(ω,c)-Asymptotically periodic oscillation of cellular neural networks on time scales with leakage delays and mixed time-varying delays

In this paper, we introduce the concept of (ω,c)-asymptotic periodicity within the context of translation-invariant time scales. This concept generalizes various types of function, including asymptotically periodic, asymptotically antiperiodic, asymptotically Bloch periodic, and certain unbounded functions on time scales. We investigate some fundamental properties of this class of functions and apply our findings to cellular neural network (CNN) dynamic equations with leakage and mixed time-varying delays. Using time-scale calculus and a method of contradiction, we establish sufficient conditions for the existence of a unique (ω,c)-asymptotically periodic solution for the considered CNNs and their global exponential stability. These results are completely new across all time domains. In addition, we provide numerical examples and simulations to illustrate the effectiveness of our results for various time scales.

Probabilistic-sampling-based asynchronous control for semi-Markov jumping neural networks with reaction-diffusion terms

This paper investigates the probabilistic-sampling-based asynchronous control problem for semi-Markov reaction-diffusion neural networks (SMRDNNs). Aiming at mitigating the drawback of the well-known fixed-sampling control law, a more general probabilistic-sampling-based control strategy is developed to characterize the randomly sampling period. The system mode is considered to be related to the sojourn-time and undetectable. The jumping of the controller depends on the observation mode, and is asynchronous with the jumping of the system mode. By utilizing the established hidden semi-Markov model and a stochastic analysis approach, some sufficient conditions are obtained to ensure the asymptotically stable of the SMRDNNs. Finally, an example is given to prove the validity and superiority of the conclusion.

Iterative neural networks for improving memory capacity

In recent years, the problem of the multistability of neural networks has been studied extensively. From the research results obtained, the number of stable equilibrium points depends only on a power form of the network dimension. However, in practical applications, the number of stable equilibrium points needed is often not expressed in power form. Therefore, can we determine an appropriate activation function so that the neural network has exactly the required number of stable equilibrium points? This paper provides a new way to study this problem by means of an iteration method. The necessary activation function is constructed by an appropriate iteration method, and the neural network model is established. Based on the mathematical theories of matrix analysis and functional analysis and on the inequality method, the number and distribution of the network equilibrium points are determined by dividing the state space reasonably, and some multistability criteria that are related to the number of iterations and are independent of the network dimension are established.

The combined Lyapunov functionals method for stability analysis of neutral Cohen-Grossberg neural networks with multiple delays

This research article will employ the combined Lyapunov functionals method to deal with stability analysis of a more general type of Cohen-Grossberg neural networks which simultaneously involve constant time and neutral delay parameters. By utilizing some combinations of various Lyapunov functionals, we determine novel criteria ensuring global stability of such a model of neural systems that employ Lipschitz continuous activation functions. These proposed results are totally stated independently of delay terms and they can be completely characterized by the constants parameters involved in the neural system. By making some detailed analytical comparisons between the stability results derived in this research article and the existing corresponding stability criteria obtained in the past literature, we prove that our proposed stability results lead to establishing some sets of stability conditions and these conditions may be evaluated as different alternative results to the previously reported corresponding stability criteria. A numerical example is also presented to show the applicability of the proposed stability results.

Multistability and Robustness of Competitive Neural Networks With Time-Varying Delays

This article is devoted to analyzing the multistability and robustness of competitive neural networks (NNs) with time-varying delays. Based on the geometrical structure of activation functions, some sufficient conditions are proposed to ascertain the coexistence of equilibrium points, of them are locally exponentially stable, where represents a dimension of system and is the parameter related to activation functions. The derived stability results not only involve exponential stability but also include power stability and logarithmical stability. In addition, the robustness of stable equilibrium points is discussed in the presence of perturbations. Compared with previous papers, the conclusions proposed in this article are easy to verify and enrich the existing stability theories of competitive NNs. Finally, numerical examples are provided to support theoretical results.

Deep learning assisted quantitative detection of cardiac troponin I in hierarchical dendritic copper-nickel nanostructure lateral flow immunoassay

The rising demand for point-of-care testing (POCT) in disease diagnosis has made LFIA sensors based on dendritic metal thin film (HD-nanometal) and background fluorescence technology essential for rapid and accurate disease marker detection, thanks to their integrated design, high sensitivity, and cost-effectiveness. However, their unique 3D nanostructures cause significant fluorescence variation, challenging traditional image processing methods in segmenting weak fluorescence regions. This paper develops a deep learning method to efficiently segment target regions in HD-nanometal LFIA sensor images, improving quantitative detection accuracy. We propose an improved UNet++ network with attention and residual modules, accurately segmenting varying fluorescence intensities, especially weak ones. We evaluated the method using IoU and Dice coefficients, comparing it with UNet, Deeplabv3, and UNet++. We used an HD-nanoCu-Ni LFIA sensor for cardiac troponin I (cTnI) as a case study to validate the method's practicality. The proposed method achieved a 96.3% IoU, outperforming other networks. The R2 between characteristic quantity and cTnI concentration reached 0.994, confirming the method's accuracy and reliability. This enhances POCT accuracy and provides a reference for future fluorescence immunochromatography expansion.

Improved Stability Analysis Results of Generalized Neural Networks With Time-Varying Delays

This article studies the stability problem of generalized neural networks (GNNs) with time-varying delay. The delay has two cases: the first case is that the delay's derivative has only upper bound, the other case has no information of its derivative or itself is not differentiable. For both two cases, we provide novel stability criteria based on novel Lyapunov-Krasovskii functionals (LKFs) and new negative definite conditions (NDCs) of matrix-valued cubic polynomials. In contrast with the existing methods, in this article, the proposed criteria do not need to introduce extra state variables, and the positive-definite constraint on the novel LKF is relaxed. Moreover, based on free-matrix-based inequality (FMBI) and new NDCs, the stability conditions are expressed as linear matrix inequalities (LMIs). Eventually, the merits and efficiency of the proposed criteria are checked through some classical numerical examples.

Almost Surely Exponential Convergence Analysis of Time Delayed Uncertain Cellular Neural Networks Driven by Liu Process via Lyapunov-Krasovskii Functional Approach

As with probability theory, uncertainty theory has been developed, in recent years, to portray indeterminacy phenomena in various application scenarios. We are concerned, in this paper, with the convergence property of state trajectories to equilibrium states (or fixed points) of time delayed uncertain cellular neural networks driven by the Liu process. By applying the classical Banach's fixed-point theorem, we prove, under certain conditions, that the delayed uncertain cellular neural networks, concerned in this paper, have unique equilibrium states (or fixed points). By carefully designing a certain Lyapunov-Krasovskii functional, we provide a convergence criterion, for state trajectories of our concerned uncertain cellular neural networks, based on our developed Lyapunov-Krasovskii functional. We demonstrate under our proposed convergence criterion that the existing equilibrium states (or fixed points) are exponentially stable almost surely, or equivalently that state trajectories converge exponentially to equilibrium states (or fixed points) almost surely. We also provide an example to illustrate graphically and numerically that our theoretical results are all valid. There seem to be rare results concerning the stability of equilibrium states (or fixed points) of neural networks driven by uncertain processes, and our study in this paper would provide some new research clues in this direction. The conservatism of the main criterion obtained in this paper is reduced by introducing quite general positive definite matrices in our designed Lyapunov-Krasovskii functional.

Graphene-based RRAM devices for neural computing

Resistive random access memory is very well known for its potential application in in-memory and neural computing. However, they often have different types of device-to-device and cycle-to-cycle variability. This makes it harder to build highly accurate crossbar arrays. Traditional RRAM designs make use of various filament-based oxide materials for creating a channel that is sandwiched between two electrodes to form a two-terminal structure. They are often subjected to mechanical and electrical stress over repeated read-and-write cycles. The behavior of these devices often varies in practice across wafer arrays over these stresses when fabricated. The use of emerging 2D materials is explored to improve electrical endurance, long retention time, high switching speed, and fewer power losses. This study provides an in-depth exploration of neuro-memristive computing and its potential applications, focusing specifically on the utilization of graphene and 2D materials in RRAM for neural computing. The study presents a comprehensive analysis of the structural and design aspects of graphene-based RRAM, along with a thorough examination of commercially available RRAM models and their fabrication techniques. Furthermore, the study investigates the diverse range of applications that can benefit from graphene-based RRAM devices.

Novel results on asymptotic stability and synchronization of fractional-order memristive neural networks with time delays: The 0<δ≤1 case

This paper investigates the asymptotic stability and synchronization of fractional-order (FO) memristive neural networks with time delays. Based on the FO comparison principle and inverse Laplace transform method, the novel sufficient conditions for the asymptotic stability of a FO nonlinear system are given. Then, based on the above conclusions, the sufficient conditions for the asymptotic stability and synchronization of FO memristive neural networks with time delays are investigated. The results in this paper have a wider coverage of situations and are more practical than the previous related results. Finally, the validity of the results is checked by two examples.

Stability Analysis for Delayed Neural Networks via a Generalized Reciprocally Convex Inequality

This article deals with the stability of neural networks (NNs) with time-varying delay. First, a generalized reciprocally convex inequality (RCI) is presented, providing a tight bound for reciprocally convex combinations. This inequality includes some existing ones as special case. Second, in order to cater for the use of the generalized RCI, a novel Lyapunov-Krasovskii functional (LKF) is constructed, which includes a generalized delay-product term. Third, based on the generalized RCI and the novel LKF, several stability criteria for the delayed NNs under study are put forward. Finally, two numerical examples are given to illustrate the effectiveness and advantages of the proposed stability criteria.

Lyapunov approach to manifolds stability for impulsive Cohen-Grossberg-type conformable neural network models

In this paper, motivated by the advantages of the generalized conformable derivatives, an impulsive conformable Cohen-Grossberg-type neural network model is introduced. The impulses, which can be also considered as a control strategy, are at fixed instants of time. We define the notion of practical stability with respect to manifolds. A Lyapunov-based analysis is conducted, and new criteria are proposed. The case of bidirectional associative memory (BAM) network model is also investigated. Examples are given to demonstrate the effectiveness of the established results.

Design of continuous-time recurrent neural networks with piecewise-linear activation function for generation of prescribed sequences of bipolar vectors

A recurrent neural network (RNN) can generate a sequence of patterns as the temporal evolution of the output vector. This paper focuses on a continuous-time RNN model with a piecewise-linear activation function that has neither external inputs nor hidden neurons, and studies the problem of finding the parameters of the model so that it generates a given sequence of bipolar vectors. First, a sufficient condition for the model to generate the desired sequence is derived, which is expressed as a system of linear inequalities in the parameters. Next, three approaches to finding solutions of the system of linear inequalities are proposed: One is formulated as a convex quadratic programming problem and others are linear programming problems. Then, two types of sequences of bipolar vectors that can be generated by the model are presented. Finally, the case where the model generates a periodic sequence of bipolar vectors is considered, and a sufficient condition for the trajectory of the state vector to converge to a limit cycle is provided.

Aperiodic switching event-triggered stabilization of continuous memristive neural networks with interval delays

The stabilization problem is studied for memristive neural networks with interval delays under aperiodic switching event-triggered control. Note that, most of delayed memristive neural networks models studied are discontinuous, which are not the real memristive neural networks. First, a real model of memristive neural networks is proposed by continuous differential equations, furthermore, it is simplified to neural networks with interval matrix uncertainties. Secondly, an aperiodic switching event-trigger is given, and the considered system switches between aperiodic sampled-data system and continuous event-triggered system. Thirdly, by constructing a time-dependent piecewise-defined Lyapunov functional, the stability criterion and the feedback gain design are obtained by linear matrix inequalities. Compared with the existing results, the stability criterion is with lower conservatism. Finally, two neurons are taken as examples to ensure the feasibility of the results.

Robust exponential stability of discrete-time uncertain impulsive stochastic neural networks with delayed impulses

This paper is devoted to the study of the robust exponential stability (RES) of discrete-time uncertain impulsive stochastic neural networks (DTUISNNs) with delayed impulses. Using Lyapunov function methods and Razumikhin techniques, a number of sufficient conditions for mean square (RES-ms) robust exponential stability are derived. The obtained results show that the hybrid dynamic is RES-ms with regard to lower boundary of impulse interval if the discrete-time stochastic neural networks (DTSNNs) is RES-ms and that the impulsive effects are instable. Conversely, if DTSNNs is not RES-ms, impulsive effects can induce unstable neural networks (NNs) to stabilize again concerning an upper bound of the impulsive interval. The results obtained in this study have a broader scope of application than some previously existing findings. Two numerical examples were presented to verify the availability and advantages of the results.

An Overview of the Stability Analysis of Recurrent Neural Networks With Multiple Equilibria

The stability analysis of recurrent neural networks (RNNs) with multiple equilibria has received extensive interest since it is a prerequisite for successful applications of RNNs. With the increasing theoretical results on this topic, it is desirable to review the results for a systematical understanding of the state of the art. This article provides an overview of the stability results of RNNs with multiple equilibria including complete stability and multistability. First, preliminaries on the complete stability and multistability analysis of RNNs are introduced. Second, the complete stability results of RNNs are summarized. Third, the multistability results of various RNNs are reviewed in detail. Finally, future directions in these interesting topics are suggested.

Deep Cellular Recurrent Network for Efficient Analysis of Time-Series Data With Spatial Information

Efficient processing of large-scale time-series data is an intricate problem in machine learning. Conventional sensor signal processing pipelines with hand-engineered feature extraction often involve huge computational costs with high dimensional data. Deep recurrent neural networks have shown promise in automated feature learning for improved time-series processing. However, generic deep recurrent models grow in scale and depth with the increased complexity of the data. This is particularly challenging in presence of high dimensional data with temporal and spatial characteristics. Consequently, this work proposes a novel deep cellular recurrent neural network (DCRNN) architecture to efficiently process complex multidimensional time-series data with spatial information. The cellular recurrent architecture in the proposed model allows for location-aware synchronous processing of time-series data from spatially distributed sensor signal sources. Extensive trainable parameter sharing due to cellularity in the proposed architecture ensures efficiency in the use of recurrent processing units with high-dimensional inputs. This study also investigates the versatility of the proposed DCRNN model for the classification of multiclass time-series data from different application domains. Consequently, the proposed DCRNN architecture is evaluated using two time-series data sets: a multichannel scalp electroencephalogram (EEG) data set for seizure detection, and a machine fault detection data set obtained in-house. The results suggest that the proposed architecture achieves state-of-the-art performance while utilizing substantially less trainable parameters when compared to comparable methods in the literature.

New Global Asymptotic Robust Stability of Dynamical Delayed Neural Networks via Intervalized Interconnection Matrices

This article identifies a new upper bound norm for the intervalized interconnection matrices pertaining to delayed dynamical neural networks under the parameter uncertainties. By formulating the appropriate Lyapunov functional and slope-bounded activation functions, the derived new upper bound norms provide new sufficient conditions corresponding to the equilibrium point of the globally asymptotic robust stability with respect to the delayed neural networks. The new upper bound norm also yields the optimized minimum results as compared with some existing methods. Numerical examples are given to demonstrate the effectiveness of the proposed results obtained through the new upper bound norm method.

Poisson Stability in Symmetrical Impulsive Shunting Inhibitory Cellular Neural Networks with Generalized Piecewise Constant Argument

In the paper, shunting inhibitory cellular neural networks with impulses and the generalized piecewise constant argument are under discussion. The main modeling novelty is that the impulsive part of the systems is symmetrical to the differential part. Moreover, the model depends not only on the continuous time, but also the generalized piecewise constant argument. The process is subdued to Poisson stable inputs, which cause the new type of recurrent signals. The method of included intervals, recently introduced approach of recurrent motions checking, is effectively utilized. The existence and asymptotic properties of the unique Poisson stable motion are investigated. Simulation examples for results are provided. Finally, comparing impulsive shunting inhibitory cellular neural networks with former neural network models, we discuss the significance of the components of our model.

Improved Stability Criteria for Delayed Neural Networks via a Relaxed Delay-Product-Type Lapunov–Krasovskii Functional

In this paper, the asymptotic stability problem of neural networks with time-varying delays is investigated. First, a new sufficient and necessary condition on a general polynomial inequality was developed. Then, a novel augmented Lyapunov–Krasovskii functional (LKF) was constructed, which efficiently introduces some new terms related to the previous information of neuron activation function. Furthermore, based on the suitable LKF and the stated negative condition of the general polynomial, two criteria with less conservatism were derived in the form of linear matrix inequalities. Finally, two numerical examples were carried out to confirm the superiority of the proposed criteria, and a larger allowable upper bound of delays was achieved.

Convergence of a Class of Delayed Neural Networks with Real Memristor Devices

Neural networks with memristors are promising candidates to overcome the limitations of traditional von Neumann machines via the implementation of novel analog and parallel computation schemes based on the in-memory computing principle. Of special importance are neural networks with generic or extended memristor models that are suited to accurately describe real memristor devices. The manuscript considers a general class of delayed neural networks where the memristors obey the relevant and widely used generic memristor model, the voltage threshold adaptive memristor (VTEAM) model. Due to physical limitations, the memristor state variables evolve in a closed compact subset of the space; therefore, the network can be mathematically described by a special class of differential inclusions named differential variational inequalities (DVIs). By using the theory of DVI, and the Lyapunov approach, the paper proves some fundamental results on convergence of solutions toward equilibrium points, a dynamic property that is extremely useful in neural network applications to content addressable memories and signal-processing in real time. The conditions for convergence, which hold in the general nonsymmetric case and for any constant delay, are given in the form of a linear matrix inequality (LMI) and can be readily checked numerically. To the authors knowledge, the obtained results are the only ones available in the literature on the convergence of neural networks with real generic memristors.

Distributed Adaptive Containment Control for Coupled Reaction-Diffusion Neural Networks With Directed Topology

In this article, we consider the problem of distributed adaptive leader-follower coordination of partial differential systems (i.e., reaction-diffusion neural networks, RDNNs) with directed communication topology in the case of multiple leaders. Different from the dynamical networks with ordinary differential dynamics, the design of adaptive protocols is more difficult due to the existence of spatial variables and nonlinear terms in the model. Under directed networks, a novel adaptive control protocol is proposed to solve the containment control problem of RDNNs. By constructing proper Lyapunov functional and adopting some important prior knowledge, the stability of containment for coupled RDNNs is theoretically proved. Furthermore, a corollary about the leader-follower synchronization with a leader for coupled RDNNs with directed communication topology is given. In the end, two numerical examples are provided to illustrate the obtained theoretical results.

Dynamics of Shunting Inhibitory Cellular Neural Networks with Variable Two-Component Passive Decay Rates and Poisson Stable Inputs

Shunting inhibitory cellular neural networks with continuous time-varying rates and inputs are the focus of this research. A new model is considered with compartmental passive decay rates which consist of periodic and Poisson stable components. The first component guarantees the Poisson stability of the dynamics, and the second one causes irregular oscillations. The inputs are Poisson stable to take into account the more sophisticated environment of the networks. The rates and inputs are synchronized to obtain Poisson stable outputs. A new efficient technique for checking the recurrence, the method of included intervals, is applied. Sufficient conditions for the existence of a Poisson stable solution and its asymptotic stability were obtained. Numerical simulations of Poisson stable outputs as well as inputs are provided. Examples of the model with Poisson stable rates, inputs and outputs confirm the feasibility of theoretical results. Discussions were undertaken to provide additional light on the relation of the obtained results with practical and theoretical potentials of neuroscience. Quantitative characteristics are suggested, which can be useful for the future applications of the results. In particular, the center of antisymmetry for the degree of periodicity is determined.

Stability Analysis for Delayed Neural Networks via a Novel Negative-Definiteness Determination Method

The stability of neural networks with a time-varying delay is studied in this article. First, a relaxed Lyapunov-Krasovskii functional (LKF) is presented, in which the positive-definiteness requirement of the augmented quadratic term and the delay-product-type terms are set free, and two double integral states are augmented into the single integral terms at the same time. Second, a new negative-definiteness determination method is put forward for quadratic functions by utilizing Taylor's formula and the interval-decomposition approach. This method encompasses the previous negative-definiteness determination approaches and has less conservatism. Finally, the proposed LKF and the negative-definiteness determination method are applied to the stability analysis of neural networks with a time-varying delay, whose advantages are shown by two numerical examples.

Delayed Impulsive Control for Lag Synchronization of Delayed Neural Networks Involving Partial Unmeasurable States

In the framework of impulsive control, this article deals with the lag synchronization problem of neural networks involving partially unmeasurable states, where the time delay in impulses is fully addressed. Since the complexity of external environment and uncertainty of networks, which may lead to a result that the information of partial states is unmeasurable, the key problem for lag synchronization control is how to utilize the information of measurable states to design suitable impulsive control. By using linear matrix inequality (LMI) and transition matrix method coupled with dimension expansion technique, some sufficient conditions are derived to guarantee lag synchronization, where the requirement for information of all states is needless. Moreover, our proposed conditions not only allow the existence of unmeasurable states but also reduce the restrictions on the number of measurable states, which shows the generality of our results and wide-application in practice. Finally, two illustrative examples and their numerical simulations are presented to demonstrate the effectiveness of main results.

Neuronal Constraint-Handling Technique for the Optimal Synthesis of Closed-Chain Mechanisms in Lower Limb Rehabilitation

The optimal methods for the synthesis of mechanisms in rehabilitation usually require solving constrained optimization problems. Metaheuristic algorithms are frequently used to solve these problems with the inclusion of Constraint-Handling Techniques (CHTs). Nevertheless, the most used CHTs in the synthesis of mechanisms, such as penalty function and feasibility rules, generally prioritize the search for feasible regions over the minimization of the objective function, and it notably influences the exploration and exploitation of the algorithm such that it could induce in the premature convergence to the local minimum and thus the solution quality could deteriorate. In this work, a Neuronal Constraint-Handling (NCH) technique is proposed and its performance is studied in the solution of mechanism synthesis for rehabilitation. The NCH technique uses a neural network to search for the fittest solutions into the feasible and the infeasible region to pass them to the next generation of the evolutionary process of the Differential Evolution (DE) algorithm and consequently improve the obtained solution quality. Two synthesis problems with four–bar and cam–linkage mechanisms are the study cases for developing lower-limb rehabilitation routines. The NCH is compared with four state-of-the-art constraint-handling techniques (penalty function, feasibility rules, stochastic ranking, ϵ-constrained method) included into four representative metaheuristic algorithms. The irace package is used for both the algorithm settings and neuronal network training to fairly and meaningfully compare through statistics to confirm the overall performance. The statistical results confirm that, despite changes in the rehabilitation trajectories, the proposal presents the best overall performance among selected algorithms in the studied synthesis problems for rehabilitation, followed by penalty function and feasibility rule.

A Hybrid Shuffled Frog Leaping Algorithm and Its Performance Assessment in Multi-Dimensional Symmetric Function

Ensemble learning of swarm intelligence evolutionary algorithm of artificial neural network (ANN) is one of the core research directions in the field of artificial intelligence (AI). As a representative member of swarm intelligence evolutionary algorithm, shuffled frog leaping algorithm (SFLA) has the advantages of simple structure, easy implementation, short operation time, and strong global optimization ability. However, SFLA is susceptible to fall into local optimas in the face of complex and multi-dimensional symmetric function optimization, which leads to the decline of convergence accuracy. This paper proposes an improved shuffled frog leaping algorithm of threshold oscillation based on simulated annealing (SA-TO-SFLA). In this algorithm, the threshold oscillation strategy and simulated annealing strategy are introduced into the SFLA, which makes the local search behavior more diversified and the ability to escape from the local optimas stronger. By using multi-dimensional symmetric function such as drop-wave function, Schaffer function N.2, Rastrigin function, and Griewank function, two groups (i: SFLA, SA-SFLA, TO-SFLA, and SA-TO-SFLA; ii: SFLA, ISFLA, MSFLA, DSFLA, and SA-TO-SFLA) of comparative experiments are designed to analyze the convergence accuracy and convergence time. The results show that the threshold oscillation strategy has strong robustness. Moreover, compared with SFLA, the convergence accuracy of SA-TO-SFLA algorithm is significantly improved, and the median of convergence time is greatly reduced as a whole. The convergence accuracy of SFLA algorithm on these four test functions are 90%, 100%, 78%, and 92.5%, respectively, and the median of convergence time is 63.67 s, 59.71 s, 12.93 s, and 8.74 s, respectively; The convergence accuracy of SA-TO-SFLA algorithm on these four test functions is 99%, 100%, 100%, and 97.5%, respectively, and the median of convergence time is 48.64 s, 32.07 s, 24.06 s, and 3.04 s, respectively.

Stability and dissipativity criteria for neural networks with time-varying delays via an augmented zero equality approach

This work investigates the stability and dissipativity problems for neural networks with time-varying delay. By the construction of new augmented Lyapunov-Krasovskii functionals based on integral inequality and the use of zero equality approach, three improved results are proposed in the forms of linear matrix inequalities. And, based on the stability results, the dissipativity analysis for NNs with time-varying delays was investigated. Through some numerical examples, the superiority and effectiveness of the proposed results are shown by comparing the existing works.

Adaptive Event-Triggered Synchronization of Reaction-Diffusion Neural Networks

This article focuses on the design of an adaptive event-triggered sampled-data control (ETSDC) mechanism for synchronization of reaction-diffusion neural networks (RDNNs) with random time-varying delays. Different from the existing ETSDC schemes with predetermined constant thresholds, an adaptive ETSDC mechanism is proposed for RDNNs. The adaptive ETSDC mechanism can be promptly adaptively adjusted since the threshold function is based on the current sampled and latest transmitted signals. Thus, the adaptive ETSDC mechanism can effectively save communication resources for RDNNs. By taking the influence of uncertain factors, the random time-varying delays are considered, which belongs to two intervals in a probabilistic way. Then, by constructing an appropriate Lyapunov-Krasovskii functional (LKF), new synchronization criteria are derived for RDNNs. By solving a set of linear matrix inequalities (LMIs), the desired adaptive ETSDC gain is obtained. Finally, the merits of the adaptive ETSDC mechanism and the effectiveness of the proposed results are verified by one numerical example.

Periodicity and multi-periodicity generated by impulses control in delayed Cohen-Grossberg-type neural networks with discontinuous activations

This paper discusses the periodicity and multi-periodicity in delayed Cohen-Grossberg-type neural networks (CGNNs) possessing impulsive effects, whose activation functions possess discontinuities and are allowed to be unbounded or nonmonotonic. Based on differential inclusion and cone expansion-compression fixed-point theory of set-valued mapping, several improved criteria are given to derive the positive solution with ω-periodicity and ω-multi-periodicity for delayed CGNNs under impulsive control. These ω-periodicity/ω-multi-periodicity orbits are produced by impulses control. The analytical method and theoretical results presented in this paper are of certain significance to the design of neural network models or circuits possessing discontinuous neuron activation and impulsive effects in periodic environment.

Robust Stability of Recurrent Neural Networks With Time-Varying Delays and Input Perturbation

This paper addresses the robust stability of recurrent neural networks (RNNs) with time-varying delays and input perturbation, where the time-varying delays include discrete and distributed delays. By employing the new ψ -type integral inequality, several sufficient conditions are derived for the robust stability of RNNs with discrete and distributed delays. Meanwhile, the robust boundedness of neural networks is explored by the bounded input perturbation and L¹ -norm constraint. Moreover, RNNs have a strong anti-jamming ability to input perturbation, and the robustness of RNNs is suitable for associative memory. Specifically, when input perturbation belongs to the specified and well-characterized space, the results cover both monostability and multistability as special cases. It is revealed that there is a relationship between the stability of neural networks and input perturbation. Compared with the existing results, these conditions proposed in this paper improve and extend the existing stability in some literature. Finally, the numerical examples are given to substantiate the effectiveness of the theoretical results.

Novel criteria for global robust stability of dynamical neural networks with multiple time delays

This research article considers the problem regarding global robust asymptotic stability of the general type of dynamical neural networks involving multiple constant time delays. Some new sufficient criteria are proposed for the existence, uniqueness and global asymptotic stability of the equilibrium point of this neural network model whose network parameters possess uncertainties. This paper will first address the existence and uniqueness problem for equilibrium points by utilizing the Homomorphic transformation theory. Secondly, by exploiting a novel Lyapunov functional candidate, the sufficient conditions for asymptotic stability of equilibrium points of this class of delayed neural networks will be established. The derived robust stability conditions are expressed independently of the constant time delay parameters and define some novel relationships among network parameters of the considered neural network. Thus, the applicability and validity of the obtained robust stability conditions for delayed-type neural networks can be easily tested. The comprehensive comparisons among the results of the current article and some of previously derived corresponding results will also be made by giving an illustrative numerical example.

System-Theoretic Methods for Designing Bio-Inspired Mem-Computing Memristor Cellular Nonlinear Networks

The introduction of nano-memristors in electronics may allow to boost the performance of integrated circuits beyond the Moore era, especially in view of their extraordinary capability to process and store data in the very same physical volume. However, recurring to nonlinear system theory is absolutely necessary for the development of a systematic approach to memristive circuit design. In fact, the application of linear system-theoretic techniques is not suitable to explore thoroughly the rich dynamics of resistance switching memories, and designing circuits without a comprehensive picture of the nonlinear behaviour of these devices may lead to the realization of technical systems failing to operate as desired. Converting traditional circuits to memristive equivalents may require the adaptation of classical methods from nonlinear system theory. This paper extends the theory of time- and space-invariant standard cellular nonlinear networks with first-order processing elements for the case where a single non-volatile memristor is inserted in parallel to the capacitor in each cell. A novel nonlinear system-theoretic method allows to draw a comprehensive picture of the dynamical phenomena emerging in the memristive mem-computing array, beautifully illustrated in the so-called Primary Mosaic for the class of uncoupled memristor cellular nonlinear networks. Employing this new analysis tool it is possible to elucidate, with the support of illustrative examples, how to design variability-tolerant bio-inspired cellular nonlinear networks with second-order memristive cells for the execution of computing tasks or of memory operations. The capability of the class of memristor cellular nonlinear networks under focus to store and process information locally, without the need to insert additional memory units in each cell, may allow to increase considerably the spatial resolution of state-of-the-art purely CMOS sensor-processor arrays. This is of great appeal for edge computing applications, especially since the Internet-of-Things industry is currently calling for the realization of miniaturized, lightweight, low-power, and high-speed mem-computers with sensing capability on board.

Exponential Stability of Discrete-Time Neural Networks With Large Delay

We study the exponential stability of discrete-time neural networks (NNs) with a time-varying delay which contains a few intermittent large delays (LDs). By modeling the considered discrete-time NN as a discrete-time switched NN which contains two subsystems and one of them may be unstable over the LD periods (LDPs), switching techniques are employed to analyze the problem. Delay-dependent exponential stability conditions to check the frequency and the length of the LDs allowed for guaranteeing the exponential stability are proposed by applying a novel Lyapunov-Krasovskii functional (LKF) with LDP-based terms, Wirtinger-based summation inequality, and reciprocally convex combination technique. Based on these conditions, associated evaluation algorithms are developed. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.

Multistability of delayed fractional-order competitive neural networks

This paper is concerned with the multistability of fractional-order competitive neural networks (FCNNs) with time-varying delays. Based on the division of state space, the equilibrium points (EPs) of FCNNs are given. Several sufficient conditions and criteria are proposed to ascertain the multiple O(t^-α)-stability of delayed FCNNs. The O(t^-α)-stability is the extension of Mittag-Leffler stability of fractional-order neural networks, which contains monostability and multistability. Moreover, the attraction basins of the stable EPs of FCNNs are estimated, which shows the attraction basins of the stable EPs can be larger than the divided subsets. These conditions and criteria supplement and improve the previous results. Finally, the results are illustrated by the simulation examples.

Three-Dimensional Deep Noninvasive Radiomics for the Prediction of Disease Control in Patients With Metastatic Urothelial Carcinoma treated With Immunotherapy

INTRODUCTION

Immunotherapy is effective in a small percentage of patients with cancer and no reliable predictive biomarkers are currently available. Artificial Intelligence algorithms may automatically quantify radiologic characteristics associated with disease response to medical treatments.

METHODS

We investigated an innovative approach based on a 3-dimensional (3D) deep radiomics pipeline to classify visual features of chest-abdomen computed tomography (CT) scans with the aim of distinguishing disease control from progressive disease to immune checkpoint inhibitors (ICIs). Forty-two consecutive patients with metastatic urothelial cancer had progressed on first-line platinum-based chemotherapy and had baseline CT scans at immunotherapy initiation. The 3D-pipeline included self-learned visual features and a deep self-attention mechanism. According to the outcome to the ICIs, a 3D deep classifier semiautomatically categorized the most discriminative region of interest on the CT scans.

RESULTS

With a median follow-up of 13.3 months (95% CI, 11.1-15.6), the median overall survival was 8.5 months (95% CI, 3.1-13.8). According to disease response to immunotherapy, the median overall survival was 3.6 months (95% CI, 2.0-5.2) for patients with progressive disease; it was not yet reached for those with disease control. The predictive accuracy of the 3D-pipeline was 82.5% (sensitivity 96%; specificity, 60%). The addition of baseline clinical factors increased the accuracy to 92.5% by improving specificity to 87%; the accuracy of other architectures ranged from 72.5% to 90%.

CONCLUSION

Artificial Intelligence by 3D deep radiomics is a potential noninvasive biomarker for the prediction of disease control to ICIs in metastatic urothelial cancer and deserves validation in larger series.

Dissipativity Analysis for Neural Networks With Time-Varying Delays via a Delay-Product-Type Lyapunov Functional Approach

This article is concerned with the problem of dissipativity and stability analysis for a class of neural networks (NNs) with time-varying delays. First, a new augmented Lyapunov-Krasovskii functional (LKF), including some delay-product-type terms, is proposed, in which the information on time-varying delay and system states is taken into full consideration. Second, by employing a generalized free-matrix-based inequality and its simplified version to estimate the derivative of the proposed LKF, some improved delay-dependent conditions are derived to ensure that the considered NNs are strictly ( Q , S , R )- γ -dissipative. Furthermore, the obtained results are applied to passivity and stability analysis of delayed NNs. Finally, two numerical examples and a real-world problem in the quadruple tank process are carried out to illustrate the effectiveness of the proposed method.

Reachable Set Estimation for Discrete-Time Markovian Jump Neural Networks With Generally Incomplete Transition Probabilities

This paper is concerned with the problem of reachable set estimation for discrete-time Markovian jump neural networks with generally incomplete transition probabilities (TPs). This kind of TP may be exactly known, merely known with lower and upper bounds, or unknown. The aim of this paper is to derive a precise reachable set description for the considered system via the Lyapunov-Krasovskii functional (LKF) approach. By constructing an augmented LKF, using an equivalent transformation method to deal with the unknown TPs and utilizing the extended reciprocally convex matrix inequality, and the free matrix weighting approach to estimate the forward difference of the constructed LKF, several sufficient conditions that guarantee the existence of an ellipsoidal reachable set are established. Finally, a numerical example with simulation results is given to demonstrate the effectiveness and superiority of the proposed results.