Optimal Reconstruction of Probabilistic Boolean Networks.

In gene regulatory networks (GRNs), it is important to model gene regulation based on a priori information and experimental data. As a useful mathematical model, probabilistic Boolean networks (PBNs) have been widely applied in GRNs. This article addresses the optimal reconstruction problem of PBNs based on several priori Boolean functions and sampled data. When all candidate Boolean functions are known in advance, the optimal reconstruction problem is reformulated into an optimization problem. This problem can be well solved by a recurrent neural network approach which decreases the computational cost. When parts of candidate Boolean functions are known in advance, necessary and sufficient conditions are provided for the reconstruction of PBNs. In this case, two types of reconstruction problems are further proposed: one is aimed at minimizing the number of reconstructed Boolean functions, and the other one is aimed at maximizing the selection probability of the main dynamics under noises. At last, examples in GRNs are elaborated to demonstrate the effectiveness of the main results.

Input-to-State Stability of Switched Network Control Systems Under Unknown Deception Attacks.

This article focuses on the stability issue of switched network control systems (SNCSs) under deception attacks described by a Bernoulli process with unknown probability distribution. The false information in deception attacks is unknown but bounded and may be state dependent or state independent. By means of the input-to-state stability (ISS) tool and the convex combination method, an improved lemma is first developed for SNCSs, which facilitates the derivations of our results. After that, some attack-independent sufficient conditions for the ISS of SNCSs are obtained for mode-dependent average dwell time switching and stochastic switching, respectively. Different from existing results, the concerned switching contributes to the stability of SNCSs, which benefits the ISS performance of SNCSs even though the unknown deception attacks cause all subsystems to be non-ISS. The proposed results provide an effective solution with strong robustness to deal with unknown deception attacks or denial-of-service attacks.

Fixed-time synchronization for two-dimensional coupled reaction-diffusion complex networks: Boundary conditions analysis.

This paper examines fixed-time synchronization (FxTS) for two-dimensional coupled reaction-diffusion complex networks (CRDCNs) with impulses and delay. Utilizing the Lyapunov method, a FxTS criterion is established for impulsive delayed CRDCNs. Herein, impulses encompass both synchronizing and desynchronizing variants. Subsequently, by employing a Lyapunov-Krasovskii functional, two FxTS boundary controllers are formulated for CRDCNs with Neumann and mixed boundary condition, respectively. It is observed that vanishing Dirichlet boundary contributes to the synchronization of the CRDCNs. Furthermore, this study calculates the optimal constant for the Poincaré inequality in the square domain, which is instrumental in analyzing FxTS conditions for boundary controllers. Conclusive numerical examples underscore the efficacy of the proposed theoretical findings.

Synchronization in Coupled Neural Networks With Hybrid Delayed Impulses: Average Impulsive Delay-Gain Method.

In this article, we propose a new concept called average impulsive delay-gain (AIDG) for studying the synchronization of coupled neural networks (CNNs). Based on the viewpoints of impulsive control and impulsive perturbation, we establish some globally exponential synchronization criteria for CNNs. Our methods are well-suited for addressing the synchronization problems of systems subject to hybrid delayed impulses with time-varying impulsive delay and gain. Moreover, we prove that the AIDG has both positive and negative effects on synchronization. Compared to existing research, our conclusions are more applicable and less conservative as the considered hybrid delayed impulses involve more flexible cases. Finally, we validate the effectiveness of our proposed results by applying them to small-world and scale-free network models.

Synchronization of Time-Delay Coupled Neural Networks With Stabilizing Delayed Impulsive Control.

This brief studies the distributed synchronization of time-delay coupled neural networks (NNs) with impulsive pinning control involving stabilizing delays. A novel differential inequality is proposed, where the state's past information at impulsive time is effectively extracted and used to handle the synchronization of coupled NNs. Based on this inequality, the restriction that the size of impulsive delay is always limited by the system delay is removed, and the upper bound on the impulsive delay is relaxed, which is improved the existing related results. By using the methods of average impulsive interval (AII) and impulsive delay, some relaxed criteria for distributed synchronization of time-delay coupled NNs are obtained. The proposed synchronization conditions do not impose on the upper bound of two consecutive impulsive signals, and the lower bound is more flexible. Moreover, our results reveal that the impulsive delays may contribute to the synchronization of time-delay systems. Finally, typical networks are presented to illustrate the advantage of our delayed impulsive control method.

Event-based fixed-time synchronization of neural networks under DoS attack and its applications.

In this paper, the fixed-time synchronization control for neural networks with discontinuous data communication is investigated. Due to the transmission blocking caused by DoS attack, it is intractable to establish a monotonically decreasing Lyapunov function like the conventional analysis of fixed-time stability. Therefore, by virtue of recursive and reduction to absurdity approaches, novel fixed-time stability criteria where the estimated upper bound of settling-time is inherently different from existing results are presented. Then, based on the developed conditions, an event-triggered control scheme that can avoid Zeno behavior is designed to achieve synchronization of master-slave neural networks under DoS attack within a prescribed time. For comparison, the established control scheme is further discussed under the case without DoS attack, and the circumstance that there is no attack or event-triggered mechanism, respectively. Simulation results are finally provided to illustrate the significant and validity of our theoretical research. Especially, in terms of encryption and decryption keys generated from the synchronization behavior of chaotic networks, we specifically discuss the application of the proposed fixed-time synchronization scheme to image and audio encryption.

Asymptotic Stability of Delayed Boolean Networks With Random Data Dropouts.

In real networks, communication constraints often prevent the full exchange of information between nodes, which is inevitable. This brief investigates the problem of time delay and randomly missing data in Boolean networks (BNs). A Bernoulli random variable is assigned to each node to characterize the probability of data packet dropout. Time delay and missing data are modeled by independent random variables. A novel data-sending rule that incorporates both communication constraints is proposed. An augmented system, comprising current states, delayed information, and successfully transmitted data, is established for theoretical analysis. Using the semitensor product (STP), the necessary and sufficient condition for asymptotic stability of delayed BNs with random data dropouts is derived. The convergence rate is also obtained.

A Switching Memory-Based Event-Trigger Scheme for Synchronization of Lur'e Systems With Actuator Saturation: A Hybrid Lyapunov Method.

This article is concerned with the event-triggered synchronization of Lur'e systems subject to actuator saturation. Aiming at reducing control costs, a switching-memory-based event-trigger (SMBET) scheme, which allows a switching between the sleeping interval and the memory-based event-trigger (MBET) interval, is first presented. In consideration of the characteristics of SMBET, a piecewise-defined but continuous looped-functional is newly constructed, under which the requirement of positive definiteness and symmetry on some Lyapunov matrices is dropped within the sleeping interval. Then, a hybrid Lyapunov method (HLM), which bridges the gap between the continuous-time Lyapunov theory (CTLT) and the discrete-time Lyapunov theory (DTLT), is used to make the local stability analysis of the closed-loop system. Meanwhile, using a combination of inequality estimation techniques and the generalized sector condition, two sufficient local synchronization criteria and a codesign algorithm for the controller gain and triggering matrix are developed. Furthermore, two optimization strategies are, respectively, put forward to enlarge the estimated domain of attraction (DoA) and the allowable upper bound of sleeping intervals on the premise of ensuring local synchronization. Finally, a three-neuron neural network and the classical Chua's circuit are used to carry out some comparison analyses and to display the advantages of the designed SMBET strategy and the constructed HLM, respectively. Also, an application to image encryption is provided to substantiate the feasibility of the obtained local synchronization results.

Impulsive strategies in nonlinear dynamical systems: A brief overview.

The studies of impulsive dynamical systems have been thoroughly explored, and extensive publications have been made available. This study is mainly in the framework of continuous-time systems and aims to give an exhaustive review of several main kinds of impulsive strategies with different structures. Particularly, (i) two kinds of impulse-delay structures are discussed respectively according to the different parts where the time delay exists, and some potential effects of time delay in stability analysis are emphasized. (ii) The event-based impulsive control strategies are systematically introduced in the light of several novel event-triggered mechanisms determining the impulsive time sequences. (iii) The hybrid effects of impulses are emphatically stressed for nonlinear dynamical systems, and the constraint relationships between different impulses are revealed. (iv) The recent applications of impulses in the synchronization problem of dynamical networks are investigated. Based on the above several points, we make a detailed introduction for impulsive dynamical systems, and some significant stability results have been presented. Finally, several challenges are suggested for future works.

Fixed-time and prescribed-time synchronization of quaternion-valued neural networks: A control strategy involving Lyapunov functions.

A control strategy containing Lyapunov functions is proposed in this paper. Based on this strategy, the fixed-time synchronization of a time-delay quaternion-valued neural network (QVNN) is analyzed. This strategy is extended to the prescribed-time synchronization of the QVNN. Furthermore, an improved two-step switching control strategy is also proposed based on this flexible control strategy. Compared with some existing methods, the main method of this paper is a non-decomposition one, does not contain a sign function in the controller, and has better synchronization accuracy. Two numerical examples verify the above advantages.

Minimal Pinning Control for Oscillatority of Boolean Networks.

In this article, minimal pinning control for oscillatority (i.e., instability) of Boolean networks (BNs) under algebraic state space representations method is studied. First, two criteria for oscillatority of BNs are obtained from the aspects of state transition matrix (STM) and network structure (NS) of BNs, respectively. A distributed pinning control (DPC) from these two aspects is proposed: one is called STM-based DPC and the other one is called NS-based DPC, both of which are only dependent on local in-neighbors. As for STM-based DPC, one arbitrary node can be chosen to be controlled, based on certain solvability of several equations, meanwhile a hybrid pinning control (HPC) combining DPC and conventional pinning control (CPC) is also proposed. In addition, as for NS-based DPC, pinning control nodes (PCNs) can be found using the information of NS, which efficiently reduces the high computational complexity. The proposed STM-based DPC and NS-based DPC in this article are shown to be simple and concise, which provide a new direction to dramatically reduce control costs and computational complexity. Finally, gene networks are simulated to discuss the effectiveness of theoretical results.

A Comprehensive Review of Continuous-/Discontinuous-Time Fractional-Order Multidimensional Neural Networks.

The dynamical study of continuous-/discontinuous-time fractional-order neural networks (FONNs) has been thoroughly explored, and several publications have been made available. This study is designed to give an exhaustive review of the dynamical studies of multidimensional FONNs in continuous/discontinuous time, including Hopfield NNs (HNNs), Cohen-Grossberg NNs, and bidirectional associative memory NNs, and similar models are considered in real ( [Formula: see text]), complex ( [Formula: see text]), quaternion ( [Formula: see text]), and octonion ( [Formula: see text]) fields. Since, in practice, delays are unavoidable, theoretical findings from multidimensional FONNs with various types of delays are thoroughly evaluated. Some required and adequate stability and synchronization requirements are also mentioned for fractional-order NNs without delays.

Synchronization of Complex Dynamical Networks Subject to DoS Attacks: An Improved Coding-Decoding Protocol.

This article investigates the synchronization of communication-constrained complex dynamic networks subject to malicious attacks. An observer-based controller is designed by virtue of the bounded encode sequence derived from an improved coding-decoding communication protocol. Moreover, taking the security of data transmission into consideration, the denial-of-service attacks with the frequency and duration characterized by the average dwell-time constraint are introduced into data communication, and their influence on the coder string is analyzed explicitly. Thereafter, by imposing reasonable restrictions on the transmission protocol and the occurrence of attacks, the boundedness of coding intervals can be obtained. Since the precision of data is generally limited, it may lead to the situation that the signal to be encoded overflows the coding interval such that it results in the unavailability of the developed coding scheme. To cope with this problem, a dynamic variable is introduced to the design of the protocol. Subsequently, based on the Lyapunov stability theory, sufficient conditions for ensuring the input-to-state stability of the synchronization error systems under the communication-constrained condition and malicious attacks are presented. The validity of the developed method is finally verified by a simulation example of chaotic networks.

Impulsive-Based Almost Surely Synchronization for Neural Network Systems Subject to Deception Attacks.

This article is dedicated to investigating the impulsive-based almost surely synchronization issue of neural network systems (NSSs) with quality-of-service constraints. First, the communication network considered suffers from random double deception attacks, which are modeled as a nonlinear function and a desynchronizing impulse sequence, respectively. Meanwhile, the impulsive instants and impulsive gains are randomly and only their expectations are available. Second, by taking two different types of random deception attacks into consideration, a novel mathematical model for vulnerable NSSs is constructed. Then, almost surely synchronization criteria are established by using Borel-Cantelli lemma. Furthermore, based on the derived strong and weak sufficient conditions, the almost surely synchronization of NSSs is achieved. Finally, the section of numerical example is shown to illustrate the effectiveness of the proposed method.

Feedback Stabilization of Boolean Control Networks With Missing Data.

Data loss is often random and unavoidable in realistic networks due to transmission failure or node faults. When it comes to Boolean control networks (BCNs), the model actually becomes a delayed system with unbounded time delays. It is difficult to find a suitable way to model it and transform it into a familiar form, so there have been no available results so far. In this article, the stabilization of BCNs is studied with Bernoulli-distributed missing data. First, an augmented probabilistic BCN (PBCN) is constructed to estimate the appearance of data loss items in the model form. Based on this model, some necessary and sufficient conditions are proposed based on the construction of reachable matrices and one-step state transition probability matrices. Moreover, algorithms are proposed to complete the state feedback stabilizability analysis. In addition, a constructive method is developed to design all feasible state feedback controllers. Finally, illustrative examples are given to show the effectiveness of the proposed results.

State-Feedback Set Stabilization of Boolean Networks With State-Dependent Random Impulses.

In this article, we are devoted to addressing the state-feedback set stabilization of Boolean control networks with state-dependent random impulses by utilizing a hybrid index model. By comparison with the previous impulsive Boolean networks, this model can be used to describe the instantaneousness of various impulsive behaviors more clearly. In order to avoid the occurrence of Zeno phenomenon, we first introduce the basic concept of forward completeness and further establish the judging criterion. After that, an algorithm is presented to derive the largest control invariant subset of a given subset. Based on this, we derive a necessary and sufficient criterion for finite-time feedback set stabilizability. Similarly, the result is also obtained for the asymptotic case, and the asymptotic set stabilizers are designed by dividing the whole state space into several layers. Moreover, we also investigate the relationships between different stabilizabilities. Last, two illustrative examples are presented to demonstrate the efficiency of the theoretical results.

Finite-time synchronization of quaternion-valued neural networks with delays: A switching control method without decomposition.

For a class of quaternion-valued neural networks (QVNNs) with discrete and distributed time delays, its finite-time synchronization (FTSYN) is addressed in this paper. Instead of decomposition, a direct analytical method named two-step analysis is proposed. That method can always be used to study FTSYN, under either 1-norm or 2-norm of quaternion. Compared with the decomposing method, the two-step method is also suitable for models that are not easily decomposed. Furthermore, a switching controller based on the two-step method is proposed. In addition, two criteria are given to realize the FTSYN of QVNNs. At last, three numerical examples illustrate the feasibility, effectiveness and practicability of our method.

Stabilizing Large-Scale Probabilistic Boolean Networks by Pinning Control.

This article aims to stabilize probabilistic Boolean networks (PBNs) via a novel pinning control strategy. In a PBN, the state evolution of each gene switches among a collection of candidate Boolean functions with preassigned probability distributions, which govern the activation frequency of each Boolean function. Due to the existence of stochasticity, the mode-independent pinning controller might be disabled. Thus, both mode-independent and mode-dependent pinning controller are required here. Moreover, a criterion is derived to determine whether mode-independent controllers are applicable while the pinned nodes are given. It is worth pointing out that this pinning control is based on the n×n network structure rather than 2n ×2n state transition matrix. Therefore, compared with the existing results, this pinning control strategy is more practicable and has the ability to handle large-scale networks, especially sparsely connected networks. To demonstrate the effectiveness of the designed control scheme, a PBN that describes the mammalian cell-cycle encountering a mutated phenotype is discussed as a simulation.

Synchronization of Chaotic Neural Networks: Average-Delay Impulsive Control.

In the brief, delayed impulsive control is investigated for the synchronization of chaotic neural networks. In order to overcome the difficulty that the delays in impulsive control input can be flexible, we utilize the concept of average impulsive delay (AID). To be specific, we relax the restriction on the upper/lower bound of such delays, which is not well addressed in most existing results. Then, by using the methods of average impulsive interval (AII) and AID, we establish a Lyapunov-based relaxed condition for the synchronization of chaotic neural networks. It is shown that the time delay in impulsive control input may bring a synchronizing effect to the chaos synchronization. Furthermore, we use the method of linear matrix inequality (LMI) for designing average-delay impulsive control, in which the delays satisfy the AID condition. Finally, an illustrative example is given to show the validity of the derived results.

Metagenomic and metabolomic remodeling in nonagenarians and centenarians and its association with genetic and socioeconomic factors.

A better understanding of the biological and environmental variables that contribute to exceptional longevity has the potential to inform the treatment of geriatric diseases and help achieve healthy aging. Here, we compared the gut microbiome and blood metabolome of extremely long-lived individuals (94-105 years old) to that of their children (50-79 years old) in 116 Han Chinese families. We found extensive metagenomic and metabolomic remodeling in advanced age and observed a generational divergence in the correlations with socioeconomic factors. An analysis of quantitative trait loci revealed that genetic associations with metagenomic and metabolomic features were largely generation-specific, but we also found 131 plasma metabolic quantitative trait loci associations that were cross-generational with the genetic variants concentrated in six loci. These included associations between FADS1/2 and arachidonate, PTPA and succinylcarnitine and FLVCR1 and choline. Our characterization of the extensive metagenomic and metabolomic remodeling that occurs in people reaching extreme ages may offer new targets for aging-related interventions.