This chapter summarises techniques that are suitable for performance and resilience modelling and analysis of massive stochastic systems. We will introduce scalable techniques that can be applied to models constructed using DTMCs and CTMCs as well as compositional formalisms such as stochastic automata networks, stochastic process algebras and queueing networks. We will briefly show how techniq...

This paper deals with the problem of passivity analysis for stochastic neural networks with leakage, discrete and distributed delays. By using delay partitioning technique, free weighting matrix method and stochastic analysis technique, several sufficient conditions for the passivity of the addressed neural networks are established in terms of linear matrix inequalities (LMIs), in which both th...

We describe a new stochastic search algorithm for linear regression models called the bounded mode stochastic search (BMSS). We make use of BMSS to perform variable selection and classification as well as to construct sparse dependency networks. Furthermore, we show how to determine genetic networks from genome-wide data that involves any combination of continuous and discrete variables. We ill...

Stochastic processing networks arise as models in manufacturing, telecommunications, computer systems and the service industry. Common characteristics of these networks are that they have entities, such as jobs, customers or packets, that move along routes, wait in buffers, receive processing from various resources, and are subject to the effects of stochastic variability through such quantitie...

In this paper, the natural gradient descent method for the multilayer stochastic complex-valued neural networks is considered, and the natural gradient is given for a single stochastic complex-valued neuron as an example. Since the space of the learnable parameters of stochastic complex-valued neural networks is not the Euclidean space but a curved manifold, the complex-valued natural gradient ...

Clustering is an important task in network analysis, with applications in fields such as biology and the social sciences. We present a novel inference algorithm for the Stochastic Block Model (SBM), a well known network clustering model. Previous inference in this model typically utilizes Markov Chain Monte Carlo or Variational Bayes, but our method is the first to utilize Stochastic Variationa...

This paper deals with an impulsive stochastic fuzzy cellular neural networks with both time-varying and infinite distributed delays. Based on M-matrix theory and stochastic analysis technique, a sufficient condition is obtained to ensure the existence, uniqueness, and global exponential p−stability of the equilibrium point for the addressed impulsive stochastic fuzzy cellular neural network wit...

In this paper, the problem of stochastic synchronization analysis is investigated for complex networks perturbed by the Poisson noise. By using the key tool such as the infinites-imal operator for stochastic differential equations driven by the Poisson process, this paper proposes a globally exponentially synchronization criterion in mean square for complex networks perturbed by the Poisson noi...

The synchronization of nonlinear systems connected over large-scale networks has gained popularity in a variety of applications, such as power grids, sensor networks, and biology. Stochastic uncertainty in the interconnections is a ubiquitous phenomenon observed in these physical and biological networks. We provide a size-independent network sufficient condition for the synchronization of scala...