We propose a new localization result for the leading eigenvalue and eigenvector of a symmetric matrix A. The result exploits the Frobenius inner product between A and a given rank-one landmark matrix X. Different choices for X may be used, depending upon the problem under investigation. In particular, we show that the choice where X is the all-ones matrix allows to estimate the signature of the...

Many communication networks such as wireless networks only provide stochastic service guarantees. For analyzing stochastic service guarantees, research effort has been made in the past few years to develop stochastic network calculus, a probabilistic version of (min, +) deterministic network calculus. However, many challenges have made the development difficult. Some of them are closely related...

In this paper we present a systematic approach to constructing neural network classi ers based on stochastic model theory. A two step process is described where the rst problem is to model the stochastic relationship between sample patterns and their classes using a stochastic neural network. Then we convert the stochastic network to a deterministic one, which calculates the a-posteriori probab...

This paper is concerned with the synchronization problem for a new class of continuous-time delayed complex networks with stochastic nonlinearities (randomly occurred nonlinearities), interval time-varying delays, unbounded distributed delays as well as multiple stochastic disturbances. The stochastic nonlinearities and multiple stochastic disturbances are investigated here in order to reflect ...

The solution of a multistage stochastic programming problem needs a suitable representation of uncertainty which may be obtained through a satisfactory scenario tree construction. Unfortunately there is a trade-off between the level of accuracy in the description of the stochastic component and the computational tractability of the resulting scenario-based problem. In this contribution we addre...

Quantitative stability of linear multistage stochastic programs is studied. It is shown that the infima of such programs behave (locally) Lipschitz continuous with respect to the sum of an Lr-distance and of a distance measure for the filtrations of the original and approximate stochastic (input) processes. Various issues of the result are discussed and an illustrative example is given. Consequ...

The time-ordered product framework of quantum field theory can also be used to understand salient phenomena in stochastic biochemical networks. It is used here to derive Gillespie's stochastic simulation algorithm (SSA) for chemical reaction networks; consequently, the SSA can be interpreted in terms of Feynman diagrams. It is also used here to derive other, more general simulation and paramete...

Many exist studies always use Markov decision processes (MDPs) in modeling optimal route choice in stochastic, time-varying networks. However, taking many variable traffic data and transforming them into optimal route decision is a computational challenge by employing MDPs in real transportation networks. In this paper we model finite horizon MDPs using directed hypergraphs. It is shown that th...

The growing complexity of modern systems has escalated the need for performance metrics. Stochastic models such as queuing networks and stochastic Petri nets have been used to model these systems so that their performance measures can be evaluated analytically. Product-form solutions are equilibrium state probabilities in networks of stochastic nodes (e.g. queues) in the form of a product of te...