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Interactive programming environments are powerful tools for promoting innovative network thinking, teaching science of complexity, and exploring emergent phenomena. This paper reports on our recent development of the deterministic random…
The evolution of many dynamical systems that describe relationships or interactions between objects can be effectively modeled by temporal networks, which are typically represented as a sequence of static network snapshots. In this paper,…
We consider the two-dimensional simple random walk conditioned on never hitting the origin. This process is a Markov chain, namely it is the Doob $h$-transform of the simple random walk with respect to the potential kernel. It is known to…
We consider discrete, iterative load balancing via matchings on arbitrary graphs. Initially each node holds a certain number of tokens, defining the load of the node, and the objective is to redistribute the tokens such that eventually each…
We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…
Wireless network applications, such as, searching, routing, self stabilization and query processing can be modeled as random walks on graphs. Stateless Opportunistic routing technique is a robust distributed routing technique based on…
We define a general model of stochastically-evolving graphs, namely the \emph{Edge-Uniform Stochastically-Evolving Graphs}. In this model, each possible edge of an underlying general static graph evolves independently being either alive or…
Control and characterization of networks is a paramount step for the development of many quantum technologies. Even for moderate-sized networks, this amounts to explore an extremely vast parameters space in search for the couplings defining…
Quantum walks are a well-established model for the study of coherent transport phenomena and provide a universal platform in quantum information theory. Dynamically influencing the walker's evolution gives a high degree of flexibility for…
In the classical stochastic resetting problem, a particle, moving according to some stochastic dynamics, undergoes random interruptions that bring it to a selected domain, and then, the process recommences. Hitherto, the resetting mechanism…
This paper deals with the classical problem of exploring a ring by a cohort of synchronous robots. We focus on the perpetual version of this problem in which it is required that each node of the ring is visited by a robot infinitely often.…
In this paper we present a combinatorial optimisation view on the routing problem for connectionless packet networks by using the metaphor of a landscape. We examine the main properties of the routing landscapes as we define them and how…
A comparison technique for finite random walks on finite graphs is introduced, using the well-known interlacing method. It yields improved return probability bounds. A key feature is the incorporation of parts of the spectrum of the…
The spectral theory of random walks on networks of arbitrary topology can be readily extended to study random walks and L\'evy flights subject to resetting on these structures. When a discrete-time process is stochastically brought back…
Randomness plays a key role in the design of attacks on cryptographic systems and cyber security algorithms in general. Random walks and quantum walks are powerful tools for mastering random phenomena. In this article, I propose a…
We consider random walks in a balanced random environment in $\mathbb{Z}^d$, $d\geq 2$. We first prove an invariance principle (for $d\ge2$) and the transience of the random walks when $d\ge 3$ (recurrence when $d=2$) in an ergodic…
Performing random walks in networks is a fundamental primitive that has found numerous applications in communication networks such as token management, load balancing, network topology discovery and construction, search, and peer-to-peer…
Using both numerical simulations and scaling arguments, we study the behavior of a random walker on a one-dimensional small-world network. For the properties we study, we find that the random walk obeys a characteristic scaling form. These…
We study a random walk problem on the hierarchical network which is a scale-free network grown deterministically. The random walk problem is mapped onto a dynamical Ising spin chain system in one dimension with a nonlocal spin update rule,…
We consider a two dimensional reflecting random walk on the nonnegative integer quadrant. It is assumed that this reflecting random walk has skip free transitions. We are concerned with its time reversed process assuming that the stationary…