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The brain's connectome and the vascular system are examples of physical networks whose tangible nature influences their structure, layout, and ultimately their function. The material resources required to build and maintain these networks…
When greedy search algorithms encounter a local minima or plateau, the search typically devolves into a breadth-first search (BrFS), or a local search technique is used in an attempt to find a way out. In this work, we formally analyze the…
Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not…
This study deals with polymer looping, an important process in many chemical and biological systems. We investigate basic questions on the looping dynamics of a polymer under tension using the freely-jointed chain (FJC) model. Previous…
The explicit determinations of the mean first-passage time (MFPT) for trapping problem are limited to some simple structure, e.g., regular lattices and regular geometrical fractals, and determining MFPT for random walks on other media,…
Network flow is a powerful mathematical framework to systematically explore the relationship between structure and function in biological, social, and technological networks. We introduce a new pipelining model of flow through networks…
We present exact analytical results for the distribution of shortest path lengths (DSPL) in a directed network model that grows by node duplication. Such models are useful in the study of the structure and growth dynamics of gene regulatory…
Modeling the locations of nodes as a uniform binomial point process (BPP), we present a generic mathematical framework to characterize the performance of an arbitrarily-located reference receiver in a finite wireless network. Different from…
Samples of dynamic or time-varying networks and other random object data such as time-varying probability distributions are increasingly encountered in modern data analysis. Common methods for time-varying data such as functional data…
Burst contention is a well-known challenging problem in Optical Burst Switching (OBS) networks. Contention resolution approaches are always reactive and attempt to minimize the BLR based on local information available at the core node. On…
A long series of recent results and breakthroughs have led to faster and better distributed approximation algorithms for single source shortest paths (SSSP) and related problems in the CONGEST model. The runtime of all these algorithms,…
Analytical results for the distribution of first hitting times of random walks on Erd\H{o}s-R\'enyi networks are presented. Starting from a random initial node, a random walker hops between adjacent nodes until it hits a node which it has…
In the present work, four series of simulations are analyzed: entangled model networks of a) mono-disperse or b) poly-disperse weight distribution between the crosslinks, c) non-entangled phantom model networks and d) non-entangled model…
We study the problem of maintaining a breadth-first spanning tree (BFS tree) in partially dynamic distributed networks modeling a sequence of either failures or additions of communication links (but not both). We present deterministic…
This work considers the problem of computing distances between structured objects such as undirected graphs, seen as probability distributions in a specific metric space. We consider a new transportation distance (i.e. that minimizes a…
In biochemical reaction networks, the first passage time (FPT) of a reaction quantifies the time it takes for the reaction to first occur, from the initial state. While the mean FPT historically served as a summary metric, a far more…
In this paper we present a computer simulation study of ionic conductivity in solid polymeric electrolytes. The multiphase nature of the material is taken into account. The polymer is represented by a regular lattice whose sites represent…
The problem of mapping human close-range proximity networks has been tackled using a variety of technical approaches. Wearable electronic devices, in particular, have proven to be particularly successful in a variety of settings relevant…
Random walks are gaining much attention from the networks research community. They are the basis of many proposals aimed to solve a variety of network-related problems such as resource location, network construction, nodes sampling, etc.…
Soft Random Geometric Graphs (SRGGs) have been widely applied to various models including those of wireless sensor, communication, social and neural networks. SRGGs are constructed by randomly placing nodes in some space and making pairwise…