Robust filtering for stochastic genetic regulatory networks with time-varying delay

A Noise-Tolerating Gene Association Network Uncovering an Oncogenic Regulatory Motif in Lymphoma Transcriptomics

In cancer genomics research, gene expressions provide clues to gene regulations implicating patients' risk of survival. Gene expressions, however, fluctuate due to noises arising internally and externally, making their use to infer gene associations, hence regulation mechanisms, problematic. Here, we develop a new regression approach to model gene association networks while considering uncertain biological noises. In a series of simulation experiments accounting for varying levels of biological noises, the new method was shown to be robust and perform better than conventional regression methods, as judged by a number of statistical measures on unbiasedness, consistency and accuracy. Application to infer gene associations in germinal-center B cells led to the discovery of a three-by-two regulatory motif gene expression and a three-gene prognostic signature for diffuse large B-cell lymphoma.

State Estimation for Delayed Genetic Regulatory Networks With Reaction-Diffusion Terms

This paper addresses the problem of state estimation for delayed genetic regulatory networks (DGRNs) with reaction-diffusion terms using Dirichlet boundary conditions. The nonlinear regulation function of DGRNs is assumed to exhibit the Hill form. The aim of this paper is to design a state observer to estimate the concentrations of mRNAs and proteins via available measurement techniques. By introducing novel integral terms into the Lyapunov-Krasovskii functional and by employing the Wirtinger-type integral inequality, the convex approach, Green's identity, the reciprocally convex approach, and Wirtinger's inequality, an asymptotic stability criterion of the error system was established in terms of linear matrix inequalities (LMIs). The stability criterion depends upon the bounds of delays and their derivatives. It should be noted that if the set of LMIs is feasible, then the desired observation of DGRNs is possible, and the state estimation can be determined. Finally, two numerical examples are presented to illustrate the availability and applicability of the proposed scheme design.

Exponential H∞ filtering for discrete-time switched neural networks with random delays

This paper addresses the exponential H∞ filtering problem for a class of discrete-time switched neural networks with random time-varying delays. The involved delays are assumed to be randomly time-varying which are characterized by introducing a Bernoulli stochastic variable. Effects of both variation range and distribution probability of the time delays are considered. The nonlinear activation functions are assumed to satisfy the sector conditions. Our aim is to estimate the state by designing a full order filter such that the filter error system is globally exponentially stable with an expected decay rate and a H∞ performance attenuation level. The filter is designed by using a piecewise Lyapunov-Krasovskii functional together with linear matrix inequality (LMI) approach and average dwell time method. First, a set of sufficient LMI conditions are established to guarantee the exponential mean-square stability of the augmented system and then the parameters of full-order filter are expressed in terms of solutions to a set of LMI conditions. The proposed LMI conditions can be easily solved by using standard software packages. Finally, numerical examples by means of practical problems are provided to illustrate the effectiveness of the proposed filter design.

State estimation for delayed genetic regulatory networks based on passivity theory

This paper is concerned with the state estimation problem for delayed genetic regulatory networks (GRNs) based on passivity analysis approach. The main purpose of the problem is to design the estimator to approximate the true concentrations of the mRNA and protein through available measurement outputs. Time-varying delays are explicitly assumed to be non-differentiable and constraint on the derivative of the time-varying delay is less than one can be removed. Based on the Lyapunov-Krasovskii functionals involving triple integral terms, using some integral inequalities and convex combination technique, a delay-dependent passivity criterion is established for GRNs in terms of linear matrix inequalities (LMIs) that can efficiently be solved by any available LMI solvers. Finally, numerical examples and simulation are presented to demonstrate the efficiency of the proposed estimation schemes.