Related papers: Jackson network in a random environment: strong ap…
Social networks are organized into communities with dense internal connections, giving rise to high values of the clustering coefficient. In addition, these networks have been observed to be assortative, i.e. highly connected vertices tend…
In this work, we focus on the stationary analysis of a specific class of continuous time Markov-modulated reflected random walks in the quarter plane with applications in the modelling of two-node Markov-modulated queueing networks with…
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…
Networks of model neurons with balanced recurrent excitation and inhibition produce irregular and asynchronous spiking activity. We extend the analysis of balanced networks to include the known dependence of connection probability on the…
Two networks of queues models, presented initially by Jackson, in the open case, and Gordon and Newell, in the closed case, stochastic processes are presented and studied in some of their details and problems. The service times are…
The Transformer architecture is widely applied in sequence modeling applications, yet the theoretical understanding of its working principles remains limited. In this work, we investigate the approximation rate for single-layer Transformers…
In stochastic models for queues and their networks, random events evolve in time. A process for their backward evolution is referred to as a time reversed process. It is often greatly helpful to view a stochastic model from two different…
We consider a load balancing model where a Poisson stream of jobs arrive at a system of many servers whose service time distribution possesses a finite second moment. A small fraction of arrivals pass through the so called power-of-choice…
A machine-learning approach called "reservoir computing" has been used successfully for short-term prediction and attractor reconstruction of chaotic dynamical systems from time series data. We present a theoretical framework that describes…
We study the properties of discrete-time random walks on networks formed by randomly interconnected cliques, namely, random networks of cliques. Our purpose is to derive the parameters that define the network structure -- specifically, the…
Correlations and other collective phenomena in a schematic model of heterogeneous binary agents (individual spin-glass samples) are considered on the complete graph and also on 2d and 3d regular lattices. The system's stochastic dynamics is…
In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected…
Let $X_n(k)$ be the number of vertices at level $k$ in a random recursive tree with $n+1$ vertices. We prove a functional limit theorem for the vector-valued process $(X_{[n^t]}(1),\ldots, X_{[n^t]}(k))_{t\geq 0}$, for each $k\in\mathbb N$.…
When dense granular systems are exposed to external forcing, they evolve on the time scale that is typically related to the externally imposed one (shear or compression rate, for example). This evolution could be characterized by observing…
The mathematical analysis of random phylogenetic networks via analytic and algorithmic methods has received increasing attention in the past years. In the present work we introduce branching process methods to their study. This approach…
We consider transient nearest neighbor random walks on the positive part of the real line. We give criteria for the finiteness of the number of cutpoints and strong cutpoints. Examples and open problems are presented.
Queuing systems with an unlimited number of devices with an incoming nonstationary Poisson flow and a random flow controlled by a Markov chain are investigated. The inexpediency of ap-proximation of the birth process by Poisson flows in…
Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper we…
The extraordinary computational power of the brain may be related in part to the fact that each of the smaller neural networks that compose it can behave transiently in many different ways, depending on its inputs. Mathematically, input…
The goal of this paper is to identify exponential convergence rates and to find computable bounds for them for Markov processes representing unreliable Jackson networks. First we use the bounds of Lawler and Sokal in order to show that, for…