Related papers: Flow coupling and stochastic ordering of throughpu…

Stochastic orders on point processes are partial orders which capture notions like being larger or more variable. Laplace functional ordering of point processes is a useful stochastic order for comparing spatial deployments of wireless…

We consider a Markov chain of point processes such that each state is a super position of an independent cluster process with the previous state as its centre process together with some independent noise process. The model extends earlier…

The problem of reliability of a large distributed system is analyzed via a new mathematical model. A typical framework is a system where a set of files are duplicated on several data servers. When one of these servers breaks down, all…

Interacting networks are different in nature to single networks. The study of queuing processes on interacting networks is underdeveloped. It presents new mathematical challenges and is of importance to applications. This area of operations…

In networking applications, one often wishes to obtain estimates about the number of objects at different parts of the network (e.g., the number of cars at an intersection of a road network or the number of packets expected to reach a node…

A model for traffic flow in street networks or material flows in supply networks is presented, that takes into account the conservation of cars or materials and other significant features of traffic flows such as jam formation, spillovers,…

In this paper, we equip the conventional discrete-time queueing network with a Markovian input process, that, in addition to the usual short-term stochastics, governs the mid- to long-term behavior of the links between the network nodes.…

Developing of an effective flow control algorithm to avoid congestion is a hot topic in computer network society. This document gives a mathematical model for general network at the beginning, and then discrete control theory is proposed as…

To understand the collective spiking activity in neuronal populations, it is essential to reveal basic circuit variables responsible for these emergent functional states. Here, I develop a mean field theory for the population coupling…

In this paper, a link between monotonicity of deterministic dynamical systems and propagation of order by Markov processes is established. The order propagation has received considerable attention in the literature, however, this notion is…

We propose a framework for surrogate modelling of spiking systems. These systems are often described by stiff differential equations with high-amplitude oscillations and multi-timescale dynamics, making surrogate models an attractive tool…

Machine learning methods have shown promise in learning chaotic dynamical systems, enabling model-free short-term prediction and attractor reconstruction. However, when applied to large-scale, spatiotemporally chaotic systems, purely…

We consider in-network computation of an arbitrary function over an arbitrary communication network. A network with capacity constraints on the links is given. Some nodes in the network generate data, e.g., like sensor nodes in a sensor…

We consider the problem of online allocation (matching and assortments) of reusable resources where customers arrive sequentially in an adversarial fashion and allocated resources are used or rented for a stochastic duration that is drawn…

Empirical studies of graphs have contributed enormously to our understanding of complex systems. Known today as network science, what was originally a theoretical study of graphs has grown into a more scientific exploration of communities…

The problem of appropriately matching items subject to compatibility constraints arises in a number of important applications. While most of the literature on matching theory focuses on a static setting with a fixed number of items, several…

This paper studies a scheduling control problem for a single-server multiclass queueing network in heavy traffic, operating in a changing environment. The changing environment is modeled as a finite state Markov process that modulates the…

Flow matching has recently emerged as a powerful paradigm for generative modeling and has been extended to probabilistic time series forecasting in latent spaces. However, the impact of the specific choice of probability path model on…

We study the mean-field limit and stationary distributions of a pulse-coupled network modeling the dynamics of a large neuronal assemblies. Our model takes into account explicitly the intrinsic randomness of firing times, contrasting with…

Recent advances in variational inference enable the modelling of highly structured joint distributions, but are limited in their capacity to scale to the high-dimensional setting of stochastic neural networks. This limitation motivates a…