Simple lower and upper bounds on mean cycle time in stochastic acyclic fork-join queueing networks are derived using a (max,+)algebra based representation of network dynamics. The behaviour of the bounds under various assumptions concerning the service times in the networks is discussed, and related numerical examples are presented. Key-Words: (max,+)-algebra, dynamic state equation, acyclic fo...

Gene expression and gene regulatory networks dynamics are stochastic. The noise in the temporal amounts of proteins and RNA molecules in cells arises from the stochasticity of transcription initiation and elongation (e.g., due to RNA polymerase pausing), translation, and post-transcriptional regulation mechanisms, such as reversible phosphorylation and splicing. This is further enhanced by the ...

the main objective of this paper is to introduce a new intelligent optimization technique that uses a predictioncorrectionstrategy supported by a recurrent neural network for finding a near optimal solution of a givenobjective function. recently there have been attempts for using artificial neural networks (anns) in optimizationproblems and some types of anns such as hopfield network and boltzm...

The product form results recently published for Stochastic Petri Nets are combined with the well known product form results for Queueing Networks in the model formalism of Queueing Petri Nets yielding the class of product form Queueing Petri Nets. This model class includes Stochastic Petri Nets with product form solution and BCMP Queueing Networks as special cases. We introduce an arrival theor...

Stochastic processing networks arise as models in manufacturing, telecommunications, transportation, computer systems, the customer service industry and biochemical reaction networks. Common characteristics of these networks are that they have entities, such as jobs, packets, vehicles, customers or molecules, that move along routes, wait in buffers, receive processing from various resources, an...

In this report, we present a formal approach that addresses the problem of emergence of phase transitions in stochastic and attractive nonlinear threshold Boolean automata networks. Nonlinear networks considered are informally defined on the basis of classical stochastic threshold Boolean automata networks in which specific interaction potentials of neighbourhood coalition are taken into accoun...

In this paper, we outline the theory of epidemic percolation networks and their use in the analysis of stochastic susceptible-infectious-removed (SIR) epidemic models on undirected contact networks. We then show how the same theory can be used to analyze stochastic SIR models with random and proportionate mixing. The epidemic percolation networks for these models are purely directed because und...

Leveraging advances in variational inference, we propose to enhance recurrent neural networks with latent variables, resulting in Stochastic Recurrent Networks (STORNs). The model i) can be trained with stochastic gradient methods, ii) allows structured and multi-modal conditionals at each time step, iii) features a reliable estimator of the marginal likelihood and iv) is a generalisation of de...

We prove some new pathwise comparison results for single class stochastic fluid networks. Under fairly general conditions, monotonicity with respect to the (stateand time-dependent) routing matrices is shown. Under more restrictive assumptions, monotonicity with respect to the service rates is shown as well. We conclude by using the comparison results to establish a moment bound, a stability re...