Final epidemic size and critical times for susceptible-infectious-recovered models with a generalized contact rate.

During the spread of an infectious disease, the contact rate or the incidence rate may affect disease characteristics. For simplicity, most disease models assume standard incidence or mass action rates to calculate the basic reproduction number, final epidemic size, and peak time of an epidemic. For standard incidence, the contact rate remains constant resulting in the incidence rate is inversely proportional to the population size, while for the mass action rate, this contact rate is proportional to the total population size resulting in the incidence rate is independent of the population size. In this paper, we consider susceptible-infectious-recovered epidemic models with a generalized contact rate C(N) and a nonlinear incidence rate in view of the behavioral change from susceptible or infectious individuals when an infectious disease appears. The basic reproduction number and the final size equation are derived. The impact of different types of contact rates on them is studied. Moreover, two critical times (peak time and epidemic duration) of an epidemic are considered. Explicit formulas for the peak time and epidemic duration are obtained. These formulas are helpful not only for taking early effective epidemic precautions but also for understanding how the epidemic duration can be changed by acting on the model parameters, especially when the epidemic model is used to make public health policy.

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

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

How to regulate pattern formations for malware propagation in cyber-physical systems.

Malware propagation can be fatal to cyber-physical systems. How to detect and prevent the spatiotemporal evolution of malware is the major challenge we are facing now. This paper is concerned with the control of Turing patterns arising in a malware propagation model depicted by partial differential equations for the first time. From the control theoretic perspective, the goal is not only to predict the formation and evolution of patterns but also to design the spatiotemporal state feedback scheme to modulate the switch of patterns between different modes. The Turing instability conditions are obtained for the controlled malware propagation model with cross-diffusion. Then, the multi-scale analysis is carried out to explore the amplitude equations near the threshold of Turing bifurcation. The selection and stability of pattern formations are determined based on the established amplitude equations. It is proved that the reaction-diffusion propagation model has three types of patterns: hexagonal pattern, striped pattern, and mixed pattern, and selecting the appropriate control parameters can make the pattern transform among the three patterns. The results of the analysis are numerically verified and provide valuable insights into dynamics and control of patterns embedded in reaction-diffusion systems.

Mathematical Analysis of Epidemic Models with Treatment in Heterogeneous Networks.

In this paper, we formulate two different network-based epidemic models to investigate the effect of partly effective treatment on disease dynamics. The first network model represents the individuals with heterogeneous number of contacts in a population as choosing a new partner at each moment, whereas the second one assumes the individuals have fixed or stable neighbors. The basic reproduction number [Formula: see text] is computed for each model, using the next generation matrix method. In particular, the critical treatment rate is defined for the model, above which the disease can be eliminated through the treatment. The final epidemic size relations are derived, and the solvability of these implicit equations is studied. In particular, a unique solution of the implicit equation for the final epidemic size is determined, and by rewriting the implicit equation as a suitable fixed point problem, it is proved that the iteration of the fixed point problem converges to the unique solution. Stochastic simulations and numerical simulations, including in comparison with the model outputs and the joint influence of network topology and treatment on the final epidemic size, are conducted to illustrate the theoretical results.

Fractional order-induced bifurcations in a delayed neural network with three neurons.

This paper reports the novel results on fractional order-induced bifurcation of a tri-neuron fractional-order neural network (FONN) with delays and instantaneous self-connections by the intersection of implicit function curves to solve the bifurcation critical point. Firstly, it considers the distribution of the root of the characteristic equation in depth. Subsequently, it views fractional order as the bifurcation parameter and establishes the transversal condition and stability interval. The main novelties of this paper are to systematically analyze the order as a bifurcation parameter and concretely establish the order critical value through an implicit function array, which is a novel idea to solve the critical value. The derived results exhibit that once the value of the fractional order is greater than the bifurcation critical value, the stability of the system will be smashed and Hopf bifurcation will emerge. Ultimately, the validity of the developed key fruits is elucidated via two numerical experiments.

Observers-based event-triggered adaptive fuzzy backstepping synchronization of uncertain fractional order chaotic systems.

In this paper, for a class of uncertain fractional order chaotic systems with disturbances and partially unmeasurable states, an observer-based event-triggered adaptive fuzzy backstepping synchronization control method is proposed. Fuzzy logic systems are employed to estimate unknown functions in the backstepping procedure. To avoid the explosion of the complexity problem, a fractional order command filter is designed. Simultaneously, in order to reduce the filter error and improve the synchronization accuracy, an effective error compensation mechanism is devised. In particular, a disturbance observer is devised in the case of unmeasurable states, and a state observer is established to estimate the synchronization error of the master-slave system. The designed controller can ensure that the synchronization error converges to a small neighborhood around the origin finally and all signals are semiglobal uniformly ultimately bounded, and meanwhile, it is conducive to avoiding Zeno behavior. Finally, two numerical simulations are given to verify the effectiveness and accuracy of the proposed scheme.

Distributed inertial online game algorithm for tracking generalized Nash equilibria.

This paper is concerned with the distributed generalized Nash equilibrium (GNE) tracking problem of noncooperative games in dynamic environments, where the cost function and/or the coupled constraint function are time-varying and revealed to each agent after it makes a decision. We first consider the case without coupled constraints and propose a distributed inertial online game (D-IOG) algorithm based on the mirror descent method. The proposed algorithm is capable of tracking Nash equilibrium (NE) through a time-varying communication graph and has the potential of achieving a low average regret. With an appropriate non-increasing stepsize sequence and an inertial parameter, the regrets can grow sublinearly if the deviation of the NE sequence grows sublinearly. Second, the time-varying coupled constraints are further investigated, and a modified D-IOG algorithm for tracking GNE is proposed based on the primal-dual and mirror descent methods. Then, the upper bounds of regrets and constraint violation are derived. Moreover, inertia and two information transmission modes are discussed. Finally, two simulation examples are provided to illustrate the effectiveness of the D-IOG algorithms.

Early warning of tipping in a chemical model with cross-diffusion via spatiotemporal pattern formation and transition.

The spatiotemporal pattern formation and transition driven by cross-diffusion of the Gray-Scott model are investigated for the early warning of tipping in this paper. The mathematical analyses of the corresponding non-spatial model and spatial model are performed first, which enable us to have a comprehensive understanding. Then, the linear stability analysis and the multiple scale analysis method exhibit that cross-diffusion is the key mechanism for the evolution of spatiotemporal patterns. Through selecting a cross-diffusion coefficient as the bifurcation parameter, the amplitude equations that can describe structural transition and determine the stability of different types of Turing patterns are derived. Ultimately, numerical simulations verify the validity of the theoretical results. It is demonstrated that in the absence of cross-diffusion, the spatiotemporal distribution of substances is homogeneous. Nevertheless, when the cross-diffusion coefficient exceeds its threshold value, the spatiotemporal distribution of substances will become inhomogeneous in space. As the cross-diffusion coefficient increases, the Turing instability region will be extended, leading to various types of Turing patterns: spots, stripes, and a mixture of spots and stripes.

A Brief Survey of Recent Advances and Methodologies for the Security Control of Complex Cyber-Physical Networks.

Complex cyber-physical networks combine the prominent features of complex networks and cyber-physical systems (CPSs), and the interconnections between the cyber layer and physical layer usually pose significant impacts on its normal operation. Many vital infrastructures, such as electrical power grids, can be effectively modeled as complex cyber-physical networks. Given the growing importance of complex cyber-physical networks, the issue of their cybersecurity has become a significant concern in both industry and academic fields. This survey is focused on some recent developments and methodologies for secure control of complex cyber-physical networks. Besides the single type of cyberattack, hybrid cyberattacks are also surveyed. The examination encompasses both cyber-only hybrid attacks and coordinated cyber-physical attacks that leverage the strengths of both physical and cyber attacks. Then, special focus will be paid to proactive secure control. Reviewing existing defense strategies from topology and control perspectives aims to proactively enhance security. The topological design allows the defender to resist potential attacks in advance, while the reconstruction process can aid in reasonable and practical recovery from unavoidable attacks. In addition, the defense can adopt active switching-based control and moving target defense strategies to reduce stealthiness, increase the cost of attacks, and limit the attack impacts. Finally, conclusions are drawn and some potential research topics are suggested.

Multi-Modal Fake News Detection via Bridging the Gap between Modals.

Multi-modal fake news detection aims to identify fake information through text and corresponding images. The current methods purely combine images and text scenarios by a vanilla attention module but there exists a semantic gap between different scenarios. To address this issue, we introduce an image caption-based method to enhance the model's ability to capture semantic information from images. Formally, we integrate image description information into the text to bridge the semantic gap between text and images. Moreover, to optimize image utilization and enhance the semantic interaction between images and text, we combine global and object features from the images for the final representation. Finally, we leverage a transformer to fuse the above multi-modal content. We carried out extensive experiments on two publicly available datasets, and the results show that our proposed method significantly improves performance compared to other existing methods.

Optimizing protection resource allocation for traffic-driven epidemic spreading.

Optimizing the allocation of protection resources to control the spreading process in networks is a central problem in public health and network security. In this paper, we propose a comprehensive adjustable resource allocation mechanism in which the over allocation of resources can be also numerically reflected and study the effects of this mechanism on traffic-driven epidemic spreading. We observe that an inappropriate resource allocation scheme can induce epidemic spreading, while an optimized heterogeneous resource allocation scheme can significantly suppress the outbreak of the epidemic. The phenomenon can be explained by the role of nodes induced by the heterogeneous network structure and traffic flow distribution. Theoretical analysis also gives an exact solution to the epidemic threshold and reveals the optimal allocation scheme. Compared to the uniform allocation scheme, the increase in traffic flow will aggravate the decline of the epidemic threshold for the heterogeneous resource allocation scheme. This indicates that the uneven resource allocation makes the network performance of suppressing epidemic degrade with the traffic load level. Finally, it is demonstrated that real-world network topology also confirms the results.

FCF: Feature complement fusion network for detecting COVID-19 through CT scan images.

COVID-19 spreads and contracts people rapidly, to diagnose this disease accurately and timely is essential for quarantine and medical treatment. RT-PCR plays a crucial role in diagnosing the COVID-19, whereas computed tomography (CT) delivers a faster result when combining artificial assistance. Developing a Deep Learning classification model for detecting the COVID-19 through CT images is conducive to assisting doctors in consultation. We proposed a feature complement fusion network (FCF) for detecting COVID-19 through lung CT scan images. This framework can extract both local features and global features by CNN extractor and ViT extractor severally, which successfully complement the deficiency problem of the receptive field of the other. Due to the attention mechanism in our designed feature complement Transformer (FCT), extracted local and global feature embeddings achieve a better representation. We combined a supervised with a weakly supervised strategy to train our model, which can promote CNN to guide the VIT to converge faster. Finally, we got a 99.34% accuracy on our test set, which surpasses the current state-of-art popular classification model. Moreover, this proposed structure can easily extend to other classification tasks when changing other proper extractors.

A novel Lyapunov theorem on finite/fixed-time stability of discontinuous impulsive systems.

This paper deals with the Finite/Fixed-Time Stability (FTS) problem of the discontinuous impulsive differential equation. Under the framework on differential inclusion, this problem can be transformed into the FTS problem of impulsive differential inclusion. A uniform criterion on FTS of nonlinear discontinuous impulsive differential systems with pre-given finite impulse instances is established, which is effective for both stabilizing impulses and destabilizing impulses. During this process, we propose an improved Lyapunov method, where the derivative of the Lyapunov Function (LF) may not exist in some instances. Moreover, the upper-bound estimation for the derivative of LF is allowed to be a time-varying function and takes both positive and negative values. Finally, the proposed criterion is supported by two numerical examples.

A novel mathematical approach of COVID-19 with non-singular fractional derivative.

We analyze a proposition which considers new mathematical model of COVID-19 based on fractional ordinary differential equation. A non-singular fractional derivative with Mittag-Leffler kernel has been used and the numerical approximation formula of fractional derivative of function ( t - a ) n is obtained. A new operational matrix of fractional differentiation on domain [0, a], a ≥ 1, a ∈ N by using the extended Legendre polynomial on larger domain has been developed. It is shown that the new mathematical model of COVID-19 can be solved using Legendre collocation method. Also, the accuracy and validity of our developed operational matrix have been tested. Finally, we provide numerical evidence and theoretical arguments that our new model can estimate the output of the exposed, infected and asymptotic carrier with higher fidelity than the previous models, thereby motivating the use of the presented model as a standard tool for examining the effect of contact rate and transmissibility multiple on number of infected cases are depicted with graphs.

An integral sliding mode observer for CPS cyber security attack detection.

Cyber-physical system (CPS) is a next-generation intelligent system integrating computing, communication, and control. As a unit of computing process and physical process, CPS is a new research field, where cooperative adaptive cruise control (CACC) is not only a microcosm of CPS but also a prerequisite for unmanned systems. CACC relies on the wireless communication network technology to achieve cooperative platooning control through vehicle-to-vehicle collaborative control methods. It can improve traffic efficiency and ensure safe driving. Once the wireless network is introduced by each vehicle to exchange information, it is vulnerable to cyber attacks, making attack detection necessary. In this paper, an integral sliding mode observer is designed to monitor malicious attacks. The proposed sliding mode observer not only retains the performance of traditional sliding mode control but also realizes the finite-time observation, avoiding the singular phenomenon that may occur in the traditional terminal sliding mode.

Fully Convolutional Network-Based Multifocus Image Fusion.

As the optical lenses for cameras always have limited depth of field, the captured images with the same scene are not all in focus. Multifocus image fusion is an efficient technology that can synthesize an all-in-focus image using several partially focused images. Previous methods have accomplished the fusion task in spatial or transform domains. However, fusion rules are always a problem in most methods. In this letter, from the aspect of focus region detection, we propose a novel multifocus image fusion method based on a fully convolutional network (FCN) learned from synthesized multifocus images. The primary novelty of this method is that the pixel-wise focus regions are detected through a learning FCN, and the entire image, not just the image patches, are exploited to train the FCN. First, we synthesize 4500 pairs of multifocus images by repeatedly using a gaussian filter for each image from PASCAL VOC 2012, to train the FCN. After that, a pair of source images is fed into the trained FCN, and two score maps indicating the focus property are generated. Next, an inversed score map is averaged with another score map to produce an aggregative score map, which take full advantage of focus probabilities in two score maps. We implement the fully connected conditional random field (CRF) on the aggregative score map to accomplish and refine a binary decision map for the fusion task. Finally, we exploit the weighted strategy based on the refined decision map to produce the fused image. To demonstrate the performance of the proposed method, we compare its fused results with several start-of-the-art methods not only on a gray data set but also on a color data set. Experimental results show that the proposed method can achieve superior fusion performance in both human visual quality and objective assessment.

Edge-based epidemic spreading in degree-correlated complex networks.

Networks that grow through the addition of new nodes or edges may acquire degree-degree correlations. When one considers a short epidemic on a slowly growing network, such as the spread of a strain of influenza in a population for one season, it is reasonable to assume that the degree-correlated network is static during the course of an epidemic. In this case using only information about the network degree distribution is not enough to capture the exponential growth phase, the epidemic peak or the final epidemic size. Hence, in this paper we formulate an edge-based SIR epidemic model on degree-correlated networks, which includes the Miller model on configuration networks as a special case. The model is relatively low-dimensional; in particular, considering the fact that it captures degree correlations. Moreover, we derive rate equations to compute two node degree correlations in a growing network. Predictions of our model agree well with the corresponding stochastic SIR process on degree-correlated networks, such as the exponential growth phase, the epidemic peak and the final epidemic size. The basic reproduction number R0 and the final epidemic size are theoretically derived, which are equivalent to those based on the percolation theory. However, our model has the advantage that it can trace the dynamic spread of an epidemic on degree-correlated networks. This provides us with more accurate information to predict and control the spread of diseases in growing populations with biased-mixing. Finally, our model is tested on degree-correlated networks with clustering, and it is shown that our model is robust to degree-correlated networks with small clustering.

Synchronization in Fractional-Order Complex-Valued Delayed Neural Networks.

This paper discusses the synchronization of fractional order complex valued neural networks (FOCVNN) at the presence of time delay. Synchronization criterions are achieved through the employment of a linear feedback control and comparison theorem of fractional order linear systems with delay. Feasibility and effectiveness of the proposed system are validated through numerical simulations.

Lag Synchronization Criteria for Memristor-Based Coupled Neural Networks via Parameter Mismatches Analysis Approach.

This letter focuses on lag synchronization control analysis for memristor-based coupled neural networks with parameter mismatches. Due to the parameter mismatches, lag complete synchronization in general cannot be achieved. First, based on the [Formula: see text]-measure method, generalized Halanay inequality, together with control algorithms, some sufficient conditions are obtained to ensure that coupled memristor-based neural networks are in a state of lag synchronization with an error. Moreover, the error level is estimated. Second, we show that memristor-based coupled neural networks with parameter mismatches can reach lag complete synchronization under a discontinuous controller. Finally, two examples are given to illustrate the effectiveness of the proposed criteria and well support theoretical results.

Sampled-Data State Feedback Stabilization of Boolean Control Networks.

In this letter, we investigate the sampled-data state feedback control (SDSFC) problem of Boolean control networks (BCNs). Some necessary and sufficient conditions are obtained for the global stabilization of BCNs by SDSFC. Different from conventional state feedback controls, new phenomena observed the study of SDSFC. Based on the controllability matrix, we derive some necessary and sufficient conditions under which the trajectories of BCNs can be stabilized to a fixed point by piecewise constant control (PCC). It is proved that the global stabilization of BCNs under SDSFC is equivalent to that by PCC. Moreover, algorithms are given to construct the sampled-data state feedback controllers. Numerical examples are given to illustrate the efficiency of the obtained results.