How to better evaluate the capabilities of Large Language Models (LLMs) is the focal point and hot topic in current LLMs research. Previous work has noted that due to the extremely high cost of iterative updates of LLMs, they are often unable to answer the latest dynamic questions well. To promote the improvement of Chinese LLMs’ ability to answer dynamic questions, in this paper, we introduce CDQA, a Chinese Dynamic QA benchmark containing question-answer pairs related to the latest news on the Chinese Internet. We obtain high-quality data through a pipeline that combines humans and models, and carefully classify the samples according to the frequency of answer changes to facilitate a more fine-grained observation of LLMs’ capabilities. We have also evaluated and analyzed mainstream and advanced Chinese LLMs on CDQA. Extensive experiments and valuable insights suggest that our proposed CDQA is challenging and worthy of more further study. We believe that the benchmark we provide will become one of the key data resources for improving LLMs’ Chinese question-answering ability in the future.

Leveraging mathematical Large Language Models (LLMs) for proof generation is a fundamental topic in LLMs research. We argue that the ability of current LLMs to prove statements largely depends on whether they have encountered the relevant proof process during training. This reliance limits their deeper understanding of mathematical theorems and related concepts. Inspired by the pedagogical method of "proof by counterexamples" commonly used in human mathematics education, our work aims to enhance LLMs’ ability to conduct mathematical reasoning and proof through counterexamples. Specifically, we manually create a high-quality, university-level mathematical benchmark, COUNTERMATH, which requires LLMs to prove mathematical statements by providing counterexamples, thereby assessing their grasp of mathematical concepts. Additionally, we develop a data engineering framework to automatically obtain training data for further model improvement. Extensive experiments and detailed analyses demonstrate that COUNTERMATH is challenging, indicating that LLMs, such as OpenAI o1, have insufficient counterexample-driven proof capabilities. Moreover, our exploration into model training reveals that strengthening LLMs’ counterexample-driven conceptual reasoning abilities is crucial for improving their overall mathematical capabilities. We believe that our work offers new perspectives on the community of mathematical LLMs.

The Forward-Forward (FF) learning algorithm provides a bottom-up alternative to backpropagation (BP) for training neural networks, relying on a layer-wise "goodness" function with well-designed negative samples for contrastive learning. Existing goodness functions are typically defined as the sum of squared postsynaptic activations, neglecting correlated variability between neurons. In this work, we propose a novel goodness function termed dimensionality compression that uses the effective dimensionality (ED) of fluctuating neural responses to incorporate second-order statistical structure. Our objective minimizes ED for noisy copies of individual inputs while maximizing it across the sample distribution, promoting structured representations without the need to prepare negative samples. We demonstrate that this formulation achieves competitive performance compared to other non-BP methods. Moreover, we show that noise plays a constructive role that can enhance generalization and improve inference when predictions are derived from the mean of squared output, which is equivalent to making predictions based on an energy term. Our findings contribute to the development of more biologically plausible learning algorithms and suggest a natural fit for neuromorphic computing, where stochasticity is a computational resource rather than a nuisance. The code is available at https://github.com/ZhichaoZhu/StochasticForwardForward.

Lane detection is crucial for autonomous driving. Recent advancements have expanded traditional two-dimensional (2D) lane detection to three-dimensional (3D) by predicting lane positions in 3D space. These methods rely on fully supervised learning, requiring high-quality 3D labels, which are difficult to obtain. This challenge motivates a weakly supervised approach leveraging abundant and easily scalable 2D lane annotations. Specifically, we systematically analyze lane geometric structure priors and introduce Lane Geometry Supervision (LGS), which relies solely on 2D lane labels. Extensive experiments on both synthetic and real-world datasets demonstrate that our method achieves performance comparable to fully supervised approaches using direct 3D labels. Moreover, incorporating LGS as a regularization term further enhances the performance of existing fully supervised methods. Finally, we show that LGS enables a label-efficient training methodology for 3D monocular lane detection, effectively utilizing both scarce yet complete 3D lane labels and abundant but incomplete 2D lane labels.

Spiking neural networks (SNNs) have attracted significant interest in the development of brain-inspired computing systems due to their energy efficiency and similarities to biological information processing. In contrast to continuous-valued artificial neural networks, which produce results in a single step, SNNs require multiple steps during inference to achieve a desired accuracy level, resulting in a burden in real-time response and energy efficiency. Inspired by the tradeoff between speed and accuracy in human and animal decision-making processes, which exhibit correlations among reaction times, task complexity, and decision confidence, an inquiry emerges regarding how an SNN model can benefit by implementing these attributes. Here, we introduce a theory of decision making in SNNs by untangling the interplay between signal and noise. Under this theory, we introduce a new learning objective that trains an SNN not only to make the correct decisions but also to shape its confidence. Numerical experiments demonstrate that SNNs trained in this way exhibit improved confidence expression, reduced trial-to-trial variability, and shorter latency to reach the desired accuracy. We then introduce a stopping policy that can stop inference in a way that further enhances the time efficiency of SNNs. The stopping time can serve as an indicator to whether a decision is correct, akin to the reaction time in animal behavior experiments. By integrating stochasticity into decision making, this study opens up new possibilities to explore the capabilities of SNNs and advance SNNs and their applications in complex decision-making scenarios where model performance is limited.

This article investigates distributed adaptive algorithms for intralayer synchronization of multiplex networks, both with and without pinning control. Two types of distributed adaptive algorithms are considered based on the parameters being adjusted: 1) node-based algorithms, which adapt the coupling strength of each node using the relative information from its neighborhood and itself, and 2) edge-based algorithms, which update the coupling weight of each edge based on the relative information between the two connected nodes. Using the Lyapunov function method, we prove that, under mild conditions on the uncoupled node dynamics, the proposed adaptive strategies guarantee intralayer synchronization for any multiplex network with strongly connected intralayer topologies.

In this article, we discuss synchronization in multiplex networks of different layers. Both the topologies and the uncoupled node dynamics in different layers are different. Novel sufficient criteria are derived for intralayer synchronization and interlayer quasisynchronization, in terms of the coupling matrices, the coupling strengths, and the intrinsic function of the uncoupled systems. We also investigate interlayer synchronization of multiplex networks with identical uncoupled node dynamics. Finally, we give some numerical examples to validate the effectiveness of these theoretical results.

Combinatorial optimization problems are widespread but inherently challenging due to their discrete nature. The primary limitation of existing methods is that they can only access a small fraction of the solution space at each iteration, resulting in limited efficiency for searching the global optimal. To overcome this challenge, diverging from conventional efforts of expanding the solver's search scope, we focus on enabling information to actively propagate to the solver through heat diffusion. By transforming the target function while preserving its optima, heat diffusion facilitates information flow from distant regions to the solver, providing more efficient navigation. Utilizing heat diffusion, we propose a framework for solving general combinatorial optimization problems. The proposed methodology demonstrates superior performance across a range of the most challenging and widely encountered combinatorial optimizations. Echoing recent advancements in harnessing thermodynamics for generative artificial intelligence, our study further reveals its significant potential in advancing combinatorial optimization.

Neural activity in the cortex exhibits a wide range of firing variability and rich correlation structures. Studies on neural coding indicate that correlated neural variability can influence the quality of neural codes, either beneficially or adversely. However, the mechanisms by which correlated neural variability is transformed and processed across neural populations to achieve meaningful computation remain largely unclear. Here we propose a theory of covariance computation with spiking neurons which offers a unifying perspective on neural representation and computation with correlated noise. We employ a recently proposed computational framework known as the moment neural network to resolve the nonlinear coupling of correlated neural variability with a task-driven approach to constructing neural network models for performing covariance-based perceptual tasks. In particular, we demonstrate how perceptual information initially encoded entirely within the covariance of upstream neurons' spiking activity can be passed, in a near-lossless manner, to the mean firing rate of downstream neurons, which in turn can be used to inform inference. The proposed theory of covariance computation addresses an important question of how the brain extracts perceptual information from noisy sensory stimuli to generate a stable perceptual whole and indicates a more direct role that correlated variability plays in cortical information processing.

In this paper, we address matrix-valued distributed stochastic optimization with inequality and equality constraints, where the objective function is a sum of multiple matrix-valued functions with stochastic variables and the considered problems are solved in a distributed manner. A penalty method is derived to deal with the constraints, and a selection principle is proposed for choosing feasible penalty functions and penalty gains. A distributed optimization algorithm based on the gossip model is developed for solving the stochastic optimization problem, and its convergence to the optimal solution is analyzed rigorously. Two numerical examples are given to demonstrate the viability of the main results.

Neural activity in the brain exhibits correlated fluctuations that may strongly influence the properties of neural population coding. However, how such correlated neural fluctuations may arise from the intrinsic neural circuit dynamics and subsequently affect the computational properties of neural population activity remains poorly understood. The main difficulty lies in resolving the nonlinear coupling between correlated fluctuations with the overall dynamics of the system. In this study, we investigate the emergence of synergistic neural population codes from the intrinsic dynamics of correlated neural fluctuations in a neural circuit model capturing realistic nonlinear noise coupling of spiking neurons. We show that a rich repertoire of spatial correlation patterns naturally emerges in a bump attractor network and further reveals the dynamical regime under which the interplay between differential and noise correlations leads to synergistic codes. Moreover, we find that negative correlations may induce stable bound states between two bumps, a phenomenon previously unobserved in firing rate models. These noise-induced effects of bump attractors lead to a number of computational advantages including enhanced working memory capacity and efficient spatiotemporal multiplexing and can account for a range of cognitive and behavioral phenomena related to working memory. This study offers a dynamical approach to investigating realistic correlated neural fluctuations and insights to their roles in cortical computations.

This article considers the fully distributed leaderless synchronization in a complex network by only utilizing local neighboring information to design and tune the coupling strength of each node such that the synchronization problem can be solved without involving any global information of the network. For an undirected network, a fully distributed synchronization algorithm is presented to adjust the coupling strength of each node based on a simple adaptive law. When the topology of a network is directed, two different types of adaptive algorithms are developed to achieve synchronization in a fully distributed manner, where the coupling strength of each node is designed to be either the sum or product of two non-negative scalar functions. The fully distributed leaderless synchronization of a directed network is investigated in a leader-follower framework, where the leader subnetwork is analyzed by using the techniques from constrained Rayleigh quotients and the follower subnetwork is addressed by employing the properties of nonsingular M -matrices. Simulations are given to illustrate the theoretical results.

In this article, we discuss quadratic condition (QUAD-condition) for general models of synchronization of complex networks and consensus of multiagents with or without pinning controller in detail. Synchronization analysis consists of two parts. One is connection structure, which is described with coupling matrix. The other one is the intrinsic property of the uncoupled system. QUAD-conditions play a key role in describing the intrinsic property of the uncoupled system. With QUAD-conditions, we unify synchronization and consensus of multiagents in a framework. It is interesting that anti-synchronization can be easily transformed to synchronization by introducing suitable QUAD-condition.

Detection and segmentation of the substation equipments is the important first step towards establishing an AI-based thermal fault detection of substation equipments. The traditional detection and segmentation methods have been built up based on the single mode of thermal or visible light image. In this paper, we propose the framework of bimodal fusion: the visible-light images and the temperature map, to establish the deep neural network models for object detection and instance segmentation of the substation equipments, based on the Mask R-CNN. In our private fused dataset, we realize and compare diverse fusion methods, including the pixel-based fusion, feature-based fusion and decision-level fusion methods for the detection and segmentation task of substation equipments. The comparison experiments shown that the FPN feature layer fusion model in the feature-based fusion can achieve better detection and segmentation effects than the others and the models of the single mode. We also demonstrate that the fused method can slightly improve the performance in the night scene by simulation. However, the improvement of performance measured by the mAP and AR of these method are all slight.

In this paper, we propose a camera control system towards occasionally videoing preassigned objects. Based on the technique of real-time visual detection and tracking, using the Kalman filter and re-identification (ReID), we propose continuous composition of lens, based on the atomic rules of shots, and give the trajectory planning of the camera, to generate the PID controller to the pan-tilt. By both simulation and emulation by frame-wise cropping of video clips, we illustrate the efficiency of this method. Based on this model, we design and produce an AI automatic camera for lively photography and clip videoing.

Product theory of stochastic matrices provides a powerful tool in the consensus analysis of discrete-time multiagent systems. However, the classic theory cannot deal with networks with general coupling coefficients involving negative ones, which have been discussed only in very few papers due to the technicalities involved. Motivated by these works, here we developed some new results for the products of matrices which generalize that of the classical stochastic matrices by admitting negative entries. Particularly, we obtained a generalized version of the classic Hajnal inequality on this generalized matrix class. Based on these results, we proved some convergence results for a class of discrete-time consensus algorithms with time-varying delays and general coupling coefficients. At last, these results were applied to the analysis of a class of continuous-time consensus algorithms with discrete-time controller updates in the existence of communication/actuation delays.

The main objective of this article is to explore the issue of how to improve the performance of discrete-time sliding mode control (DSMC) law for a class of discrete-time dynamic systems with both matched and mismatched disturbances. By using tools from mismatched disturbance compensation technique, a new kind of discrete-time sliding surface is constructed and subsequently utilized in designing the desirable DSMC laws. Specifically, two different types of DSMC laws, i.e., the equivalent-control-based DSMC law and the reaching-law-based DSMC law, are respectively constructed based upon the developed sliding surface. Rigorous analysis on stability of the corresponding closed-loop system is performed where it is shown that the mismatched disturbances could be successfully attenuated from the output channel in steady state. The effectiveness of the analytic result is supported by the experimental studies as well as numerical simulations.

Inference, estimation, sampling and likelihood evaluation are four primary goals of probabilistic modeling. Practical considerations often force modeling approaches to make compromises between these objectives. We present a novel probabilistic learning framework, called Fenchel Mini-Max Learning (FML), that accommodates all four desiderata in a flexible and scalable manner. Our derivation is rooted in classical maximum likelihood estimation, and it overcomes a longstanding challenge that prevents unbiased estimation of unnormalized statistical models. By reformulating MLE as a mini-max game, FML enjoys an unbiased training objective that (i) does not explicitly involve the intractable normalizing constant and (ii) is directly amendable to stochastic gradient descent optimization. To demonstrate the utility of the proposed approach, we consider learning unnormalized statistical models, nonparametric density estimation and training generative models, with encouraging empirical results presented.

A class of the preventive and reactive cyber defense dynamics has recently been proven to be globally convergent, meaning that the dynamics always converges to a unique equilibrium whose location only depends on the values of the model parameters (but not the initial state of the dynamics). In this paper, we unify the aforementioned class of preventive and reactive cyber defense dynamics models and the closely related class of N-intertwined epidemic models into a single framework. We prove that the unified dynamics is still globally convergent under some mild conditions, which are naturally satisfied by the two specific classes of dynamics models mentioned above and are inevitable when analyzing a more general framework. We also characterize the convergence speed of the unified dynamics. As a corollary, we obtain that the N-intertwined epidemic model and its extension are globally convergent, together with a full characterization on their convergence speed, which is only partially addressed in the literature.

Inspired by the recent neuroscience studies on the left-right asymmetry of the human brain in processing low and high spatial frequency information, this paper introduces a dual skipping network which carries out coarse-to-fine object categorization. Such a network has two branches to simultaneously deal with both coarse and fine-grained classification tasks. Specifically, we propose a layer-skipping mechanism that learns a gating network to predict which layers to skip in the testing stage. This layer-skipping mechanism endows the network with good flexibility and capability in practice. Evaluations are conducted on several widely used coarse-to-fine object categorization benchmarks, and promising results are achieved by our proposed network model.

This paper mainly investigates consensus problem with a pull-based event-triggered feedback control. For each agent, the diffusion coupling feedbacks are based on the states of its in-neighbors at its latest triggering time, and the next triggering time of this agent is determined by its in-neighbors' information. The general directed topologies, including irreducible and reducible cases, are investigated. The scenario of distributed continuous communication is considered first. It is proved that if the network topology has a spanning tree, then the event-triggered coupling algorithm can realize the consensus for the multiagent system. Then, the results are extended to discontinuous communication, i.e., self-triggered control, where each agent computes its next triggering time in advance without having to observe the system's states continuously. The effectiveness of the theoretical results is illustrated by a numerical example finally.

In this paper, stability of linearly coupled dynamical systems with feedback pinning is studied. Event-triggered rules are employed on both diffusion coupling and feedback pinning to reduce the updating load of the coupled system. Here, both the coupling matrix and the set of pinned-nodes vary with time are induced by a homogeneous Markov chain. For each node, the diffusion coupling is set up from the state information of its neighbors' at their latest triggered time and the feedback pinning uses the target's (if pinned) information at the node's latest event time. The next event time is triggered by some specified criteria. Two event-triggering rules are proposed and it is proved that if the system with time-average coupling and pinning gains are stable, the event-triggered strategies can stabilize the system if the switching is sufficiently fast. Moreover, Zeno behaviors are excluded in some cases. Finally, numerical examples are presented to illustrate the theoretical results.

Data assimilation (DA) has proved to be an efficient framework for estimation problems in real-world complex dynamical systems arising in geoscience, and it has also begun to show its power in computational neuroscience. The ensemble Kalman filter (EnKF) is believed to be a powerful tool of DA in practice. In comparison to the other filtering methods of DA, such as the bootstrap filter (BF) and optimal sequential importance re-sampling (OPT-SIRS), it is considered more convenient in many applications, but with the theoretical flaw of Gaussian assumption. In this paper, we apply the EnKF, the BF and the OPT-SIRS to the estimation and prediction of a single computational neuron model with ten parameters and conduct a comparison study of these three DA filtering methods on this model. It is numerically shown that the EnKF presents the best performance in both accuracy and computation load. We argue that the EnKF will be a promising tool in the large-scale DA problem occurring in computational neuroscience with experimental data.

In this paper, we investigate stability of a class of analytic neural networks with the synaptic feedback via event-triggered rules. This model is general and include Hopfield neural network as a special case. These event-trigger rules can efficiently reduces loads of computation and information transmission at synapses of the neurons. The synaptic feedback of each neuron keeps a constant value based on the outputs of the other neurons at its latest triggering time but changes at its next triggering time, which is determined by a certain criterion. It is proved that every trajectory of the analytic neural network converges to certain equilibrium under this event-triggered rule for all the initial values except a set of zero measure. The main technique of the proof is the Łojasiewicz inequality to prove the finiteness of trajectory length. The realization of this event-triggered rule is verified by the exclusion of Zeno behaviors. Numerical examples are provided to illustrate the efficiency of the theoretical results.

In this paper, we provide a theoretical analysis for nonlinear discontinuous consensus protocols in networks of multiagents over weighted directed graphs. By integrating the analytic tools from nonsmooth stability analysis and graph theory, we investigate networks with both fixed topology and randomly switching topology. For networks with a fixed topology, we provide a sufficient and necessary condition for asymptotic consensus, and the consensus value can be explicitly calculated. As to networks with switching topologies, we provide a sufficient condition for the network to realize consensus almost surely. In particular, we consider the case that the switching sequence is independent and identically distributed. As applications of the theoretical results, we introduce a generalized blinking model and show that consensus can be realized almost surely under the proposed protocols. Numerical simulations are also provided to illustrate the theoretical results.

In this paper, we utilize event-triggered coupling configurations to realize synchronization of linearly coupled dynamical systems. Here, the diffusion couplings are set up from the latest observations of the nodes and their neighborhood and the next observation time is triggered by the proposed criteria based on the local neighborhood information as well. Two scenarios are considered: 1) continuous monitoring, in which each node can observe its neighborhood's instantaneous states and 2) discrete monitoring, in which each node can obtain only its neighborhood's states at the same time point when the coupling term is triggered. In both the cases, we prove that if the system with persistent coupling can synchronize, then these event-triggered coupling strategies can synchronize the system too.

In this paper, we give a stability analysis of multi-agent system with a local pinning control algorithm for very general network topologies. These include determinately directed time varying topologies, the stochastically switching topologies. The pinned vertex set also varies with time, including deterministic and stochastic time-variations. We present sufficient conditions to guarantee the convergence of the pinning process: for the deterministic case, a time-varying pinned vertex set can stabilize the network of multi-agents with time-varying topologies if any vertex in the networks can be accessed by directed paths by at least one vertex in the pinned vertex set across all time intervals that are pre-defined; Similar results are also given for the stochastically switching case. As applications, numerical simulations based on the random waypoint model are given to verify our theoretical results.

This paper investigates the convergence of Hop-field neural networks with an event-triggered rule to reduce the frequency of the neuron output feedbacks. The output feedback of each neuron is based on the outputs of its neighbours at its latest triggering time and the next triggering time of this neuron is determined by a criterion based on its neighborhood information as well. It is proved that the Hopfield neural networks are completely stable under this event-triggered rule. The main technique of proof is to prove the finiteness of trajectory length by the Łojasiewicz inequality. The realization of this event-triggered rule is verified by the exclusion of Zeno behaviors. Numerical examples are provided to illustrate the theoretical results and present the goal-seeking capability of the networks. Our result can be easily extended to a large class of neural networks.

Theoretical modeling of computer virus/worm epidemic dynamics is an important problem that has attracted many studies. However, most existing models are adapted from biological epidemic ones. Although biological epidemic models can certainly be adapted to capture some computer virus spreading scenarios (especially when the so-called homogeneity assumption holds), the problem of computer virus spreading is not well understood because it has many important perspectives that are not necessarily accommodated in the biological epidemic models. In this article, we initiate the study of such a perspective, namely that ofadaptivedefense against epidemic spreading in arbitrary networks. More specifically, we investigate a nonhomogeneous Susceptible-Infectious-Susceptible (SIS) model where the model parameters may vary with respect to time. In particular, we focus on two scenarios we callsemi-adaptivedefense andfully adaptivedefense, which accommodate implicit and explicit dependency relationships between the model parameters, respectively. In the semi-adaptive defense scenario, the model’s input parameters are given; the defense is semi-adaptive because the adjustment is implicitly dependent upon the outcome of virus spreading. For this scenario, we present a set of sufficient conditions (some are more general or succinct than others) under which the virus spreading will die out; such sufficient conditions are also known asepidemic thresholdsin the literature. In the fully adaptive defense scenario, some input parameters are not known (i.e., the aforementioned sufficient conditions are not applicable) but the defender can observe the outcome of virus spreading. For this scenario, we present adaptive control strategies under which the virus spreading will die out or will be contained to a desired level.

In this paper, cluster consensus of multiagent systems is studied via inter-cluster nonidentical inputs. Here, we consider general graph topologies, which might be time-varying. The cluster consensus is defined by two aspects: intracluster synchronization, the state at which differences between each pair of agents in the same cluster converge to zero, and inter-cluster separation, the state at which agents in different clusters are separated. For intra-cluster synchronization, the concepts and theories of consensus, including the spanning trees, scramblingness, infinite stochastic matrix product, and Hajnal inequality, are extended. As a result, it is proved that if the graph has cluster spanning trees and all vertices self-linked, then the static linear system can realize intra-cluster synchronization. For the time-varying coupling cases, it is proved that if there exists T > 0 such that the union graph across any T-length time interval has cluster spanning trees and all graphs has all vertices self-linked, then the time-varying linear system can also realize intra-cluster synchronization. Under the assumption of common inter-cluster influence, a sort of inter-cluster nonidentical inputs are utilized to realize inter-cluster separation, such that each agent in the same cluster receives the same inputs and agents in different clusters have different inputs. In addition, the boundedness of the infinite sum of the inputs can guarantee the boundedness of the trajectory. As an application, we employ a modified non-Bayesian social learning model to illustrate the effectiveness of our results.

This issue marks the first anniversary issue of IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS after it changed its name from IEEE TRANSACTIONS ON NEURAL NETWORKS. I am happy to report that we had a great year! The number of new submissions in a year exceeded 1,000 for the first time in the history of TNN/TNNLS. IEEE TNN had a very successful development for 22 years from 1990 to 2011, and we have good reasons to believe that IEEE TNNLS will have many more years of successful growth.

In this paper, we discuss pinning consensus in networks of multiagents via impulsive controllers. In particular, we consider the case of using only one impulsive controller. We provide a sufficient condition to pin the network to a prescribed value. It is rigorously proven that in case the underlying graph of the network has spanning trees, the network can reach consensus on the prescribed value when the impulsive controller is imposed on the root with appropriate impulsive strength and impulse intervals. Interestingly, we find that the permissible range of the impulsive strength completely depends on the left eigenvector of the graph Laplacian corresponding to the zero eigenvalue and the pinning node we choose. The impulses can be very sparse, with the impulsive intervals being lower bounded. Examples with numerical simulations are also provided to illustrate the theoretical results.

In this paper, the adaptive Lpregularization is proposed for parameter estimation and variable selection. In particular, we focus on the (0 < p < 1) case when the adaptive Lpregularizer has a nonconvex penalty. Besides some traditional properties for penalized linear regression model, such as unbiasedness and sparsity, we have shown that the adaptive Lpregularization also enjoy the oracle property. A modified iterative algorithm is utilized to solve the adaptive Lp. By comparing with ordinary least square, adaptive lasso and Lp, the numerical results show that the adaptive Lpis more accurate and sparse.

Understanding the dynamics of computer virus (malware, worm) in cyberspace is an important problem that has attracted a fair amount of attention. Early investigations for this purpose adapted biological epidemic models, and thus inherited the so-called homogeneity assumption that each node is equally connected to others. Later studies relaxed this often unrealistic homogeneity assumption, but still focused on certain power-law networks. Recently, researchers investigated epidemic models inarbitrarynetworks (i.e., no restrictions on network topology). However, all these models only capturepush-basedinfection, namely that an infectious node always actively attempts to infect its neighboring nodes. Very recently, the concept ofpull-basedinfection was introduced but was not treated rigorously. Along this line of research, the present article investigates push- and pull-based epidemic spreading dynamics in arbitrary networks, using a nonlinear dynamical systems approach. The article advances the state-of-the-art as follows: (1) It presents a more general and powerful sufficient condition (also known as epidemic threshold in the literature) under which the spreading will become stable. (2) It gives both upper and lower bounds on the global mean infection rate, regardless of the stability of the spreading. (3) It offers insights into, among other things, the estimation of the global mean infection rate through localized monitoring of a smallconstantnumber of nodes,withoutknowing the values of the parameters.

Understanding the spreading dynamics of computer viruses (worms, attacks) is an important research problem, and has received much attention from the communities of both computer security and statistical physics. However, previous studies have mainly focused on single-virus spreading dynamics. In this paper, we study multivirus spreading dynamics, where multiple viruses attempt to infect computers while possibly combating against each other because, for example, they are controlled by multiple botmasters. Specifically, we propose and analyze a general model (and its two special cases) of multivirus spreading dynamics in arbitrary networks (i.e., we do not make any restriction on network topologies), where the viruses may or may not coreside on computers. Our model offers analytical results for addressing questions such as: What are the sufficient conditions (also known as epidemic thresholds) under which the multiple viruses will die out? What if some viruses can "rob” others? What characteristics does the multivirus epidemic dynamics exhibit when the viruses are (approximately) equally powerful? The analytical results make a fundamental connection between two types of factors: defense capability and network connectivity. This allows us to draw various insights that can be used to guide security defense.

In this brief, we discuss some variants of generalized Halanay inequalities that are useful in the discussion of dissipativity and stability of delayed neural networks, integro-differential systems, and Volterra functional differential equations. We provide some generalizations of the Halanay inequality, which is more accurate than the existing results. As applications, we discuss invariant set, dissipative synchronization, and global asymptotic stability for the Hopfield neural networks with infinite delays. We also prove that the dynamical systems with unbounded time-varying delays are globally asymptotically stable.

In this paper, we study the distribution of attraction basins of multiple equilibrium points of cellular neural networks (CNNs). Under several conditions, the boundaries of the attracting basins of the stable equilibria of a completely stable CNN system are composed of the closures of the stable manifolds of unstable equilibria of (n - 1) dimensions. As demonstrations of this idea, under the conditions proposed in the literature which depicts stable and unstable equilibria, we identify the attraction basin of each stable equilibrium of which the boundary is composed of the stable manifolds of the unstable equilibria precisely. We also investigate the attracting basins of a simple class of symmetric 1-D CNNs via identifying the unstable equilibria of which the stable manifold is (n - 1) dimensional and the completely stable asymmetric CNNs with stable equilibria less than 2(n).

Can you retrieve the underlying neuronal network topology which generates an ensemble of desired spiking trains? This is one of the key questions if one wants to implement learning in spiking neuronal network. We propose an approach to solve the question. Our approach ensures that the retrieved spiking neuronal network not only generates the desired spike timing pattern but also has a sparse topology. We analyze the solvability and robustness of our algorithm in details based on the linear programming theory. Two numerical examples are included to illustrate the approach. One example is artificial and the spike trains are generated by a leaky integrate-and-fire neuronal network. The other is from experimental data of the neuronal spikes recorded in hippocampal CA3 area. Our results demonstrate that the approach can provide us with a framework to deal with the learning problem in spiking neuronal networks.

A novel model is proposed to describe the rich dynamics of spiking activities of leaky integrate-and-fire (LIF) neuronal networks via the moment neuronal network approach. Different from the existing neuronal field model (for example, Wilson-Cowan-Amari model) which only takes the first-order moment (mean firing rate) into considerations, we develop a Gaussian random field to qualitatively describe the spatio-temporal distribution of the first- and second-order moments: mean firing rate, variance or coefficient of variation (CV) equivalently, and the coefficient of correlation (CC), of spiking trains. By this neuronal field model, we find out that the firing rate response with respect to the input may be not sigmoidal or even monotonic if the inhibition is stronger than excitation, which leads fruitful dynamical behaviors, in comparison with the sigmoidal response. In addition, within this framework, we can analyse the synchronisation propagation in the LIF neuronal network. We use our Gaussian random field model to investigate how the three key factors: the ratio between inhibition and excitation, the size of synchronous cluster, and the background firing rate, decide the stability of a synfire chain.

In this paper, we are concerned with the multistability of almost periodic solutions of a class of delayed neural networks. We derive conditions guaranteeing 2nasymptotically stable almost periodic trajectories for neural networks with n-neurons. Furthermore, we investigate the attraction basin of each almost periodic solution. Compared with the existing literature, we obtain a more general criteria for the multistability of delayed neural networks and depict the attraction basins more precisely.

In this paper, we propose a new selective pinning strategy, the BC-based pinning strategy, to control a complex network, i.e., placing the local feedback controllers on the vertices with high betweenness centrality (BC). To verify that the stabilizability bounds of a network depend on not only degrees of the pinned vertices, but also the distance between the pinned vertex set and the unpinned vertex set, we pin two real-world networks, the protein-protein network in yeast and the U.S.A. airline routing map, through the BC-based strategy, where the vertices' BC are weakly correlated with their degrees. Since the vertex's BC contain more information with the degree as well as the shortest path, our investigation shows that the former method yields better stabilizability than the latter one.

In this paper, we investigate multistability of almost-periodic solutions of recurrently connected neural networks with delays (simply called delayed neural networks). We will reveal that under some conditions, the space R(n) can be divided into 2(n) subsets, and in each subset, the delayed n-neuron neural network has a locally stable almost-periodic solution. Furthermore, we also investigate the attraction basins of these almost-periodic solutions. We reveal that the attraction basin of almost-periodic trajectory is larger than the subset, where the corresponding almost-periodic trajectory is located. In addition, several numerical simulations are presented to corroborate the theoretical results.

We use the concept of the Filippov solution to study the dynamics of a class of delayed dynamical systems with discontinuous right-hand side, which contains the widely studied delayed neural network models with almost periodic self-inhibitions, interconnection weights, and external inputs. We prove that diagonal-dominant conditions can guarantee the existence and uniqueness of an almost periodic solution, as well as its global exponential stability. As special cases, we derive a series of results on the dynamics of delayed dynamical systems with discontinuous activations and periodic coefficients or constant coefficients, respectively. From the proof of the existence and uniqueness of the solution, we prove that the solution of a delayed dynamical system with high-slope activations approximates to the Filippov solution of the dynamical system with discontinuous activations.

In this letter, without assuming the boundedness of the activation functions, we discuss the dynamics of a class of delayed neural networks with discontinuous activation functions. A relaxed set of sufficient conditions is derived, guaranteeing the existence, uniqueness, and global stability of the equilibrium point. Convergence behaviors for both state and output are discussed. The constraints imposed on the feedback matrix are independent of the delay parameter and can be validated by the linear matrix inequality technique. We also prove that the solution of delayed neural networks with discontinuous activation functions can be regarded as a limit of the solutions of delayed neural networks with high-slope continuous activation functions.

Research of delayed neural networks with varying self-inhibitions, interconnection weights, and inputs is an important issue. In the real world, self-inhibitions, interconnection weights, and inputs should vary as time varies. In this letter, we discuss a large class of delayed neural networks with periodic inhibitions, interconnection weights, and inputs. We prove that if the activation functions are of Lipschitz type and some set of inequalities, for example, the set of inequalities 3.1 in theorem 1, is satisfied, the delayed system has a unique periodic solution, and any solution will converge to this periodic solution. We also prove that if either set of inequalities 3.20 in theorem 2 or 3.23 in theorem 3 is satisfied, then the system is exponentially stable globally. This class of delayed dynamical systems provides a general framework for many delayed dynamical systems. As special cases, it includes delayed Hopfield neural networks and cellular neural networks as well as distributed delayed neural networks with periodic self-inhibitions, interconnection weights, and inputs. Moreover, the entire discussion applies to delayed systems with constant self-inhibitions, interconnection weights, and inputs.

Blind source separation (BSS)/ independent component analysis (ICA) is an emerging research field in both theory and applications. It has been motivated by practical applications that involve multiple source signals and observation sensors and share a common objective, that is to separate source signals and estimate channel parameters without knowing the characteristics of the transmission channel. In this paper, we propose an algorithm, analyze its dynamical behaviors and answer the problem whether the resulting signals are the source signals.

In this paper, without assuming the boundedness, strict monotonicity and differentiability of the activation functions, we utilize a new Lyapunov function to analyze the global convergence of a class of neural networks models with time delays. A new sufficient condition guaranteeing the existence, uniqueness and global exponential stability of the equilibrium point is derived. This stability criterion imposes constraints on the feedback matrices independently of the delay parameters. The result is compared with some previous works. Furthermore, the condition may be less restrictive in the case that the activation functions are hyperbolic tangent.

In this letter, we discuss the dynamics of the Cohen-Grossberg neural networks. We provide a new and relaxed set of sufficient conditions for the Cohen-Grossberg networks to be absolutely stable and exponentially stable globally. We also provide an estimate of the rate of convergence.

We discuss recurrently connected neural networks, investigating their global exponential stability (GES). Some sufficient conditions for a class of recurrent neural networks belonging to GES are given. Sharp convergence rate is given too.