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We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…
Complex systems are very often organized under the form of networks where nodes and edges are embedded in space. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks, neural…
We consider $n$-dimensional discrete motions such that any two neighbouring positions correspond in a pure rotation ("rotating motions"). In the Study quadric model of Euclidean displacements these motions correspond to quadrilateral nets…
Spatio-temporal network dynamics is an emergent property of many complex systems which remains poorly understood. We suggest a new approach to its study based on the analysis of dynamical motifs -- small subnetworks with periodic and…
We apply an information theoretic treatment of action potential time series measured with microelectrode arrays to estimate the connectivity of mammalian neuronal cell assemblies grown {\it in vitro}. We infer connectivity between two…
We provide a numerical study of the macroscopic model of [3] derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodelling process is very fast, the…
We present a microscopic approach for the coupling of cortical activity, as resulting from proper dipole currents of pyramidal neurons, to the electromagnetic field in extracellular fluid in presence of diffusion and Ohmic conduction.…
This paper studies the information-theoretic secrecy performance in large-scale cellular networks based on a stochastic geometry framework. The locations of both base stations and mobile users are modeled as independent two-dimensional…
We introduce new geometric objects called spectral networks. Spectral networks are networks of trajectories on Riemann surfaces obeying certain local rules. Spectral networks arise naturally in four-dimensional N=2 theories coupled to…
Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…
The mathematical theory of pattern formation in electrically coupled networks of excitable neurons forced by small noise is presented in this work. Using the Freidlin-Wentzell large deviation theory for randomly perturbed dynamical systems…
To understand large, connected systems, we cannot only zoom into the details. We also need to see the large-scale features from afar. One way to take a step back and get the whole picture is to model the systems as a network. However, many…
Quantifying the outcomes of cells collisions is a crucial step in building the foundations of a kinetic theory of living matter. Here, we develop a mechanical theory of such collisions by first representing individual cells as extended…
Starting from the concept of binary interactions between pairs of particles, a kinetic framework for the description of the action potential dynamics on a neural network is proposed. It consists of two coupled levels: the description of a…
The study of neuronal morphology is important not only for its potential relationship with neuronal dynamics, but also as a means to classify diverse types of cells and compare than among species, organs, and conditions. In the present…
Prediction and control of the dynamics of complex networks is a central problem in network science. Structural and dynamical similarities of different real networks suggest that some universal laws might accurately describe the dynamics of…
Systems which consist of many localized constituents interacting with each other can be represented by complex networks. Consistently, network science has become highly popular in vast fields focusing on natural, artificial and social…
We consider atoms interacting each other through the topological structure of a complex network and investigate lattice vibrations of the system, the quanta of which we call {\em netons} for convenience. The density of neton levels,…
The fractal nature of graphs has traditionally been investigated by using the nodes of networks as the basic units. Here, instead, we propose to concentrate on the graph edges, and introduce a practical and computationally not demanding…
Being cognizant of the abundance of multi-body interactions in various complex systems, here we investigate a possible way to incorporate multi-body interactions in dynamical networks. Adopting hypergraph as the underlying architecture aids…