modularity may arise from evolutionary selection. We show that finding the modularity of a network is analogous to…

Biological networks have two modes. The first mode is static: a network is a passage on which something flows. The second mode is dynamic: a network is a pattern constructed by gluing functions of entities constituting the network. In this…

The concept of structured occurrence nets is an extension of that of occurrence nets which are directed acyclic graphs that represent causality and concurrency information concerning a single execution of a distributed system. The formalism…

We propose a new framework for the study of continuous time dynamical systems on networks. We view such dynamical systems as collections of interacting control systems. We show that a class of maps between graphs called graph fibrations…

Neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of…

We consider a finite collection of reinforced stochastic processes with a general network-based interaction among them. We provide sufficient and necessary conditions in order to have some form of almost sure asymptotic synchronization,…

Real-world networks often benefit from capturing both local and global interactions. Inspired by multi-modal analysis in brain imaging, where structural and functional connectivity offer complementary views of network organization, we…

Complex networks are the subject of fundamental interest from the scientific community at large. Several metrics have been introduced to characterize the structure of these networks, such as the degree distribution, degree correlation, path…

Networks are representations of complex underlying social processes. However, the same given network may be more suitable to model one behavior of individuals than another. In many cases, aggregate population models may be more effective…

In many natural synchronization phenomena, communication between individual elements occurs not directly, but rather through the environment. One of these instances is bacterial quorum sensing, where bacteria release signaling molecules in…

Many physical and biological systems can be studied using complex network theory, a new statistical physics understanding of graph theory. The recent application of complex network theory to the study of functional brain networks generated…

We seek to develop network algorithms for function computation in sensor networks. Specifically, we want dynamic joint aggregation, routing, and scheduling algorithms that have analytically provable performance benefits due to in-network…

Recurrent neural network architectures can have useful computational properties, with complex temporal dynamics and input-sensitive attractor states. However, evaluation of recurrent dynamic architectures requires solution of systems of…

This paper focuses on computing the frequency response and transfer functions for large self-similar networks under different circumstances. Modeling large scale systems is difficult due, typically, to the dimension of the problem, and…

We extend recent theoretical approximations describing the transition to synchronization in large undirected networks of coupled phase oscillators to the case of directed networks. We also consider extensions to networks with mixed…

In this paper, we are introducing a novel model of artificial intelligence, the functional neural network for modeling of human decision-making processes. This neural network is composed of multiple artificial neurons racing in the network.…

Contrasts with existing works which all consider nodes as functions and use edges to represent the relationships between different functions. We target at network modeling whose edges are functional data and transform the adjacency matrix…