Related papers: Markov Chain Methods For Analyzing Complex Transpo…

We consider the problem of estimating the expected time to find a maximum degree node on a graph using a (parameterized) biased random walk. For assortative graphs the positive degree correlation serves as a local gradient for which a bias…

Built upon the shoulders of graph theory, the field of complex networks has become a central tool for studying real systems across various fields of research. Represented as graphs, different systems can be studied using the same analysis…

We propose a family of lagged random walk sampling methods in simple undirected graphs, where transition to the next state (i.e. node) depends on both the current and previous states -- hence, lagged. The existing random walk sampling…

We develop a general theory of Markov chains realizable as random walks on $\mathscr R$-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via…

Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into…

In this paper, urban traffic is modeled using dual graph representation of urban transportation network where roads are mapped to nodes and intersections are mapped to links. The proposed model considers both the navigation of vehicles on…

To better understand the flows of ideas or information through social and biological systems, researchers develop maps that reveal important patterns in network flows. In practice, network flow models have implied memoryless first-order…

Major cities worldwide experience problems with the performance of their road transportation networks, and the continuous increase in traffic demand presents a substantial challenge to the optimal operation of urban road networks and the…

Robust estimates for the performance of complicated queueing networks can be obtained by showing that the number of jobs in the network is stochastically comparable to a simpler, analytically tractable reference network. Classical coupling…

We study ergodic properties of a family of traffic maps acting in the space of bi-infinite sequences of real numbers. The corresponding dynamics mimics the motion of vehicles in a simple traffic flow, which explains the name. Using…

Locally Markov walks are natural generalizations of classical Markov chains, where instead of a particle moving independently of the past, it decides where to move next depending on the last action performed at the current location. We…

Temporal networks model how the interaction between elements in a complex system evolve over time. Just like complex systems display collective dynamics, here we interpret temporal networks as trajectories performing a collective motion in…

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…

Recently, De Martino et al have presented a general framework for the study of transportation phenomena on complex networks. One of their most significant achievements was a deeper understanding of the phase transition from the uncongested…

We study the linearization of a discrete transportation distance between probability distributions on finite weighted graphs originally due to Maas (``Gradient flows of the entropy for finite {M}arkov chains,'' J. Funct. Anal. 261(8), 2011)…

We present here a general framework and a specific algorithm for predicting the destination, route, or more generally a pattern, of an ongoing journey, building on the recent work of [Y. Lassoued, J. Monteil, Y. Gu, G. Russo, R. Shorten,…

We consider an elementary model for self-organised criticality, the activated random walk on the complete graph. We introduce a discrete time Markov chain as follows. At each time step, we add an active particle at a random vertex and let…

We study the biased random walk process in random uncorrelated networks with arbitrary degree distributions. In our model, the bias is defined by the preferential transition probability, which, in recent years, has been commonly used to…

We study the problem of learning the Markov order in categorical sequences that represent paths in a network, i.e. sequences of variable lengths where transitions between states are constrained to a known graph. Such data pose challenges…

We address the problem of inferring the topology of a wireless network using limited observational data. Specifically, we assume that we can detect when a node is transmitting, but no further information regarding the transmission is…