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We present results relating mixing times to the intersection time of branching random walk (BRW) in which the logarithm of the expected number of particles grows at rate of the spectral-gap $\mathrm{gap}$ . This is a finite state space…
An intense research on financial market microstructure is presently in progress. Continuous time random walks (CTRWs) are general models capable to capture the small-scale properties that high frequency data series show. The use of CTRW…
Long flows contribute huge volumes of traffic over inter-datacenter WAN. The Flow Completion Time (FCT) is a vital network performance metric that affects the running time of distributed applications and the users' quality of experience.…
The co-evolution between network structure and functional performance is a fundamental and challenging problem whose complexity emerges from the intrinsic interdependent nature of structure and function. Within this context, we investigate…
Breadth First Search (BFS) and other graph traversal techniques are widely used for measuring large unknown graphs, such as online social networks. It has been empirically observed that an incomplete BFS is biased toward high degree nodes.…
The kinetics of a variety of transport-controlled processes can be reduced to the problem of determining the mean time needed to arrive at a given location for the first time, the so called mean first passage time (MFPT) problem. The…
Single linear polymer chains in dilute solutions under good solvent conditions are studied by Monte Carlo simulations with the pruned-enriched Rosenbluth method up to the chain length $N \sim {\cal O}(10^4)$. Based on the standard simple…
Optimizing paths on networks is crucial for many applications, from subway traffic to Internet communication. As global path optimization that takes account of all path-choices simultaneously is computationally hard, most existing routing…
We review various features of the statistics of random paths on graphs. The relationship between path statistics and Quantum Mechanics (QM) leads to two canonical ways of defining random walk on a graph, which have different statistics and…
The polymer model framework is a classical tool from statistical mechanics that has recently been used to obtain approximation algorithms for spin systems on classes of bounded-degree graphs; examples include the ferromagnetic Potts model…
Distribution of loops in a one-dimensional random walk (RW), or, equivalently, neutral segments in a sequence of positive and negative charges is important for understanding the low energy states of randomly charged polymers. We investigate…
We present analytical results for the distribution of cover times of random walks (RWs) on random regular graphs consisting of $N$ nodes of degree $c$ ($c \ge 3$). Starting from a random initial node at time $t=1$, at each time step $t \ge…
We analyze generalized space-time fractional motions on undirected networks and lattices. The continuous-time random walk (CTRW) approach of Montroll and Weiss is employed to subordinate a space fractional walk to a generalization of the…
We consider a continuous-time branching random walk on a multidimensional lattice in a random branching medium. It is theoretically known that, in such branching random walks, large rare fluctuations of the medium may lead to anomalous…
Belief propagation (BP) is a message-passing heuristic for statistical inference in graphical models such as Bayesian networks and Markov random fields. BP is used to compute marginal distributions or maximum likelihood assignments and has…
We propose the first return time distribution (FRTD) of a random walk as an interpretable and mathematically grounded node embedding. The FRTD assigns a probability mass function to each node, allowing us to define a distance between any…
Intrachain contact formation rates, fundamental to the dynamics of biopolymer self-organization such as protein folding, can be monitored in the laboratory through fluorescence quenching measurements. The common approximations for the…
Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen…
How to enable efficient analytics over such data has been an increasingly important research problem. Given the sheer size of such social networks, many existing studies resort to sampling techniques that draw random nodes from an online…
Due to dynamic network conditions, routing is the most critical part in WMNs and needs to be optimised. The routing strategies developed for WMNs must be efficient to make it an operationally self configurable network. Thus we need to…