Related papers: Transport Networks Revisited: Why Dual Graphs?
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
We have revealed general physical conditions for the {\it maximization} of the network throughput at which free flow conditions are ensured, i.e., traffic breakdown cannot occur in the whole traffic or transportation network. A physical…
We quantize graphs (networks) which consist of a finite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrix theory. We also define a classical phase space for the…
We study transport in topologically disordered networks that are subjected to an environment that induces classical diffusion. The dynamics is phenomenologically described within the framework of the recently introduced quantum stochastic…
Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and…
We introduce the notion of a network's conduciveness, a probabilistically interpretable measure of how the network's structure allows it to be conducive to roaming agents, in certain conditions, from one portion of the network to another.…
A heterogeneous continuous time random walk is an analytical formalism for studying and modeling diffusion processes in heterogeneous structures on microscopic and macroscopic scales. In this paper we study both analytically and numerically…
We use complex network concepts to analyze statistical properties of urban public transport networks (PTN). To this end, we present a comprehensive survey of the statistical properties of PTNs based on the data of fourteen cities of so far…
We study symmetric queuing networks with moving servers and FIFO service discipline. The mean-field limit dynamics demonstrates unexpected behavior which we attribute to the meta-stability phenomenon. Large enough finite symmetric networks…
By constructing jointly a random graph and an associated exploration process, we define the dynamics of a "parking process" on a class of uniform random graphs as a measure-valued Markov process, representing the empirical degree…
We introduce graphs associated to transport problems between discrete marginals, that allow to characterize the set of all optimizers given one primal optimizer. In particular, we establish that connectivity of those graphs is a necessary…
We propose a one parameter family of random walk processes on hypergraphs, where a parameter biases the dynamics of the walker towards hyperedges of low or high cardinality. We show that for each value of the parameter the resulting process…
In this paper we investigate the growth rate of the number of all possible paths in graphs with respect to their length in an exact analytical way. Apart from the typical rates of growth, i.e. exponential or polynomial, we identify…
In real-world systems, the relationships and connections between components are highly complex. Real systems are often described as networks, where nodes represent objects in the system and edges represent relationships or connections…
We recently introduced a formalism for the modeling of temporal networks, that we call stream graphs. It emphasizes the streaming nature of data and allows rigorous definitions of many important concepts generalizing classical graphs. This…
We propose a simple model to analyze the traffic of droplets in microfluidic ``dual networks''. Such functional networks which consist of two types of channels, namely those accessible or forbidden to droplets, often display a complex…
We compare several approaches to learn an Optimal Map, represented as a neural network, between probability distributions. The approaches fall into two categories: ``Heuristics'' and approaches with a more sound mathematical justification,…
In the area of urban transportation networks, a growing number of day-to-day (DTD) traffic dynamic theories have been proposed to describe the network flow evolution, and an increasing amount of laboratory experiments have been conducted to…
A novel constructive mathematical model based on the multifractal formalism in order to accurately characterizing the localized fluctuations present in the course of traffic flows today high-speed computer networks is presented. The…
We introduce a broad class of analytically solvable processes on networks. In the special case, they reduce to random walk and consensus process - two most basic processes on networks. Our class differs from previous models of interactions…