Search Results (98)

In this digital era, social images are the most vital information carrier on multimedia social platforms. More and more users are interested in sharing social images with mobile terminals on multimedia social platforms. Social image sharing also faces potential risks from malicious use, such as illegal sharing, piracy, and misappropriation. This paper mainly concentrates on secure social image sharing. To address how to share social images in a safe way, a social image security scheme is proposed. The technology addresses the social image security problem and the active tracing problem. First, discrete wavelet transform (DWT) is performed directly from the JPEG image. Then, the high-bit planes of the LL, LH, and HL are permuted with cellular automation (CA), bit-XOR, and singular value decomposition (SVD) computing, and their low-bit planes are chosen to embed a watermark. In the end, the encrypted and watermarked image is again permuted with cellular automation in the discrete cosine transform (DCT) domain. Experimental results and security analysis show that the social image security method not only has good performance in robustness, security, and time complexity but can also actively trace the illegal distribution of social images. The proposed social image security method can provide double-level security for multimedia social platforms. Full article

This manuscript introduces a simple third-order Hopfield neural network. Its dynamics, implementation with a microcontroller and application to random number generation are explored. The model includes three coupled neurons with no synaptic weights between the first neuron and the third, and between the third and the second. The fundamental features (i.e., symmetry, dissipation and the requirement of existence of an attractor) of the model are studied. The results suggest that the model is asymmetric, dissipative and capable of supporting attractors. The dynamic analysis of the model is conducted through computer explorations, and the findings reveal that it develops complex behaviors like chaos and the coexistence of patterns. The coexistence of patterns is controlled using the linear augmentation method. The coexisting patterns are destroyed, and the multistable system is transformed into a monostable one. In order to confirm the numerical findings, a microcontroller implementation of the considered HNN model is carried out, and the findings of both approaches are concordant. Finally, the elaborated third-order HNN chaotic model is designed for random number generation application. The NIST statistical tests are provided in order to confirm the random features of the generated signals. Full article

Neurons in the brain are interconnected through synapses. Local active memristors can both simulate the synaptic behavior of neurons and the action potentials of neurons. Currently, the hyperbolic tangent function-type memristors used for coupling neural networks do not belong to local active memristors. To take advantage of local active memristors and consider the multi-equilibrium point problem, a cosine function is introduced into the state equation, resulting in the design of an absolute value hyperbolic tangent-type double local active memristor, and it is used as a coupling synapse to replace a synaptic weight in a 3-neuron HNN. Then, basic dynamical analysis methods are used to study the effects of different memristor synapse coupling strengths and different initial conditions on the dynamics of the neural network. The research results indicate that dynamical behavior of memristor Hopfield neural network is closely related to the synaptic coupling strengths and the initial conditions, and this neural network exhibits rich dynamical behaviors, including the coexistence of chaotic and periodic attractors, super-multistability phenomena, etc. Finally, the neural network was implemented using an FPGA development board, verifying the hardware feasibility of this system. Full article

Locally active memristors with an Edge-of-Chaos kernel (EOCK) represent a significant advancement in the simulation of neuromorphic dynamics. However, current research on memristors with an EOCK remains at the circuit level, without further analysis of their feasibility. In this context, we designed a memristor and installed it in a third-order circuit, where it showed local activity and stability under defined voltage and inductance parameters. This behavior ensured that by varying the input voltage and inductance, the memristor could effectively simulate various neural activities, including inhibitory postsynaptic potential and chaotic waveforms. By subsequently integrating the memristor with an EOCK into a Hopfield neural network (HNN) framework and substituting the self-coupling weight, we observed a rich spectrum of dynamic behaviors, including the rare phenomenon of antimonotonicity bubble bifurcation. Finally, we used hardware circuits to realize these generated dynamic phenomena, confirming the feasibility of the memristor. By introducing the HNN and studying its dynamic behavior and hardware circuit implementation, this study provides theoretical insights into and an empirical basis for developing circuits and systems that replicate the complexity of human brain functions. This study provides a reference for the development and application of EOCK in the future. Full article

The Hopfield Recurrent Neural Network (HRNN) is a single-point descent metaheuristic that uses a single potential solution to explore the search space of optimization problems, whose constraints and objective function are aggregated into a typical energy function. The initial point is usually randomly initialized, then moved by applying operators, characterizing the discrete dynamics of the HRNN, which modify its position or direction. Like all single-point metaheuristics, HRNN has certain drawbacks, such as being more likely to get stuck in local optima or miss global optima due to the use of a single point to explore the search space. Moreover, it is more sensitive to the initial point and operator, which can influence the quality and diversity of solutions. Moreover, it can have difficulty with dynamic or noisy environments, as it can lose track of the optimal region or be misled by random fluctuations. To overcome these shortcomings, this paper introduces a population-based fuzzy version of the HRNN, namely Gaussian Takagi–Sugeno Hopfield Recurrent Neural Network (G-TS-HRNN). For each neuron, the G-TS-HRNN associates an input fuzzy variable of d values, described by an appropriate Gaussian membership function that covers the universe of discourse. To build an instance of G-TS-HRNN(s) of size s, we generate s n-uplets of fuzzy values that present the premise of the Takagi–Sugeno system. The consequents are the differential equations governing the dynamics of the HRNN obtained by replacing each premise fuzzy value with the mean of different Gaussians. The steady points of all the rule premises are aggregated using the fuzzy center of gravity equation, considering the level of activity of each rule. G-TS-HRNN is used to solve the random optimization method based on the support vector model. Compared with HRNN, G-TS-HRNN performs better on well-known data sets. Full article

Memristor-based fractional-order chaotic systems can record information from the past, present, and future, and describe the real world more accurately than integer-order systems. This paper proposes a novel memristor model and verifies its characteristics through the pinched loop (PHL) method. Subsequently, a new fractional-order memristive Hopfield neural network (4D-FOMHNN) is introduced to simulate induced current, accompanied by Caputo’s definition of fractional order. An Adomian decomposition method (ADM) is employed for system solution. By varying the parameters and order of the 4D-FOMHNN, rich dynamic behaviors including transient chaos, chaos, and coexistence attractors are observed using methods such as bifurcation diagrams and Lyapunov exponent analysis. Finally, the proposed FOMHNN system is implemented on a field-programmable gate array (FPGA), and the oscilloscope observation results are consistent with the MATLAB numerical simulation results, which further validate the theoretical analysis of the FOMHNN system and provide a theoretical basis for its application in the field of encryption. Full article

Systems of incommensurate delay fractional differential equations (DFDEs) with non-vanishing constant delay of retarded type are investigated. It is shown that the mild solutions are well-posed in Hadamard sense on the space of continuous functions. The analysis is local and carried out for finite intervals. The strong results are obtained with weak conditions by using state-of-the-art new methods. No condition on the Lipschitz parameter is added for well-posedness results. Application of this theorem for the Hopfield neural network is carried out. Full article

Memristors have become important components in artificial synapses due to their ability to emulate the information transmission and memory functions of biological synapses. Unlike their biological counterparts, which adjust synaptic weights, memristor-based artificial synapses operate by altering conductance or resistance, making them useful for enhancing the processing capacity and storage capabilities of neural networks. When integrated into systems like Hopfield neural networks, memristors enable the study of complex dynamic behaviors, such as chaos and multistability. Moreover, fractional calculus is significant for their ability to model memory effects, enabling more accurate simulations of complex systems. Fractional-order Hopfield networks, in particular, exhibit chaotic and multistable behaviors not found in integer-order models. By combining memristors with fractional-order Hopfield neural networks, these systems offer the possibility of investigating different dynamic phenomena in artificial neural networks. This study investigates the dynamical behavior of a fractional-order Hopfield neural network (HNN) incorporating a memristor with a piecewise segment function in one of its synapses, highlighting the impact of fractional-order derivatives and memristive synapses on the stability, robustness, and dynamic complexity of the system. Using a network of four neurons as a case study, it is demonstrated that the memristive fractional-order HNN exhibits multistability, coexisting chaotic attractors, and coexisting limit cycles. Through spectral entropy analysis, the regions in the initial condition space that display varying degrees of complexity are mapped, highlighting those areas where the chaotic series approach a pseudo-random sequence of numbers. Finally, the proposed fractional-order memristive HNN is implemented on a Field-Programmable Gate Array (FPGA), demonstrating the feasibility of real-time hardware realization. Full article

The continuous Hopfield network (CHN) is a common recurrent neural network. The CHN tool can be used to solve a number of ranking and optimization problems, where the equilibrium states of the ordinary differential equation (ODE) related to the CHN give the solution to any given problem. Because of the non-local characteristic of the “infinite memory” effect, fractional-order (FO) systems have been proved to describe more accurately the behavior of real dynamical systems, compared to the model’s ODE. In this paper, a fractional-order variant of a Hopfield neural network is introduced to solve a Quadratic Knap Sac Problem (QKSP), namely the fractional CHN (FRAC-CHN). Firstly, the system is integrated with the quadratic method for fractional-order equations whose trajectories have shown erratic paths and jumps to other basin attractions. To avoid these drawbacks, a new algorithm for obtaining an equilibrium point for a CHN is introduced in this paper, namely the optimal fractional CHN (OPT-FRAC-CHN). This is a variable time-step method that converges to a good local minima in just a few iterations. Compared with the non-variable time-stepping CHN method, the optimal time-stepping CHN method (OPT-CHN) and the FRAC-CHN method, the OPT-FRAC-CHN method, produce the best local minima for random CHN instances and for the optimal feeding problem. Full article

The memristor, a revolutionary electronic component, mimics both neural synapses and electromagnetic induction phenomena. Recent study challenges are the development of effective neural models and discovering their dynamics. In this study, we propose a novel Hopfield neural network model leveraging multistable memristors, showcasing its efficacy in encoding biomedical images. We investigate the equilibrium states and dynamic behaviors of our designed model through comprehensive numerical simulations, revealing a rich array of phenomena including periodic orbits, chaotic dynamics, and homogeneous coexisting attractors. The practical realization of our model is achieved using a microcontroller, with experimental results demonstrating strong agreement with theoretical analyses. Furthermore, harnessing the chaos inherent in the neural network, we develop a robust biomedical image encryption technique, validated through rigorous computational performance tests. Full article

The purpose of this paper is to study the dynamics of Hopfield neural networks with impulsive effects, focusing on Poisson stable rates, synaptic connections, and unpredictable external inputs. Through the symmetry of impulsive and differential compartments of the model, we follow and extend the principal dynamical ideas of the founder. Specifically, the research delves into the phenomena of unpredictability and Poisson stability, which have been examined in previous studies relating to models of continuous and discontinuous neural networks with constant components. We extend the analysis to discontinuous models characterized by variable impulsive actions and structural ingredients. The method of included intervals based on the B-topology is employed to investigate the networks. It is a novel approach that addresses the unique challenges posed by the sophisticated recurrence. Full article

The electro-hydraulic servo system has advantages such as high pressure, large flow, and high power, etc., which can also realize stepless regulation, so it is widely used in many engineering machineries. A linear model is sometimes only a simple approximation of an idealized model, but in an actual system, there may be nonlinear and transient variation characteristics in the systems. Coupling is reflected in the fact that the components or functional structures implemented by each system used for the design of hydraulic systems are not completely or independently related to each other, but affect each other. The nonlinear clearance between the actuator and the load reduces the control accuracy of the system and increases the impact, thus losing stable working conditions. In the paper, based on the nonlinear clearance problem of the electro-hydraulic servo system, a mathematical transfer model with clearance is established, and on this basis, a clearance compensation method based on the Hopfield neural network is proposed. In this way, clearance compensation can be realized by adjusting the parameters of neural network nodes, through simple and convenient operation. Finally, by setting different clearance values, the results of the step response and sine response curve before and after clearance compensation of the hydraulic system are compared, and the effectiveness of Hopfield neural network compensation clearance control is verified based on the comparison simulation results. Full article

Uncovering the mechanisms behind long-term memory is one of the most fascinating open problems in neuroscience and artificial intelligence. Artificial associative memory networks have been used to formalize important aspects of biological memory. Generative diffusion models are a type of generative machine learning techniques that have shown great performance in many tasks. Similar to associative memory systems, these networks define a dynamical system that converges to a set of target states. In this work, we show that generative diffusion models can be interpreted as energy-based models and that, when trained on discrete patterns, their energy function is (asymptotically) identical to that of modern Hopfield networks. This equivalence allows us to interpret the supervised training of diffusion models as a synaptic learning process that encodes the associative dynamics of a modern Hopfield network in the weight structure of a deep neural network. Leveraging this connection, we formulate a generalized framework for understanding the formation of long-term memory, where creative generation and memory recall can be seen as parts of a unified continuum. Full article

The primary objective of introducing metaheuristic algorithms into traditional systematic logic is to minimize the cost function. However, there is a lack of research on the impact of introducing metaheuristic algorithms on the cost function under different proportions of positive literals. In order to fill in this gap and improve the efficiency of the metaheuristic algorithm in systematic logic, we proposed a metaheuristic algorithm based on mutation tabu search and embedded it in probabilistic satisfiability logic in discrete Hopfield neural networks. Based on the traditional tabu search algorithm, the mutation operators of the genetic algorithm were combined to improve its global search ability during the learning phase and ensure that the cost function of the systematic logic converged to zero at different proportions of positive literals. Additionally, further optimization was carried out in the retrieval phase to enhance the diversity of solutions. Compared with nine other metaheuristic algorithms and exhaustive search algorithms, the proposed algorithm was superior to other algorithms in terms of time complexity and global convergence, and showed higher efficiency in the search solutions at the binary search space, consolidated the efficiency of systematic logic in the learning phase, and significantly improved the diversity of the global solution in the retrieval phase of systematic logic. Full article

The digital elevation model (DEM) and its derived morphometric factors, i.e., slope, aspect, profile and plan curvatures, and topographic wetness index (TWI), are essential for natural hazard modeling and prediction as they provide critical information about the terrain’s characteristics that can influence the likelihood and severity of natural hazards. Therefore, increasing the accuracy of the DEM and its derived factors plays a critical role. The primary aim of this study is to evaluate and compare the effects of resampling and downscaling the DEM from low to medium resolution and from medium to high resolutions using four methods: namely the Hopfield Neural Network (HNN), Bilinear, Bicubic, and Kriging, on five morphometric factors derived from it. A geospatial database was established, comprising five DEMs with different resolutions: specifically, a SRTM DEM with 30 m resolution, a 20 m resolution DEM derived from topographic maps at a scale of 50,000, a 10 m resolution DEM generated from topographic maps at a scale of 10,000, a 5 m resolution DEM created using surveying points with total stations, and a 5 m resolution DEM constructed through drone photogrammetry. The accuracy of the resampling and downscaling was assessed using Root Mean Square Error (RMSE) and mean absolute error (MAE) as statistical metrics. The results indicate that, in the case of downscaling from low to medium resolution, all four methods—HNN, Bilinear, Bicubic, and Kriging—significantly improve the accuracy of slope, aspect, profile and plan curvatures, and TWI. However, for the case of medium to high resolutions, further investigations are needed as the improvement in accuracy observed in the DEMs does not necessarily translate to the improvement of the second derivative morphometric factors such as plan and profile curvatures and TWI. While RMSEs of the first derivatives of DEMs, such as slope and aspect, reduced in a range of 8% to 55% in all five datasets, the RMSEs of curvatures and TWI slightly increased in cases of downscaling and resampling of Dataset 4. Among the four methods, the HNN method provides the highest accuracy, followed by the bicubic method. The statistics showed that in all five cases of the experiment, the HNN downscaling reduced the RMSE and MAE by 55% for the best case and 10% for the worst case for slope, and it reduced the RMSE by 50% for the best case of aspect. Both the HNN and the bicubic methods outperform the Kriging and bilinear methods. Therefore, we highly recommend using the HNN method for downscaling DEMs to produce more accurate morphometric factors, slope, aspect, profile and plan curvatures, and TWI. Full article