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Zou C, Zhou C, Zhang Q, He X, Huang C. State estimation for delayed genetic regulatory networks with reaction diffusion terms and Markovian jump. COMPLEX INTELL SYST 2023. [DOI: 10.1007/s40747-023-01001-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/19/2023]
Abstract
AbstractRobust state estimation for delayed genetic regulatory networks with reaction–diffusion terms and uncertainties terms under Dirichlet boundary conditions is addressed in this article. The main purpose of the problem investigation is to design a novel state observer for estimate the true concentrations of mRNA and protein by available measurement outputs. Based on Lyapunov–Krasovskii functions and linear matrix inequalities (LMI), sufficient conditions are given to ensure the robust stability of the estimation error networks. Two examples are presented to illustrate the effectiveness of the proposed approach.
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Mohammadian M, Sufi Karimi H. Decentralized PI Controller Design for Robust Perfect Adaptation in Noisy Time-Delayed Genetic Regulatory Networks. Neural Process Lett 2023. [DOI: 10.1007/s11063-023-11162-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/11/2023]
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Wang B. Random periodic sequence of globally mean-square exponentially stable discrete-time stochastic genetic regulatory networks with discrete spatial diffusions. ELECTRONIC RESEARCH ARCHIVE 2023; 31:3097-3122. [DOI: 10.3934/era.2023157] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
Abstract
<abstract><p>This paper regards the dual effects of discrete-space and discrete-time in stochastic genetic regulatory networks via exponential Euler difference and central finite difference. Firstly, the global exponential stability of such discrete networks is investigated by using discrete constant variation formulation. In particular, the optimal exponential convergence rate is explored by solving a nonlinear optimization problem under nonlinear constraints, and an implementable computer algorithm for computing the optimal exponential convergence rate is given. Secondly, random periodic sequence for such discrete networks is investigated based on the theory of semi-flow and metric dynamical systems. The researching findings show that the spatial diffusions with nonnegative intensive coefficients have no influence on global mean square boundedness and stability, random periodicity of the networks. This paper is pioneering in considering discrete spatial diffusions, which provides a research basis for future research on genetic regulatory networks.</p></abstract>
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Song X, Li X, Song S, Ahn CK. State Observer Design of Coupled Genetic Regulatory Networks With Reaction-Diffusion Terms via Time-Space Sampled-Data Communications. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2022; 19:3704-3714. [PMID: 34550890 DOI: 10.1109/tcbb.2021.3114405] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
In this paper, state observation of coupled reaction-diffusion genetic regulatory networks (GRNs) with time-varying delays is investigated under Dirichlet boundary conditions. First, the above GRNs are constructed to model gene regulatory properties, where the feedback regulation function of the GRNs is assumed to exhibit the Hill form and a novel method to deal with it is introduced. Then a time-space sampled-data state observer is designed for the mentioned networks and new criteria are established by utilizing the Lyapunov stability theory and the inequality techniques of Halanay et al. Finally, the validity of the theoretical results is proved by numerical examples.
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Yan M, Liu C, Zhang X, Wang Y. State observer for coupled cyclic genetic regulatory networks with time delays. J EXP THEOR ARTIF IN 2022. [DOI: 10.1080/0952813x.2022.2115146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
Affiliation(s)
- Minde Yan
- School of Mathematical Science, Heilongjiang University, Harbin, China
- Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, Heilongjiang University, Harbin, China
| | - Chunyan Liu
- School of Information Management, Heilongjiang University, Harbin, P. R. China
| | - Xian Zhang
- School of Mathematical Science, Heilongjiang University, Harbin, China
- Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, Heilongjiang University, Harbin, China
| | - Yantao Wang
- School of Mathematical Science, Heilongjiang University, Harbin, China
- Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, Heilongjiang University, Harbin, China
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Qin Y, Li F, Wang J, Shen H. Extended Dissipative Synchronization of Reaction–Diffusion Genetic Regulatory Networks Based on Sampled-data Control. Neural Process Lett 2022. [DOI: 10.1007/s11063-022-11003-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Wang J, Wang H, Shen H, Wang B, Park JH. Finite-Time H ∞ State Estimation for PDT-Switched Genetic Regulatory Networks With Randomly Occurring Uncertainties. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2022; 19:1651-1660. [PMID: 33242311 DOI: 10.1109/tcbb.2020.3040979] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
This article is concerned with the problem of finite-time H∞ state estimation for switched genetic regulatory networks with randomly occurring uncertainties. The persistent dwell-time switching rule, as a more versatile class of switching rules, is considered in this paper. Besides, several random variables that obey the Bernoulli distribution are used to represent randomly occurring uncertainties. The overriding purpose of this article is to design an estimator to ensure that the estimation error system is stochastically finite-time bounded and satisfies the H∞ performance. Based on this, sufficient conditions for the explicit form of the estimator gains can be obtained by the Lyapunov method. Finally, a numerical example is given to verify the correctness and feasibility of the proposed method.
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Further results on asymptotic and finite-time stability analysis of fractional-order time-delayed genetic regulatory networks. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2021.11.088] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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Song X, Wang M, Park JH, Song S. Spatial-L ∞-Norm-Based Finite-Time Bounded Control for Semilinear Parabolic PDE Systems With Applications to Chemical-Reaction Processes. IEEE TRANSACTIONS ON CYBERNETICS 2022; 52:178-191. [PMID: 32142465 DOI: 10.1109/tcyb.2020.2972634] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
This article investigates a spatial- L∞ -norm-based reliable bounded control problem for a class of nonlinear partial differential equation systems in a finite-time interval. The main novelties are reflected in the following aspects: 1) inspired by the sector-nonlinearity approach, the considered nonlinear system is reconstructed by a Takagi-Sugeno fuzzy model, which provides an effective method for control design. Besides, several actuator failures, such as stuck faulty, outage faulty, and bias faulty, are taken into account and modeled by a novel Markov process; 2) partial areas' states are sampled and transmitted based on a new distributed event-triggered communication strategy, which reduces the cost of the system design and saves the limited network resources to some extent; and 3) on the basis of the first two works, a new piecewise fuzzy controller, which requires fewer actuators compared with the distributed control method, is constructed. Then, some sufficient conditions to guarantee the finite-time boundedness (in the sense of spatial L∞ norm) and mixed L2-L∞/H∞ disturbance attenuation performance are established, and a new linear matrix inequality relax technique is introduced to deal with the strict constraint that is caused by the asynchronous phenomenon between plant and controller. Finally, two simulation studies are given to illustrate the effectiveness and advantages of the developed controller.
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New Results on Global Exponential Stability of Genetic Regulatory Networks with Diffusion Effect and Time-Varying Hybrid Delays. Neural Process Lett 2021. [DOI: 10.1007/s11063-021-10573-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Song X, Li X, Ahn CK, Song S. Space-Dividing-Based Cluster Synchronization of Reaction-Diffusion Genetic Regulatory Networks via Intermittent Control. IEEE Trans Nanobioscience 2021; 21:55-64. [PMID: 34491897 DOI: 10.1109/tnb.2021.3111109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
In this paper, we focus on the cluster synchronization of reaction-diffusion genetic regulatory networks (RDGRNs) with time-varying delays, where the state of the system is not only time-dependent but also spatially-dependent due to the presence of the reaction-diffusion terms. First, we construct an intermittent space-dividing controller that effectively combines the two control strategies, making it more cost-effective. Furthermore, based on the activation function division approach, we propose a regulation function division method that can improve the delay upper bound of RDGRNs; meanwhile, the cluster synchronization criteria of RDGRNs under the proposed controller are derived based on the Lyapunov theory and Halanay's et al. inequality techniques. Finally, the criteria's effectiveness is demonstrated by numerical examples of the system in one- and two-dimensional space.
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Song X, Man J, Song S, Ahn CK. Gain-Scheduled Finite-Time Synchronization for Reaction-Diffusion Memristive Neural Networks Subject to Inconsistent Markov Chains. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2021; 32:2952-2964. [PMID: 32735537 DOI: 10.1109/tnnls.2020.3009081] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
An innovative class of drive-response systems that are composed of Markovian reaction-diffusion memristive neural networks, where the drive and response systems follow inconsistent Markov chains, is proposed in this article. For this kind of nonlinear parameter-varying systems, a suitable gain-scheduled controller that involves a mode and memristor-dependent item is designed, so that the error system is bounded within a finite-time interval. Moreover, by constructing a novel Lyapunov-Krasovskii functional and employing the canonical Bessel-Legendre inequality and free-weighting matrix method, the conservatism of the finite-time synchronization criterion can be greatly reduced. Finally, two numerical examples are provided to illustrate the feasibility and practicability of the obtained results.
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Farouq MW, Boulila W, Hussain Z, Rashid A, Shah M, Hussain S, Ng N, Ng D, Hanif H, Shaikh MG, Sheikh A, Hussain A. A Novel Coupled Reaction-Diffusion System for Explainable Gene Expression Profiling. SENSORS (BASEL, SWITZERLAND) 2021; 21:2190. [PMID: 33801002 PMCID: PMC8003942 DOI: 10.3390/s21062190] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/20/2021] [Revised: 03/06/2021] [Accepted: 03/08/2021] [Indexed: 12/20/2022]
Abstract
Machine learning (ML)-based algorithms are playing an important role in cancer diagnosis and are increasingly being used to aid clinical decision-making. However, these commonly operate as 'black boxes' and it is unclear how decisions are derived. Recently, techniques have been applied to help us understand how specific ML models work and explain the rational for outputs. This study aims to determine why a given type of cancer has a certain phenotypic characteristic. Cancer results in cellular dysregulation and a thorough consideration of cancer regulators is required. This would increase our understanding of the nature of the disease and help discover more effective diagnostic, prognostic, and treatment methods for a variety of cancer types and stages. Our study proposes a novel explainable analysis of potential biomarkers denoting tumorigenesis in non-small cell lung cancer. A number of these biomarkers are known to appear following various treatment pathways. An enhanced analysis is enabled through a novel mathematical formulation for the regulators of mRNA, the regulators of ncRNA, and the coupled mRNA-ncRNA regulators. Temporal gene expression profiles are approximated in a two-dimensional spatial domain for the transition states before converging to the stationary state, using a system comprised of coupled-reaction partial differential equations. Simulation experiments demonstrate that the proposed mathematical gene-expression profile represents a best fit for the population abundance of these oncogenes. In future, our proposed solution can lead to the development of alternative interpretable approaches, through the application of ML models to discover unknown dynamics in gene regulatory systems.
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Affiliation(s)
- Muhamed Wael Farouq
- Department of Statistics, Mathematics and Insurance, University of Ain Shams, Cairo 11566, Egypt;
- School of Computing, Edinburgh Napier University, Edinburgh EH11 4BN, UK
| | - Wadii Boulila
- RIADI Laboratory, National School of Computer Sciences, University of Manouba, Manouba 2010, Tunisia;
- IS Department, College of Computer Science and Engineering, Taibah University, Medina 42353, Saudi Arabia
| | - Zain Hussain
- College of Medicine and Veterinary Medicine, University of Edinburgh, Edinburgh EH8 9YL, UK; (Z.H.); (N.N.); (A.S.)
| | | | - Moiz Shah
- NHS Greater Glasgow and Clyde, Glasgow G12 0XH, UK; (M.S.); (M.G.S.)
| | - Sajid Hussain
- Albany Gastroenterology Consultants, Albany, NY 12206, USA;
| | - Nathan Ng
- College of Medicine and Veterinary Medicine, University of Edinburgh, Edinburgh EH8 9YL, UK; (Z.H.); (N.N.); (A.S.)
| | - Dominic Ng
- Faculty of Biology, Medicine and Health, University of Manchester, Manchester M13 9PL, UK; (D.N.); (H.H.)
| | - Haris Hanif
- Faculty of Biology, Medicine and Health, University of Manchester, Manchester M13 9PL, UK; (D.N.); (H.H.)
| | | | - Aziz Sheikh
- College of Medicine and Veterinary Medicine, University of Edinburgh, Edinburgh EH8 9YL, UK; (Z.H.); (N.N.); (A.S.)
| | - Amir Hussain
- School of Computing, Edinburgh Napier University, Edinburgh EH11 4BN, UK
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