相关论文: Stabilization of stochastic networks in Markovian …

Scattering transforms are non-trainable deep convolutional architectures that exploit the multi-scale resolution of a wavelet filter bank to obtain an appropriate representation of data. More importantly, they are proven invariant to…

Boolean networks have been proposed as potentially useful models for genetic control. An important aspect of these networks is the stability of their dynamics in response to small perturbations. Previous approaches to stability have assumed…

In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that…

The stable functionality of networked systems is a hallmark of their natural ability to coordinate between their multiple interacting components. Yet, strikingly, real-world networks seem random and highly irregular, apparently lacking any…

The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding a…

We address a class of Markov jump linear systems that are characterized by the underlying Markov process being time-inhomogeneous with a priori unknown transition probabilities. Necessary and sufficient conditions for uniform stochastic…

From the perspective of probability, the stability of growing network is studied in the present paper. Using the DMS model as an example, we establish a relation between the growing network and Markov process. Based on the concept and…

We study the joint occurrence of large values of a Markov random field or undirected graphical model associated to a block graph. On such graphs, containing trees as special cases, we aim to generalize recent results for extremes of Markov…

Many systems across the sciences evolve through a combination of multiplicative growth and diffusive transport. In the presence of disorder, these systems tend to form localized structures which alternate between long periods of relative…

We consider a hidden Markov model with multiplicative noise emerging from studies of software reliability. We show the stability of the optimal filter with respect to general initial conditions in the total variation- and $L^p$-norm and…

Stabilization of graphs has received substantial attention in recent years due to its connection to game theory. Stable graphs are exactly the graphs inducing a matching game with non-empty core. They are also the graphs that induce a…

We analyse the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modelling the stability of fixed points in large systems defined…

The larger the distance to instability from a matrix is, the more robustly stable the associated autonomous dynamical system is in the presence of uncertainties and typically the less severe transient behavior its solution exhibits.…

We study the problem of estimating a temporally varying coefficient and varying structure (VCVS) graphical model underlying nonstationary time series data, such as social states of interacting individuals or microarray expression profiles…

Analysis of algorithms on time-varying networks (often called evolving graphs) is a modern challenge in theoretical computer science. The edge-Markovian is a relatively simple and comprehensive model of evolving graphs: every pair of…

Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…

We consider Markov jump processes on a graph described by a rate matrix that depends on various control parameters. We derive explicit expressions for the static responses of edge currents and steady-state probabilities. We show that they…

The methodology named LIFE (Linear-in-Flux-Expressions) was developed with the purpose of simulating and analyzing large metabolic systems. With LIFE, the number of model parameters is reduced by accounting for correlations among the…

We propose a general framework for modelling network data that is designed to describe aspects of non-exchangeable networks. Conditional on latent (unobserved) variables, the edges of the network are generated by their finite growth history…

We derive a simple sufficient condition for the local asymptotic stability of spatially discrete, continuous-time reaction-diffusion systems of networked dynamical systems at a homogeneous equilibrium point. The framework explicitly…