Multilayer networks community detection plays an important role in data mining. It can discover the latent representations of network structures for effectively completing downstream tasks. However, existing community detection methods rarely consider the relationships between multilayer networks. In addition, the noise contained in the networks always leads to the degradation of detection performance. To address the above issues, this article proposes an orthogonal symmetric nonnegative matrix factorization (SNMF) with low-rank tensor representation (OSNMFTR) for multilayer networks community detection. Specifically, the proposed approach obtains the latent representation of each network via orthogonal SNMF, then a clean self-representation tensor is got based on subspace learning. Finally, to discover the high-order relationships among each network, a weighted tensor nuclear norm is utilized to constrain the tensor to make it low-rank. An algorithm based on the alternating direction method of multipliers (ADMMs) is designed to solve the OSNMFTR model. The experiments on nine datasets show the superior performance of the proposed approach.

Text-to-image models based on diffusion models are capable of generating highly realistic images from text descriptions. Nevertheless, in practical applications, the generated images frequently fail to fully satisfy user requirements regarding position and structure due to the absence of detailed location information and complex structural demands in the text descriptions. In order to improve the accuracy of the generated image in position and structure, the introduction of additional control conditions such as keypoint annotations or semantic segmentation has become an important research direction. This paper proposes a novel method based on a lightweight pre-trained diffusion model called CTIGEN-CDM. The model reduces computational costs by pruning the denoising network of the diffusion model and integrates control conditions into the denoising process through a gating mechanism to guide image generation. These control conditions encompass Canny edge detection, HED edge detection, depth maps, keypoints, and semantic segmentation. Experimental results reveal that CTIGEN-CDM possesses excellent generation quality and broad application potential. This method can generate high-quality images with precise positioning and structure while significantly saving computational resources, and it offers a promising new solution for text-to-image generation tasks.

This article investigates a class of systems of nonlinear equations (SNEs). Three distributed neurodynamic models (DNMs), namely a two-layer model (DNM-I) and two single-layer models (DNM-II and DNM-III), are proposed to search for such a system's exact solution or a solution in the sense of least-squares. Combining a dynamic positive definite matrix with the primal-dual method, DNM-I is designed and it is proved to be globally convergent. To obtain a concise model, based on the dynamic positive definite matrix, time-varying gain, and activation function, DNM-II is developed and it enjoys global convergence. To inherit DNM-II's concise structure and improved convergence, DNM-III is proposed with the aid of time-varying gain and activation function, and this model possesses global fixed-time consensus and convergence. For the smooth case, DNM-III's globally exponential convergence is demonstrated under the Polyak-Łojasiewicz (PL) condition. Moreover, for the nonsmooth case, DNM-III's globally finite-time convergence is proved under the Kurdyka-Łojasiewicz (KL) condition. Finally, the proposed DNMs are applied to tackle quadratic programming (QP), and some numerical examples are provided to illustrate the effectiveness and advantages of the proposed models.

This article presents a novel proximal gradient neurodynamic network (PGNN) for solving composite optimization problems (COPs). The proposed PGNN with time-varying coefficients can be flexibly chosen to accelerate the network convergence. Based on PGNN and sliding mode control technique, the proposed time-varying fixed-time proximal gradient neurodynamic network (TVFxPGNN) has fixed-time stability and a settling time independent of the initial value. It is further shown that fixed-time convergence can be achieved by relaxing the strict convexity condition via the Polyak-Lojasiewicz condition. In addition, the proposed TVFxPGNN is being applied to solve the sparse optimization problems with the log-sum function. Furthermore, the field-programmable gate array (FPGA) circuit framework for time-varying fixed-time PGNN is implemented, and the practicality of the proposed FPGA circuit is verified through an example simulation in Vivado 2019.1. Simulation and signal recovery experimental results demonstrate the effectiveness and superiority of the proposed PGNN.

This article presents two innovative matrix neurodynamic approaches (MNAs) designed to tackle the rank minimization problem. First, by introducing the matrix norm-normalized sign function, two variants of MNA are developed: finite-time converging MNA (FINt-MNA) and fixed-time converging MNA (FIXt-MNA). Then, the proposed approaches are shown to guarantee the existence and uniqueness of solutions, and based on Lyapunov analysis, it is demonstrated that the proposed approaches converge to the optimal solution within FINt and FIXt. In addition, upper bounds on the settling time are determined using finite-time and fixed-time lemmas, with subsequent analysis examining the influence of tunable parameters on these bounds for the two approaches through the control variable method. Finally, numerical examples and an image completion experiment confirm the effectiveness and superiority of the proposed approaches compared with the existing MNA and two classical approaches.

Aiming at the situation where the measurement matrix B has a flexible block decomposition, this article designs two novel distributed continuous- and discrete-time projection neurodynamic approaches to solve the basis pursuit (BP) problem for sparse recovery. These approaches only require information from each flexible block of the measurement matrix B, rather than from each row, column, or the entire matrix. First, with the aid of the primal-dual dynamical approach, projection operator, and second-order multiagent consensus condition, a novel distributed projection neurodynamic approach in continuous time (DPNA-CT-B) is proposed, and its optimality and global asymptotic stability are rigorously proved. Moreover, based on the forward and backward Euler methods and variable substitution methods, a corresponding distributed projection neurodynamic approach in discrete time (DPNA-DT-B) is designed. Finally, through sparse signal and image reconstruction experiments, the effectiveness and superiority of the proposed neurodynamic approaches are verified.

This paper studies the bipartite synchronization of signed networks with time-varying delays based on T-S fuzzy system, where the edges between nodes can be positive or negative. Assume that the signed graph of the network is structurally balanced. Firstly, the signed network system is described by T-S fuzzy model and then the control controller is used to control the network nodes, which can facilitate nodes to reach a synchronous state. Then some important lemmas and sufficient conditions are put forward to achieve bipartite synchronization of the signed networks. Finally, a numerical example is presented to certify the rationality of the theoretical results

The current investigation explores the leader-following consensus problem for nonlinear multiagent systems under the output feedback control mechanism and the event-triggered communication mechanism. Owing to the physical instrument constraints, a significant portion of the state variables is not readily available. Therefore, this article put forward a distributed event-based leader-following consensus protocol only using agents' relative output measurements and underlying neighbors. Furthermore, this article develops two event-triggered mechanisms simultaneously, one is the event-triggered communication mechanism in the sensor-to-controller channel, and another is the event-triggered controller update in the controller-to-actuator track. Besides that, it is proven that the developed event-triggered control protocol can settle the leader-following consensus problem of the nonlinear multiagent systems, and the Zeno behavior is excluded in both the channels. Finally, we perform two simulation examples to illustrate the efficacy of the obtained results.

Since the depth information of images facilitates the analysis of the spatial distance of objects in computer vision applications, it is necessary to protect the image depth information. Thus this article proposes a novel red-green-blue-depth (RGB-D) image protection algorithm, which is implemented with the finite-time synchronization (FTS) of neural networks (NNs) with proportional delays via the quantized intermittent control to derive the system synchronization criterion based on Lyapunov stability theory. The performance of RGB-D image protection depends on the synchronization error of the system by driving the system sequence to encrypt the RGB-D image and responding to the system sequence to decrypt the encrypted image. Subsequently, the validity of the proposed criteria is verified by simulation examples, and the practical application of RGB-D image protection is verified.

Sparse optimization problems have been successfully applied to a wide range of research areas, and useful insights and elegant methods for proving the stability and convergence of neurodynamic algorithms have been yielded in previous work. This article develops several neurodynamic algorithms for sparse signal recovery by solving the$\ell _{1}$regularization problem. First, in the framework of the locally competitive algorithm (LCA), modified LCA (MLCA) with finite-time convergence and MLCA with fixed-time convergence are designed. Then, the sliding-mode control (SMC) technique is introduced and modified, i.e., modified SMC (MSMC), which is combined with LCA to design MSMC-LCA with finite-time convergence and MSMC-LCA with fixed-time convergence. It is shown that the solutions of the proposed neurodynamic algorithms exist and are unique under the observation matrix satisfying restricted isometry property (RIP) condition, while finite-time or fixed-time convergence to the optimal points is shown via Lyapunov-based analysis. In addition, combining the notions of finite-time stability (FTS) and fixed-time stability (FxTS), upper bounds on the convergence time of the proposed neurodynamic algorithms are given, and the convergence results obtained for the MLCA and MSMC-LCA with fixed-time convergence are shown to be independent of the initial conditions. Finally, simulation experiments of signal recovery and image recovery are carried out to demonstrate the superior performance of the proposed neurodynamic algorithms.

This article investigates a fully distributed inertial neurodynamic approach for sparse recovery. The approach is based on proximal operators and inertia items. It aims to solve the$L_{1}$-norm minimization problem with consensus and linear observation constraints over directed communication networks. The proposed neurodynamic approach has the advantages of only requiring the communication network to be directed and weight-balanced, does not involve a central processing node and global parameters, which means that no single node can access the entire network and observe it at any time, so it is fully distributed. To effectively deal with the nonsmooth objective function,$L_{1}$-norm, the proximal operator method is used here. For efficiently handling linear observation and consensus constraints, a primal-dual method is applied to the inertial dynamic system. With the aid of maximal monotone operator theory and Baillon-Haddad lemmas, it reveals that the trajectories of our approach can converge to consensus solution at the optimal solution, provided that the distributed parameters satisfy technical conditions. In addition, we aim to demonstrate the weak convergence of the trajectories in our proposed neurodynamic approach toward the zeros of the optimal operator in Hilbert space, using Opial’s lemma. Finally, comparative experiments on sparse signal and image recovery confirm the efficiency and effectiveness of our proposed neurodynamic approach.

In this paper, a novel Field-Programmable-Gate-Array (FPGA) implementation framework based on Lagrange programming neural network (LPNN), projection neural network (PNN) and proximal projection neural network (PPNN) is proposed which can be used to solve smooth and nonsmooth optimization problems. First, Count Unit (CU) and Calculate Unit (CaU) are designed for smooth problems with equality constraints, and these units are used to simulate the iteration actions of neural network (NN) and form a feedback loop with other basic digital circuit operations. Then, the optimal solutions of optimization problems are mapped by the output waveforms. Second, the digital circuit structures of Path Select Unit (PSU), projection operator and proximal operator are further designed to process the box constraints and nonsmooth terms, respectively. Finally, the effectiveness and feasibility of the circuit are verified by three numerical examples on the Quartus II 13.0 sp1 platform with the Cyclone IV E series chip EP4CE10F17C8.

This paper investigates two accelerated primal-dual mirror dynamical approaches for smooth and nonsmooth convex optimization problems with affine and closed, convex set constraints. In the smooth case, an accelerated primal-dual mirror dynamical approach (APDMD) based on accelerated mirror descent and primal-dual framework is proposed and accelerated convergence properties of primal-dual gap, feasibility measure and the objective function value along with trajectories of APDMD are derived by the Lyapunov analysis method. Then, we extend APDMD into two distributed dynamical approaches to deal with two types of distributed smooth optimization problems, i.e., distributed constrained consensus problem (DCCP) and distributed extended monotropic optimization (DEMO) with accelerated convergence guarantees. Moreover, in the nonsmooth case, we propose a smoothing accelerated primal-dual mirror dynamical approach (SAPDMD) with the help of smoothing approximation technique and the above APDMD. We further also prove that primal-dual gap, objective function value and feasibility measure along with trajectories of SAPDMD have the same accelerated convergence properties as APDMD by choosing the appropriate smooth approximation parameters. Later, we propose two smoothing accelerated distributed dynamical approaches to deal with nonsmooth DEMO and DCCP to obtain accelerated and efficient solutions. Finally, numerical and comparative experiments are given to demonstrate the effectiveness and superiority of the proposed accelerated mirror dynamical approaches.

In this paper, two neurodynamic algorithms and the corresponding Field-Programmable-Gate-Array (FPGA) implementation scheme are presented, respectively. Firstly, based on Lagrange programming neural networks (LPNN) and sliding mode control technique, an algorithm with finite-time convergence and an algorithm with fixed-time convergence is proposed and used to solve constrained optimization problems. Then, the Update module, the Control module, the Gradient module, the finite-time processing (FTP) module, and the fixed-time processing (FxTP) module are designed to form an FPGA hardware implementation of neurodynamic optimization algorithms. The LPNN-based FPGA reconfigurable circuit framework can be structured by invoking the Update module, the Control module, and the Gradient module. The FTP module or the FxTP module can be called into the above framework to form the finite-time or fixed-time stable FPGA reconfiguration framework. Finally, the effectiveness and practicality of the proposed FPGA hardware implementation scheme is verified through example simulations implemented on the Vivado 2019.1 platform.

This article proposes a novel fixed-time converging proximal neurodynamic network (FXPNN) via a proximal operator to deal with equilibrium problems (EPs). A distinctive feature of the proposed FXPNN is its better transient performance in comparison to most existing proximal neurodynamic networks. It is shown that the FXPNN converges to the solution of the corresponding EP in fixed-time under some mild conditions. It is also shown that the settling time of the FXPNN is independent of initial conditions and the fixed-time interval can be prescribed, unlike existing results with asymptotical or exponential convergence. Moreover, the proposed FXPNN is applied to solve composition optimization problems (COPs),$l_{1}$-regularized least-squares problems, mixed variational inequalities (MVIs), and variational inequalities (VIs). It is further shown, in the case of solving COPs, that the fixed-time convergence can be established via the Polyak–Lojasiewicz condition, which is a relaxation of the more demanding convexity condition. Finally, numerical examples are presented to validate the effectiveness and advantages of the proposed neurodynamic network.

This article considers constrained nonsmooth generalized convex and strongly convex optimization problems. For such problems, two novel distributed smoothing projection neurodynamic approaches (DSPNAs) are proposed to seek their optimal solutions with faster convergence rates in a distributed manner. First, we equivalently transform the original constrained optimal problem into a standard smoothing distributed problem with only local set constraints based on an exact penalty and smoothing approximation methods. Then, to deal with nonsmooth generally convex optimization, we propose a novel DSPNA based on continuous variant of Nesterov’s acceleration (called DSPNA-N), which has a faster convergence rate$\mathcal {O} ({1}/{t^{2}})$, and we design a novel DSPNA inspired by the continuous variant of Polyak’s heavy ball method (called DSPNA-P) to address the nonsmooth strongly convex optimal problem with an explicit exponential convergent rate. In addition, the existence, uniqueness, and feasibility of the solution of our proposed DSPNAs are also provided. Finally, numerical results demonstrate the effectiveness of DSPNAs.

This letter develops a novel fixed-time stable neurodynamic flow (FTSNF) implemented in a dynamical system for solving the nonconvex, nonsmooth model L1-β2, β∈[0,1] to recover a sparse signal. FTSNF is composed of many neuron-like elements running in parallel. It is very efficient and has provable fixed-time convergence. First, a closed-form solution of the proximal operator to model L1-β2, β∈[0,1] is presented based on the classic soft thresholding of the L1-norm. Next, the proposed FTSNF is proven to have a fixed-time convergence property without additional assumptions on the convexity and strong monotonicity of the objective functions. In addition, we show that FTSNF can be transformed into other proximal neurodynamic flows that have exponential and finite-time convergence properties. The simulation results of sparse signal recovery verify the effectiveness and superiority of the proposed FTSNF.

This article proposes a novel fixed-time converging forward-backward-forward neurodynamic network (FXFNN) to deal with mixed variational inequalities (MVIs). A distinctive feature of the FXFNN is its fast and fixed-time convergence, in contrast to conventional forward-backward-forward neurodynamic network and projected neurodynamic network. It is shown that the solution of the proposed FXFNN exists uniquely and converges to the unique solution of the corresponding MVIs in fixed time under some mild conditions. It is also shown that the fixed-time convergence result obtained for the FXFNN is independent of initial conditions, unlike most of the existing asymptotical and exponential convergence results. Furthermore, the proposed FXFNN is applied in solving sparse recovery problems, variational inequalities, nonlinear complementarity problems, and min-max problems. Finally, numerical and experimental examples are presented to validate the effectiveness of the proposed neurodynamic network.

-minimization problem is proposed, which is based on classic PNN and sliding mode control technique. Furthermore, the proposed network can be used to make sparse signal reconstruction and image reconstruction. First, a sign function is introduced into the PNN model to design fixed-time PNN (FPNN). Then, under the condition that the projection matrix satisfies the restricted isometry property (RIP), the stability and fixed-time convergence of the proposed FPNN are proved by the Lyapunov method. Finally, based on the experimental results of signal simulation and image reconstruction, the proposed FPNN shows the effectiveness and superiority compared with that of the existing PNNs.

This article develops several centralized and collective neurodynamic approaches for sparse signal reconstruction by solving the$L_{1}$-minimization problem. First, two centralized neurodynamic approaches are designed based on the augmented Lagrange method and the Lagrange method with derivative feedback and projection operator. Then, the optimality and global convergence of them are derived. In addition, considering that the collective neurodynamic approaches have the function of information protection and distributed information processing, first, under mild conditions, we transform the$L_{1}$-minimization problem into two network optimization problems. Later, two collective neurodynamic approaches based on the above centralized neurodynamic approaches and multiagent consensus theory are proposed to address the obtained network optimization problems. As far as we know, this is the first attempt to use the collective neurodynamic approaches to deal with the$L_{1}$-minimization problem in a distributed manner. Finally, several comparative experiments on sparse signal and image reconstruction demonstrate that our proposed centralized and collective neurodynamic approaches are efficient and effective.

This paper presents the impulsive average quasi-consensus algorithm for distributed constrained convex optimization. First, the constrained optimization problem can be transformed into an unconstrained problem using the interior point method, and then a distributed algorithm is modeled by means of impulsive differential equation. In the framework of the continuous-time gradient method and algebraic graph theory, each agent can deal with one local objective function with local constraints. At the impulsive instants, each agent can communicate with its neighboring agents over the network. Under certain conditions, the impulsive average quasi-consensus is achieved. It is shown that the state of average quasi-consensus is the optimal solution of the aforementioned unconstrained optimization problem, and the state of each agent can also reach the neighborhood of the optimal solution. Finally, two numerical examples show the effectiveness of the proposed impulsive average quasi-consensus algorithm. Moreover, the feasibility of the approach is verified by an application to one sensor network localization problem.

This paper proposes a novel distributed approach to solve a new dynamic economic dispatch problem (DEDP) in which environmental cost function and ramp rate constraints are taken into consideration in islanded microgrid. In our proposed optimization model, the environmental cost function with E-exponential term and ramp rate constraints are considered to make the optimization problem more practical. Then a novel fully distributed algorithm is proposed to address the DEDP based on the alternating direction method of multipliers (ADMM) and distributed consensus theory of the multiagents system. A Lambert W function is employed to tackle the E-exponential term in the environmental cost function, which is different from most existing papers which discuss the DEDP only with quadratic cost functions. A parallel projection method on account of ADMM is used to deal with the ramp rate constraints in this paper. In addition, the power balance can be guaranteed every time when the sum of initial powder output is equal to the total demand. Therefore, the proposed algorithm can deal with the supply-demand constraints, capacity limit constraints, and ramp rate constraints. Finally, simulations on IEEE14-bus are introduced to further illustrate the effectiveness of the proposed algorithm.

Cloud capability is considered to be extended to the edge of the Internet for improving the security of data transmission. Compressive sensing (CS) has been widely studied as a built-in privacy-preserving layer to provide some cryptographic features while sampling and compressing, including data confidentiality guarantees and data integrity guarantees. Unfortunately, most existing CS-based ciphers are too lightweight or highly complex to meet the requirements of both high security of transmitting the captured data over the Internet and low energy consumption of sensing devices in the Internet of Things (IoT). In this article, a secure transmission framework for CS data by combining CS-based cipher and edge computing is proposed. From the perspective of security, the double-layer encryption mechanism and double-layer authentication mechanism are rooted in it by performing some privacy-preserving operations, including CS-based encryption, CS-based hash, information splitting, strong encryption, and feature extraction. Most significantly, the proposed framework is very useful for resource-limited IoT applications.

This paper considers the cost-driven optimal energy management strategy under a complex environment, multimicrogrids system. To provide the flexibility of load in depth, the heating, ventilating, and air conditioning (HVAC) load is investigated and explicitly formulated incorporated with indoor temperature dynamic function. The operation cost of wind generation includes the basic cost and additional cost to deal with the uncertainty of wind generation, which provides the tradeoff between optimality and possibility. Furthermore, the energy management problem of multimicrogrid is presented according to different characteristics of generation devices, storage devices, and load. A distributed neurodynamic algorithm is presented to solve the nonsmooth optimization of energy management of multimicrogrids system. By this method, the only information exchanged among microgrids is the intermediate variable when computing. The simulation results validate the effectiveness of the proposed cost-driven energy management strategy.

Based on the multiagent networks, this paper introduces a continuous-time algorithm to deal with distributed convex optimization. Using nonsmooth analysis and algebraic graph theory, the distributed network algorithm is modeled by the aid of a nonautonomous differential inclusion, and each agent exchanges information from the first-order and the second-order neighbors. For any initial point, the solution of the proposed network can reach consensus to the set of minimizers if the graph has a spanning tree. In contrast to the existing continuous-time algorithms for distributed optimization, the proposed model holds the least number of state variables and relaxes the strongly connected weighted-balanced topology to the weaker case. The modified form of the proposed continuous-time algorithm is also given, and it is proven that this algorithm is suitable for solving distributed problems if the undirected network is connected. Finally, two numerical examples and an optimal placement problem confirm the effectiveness of the proposed continuous-time algorithm.

In this brief, considering the inertial term into first order neural networks(NNs), an inertial NN(INN) modeled by means of a differential inclusion is proposed for solving linear complementarity problem with P0matrix. Compared with existing NNs, the presence of the inertial term allows us to overcome some drawbacks of many NNs, which are constructed based on the steepest descent method, and this model is more convenient for exploring different optimal solution. It is proved that the proposed NN is stable in the sense of Lyapunov and any equilibrium of our NN is the optimal solution of LCP with P0matrix. Simulation results on two numerical examples show the effectiveness and performance of the proposed neural network.

The resource allocation problem is studied and reformulated by a distributed interior point method via a -logarithmic barrier. By the facilitation of the graph Laplacian, a fully distributed continuous-time multiagent system is developed for solving the problem. Specifically, to avoid high singularity of the -logarithmic barrier at boundary, an adaptive parameter switching strategy is introduced into this dynamical multiagent system. The convergence rate of the distributed algorithm is obtained. Moreover, a novel distributed primal-dual dynamical multiagent system is designed in a smart grid scenario to seek the saddle point of dynamical economic dispatch, which coincides with the optimal solution. The dual decomposition technique is applied to transform the optimization problem into easily solvable resource allocation subproblems with local inequality constraints. The good performance of the new dynamical systems is, respectively, verified by a numerical example and the IEEE six-bus test system-based simulations.

This paper proposes two second-order continuous-time algorithms to solve the economic power dispatch problem in smart grids. The collective aim is to minimize a sum of generation cost function subject to the power demand and individual generator constraints. First, in the framework of nonsmooth analysis and algebraic graph theory, one distributed second-order algorithm is developed and guaranteed to find an optimal solution. As a result, the power demand constraints can be kept all the time under appropriate initial condition. The second algorithm is under a centralized framework, and the optimal solution is robust in the sense that different initial power conditions do not change the convergence of the optimal solution. Finally, simulation results based on five-unit system, IEEE 30-bus system, and IEEE 300-bus system show the effectiveness and performance of the proposed continuous-time algorithms. The examples also show that the convergence rate of second-order algorithm is faster than that of first-order distributed algorithm.

In this paper, a dynamic economic dispatch problem (DEDP) which considers the benefit function, environmental cost function and fuel cost function is studied by the distributed strategy. We propose a distributed algorithm based on undirected graphs and alternating direction method of multipliers (ADMM). Firstly, the DEDP is decomposed into three minimization steps to solve according to ADMM. Secondly, in the first minimization iterative step, with the E exponential term introduced into the environmental cost function and coupling constraint of all generators, we proposed a distributed consensus algorithm with Lambert W function to acquire the values of first minimization iterative step; in the second minimization iterative step, we use ADMM based on parallel projection and distributed consensus strategy to gain the values of it. Based on the above designed, our algorithm is distributed, i.e., all the generators only communicate with their neighbors. Simulation results tested on IEEE14-bus system show that the proposed algorithm is capable of converging to the optimal solution of DEDP.

Various kinds of image sensors capture a large number of images in Internet of Things (IoT) every day. It is increasingly concerned how to securely store and share these big image data from IoT. In this paper, we harness the hybrid cloud to provide secure big image data storage and share service for users. The basic idea is to partition each image into a small set of sensitive data and a large set of insensitive data, which are securely stored in the private cloud and the public cloud, respectively. Specially, the private cloud divides each image into the sensitive data (80%) based on sensitivity identification approaches like Sobel edge detector. The sensitive data are encrypted in parallel at a counter mode and then stored in the private cloud. The insensitive data are encrypted-then-subsampled and then placed in the public cloud, in which the encryption employs the permutation-diffusion architecture and the subsampling utilizes compressed sampling technique. The keystreams used in encryption operations are managed by the tent-logistic system with high initial value sensitivity. Once users make a request for an image, the public cloud provides a privacy-guaranteed insensitive data reconstruction service, and the private cloud decrypts the sensitive and insensitive data and regroups them into a complete image. Experimental results demonstrate that the proposed framework can provide secure big image data service.

Recently, projection neural network (PNN) was proposed for solving monotone variational inequalities (VIs) and related convex optimization problems. In this paper, considering the inertial term into first order PNNs, an inertial PNN (IPNN) is also proposed for solving VIs. Under certain conditions, the IPNN is proved to be stable, and can be applied to solve a broader class of constrained optimization problems related to VIs. Compared with existing neural networks (NNs), the presence of the inertial term allows us to overcome some drawbacks of many NNs, which are constructed based on the steepest descent method, and this model is more convenient for exploring different Karush-Kuhn-Tucker optimal solution for nonconvex optimization problems. Finally, simulation results on three numerical examples show the effectiveness and performance of the proposed NN.

This paper proposes a generalized Hopfield network for solving general constrained convex optimization problems. First, the existence and the uniqueness of solutions to the generalized Hopfield network in the Filippov sense are proved. Then, the Lie derivative is introduced to analyze the stability of the network using a differential inclusion. The optimality of the solution to the nonsmooth constrained optimization problems is shown to be guaranteed by the enhanced Fritz John conditions. The convergence rate of the generalized Hopfield network can be estimated by the second-order derivative of the energy function. The effectiveness of the proposed network is evaluated on several typical nonsmooth optimization problems and used to solve the hierarchical and distributed model predictive control four-tank benchmark.

Synchronization of an array of linearly coupled memristor-based recurrent neural networks with impulses and time-varying delays is investigated in this brief. Based on the Lyapunov function method, an extended Halanay differential inequality and a new delay impulsive differential inequality, some sufficient conditions are derived, which depend on impulsive and coupling delays to guarantee the exponential synchronization of the memristor-based recurrent neural networks. Impulses with and without delay and time-varying delay are considered for modeling the coupled neural networks simultaneously, which renders more practical significance of our current research. Finally, numerical simulations are given to verify the effectiveness of the theoretical results.

Spike-timing-dependent plasticity (STDP) learning ability has been observed in physical memristors, but whether the STDP is caused by the neuron or the memristor is unclear. In this paper, we proved the STDP property in the model for both symmetric and asymmetric memristor. We also employed the symmetric/asymmetric memristors with STDP property and the simplified neurons to perform the STDP learning ability. At last, the sequence learning experiment of the memritive neural network (MNN) with the symmetric memristor synapse further verifies the STDP learning ability of the memristor.

In this brief, based on the method of penalty functions, a recurrent neural network (NN) modeled by means of a differential inclusion is proposed for solving the bilevel linear programming problem (BLPP). Compared with the existing NNs for BLPP, the model has the least number of state variables and simple structure. Using nonsmooth analysis, the theory of differential inclusions, and Lyapunov-like method, the equilibrium point sequence of the proposed NNs can approximately converge to an optimal solution of BLPP under certain conditions. Finally, the numerical simulations of a supply chain distribution model have shown excellent performance of the proposed recurrent NNs.

This brief reports a retarded functional differential equation modeling tri-neuron network with time delay. The Bogdanov-Takens (B-T) bifurcation is investigated by using the center manifold reduction and the normal form method. We get the versal unfolding of the norm forms at the B-T singularity and show that the model can exhibit pitchfork, Hopf, homoclinic, and double-limit cycles bifurcations. Some numerical simulations are given to support the analytic results and explore chaotic dynamics. Finally, an algorithm is given to show that chaotic tri-neuron networks can be used for encrypting a color image.