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Gualtieri CT. Genomic Variation, Evolvability, and the Paradox of Mental Illness. Front Psychiatry 2021; 11:593233. [PMID: 33551865 PMCID: PMC7859268 DOI: 10.3389/fpsyt.2020.593233] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 08/10/2020] [Accepted: 11/27/2020] [Indexed: 12/30/2022] Open
Abstract
Twentieth-century genetics was hard put to explain the irregular behavior of neuropsychiatric disorders. Autism and schizophrenia defy a principle of natural selection; they are highly heritable but associated with low reproductive success. Nevertheless, they persist. The genetic origins of such conditions are confounded by the problem of variable expression, that is, when a given genetic aberration can lead to any one of several distinct disorders. Also, autism and schizophrenia occur on a spectrum of severity, from mild and subclinical cases to the overt and disabling. Such irregularities reflect the problem of missing heritability; although hundreds of genes may be associated with autism or schizophrenia, together they account for only a small proportion of cases. Techniques for higher resolution, genomewide analysis have begun to illuminate the irregular and unpredictable behavior of the human genome. Thus, the origins of neuropsychiatric disorders in particular and complex disease in general have been illuminated. The human genome is characterized by a high degree of structural and behavioral variability: DNA content variation, epistasis, stochasticity in gene expression, and epigenetic changes. These elements have grown more complex as evolution scaled the phylogenetic tree. They are especially pertinent to brain development and function. Genomic variability is a window on the origins of complex disease, neuropsychiatric disorders, and neurodevelopmental disorders in particular. Genomic variability, as it happens, is also the fuel of evolvability. The genomic events that presided over the evolution of the primate and hominid lineages are over-represented in patients with autism and schizophrenia, as well as intellectual disability and epilepsy. That the special qualities of the human genome that drove evolution might, in some way, contribute to neuropsychiatric disorders is a matter of no little interest.
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Xiao M, Zheng WX, Jiang G. Bifurcation and Oscillatory Dynamics of Delayed Cyclic Gene Networks Including Small RNAs. IEEE TRANSACTIONS ON CYBERNETICS 2019; 49:883-896. [PMID: 29994187 DOI: 10.1109/tcyb.2017.2789331] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
It has been demonstrated in a large number of experimental results that small RNAs (sRNAs) play a vital role in gene regulation processes. Thus, the gene regulation process is dominated by sRNAs in addition to messenger RNAs and proteins. However, the regulation mechanism of sRNAs is not well understood and there are few models considering the effect of sRNAs. So it is of realistic biological background to include sRNAs when modeling gene networks. In this paper, sRNAs are incorporated into the process of gene expression and a new differential equation model is put forward to describe cyclic genetic regulatory networks with sRNAs and multiple delays. We mainly investigate the stability and bifurcation criteria for two cases: 1) positive cyclic genetic regulatory networks and 2) negative cyclic genetic regulatory networks. For a positive cyclic genetic regulatory network, it is revealed that there may exist more than one equilibrium and the multistability can appear. Sufficient conditions are established for the delay-independent stability and fold bifurcations. It is found that the dynamics of positive cyclic gene networks has no bearing on time delays, but depends on the biochemical parameters, the Hill coefficient and the equilibrium itself. For a negative cyclic genetic regulatory network, it is proved that there exists a unique equilibrium. Delay-dependent conditions for the stability are derived, and the existence of Hopf bifurcations is examined. Different from the delay-independent stability of positive gain networks, the stability of equilibrium is determined not only by the biochemical parameters, the Hill coefficient and the equilibrium itself, but also by the total delay. At last, three illustrative examples are provided to validate the major results.
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Saravanakumar R, Syed Ali M, Ahn CK, Karimi HR, Shi P. Stability of Markovian Jump Generalized Neural Networks With Interval Time-Varying Delays. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2017; 28:1840-1850. [PMID: 28113729 DOI: 10.1109/tnnls.2016.2552491] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
This paper examines the problem of asymptotic stability for Markovian jump generalized neural networks with interval time-varying delays. Markovian jump parameters are modeled as a continuous-time and finite-state Markov chain. By constructing a suitable Lyapunov-Krasovskii functional (LKF) and using the linear matrix inequality (LMI) formulation, new delay-dependent stability conditions are established to ascertain the mean-square asymptotic stability result of the equilibrium point. The reciprocally convex combination technique, Jensen's inequality, and the Wirtinger-based double integral inequality are used to handle single and double integral terms in the time derivative of the LKF. The developed results are represented by the LMI. The effectiveness and advantages of the new design method are explained using five numerical examples.
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Manivannan R, Samidurai R, Cao J, Alsaedi A, Alsaadi FE. Global exponential stability and dissipativity of generalized neural networks with time-varying delay signals. Neural Netw 2017; 87:149-159. [DOI: 10.1016/j.neunet.2016.12.005] [Citation(s) in RCA: 58] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2016] [Revised: 11/05/2016] [Accepted: 12/13/2016] [Indexed: 11/26/2022]
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Zhou G, Huang J, Tian F, Liao X. Sufficient and necessary conditions for Lyapunov stability of genetic networks with SUM regulatory logic. Cogn Neurodyn 2015; 9:447-58. [PMID: 26157517 DOI: 10.1007/s11571-015-9341-5] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2014] [Revised: 02/21/2015] [Accepted: 03/23/2015] [Indexed: 11/30/2022] Open
Abstract
In this paper, a nonlinear model for genetic regulator networks (GRNs) with SUM regulatory logic is presented. Four sufficient and necessary conditions of global asymptotical stability and global exponential stability for the equilibrium point of the GRNs are proposed, respectively. Specifically, three weak sufficient conditions and corresponding corollaries are derived by using comparing theorem and Dini derivative method. Then, a famous GRN model is used as the example to illustrate the effectiveness of our theoretical results. Comparing to the results in the previous literature, some novel ideas, study methods and interesting results are explored.
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Affiliation(s)
- Guopeng Zhou
- Institute of Engineering and Technology, Hubei University of Science and Technology, Xianning, 437100 China
| | - Jinhua Huang
- Department of Electric and Electronic Engineering, Wuhan Institute of Shipbuilding Technology, Wuhan, 430050 China
| | - Fengxia Tian
- Institute of Engineering and Technology, Hubei University of Science and Technology, Xianning, 437100 China
| | - Xiaoxin Liao
- Institute of Engineering and Technology, Hubei University of Science and Technology, Xianning, 437100 China ; College of Automation, Huazhong University of Science and Technology, Wuhan, 430074 China
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Liu X, Yu W, Cao J, Chen S. Discontinuous Lyapunov approach to state estimation and filtering of jumped systems with sampled-data. Neural Netw 2015; 68:12-22. [PMID: 25965770 DOI: 10.1016/j.neunet.2015.04.001] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2015] [Revised: 03/27/2015] [Accepted: 04/03/2015] [Indexed: 11/17/2022]
Abstract
This paper is concerned with the sampled-data state estimation and H(∞) filtering for a class of Markovian jump systems with the discontinuous Lyapunov approach. The system measurements are sampled and then transmitted to the estimator and filter in order to estimate the state of the jumped system under consideration. The corresponding error dynamics is represented by a system with two types of delays: one is from the system itself, and the other from the sampling period. As the delay due to sampling is discontinuous, a corresponding discontinuous Lyapunov functional is constructed, and sufficient conditions are established so as to guarantee both the asymptotic mean-square stability and the H(∞) performance for the filtering error systems. The explicit expressions of the desired estimator and filter are further provided. Finally, two simulation examples are given to illustrate the design procedures and performances of the proposed method.
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Affiliation(s)
- Xiaoyang Liu
- School of Computer Science & Technology, Jiangsu Normal University, Xuzhou 221116, China.
| | - Wenwu Yu
- Department of Mathematics, Southeast University, Nanjing 210096, China; Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
| | - Jinde Cao
- Department of Mathematics, Southeast University, Nanjing 210096, China; Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
| | - Shun Chen
- Department of Mathematics, City University of Hong Kong, Hong Kong
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Li Z, Chen K. Exponential Stability of Stochastic Genetic Regulatory Networks with Interval Uncertainties and Multiple Delays. ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2014. [DOI: 10.1007/s13369-014-1206-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Rakkiyappan R, Chandrasekar A, Rihan FA, Lakshmanan S. Exponential state estimation of Markovian jumping genetic regulatory networks with mode-dependent probabilistic time-varying delays. Math Biosci 2014; 251:30-53. [PMID: 24565574 DOI: 10.1016/j.mbs.2014.02.008] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2013] [Revised: 11/19/2013] [Accepted: 02/12/2014] [Indexed: 12/01/2022]
Abstract
In this paper, we investigate a problem of exponential state estimation for Markovian jumping genetic regulatory networks with mode-dependent probabilistic time-varying delays. A new type of mode-dependent probabilistic leakage time-varying delay is considered. Given the probability distribution of the time-delays, stochastic variables that satisfying Bernoulli random binary distribution are formulated to produce a new system which includes the information of the probability distribution. Under these circumstances, the state estimator is designed to estimate the true concentration of the mRNA and the protein of the GRNs. Based on Lyapunov-Krasovskii functional that includes new triple integral terms and decomposed integral intervals, delay-distribution-dependent exponential stability criteria are obtained in terms of linear matrix inequalities. Finally, a numerical example is provided to show the usefulness and effectiveness of the obtained results.
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Affiliation(s)
- R Rakkiyappan
- Department of Mathematics, Bharathiar University, Coimbatore 641 046, Tamilnadu, India.
| | - A Chandrasekar
- Department of Mathematics, Bharathiar University, Coimbatore 641 046, Tamilnadu, India
| | - F A Rihan
- Department of Mathematical Sciences, College of Science, UAE University, Al Ain 15551, United Arab Emirates
| | - S Lakshmanan
- Department of Mathematical Sciences, College of Science, UAE University, Al Ain 15551, United Arab Emirates
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Wang T, Ding Y, Zhang L, Hao K. Robust state estimation for discrete-time stochastic genetic regulatory networks with probabilistic measurement delays. Neurocomputing 2013. [DOI: 10.1016/j.neucom.2012.12.011] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Wu ZG, Shi P, Su H, Chu J. Dissipativity analysis for discrete-time stochastic neural networks with time-varying delays. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2013; 24:345-355. [PMID: 24808309 DOI: 10.1109/tnnls.2012.2232938] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
In this paper, the problem of dissipativity analysis is discussed for discrete-time stochastic neural networks with time-varying discrete and finite-distributed delays. The discretized Jensen inequality and lower bounds lemma are adopted to deal with the involved finite sum quadratic terms, and a sufficient condition is derived to ensure the considered neural networks to be globally asymptotically stable in the mean square and strictly (Q, S, R)-y-dissipative, which is delay-dependent in the sense that it depends on not only the discrete delay but also the finite-distributed delay. Based on the dissipativity criterion, some special cases are also discussed. Compared with the existing ones, the merit of the proposed results in this paper lies in their reduced conservatism and less decision variables. Three examples are given to illustrate the effectiveness and benefits of our theoretical results.
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Lakshmanan S, Park JH, Jung H, Balasubramaniam P, Lee S. Design of state estimator for genetic regulatory networks with time-varying delays and randomly occurring uncertainties. Biosystems 2013. [DOI: 10.1016/j.biosystems.2012.11.001] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Wang Y, Yu A, Zhang X. Robust stability of stochastic genetic regulatory networks with time-varying delays: a delay fractioning approach. Neural Comput Appl 2012. [DOI: 10.1007/s00521-012-1034-y] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Wu ZG, Lam J, Su H, Chu J. Stability and dissipativity analysis of static neural networks with time delay. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2012; 23:199-210. [PMID: 24808500 DOI: 10.1109/tnnls.2011.2178563] [Citation(s) in RCA: 60] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
This paper is concerned with the problems of stability and dissipativity analysis for static neural networks (NNs) with time delay. Some improved delay-dependent stability criteria are established for static NNs with time-varying or time-invariant delay using the delay partitioning technique. Based on these criteria, several delay-dependent sufficient conditions are given to guarantee the dissipativity of static NNs with time delay. All the given results in this paper are not only dependent upon the time delay but also upon the number of delay partitions. Some examples are given to illustrate the effectiveness and reduced conservatism of the proposed results.
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Finite-time robust stochastic stability of uncertain stochastic delayed reaction–diffusion genetic regulatory networks. Neurocomputing 2011. [DOI: 10.1016/j.neucom.2011.03.041] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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15
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Robust filtering of extended stochastic genetic regulatory networks with parameter uncertainties, disturbances, and time-varying delays. Neurocomputing 2011. [DOI: 10.1016/j.neucom.2011.01.018] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Balasubramaniam P, Rakkiyappan R, Krishnasamy R. Stochastic stability of Markovian jumping uncertain stochastic genetic regulatory networks with interval time-varying delays. Math Biosci 2010; 226:97-108. [DOI: 10.1016/j.mbs.2010.04.002] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2009] [Revised: 04/13/2010] [Accepted: 04/14/2010] [Indexed: 01/24/2023]
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