Stochastic neural network models for gene regulatory networks

Recent advances in gene-expression profiling technologies provide large amounts of gene expression data. This raises the possibility for a functional understanding of genome dynamics by means of mathematical modelling. As gene expression involves intrinsic noise, stochastic models are essential for better descriptions of gene regulatory networks. However, stochastic modelling for large scale gene expression data sets is still in the very early developmental stage. In this paper we present some stochastic models by introducing stochastic processes into neural network models that can describe intermediate regulation for large scale gene networks. Poisson random variables are used to represent chance events in the processes of synthesis and degradation. For expression data with normalized concentrations, exponential or normal random variables are used to realize fluctuations. Using a network with three genes, we show how to use stochastic simulations for studying robustness and stability properties of gene expression patterns under the influence of noise, and how to use stochastic models to predict statistical distributions of expression levels in population of cells. The discussion suggest that stochastic neural network models can give better description of gene regulatory networks and provide criteria for measuring the reasonableness o mathematical models

Stability assessment for multi-infeed grid-connected VSCs modeled in the admittance matrix form

© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksThe increasing use of power electronics converters to integrate renewable energy sources has been a subject of concern due to the resonance oscillatory phenomena caused by their interaction with poorly damped AC networks. Early studies are focused on assessing the controller influence of a single converter connected to simple networks, and they are no longer representative for existing systems. Lately, studies of multi-infeed grid-connected converters are of particular interest, and their main aim is to apply traditional criteria and identify their difficulties in the stability assessment. An extension of traditional criteria is commonly proposed as a result of these analysis, but they can be burdensome for large and complex power systems. The present work addresses this issue by proposing a simple criterion to assess the stability of large power systems with high-penetration of power converters. The criterion has its origin in the mode analysis and positive-net damping stability criteria, and it addresses the stability in the frequency domain by studying the eigenvalues magnitude and real component of dynamic models in the admittance matrix form. Its effectiveness is tested in two case studies developed in Matlab/Simulink which compare it with traditional criteria, proving its simplicity.Peer ReviewedPostprint (author's final draft

Application of a Stable Latency Insertion Method for Simulations of Power Distribution Networks

This paper presents an application of a stable implementation of the latency insertion method for simulations of power distribution networks (PDN). Traditionally, simulations of PDNs poses a considerable challenge due to their large circuit sizes. While the latency insertion method can be applied to simulate these networks, the existence of low latency elements results in a more stringent stability criterion which reduces the efficiency of the method. Using the improved formulation, a latency insertion method that is free from the stability criteria is obtained, which results in no limitation on the size of the time step

Mathematical problems for complex networks

Copyright @ 2012 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article is made available through the Brunel Open Access Publishing Fund.Complex networks do exist in our lives. The brain is a neural network. The global economy is a network of national economies. Computer viruses routinely spread through the Internet. Food-webs, ecosystems, and metabolic pathways can be represented by networks. Energy is distributed through transportation networks in living organisms, man-made infrastructures, and other physical systems. Dynamic behaviors of complex networks, such as stability, periodic oscillation, bifurcation, or even chaos, are ubiquitous in the real world and often reconfigurable. Networks have been studied in the context of dynamical systems in a range of disciplines. However, until recently there has been relatively little work that treats dynamics as a function of network structure, where the states of both the nodes and the edges can change, and the topology of the network itself often evolves in time. Some major problems have not been fully investigated, such as the behavior of stability, synchronization and chaos control for complex networks, as well as their applications in, for example, communication and bioinformatics

Stability of Piecewise Deterministic Markovian Metapopulation Processes on Networks

The purpose of this paper is to study a Markovian metapopulation model on a directed graph with edge-supported transfers and deterministic intra-nodal population dynamics. We first state tractable stability conditions for two typical frameworks motivated by applications: constant jump rates with multiplicative transfer amplitudes, and coercive jump rates with unitary transfers. More general criteria for boundedness, petiteness and ergodicity are then given