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In this article, we study branching random walks on graphs modeling division-mutation processes inspired by adaptive immunity. We apply the theory of expander graphs on mutation rules in evolutionary processes and obtain estimates for the…
The non-Markovianity of open quantum system dynamics is often associated with the bidirectional interchange of information between the system and its environment, and it is thought to be a resource for various quantum information tasks. We…
Statically indeterminate systems are experimentally demonstrated to be in fact dynamical at the microscopic scale. Take the classic ladder-wall problem, for instance. Depending on the Young's modulus of the wall, it may take up to twenty…
We consider a discrete-time Markovian random walk with resets on a connected undirected network. The resets, in which the walker is relocated to randomly chosen nodes, are governed by an independent discrete-time renewal process. Some nodes…
Continuous Time Random Walks (CTRW) are widely used to coarse-grain the evolution of systems jumping from a metastable sub-set of their configuration space, or trap, to another via rare intermittent events. The multi-scaled behavior typical…
Recent success in developing increasingly general purpose agents based on sequence models has led to increased focus on the problem of deploying computationally limited agents within the vastly more complex real-world. A key challenge…
We investigate the conditions under which the trace distance between two different states of a given open system increases in time due to the interaction with an environment, therefore signalling non-Markovianity. We find that the…
If the dynamics of an open quantum systems is non-Markovian, its {asymptotic} state strongly depends on the initial conditions, even if the dynamics possesses an {invariant} state. This is the very essence of memory effects. In particular,…
Rehabilitation is essential and critical for post-stroke patients, addressing both physical and cognitive aspects. Stroke predominantly affects older adults, with 75% of cases occurring in individuals aged 65 and older, underscoring the…
We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time…
We consider the statistics of occupation times, the number of visits at the origin and the survival probability for a wide class of stochastic processes, which can be classified as renewal processes. We show that the distribution of these…
Temporal hypergraphs capture time-resolved group interactions among nodes. Empirical data support that time-stamped group interactions show bursty event sequences and non-trivial temporal correlations. In the present study, we introduce…
Stochastic processes under resetting at random times have attracted a lot of attention in recent years and served as illustrations of nontrivial and interesting static and dynamic features of stochastic dynamics. In this paper, we aim to…
Excited random walks (ERWs) are a self-interacting non-Markovian random walk in which the future behavior of the walk is influenced by the number of times the walk has previously visited its current site. We study the speed of the walk,…
The amount of information generated by a discrete time stochastic processes in a single step can be quantified by the entropy rate. We investigate the differences between two discrete time walk models, the discrete time quantum walk and the…
The distribution of a population throughout the physiological age of the individuals is very relevant information in population studies. It has been modeled by the Langevin and the Fokker- Planck equations. A major problem with these…
A new timeliness metric, called Age-of-Information (AoI), has recently attracted a lot of research interests for real-time applications with information updates. It has been extensively studied for various queueing models based on the…
We study the dynamics of discrete-time quantum walk using quantum coin operations, $\hat{C}(\theta_1)$ and $\hat{C}(\theta_2)$ in time-dependent periodic sequence. For the two-period quantum walk with the parameters $\theta_1$ and…
This paper introduces a novel methodology that utilizes latency to unveil time-series dependence patterns. A customized statistical test detects memory dependence in event sequences by analyzing their inter-event time distributions.…
A continuous-time multi-state history is semi-Markovian, if an intensity to migrate from one state into another, depends on the duration in the first state. Such duration can be formalised as covariate, entering the intensity process of the…