Related papers: Markov Chain Methods For Analyzing Complex Transpo…
Spreading processes are ubiquitous in natural and artificial systems. They can be studied via a plethora of models, depending on the specific details of the phenomena under study. Disease contagion and rumor spreading are among the most…
We develop a probabilistic framework for global modeling of the traffic over a computer network. This model integrates existing single-link (-flow) traffic models with the routing over the network to capture the global traffic behavior. It…
A prominent model for transportation networks is branched transport, which seeks the optimal transportation scheme to move material from a given initial to a final distribution. The cost of the scheme encodes a higher transport efficiency…
Given a discrete source distribution $\mu$ and discrete target distribution $\nu$ on a common finite state space $\mathcal{X}$, we are tasked with transporting $\mu$ to $\nu$ using a given discrete-time Markov chain $X$ with the quickest…
We introduce a new framework for efficient sampling from complex probability distributions, using a combination of optimal transport maps and the Metropolis-Hastings rule. The core idea is to use continuous transportation to transform…
Epidemic dynamics in a stochastic network of interacting epidemic centers is considered. The epidemic and migration processes are modelled by Markov's chains. Explicit formulas for probability distribution of the migration process are…
Markovian evolving graphs are dynamic-graph models where the links among a fixed set of nodes change during time according to an arbitrary Markovian rule. They are extremely general and they can well describe important dynamic-network…
Random walks are fundamental tools for analyzing complex networked systems, including social networks, biological systems, and communication infrastructures. While classical random walks focus on pairwise interactions, many real-world…
Randomising networks using a naive `accept-all' edge-swap algorithm is generally biased. Building on recent results for nondirected graphs, we construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities for…
Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…
We consider random walks on dynamical networks where edges appear and disappear during finite time intervals. The process is grounded on three independent stochastic processes determining the walker's waiting-time, the up-time and down-time…
We study irreducible time-homogenous Markov chains with finite state space in discrete time. We obtain results on the sensitivity of the stationary distribution and other statistical quantities with respect to perturbations of the…
Network complexity has been studied for over half a century and has found a wide range of applications. Many methods have been developed to characterize and estimate the complexity of networks. However, there has been little research with…
V2V technologies bridge two infrastructures: the communications infrastructure and the transportation infrastructure. These infrastructures are interconnected and interdependent. On the one hand, the communications network enables V2V…
We consider Markov jump processes on a graph described by a rate matrix that depends on various control parameters. We derive explicit expressions for the static responses of edge currents and steady-state probabilities. We show that they…
We consider steady states of dynamics that have an underlying network structure. We study how a steady state responds to small perturbations in the network parameters and how this sensitivity is connected to the network structure. We…
We show how to map the states of an ergodic Markov chain to Euclidean space so that the squared distance between states is the expected commuting time. We find a minimax characterization of commuting times, and from this we get monotonicity…
We live in a world increasingly dominated by networks -- communications, social, information, biological etc. A central attribute of many of these networks is that they are dynamic, that is, they exhibit structural changes over time. While…
The shortest-path, commute time, and diffusion distances on undirected graphs have been widely employed in applications such as dimensionality reduction, link prediction, and trip planning. Increasingly, there is interest in using…
Many seemingly disparate Markov chains are unified when viewed as random walks on the set of chambers of a hyperplane arrangement. These include the Tsetlin library of theoretical computer science and various shuffling schemes. If only…