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In the present, the study on Alzheimer disease is exceptionally important since the number of cases are increasing by almost 10 million every year. According to World Health Organization, Alzheimer disease is one of the major effects of disability and dependency among older people and is currently the seventh leading cause of death among other diseases. There are many experiments conducted by scholars focusing on Alzheimer disease but most of them give little attention to raise awareness on the early detection of Alzheimer disease. Early detection of Alzheimer symptoms can be beneficial to help prevent the development of Alzheimer or slow the progression in people who have symptoms. One of the perspectives that integrate Alzheimer disease in Artificial Intelligence is by using a logic mining model with based Reverse Analysis method that operates in Discrete Hopfield Neural Network. In this paper, a method named Permutation 2 Satisfiability based Reverse Analysis method is implemented to obtain the logical relationship among the factors that contribute towards Alzheimer Disease. The proposed method essentially produces a pattern from analyzing the data and provides an induced logic that represents the possible outcome of the dataset with an average of 95% accuracy. The dataset used in this paper was retrieved from a reputable site of the Alzheimer Disease Neuroimaging Initiative which consists of researchers in the field of dementia science. The investigation shows that several medical factors such as the severity of gross findings in cerebral cortex atrophy, lobar atrophy, and hypopigmentation are highly contributed to the neuropathology in Alzheimer disease classification. [ABSTRACT FROM AUTHOR]

Here, in this paper, the spatial motions of a boundless collisionless electron Vlasov-Poisson gas were considered in a three-dimensional Cartesian coordinate system. Using the replacing of independent variables in the form of hydrodynamic substitution, a transition was made from the kinetic equations to an infinite system of gas-dynamic equations in the "vortex shallow water" and the Boussinesq approximations. In the process of proving the linear instability for the exact stationary solutions to the Vlasov-Poisson equations, the well-known sufficient Newcomb-Gardner-Rosenbluth condition for stability of these solutions with respect to one incomplete unclosed particular class of small spatial perturbations was reversed. An original linear differential second-order inequality with constant coefficients for the Lyapunov functional was also obtained. When the sufficient conditions found in this paper for the linear practical instability of the exact stationary solutions under research are satisfied, an a priori exponential estimate from below for the growth of small three-dimensional perturbations follows from this inequality. Since the estimate was derived without any additional restrictions on the exact stationary solutions under study, then, in this way, the absolute linear instability for the spatial dynamic equilibrium states of the electron Vlasov-Poisson gas with respect to three-dimensional perturbations was proved. [ABSTRACT FROM AUTHOR]

Associative Hopfield Memory is a very useful form of Artificial Neural Networks. This paper outlinesan optimization relaxation approach for signature verification based on the Hopfield neural network (HNN). The standard sample signature of the customer is cross matched with the one supplied on the check. The difference percentage is obtained by calculating the different pixels in both the images. The network topology is built so that each pixel in the difference image is a neuron in the network. Each neuron is categorized by its status, which in turn signifies that if the particular pixel is changed. The network converges to unwavering condition based on theenergy function which is derived in experiments. The Hopfield‟s model allows each node to take on two binary state values (changed/unchanged) for each pixel. The performance of the proposed technique is evaluated by applying it in various binary and gray scale images. This paper contributes to finding an automated scheme for verification of authentic signature on bank check. The derived energy function allows a trade-off between the influence of its neighborhood and its own criterion. This device is able to recall as well as complete partially specified inputs. The network is trained via a storage prescription that forces stable states to correspond to (local)minima of a network "energy" function. [ABSTRACT FROM AUTHOR]

League of Legends (LoL) has been on a rise in becoming an extremely favored multiplayer online battle arena (MOBA) game ever since its release in 2009. This paper presents a logic mining technique to model the results (Win / Lose) of the LoL games played in the professional league of South Korea, most commonly known as LCK. In this research, a method, namely k satisfiability based reverse analysis method (kSATRA) is brought forward to obtain the logical relationship among the gameplays and objectives in the game. The logical rule obtained from the LoL games is used to categorize the results of future games. kSATRA made use of the advantages of Hopfield Neural Network and k Satisfiability representation. The data set used in this study included the data of all 10 teams in LCK, which composed of all games from Spring Season 2018. The effectiveness of kSATRA in obtaining logical rule in LoL games is tested based on root mean square error (RMSE), mean absolute error (MAE) and CPU time. The main issue was to determine the relationship among gameplays or objectives and how they affect the outcome of the game. Results acquired from the computer simulation shows the effectiveness of kSATRA in exhibiting the performance of the LoL teams. [ABSTRACT FROM AUTHOR]

The efficiency of learning algorithm can be improved by introducing propositional satisfiability in Discrete Hopfield Neural Network and modeling the neuron structure of the neural network. To improve the flexibility of logic structure and to meet the requirements of all combinatorial problems, a special satisfiability logic structure is introduced in Discrete Hopfield Neural Network. In this paper, Exhaustive Search was harnessed as the learning algorithm to search the neuron fitness, and a constant learning trial was conducted for the sake of implementation. In order to study the learning mechanism on the special satisfiability logic, we focused on the influence of different learning trials on the structure and evaluated the performance of the model at different phases following the evaluation of indicators. We also analyzed the effect of different learning trials on synaptic weights in learning phase and discussed the quantity and quality of global solutions obtained by the model in testing phase. It has been suggested that the learning mechanism was that the higher the trial value, the better the performance in the learning phase and the testing phase. From the perspective of solution diversity, the learning mechanism embodies better solution diversity in fewer trials. [ABSTRACT FROM AUTHOR]

Logic Satisfiability in conventional Discrete Hopfield Neural Network (DHNN) has suffered major issues such as the high potential to be trapped in suboptimal solutions. This cause problem to the network because suboptimal final neuron state that is trapped in a local minima solution will be disregarded as a potential solution for any given optimization problem. Energy-Based DHNN has the advantage to move the suboptimal final neuron state into a potential global solution. This type of DHNN utilizes temperature to change the position of the solution until the network achieves a global minimum solution. In this paper, we proposed a comprehensive comparison between two conventional energy-based DHNN in doing 2 Satisfiability namely Mean Field Theory DHNN and Boltzmann DHNN. The proposed network will be compared with conventional DHNN using various performance metrics and parameter settings. Finally, results from the experiment suggest that with the right parameter setup, the performance of Boltzmann DHNN are approximately equal to the optimal Mean Field Theory DHNN. [ABSTRACT FROM AUTHOR]

2 Satisfiability (2SAT) is a language that bridges real life application to neural network optimization. 2SAT is an interesting paradigm because the outcome of this logical rule is always positive. Hopfield Neural Network (HNN) is a type of neural network that finds the solution based on energy minimization. Interesting intelligent behavior has been observed when logical rule is embedded to HNN. Increasing the storage capacity during learning phase of HNN has been a challenging problem for most neural network researchers. Ant Colony Optimization (ACO) is a population-based and nature-inspired algorithm to decipher several combinatorial optimization problems. In this paper, metaheuristic algorithm ACO will be proposed in learning 2SAT programming. To this end, all the learning model will be tested in a new restricted learning environment. In circumstances of where HNN model was not given unlimited iteration until all 2SAT clauses were fully satisfied, we would like to determine the better performing search method between exhaustive search and ACO. Results acquired from the computer simulation showed that ACO outperformed exhaustive search in restricted learning environment. [ABSTRACT FROM AUTHOR]

Hopfield Neural Network (HNN) is a sort of neural network that is strongly dependent to energy minimization of solution. Although HNN managed to solve various optimization problem, the output of HNN suffered from a lack of interpretability and variation. This has severely limited the practical usability of HNN in doing logic programming. Inspired by random neuron perturbation, Estimation of Distribution Algorithm (EDA) has been proposed to explore various optimal neuron state. EDAs employs a probabilistic model to sample the neuron state in order to move toward the various optimal location of global minimum energy. In this paper, a new Mutation Hopfield Neural Network (MHNN) will be proposed to do k Satisfiability programming. Based on the experimental result, the proposed MHNN has outperformed conventional HNN in various performance metric. [ABSTRACT FROM AUTHOR]

Developing a data mining model for commodities price plays an important role in future investments and decisions for related companies. Viewed from this perspective, this paper proposes a logic mining model for accurately showcase the behavior of the commodities' price from 2009 until 2018. This model utilizes 2 Satisfiability Reverse Analysis Method (2SATRA) integrated with Hopfield Neural Network (HNN). HNN is a single layered neural network that can be divided into learning and retrieval phase. In this case, the retrieved neuron state from HNN is an important component in 2SATRA. The inputs of the proposed model were realized by using the real commodities such as Palm oil, Latex, Gold, Crude Petroleum, Timber, Black & White Pepper and Cocoa Bean. This model discusses the implication of the 2SATRA model within the context of the discipline as well as practical application. [ABSTRACT FROM AUTHOR]

In this paper we consider an autonomous mechanical system in a finite neighborhood of the zero of the phase space of states. The system is given as a matrix differential equation in the Cauchy form with the right-hand side of the polynomial structure. We propose a method for constructing a sequence of linear inhomogeneous differential inequalities for Lyapunov functions. As a result, we obtain estimates of transient processes in the form of functional inequalities. [ABSTRACT FROM AUTHOR]

Maximum 3-Satisfiability (MAX-3SAT) is a counterpart of the Boolean satisfiability problem that can be treated as a constraint optimization problem. It deals with a conundrum of searching the maximum number of satisfied clauses in a particular 3-SAT formula. This paper presents the implementation of enhanced Hopfield network in hastening the Maximum 3-Satisfiability (MAX-3SAT) logic programming. Four post optimization techniques are investigated, including the Elliot symmetric activation function, Gaussian activation function, Wavelet activation function and Hyperbolic tangent activation function. The performances of these post optimization techniques in accelerating MAX-3SAT logic programming will be discussed in terms of the ratio of maximum satisfied clauses, Hamming distance and the computation time. Dev-C++ was used as the platform for training, testing and validating our proposed techniques. The results depict the Hyperbolic tangent activation function and Elliot symmetric activation function can be used in doing MAX-3SAT logic programming. [ABSTRACT FROM AUTHOR]

In artificial intelligence, the artificial immune system is a robust bio-inspired heuristic method, extensively used in solving many constraint optimization problems, anomaly detection, and pattern recognition. This paper discusses the implementation and performance of artificial immune system (AIS) algorithm integrated with Hopfield neural networks for VLSI circuit configuration based on 3-Satisfiability problems. Specifically, we emphasized on the clonal selection technique in our binary artificial immune system algorithm. We restrict our logic construction to 3-Satisfiability (3-SAT) clauses in order to outfit with the transistor configuration in VLSI circuit. The core impetus of this research is to find an ideal hybrid model to assist in the VLSI circuit configuration. In this paper, we compared the artificial immune system (AIS) algorithm (HNN-3SATAIS) with the brute force algorithm incorporated with Hopfield neural network (HNN-3SATBF). Microsoft Visual C++ 2013 was used as a platform for training, simulating and validating the performances of the proposed network. The results depict that the HNN-3SATAIS outperformed HNN-3SATBF in terms of circuit accuracy and CPU time. Thus, HNN-3SATAIS can be used to detect an early error in the VLSI circuit design. [ABSTRACT FROM AUTHOR]

Clonal Selection Algorithm (CSA) is a sturdy evolutionary algorithm that mimics the biological immune system mechanism, frequently implemented as a searching technique in solving complex modelling tasks such as pattern recognition and combinatorial optimization. Subsequently, 3-Satisfiability logic mining is the fundamental medium to induce real data sets in a more precise manner. In this paper, a modified clonal selection algorithm with Hopfield neural network (HNN) is proposed for 3-Satisfiability data mining. Somatic hypermutation operator in CSA can reduce the iterations during HNN training phase and retrieve the best logical rule for a minimal testing error. In addition, 3- Satisfiability logical rule provides better attributes representation of the data set. The proposed method will be applied on Amazon's Employees Resources Access data set to predict the approval or denial for an unseen set of employees in the future. The performance evaluation of the proposed method will be compared with exhaustive search (ES) by computing plausible errors such as root mean square error (RMSE), mean absolute error (MAE), sum of squared error (SSE), accuracy and computational time. The computational simulations are carried out by manipulating different number of neurons to verify the capability of the proposed method in data mining. The experimental results have shown a better performance of the proposed model in training and retrieval phase of the Amazon's Employees Resources Access data set in comparison with ES used in this research. [ABSTRACT FROM AUTHOR]

The random satisfiability (RAN-SAT) is a problem that decides whether there exists a mapping of truth values to variables that makes a given random Boolean formula satisfiable. This paper gives a brief discussion on artificial neural network, Hopfield neural networks and logic programming integration. It proposed a method of optimizing random satisfiability in Hopfield neural networks based on the model energy minimization scheme. Computer simulation is carried out to demonstrate and verify the feasibility to carrying out random satisfiability in the Hopfield network. [ABSTRACT FROM AUTHOR]

Hyperbolic activation function is examined for its ability to accelerate the performance of doing data mining by using a technique named as Reverse Analysis method. In this paper, we describe how Hopfield network perform better with hyperbolic activation function and able to induce logical rules from large database by using reverse analysis method: given the values of the connections of a network, we can hope to know what logical rules are entrenched in the database. We limit our analysis to Horn clauses. [ABSTRACT FROM AUTHOR]

Reverse analysis method is actually a data mining technique to unearth relationships between data. By knowing the connection strengths by using Hopfield network, we can extract the relationships in data sets. Hopfield networks have recognized that some relaxation schemes have a joined cost function and the states of the network converge to local minima of this function. It had performed optimization of a well-defined function. However, there is no guarantee to find the best minimum in the network. Thus, Boltzmann machine has been introduced to overcome this problem. In this paper, we integrate both approaches to enhance data mining. We limit our work to Horn clauses. [ABSTRACT FROM AUTHOR]

Discrete Hopfield Neural Network (DHNN) is very prominent in the study of Artificial Neural Network (ANN). In the DHNN, systematic logic suffers for interpretability and variation. These issues may be overcome by introducing non-systematic logical rules in the structure of DHNN. In this study, we compare the performance of a non-systematic logical rule and a systematic logical rule. Here, we consider one of the non-systematic logical structures named Random 3 Satisfiability (RAN3SAT) with the logical combination of k=2, 3 and the systematic, logical structure called 2 Satisfiability (2SAT). For example, the Exhaustive Search method incorporates the RAN3SAT and 2SAT with DHNN. To compare better, we employ performance measurements with a fixed number of neurons. The expected outcome of our experiment is that RAN3SAT (the non-systematic logical rule) can outperform 2SAT (the systematic logical rule). This finding will create a better phenomenon in the study of logic programming. [ABSTRACT FROM AUTHOR]

In this paper, we consider H∞ control problem for a class Hopfield neural networks with interval time-varying delay. The time delay is a continuous function belonging to a given interval, but not necessariry differentiable. The stabilizing controllers to be designed must satisfy some exponential stability constraints on the closed-loop poles. Based on the construction of improved Lyapunov-Krasovskii functionals combined with Newton-Leibniz formula. H∞ controller is designed via memoryless state feedback control and new sufficient conditions for the existence of the H∞ state-feedback for the system are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the obtained result. [ABSTRACT FROM AUTHOR]

Logic programming is a superior language because it operates on a higher level of mathematical or logical reasoning. Logic programming is well-suited in building the artificial intelligence systems. In this paper, we reviewed the performance of the logic programming in Hopfield Neural Network (HNN) and Radial Basis Function Neural Network (RBFNN). Logic programming by using the Embedding method will improve the performance of RBFNN. In HNN, the logic programming can be implemented by finding the optimal synaptic weight via Wan Abdullah method. RBFNN is expected to do logic programming optimally compared to HNN. This study gives an overview of HNN and RBFNN regarding architectures, learning processing, and their application in 2 Satisfiability (2SAT) logic programming. Both networks will be assessed based on accuracy, sensitivity, and robustness. Pursuing that, RBFNN is expected to outperform HNN in doing 2 Satisfiability logic programming. [ABSTRACT FROM AUTHOR]

Logic programming is extensively used to describe relations and have both a declarative and an operational meaning. A 3-Satisfiability (3-SAT) program is a class of Boolean Satisfiability problem, where strictly 3 literals per clause are involved. There are various algorithms utilized to solve the 3-Satisfiability logic program. Exhaustive Search (ES) is the standard method, where the algorithm enumerates for every possible iteration to search for a solution. Imperialist Competitive (IC) algorithm, on the other hand, an evolutionary optimization method that is inspired by the imperialistic competition model. Applying the Imperialist Competitive algorithm to 3-Satisfiability logic programming shows its ability in dealing with different types of optimization problems. In this paper, the objective was to compare IC algorithm and ES algorithm in doing 3-SAT logic programming with Hopfield Neural Network (HNN). The performance of both models were evaluated by performance evaluation metrics such as Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Global Minima Ratio and CPU Time. The expected outcome of the experiment is that the IC algorithm outperformed ES in 3-SAT logic programming. [ABSTRACT FROM AUTHOR]

In this paper, an auto-associative neural network using single-electron tunneling (SET) devices is proposed and simulated at low temperature. The nanoelectronic autoassociative network is able to converge to a stable state, previously stored during training. The recognition of the pattern involves decreasing the energy of the input state until it achieves a point of local minimum energy, which corresponds to one of the stored patterns. [ABSTRACT FROM AUTHOR]

This paper proposes an augmented Lagrange Hopfield network (ALHN) for solving economic dispatch (ED) problem in the competitive environment. The proposed ALHN is a continuous Hopfield network with its energy function based on augmented Lagrange function for efficiently dealing with constrained optimization problems. The ALHN method can overcome the drawbacks of the conventional Hopfield network such as local optimum, long computational time, and linear constraints. The proposed method is used for solving the ED problem with two revenue models of revenue based on payment for power delivered and payment for reserve allocated. The proposed ALHN has been tested on two systems of 3 units and 10 units for the two considered revenue models. The obtained results from the proposed methods are compared to those from differential evolution (DE) and particle swarm optimization (PSO) methods. The result comparison has indicated that the proposed method is very efficient for solving the problem. Therefore, the proposed ALHN could be a favorable tool for ED problem in the competitive environment. [ABSTRACT FROM AUTHOR]

This paper proposes augmented Lagrange Hopfield network (ALHN) for solving economic dispatch (ED) problems. The proposed ALHN is a new improvement of continuous Hopfield neural network by using augmented Lagrange function as its energy function. The ALHN is applied for solving different ED problems consisting of classical ED, ED with fuel constraint, ED with piecewise quadratic fuel cost, ED with prohibited operating zones, combined heat and power ED, and ED for hydrothermal systems. The proposed method has been tested on different systems and the obtained results are compared to those from other methods. The result comparison has shown that the proposed ALHN can obtain less total costs and faster computational times than many others. Therefore, ALHN could be a very powerful method for solving the ED problems. [ABSTRACT FROM AUTHOR]

This article focuses on the delay-dependent stability of Hopfield neural networks with time-varying delays. To derive the stability condition, a Lyapunov-Krasovskii functional(LKF) with the necessary conditions is considered, which contains the information of time-delays in the form of double-and triple-integrals. Besides that, some integral inequalities are utilized to estimate the double-and triple-integral terms in the derivative of LKF. Then, the delay-dependent criteria are expressed as linear matrix inequalities. Finally, numerical illustrations are given to justify the competence and potential of the results attained. [ABSTRACT FROM AUTHOR]

Some classes of switched mechanical systems with dissipative and potential forces are considered. The case, where either dissipative or potential forces are essentially nonlinear, is studied. It is assumed that the zero equilibrium position of the system is asymptotically stable at least for one operating mode. We will look for sufficient conditions which guarantee the preservation of asymptotic stability of the equilibrium position under the switching of modes. The Lyapunov direct method is used. A Lyapunov function for considered system is constructed, which satisfies the differential inequality of special form for every operating mode. This inequality is nonlinear for the chosen mode with asymptotically stable equilibrium position, and it is linear for the rest modes. The correlations between the intervals of activity of the pointed mode and the intervals of activity of the rest modes are obtained which guarantee the required properties. [ABSTRACT FROM AUTHOR]

Artificial Neural Networks (ANNs) are dependent on their own structural features. Therefore, the output of ANNs is usually overfitting and requires more diversity of solutions. Due to the restrictive number of literals allowed in each clause, the role of systematic k satisfiability (kSAT) deterred the practical advantages of the logical rule as a symbolic instruction in Discrete Hopfield Neural Network (DHNN). The distribution of negative literals in non-systematic logical structure is often neglected. This has raised a question on the effect of negative literals in non-systematic logic to govern the dynamics of an DHNN. This study proposed a novel non-systematic logical structure, namely Weighted Random 2 Satisfiability (r2SAT) with a various ratio of negative literals. Concerning to negative literals in r2SAT, a logic phase will be introduced to control the distribution of negative literals before resuming to DHNN. A comparative analysis showed r2SAT outperformed existing kSAT in terms of synaptic weight management and variation of final neuron states. [ABSTRACT FROM AUTHOR]

The logical structure of existing systematic satisfiability such as 2 Satisfiability is restricted to two literals per clause and not flexible. As a part of improving this problem, a study of non-systematic satisfiability is significant in logic programming. Therefore, this study introduces non-systematic satisfiability named Major 2 Satisfiability with three different logical structures ranging from first until third-order logic. For the main analysis, Major 2 Satisfiability will be integrated into a discrete Hopfield neural network to investigate the behavior of different logical structures. We will analyze the cost function, the number of global solutions, and neuron variations produced by our proposed model during the training and testing phase. The results show that the logical structures with second and third-order logic produce fewer training errors, consistent global minima solutions, and high neuron variations. We discuss the results in the general model of logic programming in discrete Hopfield neural networks. [ABSTRACT FROM AUTHOR]

Restricted Boolean 2 Satisfiability (2SAT) is a variant of discrete constraint satisfaction problem, commonly being applied with Hopfield neural network (HNN) as logic programming. In recent years, the binary Ant colony optimization has been formulated to solve various satisfaction and optimization problem due to the power onlooker bee phase in attaining the global convergence. The core motivation of this research is to propose a hybrid Hopfield neural network (HNN) incorporated ACO in enhancing the learning phase of new type of 2SAT logic programming. The developed hybrid model will be compared with the other conventional learning method in hybrid HNNs models such as genetic algorithm (GA) and exhaustive search (ES). The simulations were conducted by training and testing the developed model and the other counterparts with randomized simulated data sets. Therefore, the results manifested the capability of ACO in improving the learning phase of HNN as compared with GA and ES under different complexities. [ABSTRACT FROM AUTHOR]

3-Satisfiability Reverse Analysis Method (3SATRA) incorporated with Hopfield neural network is a brand-new approach in extracting the logical rule in the form of 3-Satisfiability (3-SAT) to represent the behavior of a specific medical data set. The motivation of this research is to develop a robust hybrid algorithm to be applied in extracting the information and insights in medical data set. More specifically, 3SATRA is chosen in extracting the insights in term of logical rule from medical data sets. The 3SATRA approach will be combined with 3-SAT logic and HNN as a single data mining paradigm. The proposed method is employed to test and train the medical data set such as Breast Cancer Coimbra and Statlog Heart data set, generated from the standard UCI machine learning repository. The simulation is coded and executed using Dev C++ 5.11 by employing 60% training data and 40% of testing data. The performance of the method was measured based on standard performance metrics such as Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Sum of Squared Error (SSE), accuracy and CPU Time. The overall results show that the effectiveness of the proposed method in processing the medical data, in terms of lower RMSE, MAE, SSE and faster CPU Time. Additionally, the proposed models have achieved high and consistent accuracy after each of execution. [ABSTRACT FROM AUTHOR]

This finding presents a logic mining technique to model student’s performance in terms of specialized attributes. In this study, k Satisfiability based reverse analysis method (kSATRA) will be proposed to extract the logical relationship among key student’s attribute and will be used to classify or project the outcome of the current and future performance trend. The performance of the studied trends was narrowed down to three critical components: difficulties towards assigned subject, the ability to achieve the threshold marks and the decision to continue their study to higher level education. kSATRA is a method that utilized the beneficial feature of Hopfield Neural Network and k Satisfiability representation. The dataset used in this study includes data from several schools which contain insightful features. The robustness of kSATRA in extracting logical rule in student’s performance will be evaluated based on the root mean square error (RMSE), mean absolute error (MAE) and mean percentage error (MAPE). The result obtained from the computer simulation demonstrates the effectiveness of kSATRA in representing the performance of the students. [ABSTRACT FROM AUTHOR]

This finding presents the limitation of traditional Hopfield Neural Network (HNN) in doing 2 Satisfiability problem (2SAT). More precisely, both traditional exhaustive search method (ES) and ant colony optimization (ACO) were proposed in doing 2SAT problem. Both learning method will reduce logical inconsistencies of 2SAT in HNN. Since both learning method will eventually complete the learning phase, the efficiency of both method is difficult to describe. In this study, both learning method will undergo restricted learning environment during learning phase of HNN. The robustness of ACO and ES in doing 2SAT will be evaluated based on root mean square error (RMSE), mean absolute error (MAE) and mean percentage error (MAPE). The results obtained from the computer simulation demonstrates the effectiveness of ACO in doing 2SAT in HNN. [ABSTRACT FROM AUTHOR]

We consider the Hopfield’s graded response neural network in the case when the neurons are subject to a certain impulsive state displacement at fixed moments and the duration of this displacement is not negligible small (they are known as non-instantaneous impulses). We examine the case when the present state of any neuron depends on its maximum value over a past time variable interval. The self-regulating parameters of all units as well as the functions of the connection between two neurons in the network are time varying. The stability of the equilibrium of the model is studied. The study is based on the application of Lyapunov functions. The obtained sufficient conditions are explicitly expressed in terms of the parameters of the system and hence they are easily verifiable. [ABSTRACT FROM AUTHOR]

The construction of Lyapunov-Krasovskii functionals for linear time-delay system depends on so-called Lya-punov matrix. We study the problem of finding this matrix by solving the delay-free equations with specific boundary conditions. The special boundary conditions for the delay-free problem are found and it is shown, that the problem of Lyapunov matrix’ finding as a solution of the boundary value problem with delay and the delay-free problem are equivalent. [ABSTRACT FROM AUTHOR]

Swarm intelligence is a research area that models the population of the swarm based on natural computation. Artificial bee colony (ABC) algorithm is a swarm based metaheuristic algorithm introduced by Karaboga to optimize numerical problem. Pattern-SAT is a pattern reconstruction paradigm that utilized 2SAT logical rule in representing the behavior of the desired pattern. The information of the desired pattern in terms of 2SAT logic is embedded to Hopfield neural network (HNN-P2SAT) and the desired pattern is reconstructed during the retrieval phase. Since the performance of HNN-P2SAT in Pattern-SAT deteriorates when the number of 2SAT clause increased, newly improved ABC is used to reduce the computation burden during the learning phase of HNN-P2SAT (HNN-P2SATABC). The aim of this study is to investigate the performance of Pattern-SAT produced by ABC incorporated with HNN-P2SAT and compare it with conventional standalone HNN. The comparison is examined by using Microsoft Visual Basic C++ 2013 software. The detailed comparison in doing Pattern-SAT is discussed based on global Pattern-SAT, ratio of activated clauses and computation time. The result obtained from computer simulation indicates the beneficial features of HNN-P2SATABC in doing Pattern-SAT. This finding is expected to result in a significant implication on the choice of searching method used to do Pattern-SAT. [ABSTRACT FROM AUTHOR]

Heuristic method was designed for finding optimal solution more quickly compared to classical methods which are too complex to comprehend. In this study, a hybrid approach that utilizes Hopfield network and genetic algorithm in doing maximum 2-Satisfiability problem (MAX-2SAT) was proposed. Hopfield neural network was used to minimize logical inconsistency in interpretations of logic clauses or program. Genetic algorithm (GA) has pioneered the implementation of methods that exploit the idea of combination and reproduce a better solution. The simulation incorporated with and without genetic algorithm will be examined by using Microsoft Visual 2013 C++ Express software. The performance of both searching techniques in doing MAX-2SAT was evaluate based on global minima ratio, ratio of satisfied clause and computation time. The result obtained form the computer simulation demonstrates the effectiveness and acceleration features of genetic algorithm in doing MAX-2SAT in Hopfield network. [ABSTRACT FROM AUTHOR]

The activation function is a dynamic paradigm for doing logic programming in Hopfield neural network. In neural-symbolic integration, the activation function used to metamorphose the activation level of a unit (neuron) into an output signal. The proposed activation function is Bipolar sigmoid activation function. The main goal of this research is to compare and analyze the performance of proposed activation function paradigm with another sign function, namely McCulloch-Pitts function based on Wan Abdullah's method. In this study, we evaluate experimentally the differences between both functions through computer simulations. Computer simulations are conducted to demonstrate the ability of Bipolar sigmoid function and McCulloch-Pitts function doing the logic programming in Hopfield neural network. Microsoft Visual C++ 2013 is used as a platform for training and testing. The performance of Bipolar sigmoid activation function and the McCulloch-Pitts function were discussed holistically by comparing the global minima ratio, Hamming distance and training or computation time. It was proven by computer simulations that the Bipolar sigmoid activation function has a better performance, provides good solutions and achieves an acceptable stability compared to the McCulloch-Pitts function. [ABSTRACT FROM AUTHOR]

Neural field equations (NFE) are used to model the activity of neurons in the brain, it is introduced from a single neuron 'integrate-and-fire model' starting point. The neural continuum is spatially discretized for numerical studies, and the governing equations are modeled as a system of ordinary differential equations. In this article the recurrent neural network approach is used to solve this system of ODEs. This consists of a technique developed by combining the standard numerical method of finite-differences with the Hopfield neural network. The architecture of the net, energy function, updating equations, and algorithms are developed for the NFE model. A Hopfield Neural Network is then designed to minimize the energy function modeling the NFE. Results obtained from the Hopfield-finite-differences net show excellent performance in terms of accuracy and speed. The parallelism nature of the Hopfield approaches may make them easier to implement on fast parallel computers and give them the speed advantage over the traditional methods. [ABSTRACT FROM AUTHOR]