Optimal competitive hopfield network with stochastic dynamics for maximum cut problem

In this paper, introducing stochastic dynamics into an optimal competitive Hopfield network model (OCHOM), we propose a new algorithm that permits temporary energy increases which helps the OCHOM escape from local minima. The goal of the maximum cut problem, which is an NP-complete problem, is to partition the node set of an undirected graph into two parts in order to maximize the cardinality of the set of edges cut by the partition. The problem has many important applications including the design of VLSI circuits and design of communication networks. Recently, Galán-Marín et al. proposed the OCHOM, which can guarantee convergence to a global/local minimum of the energy function, and performs better than the other competitive neural approaches. However, the OCHOM has no mechanism to escape from local minima. The proposed algorithm introduces stochastic dynamics which helps the OCHOM escape from local minima, and it is applied to the maximum cut problem. A number of instances have been simulated to verify the proposed algorithm.     

An artificial maximum neural network: a winner-take-all neuron model forcing the state of the system in a solution domain

A maximum neuron model is proposed in order to force the state of the system to converge to the solution in neural dynamics. The state of the system is always forced in a solution domain. The artificial maximum neural network is used for the module orientation problem and the bipartite subgraph problem. The usefulness of the maximum neural network is empirically demonstrated by simulating randomly generated massive nstances (examples) in both problems. In randomly generated more than one thousand instances our system always converges to the solution within one hundred iteration steps regardless of the problem size. Our simulation results show the effectiveness of our algorithms and support our claim that one class of NP-complete problems may be solvable in a polynomial time.     

A flexible annealing chaotic neural network to maximum clique problem

Based on the analysis and comparison of several annealing strategies, we present a flexible annealing chaotic neural network which has flexible controlling ability and quick convergence rate to optimization problem. The proposed network has rich and adjustable chaotic dynamics at the beginning, and then can converge quickly to stable states. We test the network on the maximum clique problem by some graphs of the DIMACS clique instances, p-random and k random graphs. The simulations show that the flexible annealing chaotic neural network can get satisfactory solutions at very little time and few steps. The comparison between our proposed network and other chaotic neural networks denotes that the proposed network has superior executive efficiency and better ability to get optimal or near-optimal solution.     

An improved transiently chaotic neural network for the maximum independent set problem

By analyzing the dynamic behaviors of the transiently chaotic neural network and greedy heuristic for the maximum independent set (MIS) problem, we present an improved transiently chaotic neural network for the MIS problem in this paper. Extensive simulations are performed and the results show that this proposed transiently chaotic neural network can yield better solutions to p-random graphs than other existing algorithms. The efficiency of the new model is also confirmed by the results on the complement graphs of some DIMACS clique instances in the second DIMACS challenge. Moreover, the improved model uses fewer steps to converge to stable state in comparison with the original transiently chaotic neural network.     

K-way neural network graph partitioning with separator vertices

A neural network for partitioning graphs into any number of subgraphs using a k-way procedure is presented. The resulting neural network optimises all subgraphs so that they contain approximately the same number of vertices with the exception of a `separator' subgraph. The latter separates all the other subgraphs and is optimised to contain a minimum number of vertices. Expressions for the neuron link weights for such a network are derived analytically, and the recall mechanism of the mean field theorem neural network is used to obtain the graph partitioning. Applications focus on partitioning graphs associated with finite element meshes which, together with parallel domain decomposition solution methods, provide the motivation for this work. Received: 14 January 1998 / Accepted in revised form: 24 November 1998     

An approach to improve Wang-Smith chaotic simulated annealing

Previous research shows that Wang-Smith chaotic simulated annealing, which employs a gradually decreasing time-step, has only a scaling effect to computational energy of the Hopfield model without changing its shape. This makes the net has sensitive dependence on the value of damping factor. Considering Chen-Aihara chaotic simulated annealing with decaying self-coupling has a shape effect to computational energy of the Hopfield model, a novel approach to improve Wang-Smith chaotic simulated annealing, which reaps the benefits of Wang-Smith model and Chen-Aihara model, is proposed in this paper. With the aid of this method the improved model can affect on computational energy of the Hopfield model from scaling and shape. By adjusting the time-step, the improved neural network can also pass from a chaotic to a non-chaotic state. From numerical simulation experiments, we know that the improved model can escape from local minima more efficiently than original Wang-Smith model.     

Parallel Clustering Algorithm for Large Data Sets with Applications in Bioinformatics

Large sets of bioinformatical data provide a challenge in time consumption while solving the cluster identification problem, and that is why a parallel algorithm is so needed for identifying dense clusters in a noisy background. Our algorithm works on a graph representation of the data set to be analyzed. It identifies clusters through the identification of densely intraconnected subgraphs. We have employed a minimum spanning tree (MST) representation of the graph and solve the cluster identification problem using this representation. The computational bottleneck of our algorithm is the construction of an MST of a graph, for which a parallel algorithm is employed. Our high-level strategy for the parallel MST construction algorithm is to first partition the graph, then construct MSTs for the partitioned subgraphs and auxiliary bipartite graphs based on the subgraphs, and finally merge these MSTs to derive an MST of the original graph. The computational results indicate that when running on 150 CPUs, our algorithm can solve a cluster identification problem on a data set with 1,000,000 data points almost 100 times faster than on single CPU, indicating that this program is capable of handling very large data clustering problems in an efficient manner. We have implemented the clustering algorithm as the software CLUMP.     

A simulation method for the firing sequences of motor units.

The firing sequences of motoneurons contain important information with regard to the underlying neural processes. Several methods have been proposed in the literature to simulate these sequences, however, one of the limitations is that they are not capable of simulating the complex neural dynamics of motor neurons, especially those of concurrently active ones, such as motor unit synchrony and motor unit common drive. In this paper, a novel model based on the Hodgkin-Huxley (HH) system is proposed, which has the ability to simulate the complex neurodynamics of the firing sequences of motor neurons. The model is presented at the cellular level and network level, and some simulation results from a simple 3-neuron network are presented to demonstrate its applications.     

Modeling brain dynamics using computational neurogenetic approach

The paper introduces a novel computational approach to brain dynamics modeling that integrates dynamic gene–protein regulatory networks with a neural network model. Interaction of genes and proteins in neurons affects the dynamics of the whole neural network. Through tuning the gene–protein interaction network and the initial gene/protein expression values, different states of the neural network dynamics can be achieved. A generic computational neurogenetic model is introduced that implements this approach. It is illustrated by means of a simple neurogenetic model of a spiking neural network of the generation of local field potential. Our approach allows for investigation of how deleted or mutated genes can alter the dynamics of a model neural network. We conclude with the proposal how to extend this approach to model cognitive neurodynamics.

A neural network designed to solve the N-Queens Problem

In this paper we discuss the Hopfield neural network designed to solve the N-Queens Problem (NQP). Our network exhibits good performance in escaping from local minima of energy surface of the problem. Only in approximately 1% of trials it settles in a false stable state (local minimum of energy). Extenive simulations indicate that the network is efficient and less sensitive to changes of its initial energy (potentials of neurons). Two strategies employed to achieve the solution and results of computer simulation are presented. Some theoretical remarks about convergence of the network are added.     

模块神经网络及其性能

提出一个不同于实现ｙ＝ｆ（ｘ）的ＢＰ网络的神经网络模型,给出了网络的结构及并行动力学方程,证明了其动力学的稳定性。通过学习算法的建立,证明网络能精确实现输入矢量对（ｘ,ｙ）映入成相联系的输出矢量ｚ,最重要的是网络能同时存诸依时变化的时序模式与静态模式。此外并给出动力学学习算法,证明此学习算法的收敛性,计算机仿真证实理论结果,最后讨论了某些可能的应用。     

The simultaneous recurrent neural network for addressing the scaling problem in static optimization.

A trainable recurrent neural network, Simultaneous Recurrent Neural network, is proposed to address the scaling problem faced by neural network algorithms in static optimization. The proposed algorithm derives its computational power to address the scaling problem through its ability to "learn" compared to existing recurrent neural algorithms, which are not trainable. Recurrent backpropagation algorithm is employed to train the recurrent, relaxation-based neural network in order to associate fixed points of the network dynamics with locally optimal solutions of the static optimization problems. Performance of the algorithm is tested on the NP-hard Traveling Salesman Problem in the range of 100 to 600 cities. Simulation results indicate that the proposed algorithm is able to consistently locate high-quality solutions for all problem sizes tested. In other words, the proposed algorithm scales demonstrably well with the problem size with respect to quality of solutions and at the expense of increased computational cost for large problem sizes.     

Novel tracking function of moving target using chaotic dynamics in a recurrent neural network model

Chaotic dynamics introduced in a recurrent neural network model is applied to controlling an object to track a moving target in two-dimensional space, which is set as an ill-posed problem. The motion increments of the object are determined by a group of motion functions calculated in real time with firing states of the neurons in the network. Several cyclic memory attractors that correspond to several simple motions of the object in two-dimensional space are embedded. Chaotic dynamics introduced in the network causes corresponding complex motions of the object in two-dimensional space. Adaptively real-time switching of control parameter results in constrained chaos (chaotic itinerancy) in the state space of the network and enables the object to track a moving target along a certain trajectory successfully. The performance of tracking is evaluated by calculating the success rate over 100 trials with respect to nine kinds of trajectories along which the target moves respectively. Computer experiments show that chaotic dynamics is useful to track a moving target. To understand the relations between these cases and chaotic dynamics, dynamical structure of chaotic dynamics is investigated from dynamical viewpoint.     

An artificial hysteresis binary neuron: a model suppressing the oscillatory behaviors of neural dynamics

A hysteresis binary McCulloch-Pitts neuron model is proposed in order to suppress the complicated oscillatory behaviors of neural dynamics. The artificial hysteresis binary neural network is used for scheduling time-multiplex crossbar switches in order to demonstrate the effects of hysteresis. Time-multiplex crossbar switching systems must control traffic on demand such that packet blocking probability and packet waiting time are minimized. The system using n×n processing elements solves an n×n crossbar-control problem with O(1) time, while the best existing parallel algorithm requires O(n) time. The hysteresis binary neural network maximizes the throughput of packets through a crossbar switch. The solution quality of our system does not degrade with the problem size.     

A neural network for the Steiner minimal tree problem

The problem of finding the shortest tree connecting a set of points is called the Steiner minimal tree problem and is nearly three centuries old. It has applications in transportation, computer networks, agriculture, telephony, building layout and very large scale integrated circuit (VLSI) design, among others, and is known to be NP-complete. We propose a neural network which self-organizes to find a minimal tree. Solutions found by the network compare favourably with the best known or optimal results on test problems from the literature. To the best of our knowledge, the proposed network is the first neural-based solution to the problem. We show that the neural network has a built-in mechanism to escape local minima.     

Modeling of the three-dimensional structure of luffin-α and its simulated reaction with the substrate oligoribonucleotide GAGA

A fundamental problem in biochemistry and molecular biology is understanding the spatial structure of macromolecules and then analyzing their functions. In this study, the three-dimensional structure of a ribosome-inactivating protein luffin-α was predicted using a neural network method and molecular dynamics simulation. A feedforward neural network with the backpropagation learning algorithm were trained on model class of homologous proteins including trichosanthin andα-momorcharin. The distance constraints for the Cα atoms in the protein backbone were utilized to generate a folded crude conformation of luffin-α by model building and the steepest descent minimization approach. The crude conformation was refined by molecular dynamics techniques and a simulated annealing procedure. The interaction between luffin-α and its analogous substrate GAGA was also simulated to understand its action mechanism.     

Pattern recall in networks of chaotic neurons

This research investigates the potential utility of chaotic dynamics in neural information processing. A novel chaotic spiking neural network model is presented which is composed of non-linear dynamic state (NDS) neurons. The activity of each NDS neuron is driven by a set of non-linear equations coupled with a threshold based spike output mechanism. If time-delayed self-connections are enabled then the network stabilises to a periodic pattern of activation. Previous publications of this work have demonstrated that the chaotic dynamics which drive the network activity ensure that an extremely large number of such periodic patterns can be generated by this network. This paper presents a major extension to this model which enables the network to recall a pattern of activity from a selection of previously stabilised patterns.     

FctClus: A Fast Clustering Algorithm for Heterogeneous Information Networks

It is important to cluster heterogeneous information networks. A fast clustering algorithm based on an approximate commute time embedding for heterogeneous information networks with a star network schema is proposed in this paper by utilizing the sparsity of heterogeneous information networks. First, a heterogeneous information network is transformed into multiple compatible bipartite graphs from the compatible point of view. Second, the approximate commute time embedding of each bipartite graph is computed using random mapping and a linear time solver. All of the indicator subsets in each embedding simultaneously determine the target dataset. Finally, a general model is formulated by these indicator subsets, and a fast algorithm is derived by simultaneously clustering all of the indicator subsets using the sum of the weighted distances for all indicators for an identical target object. The proposed fast algorithm, FctClus, is shown to be efficient and generalizable and exhibits high clustering accuracy and fast computation speed based on a theoretic analysis and experimental verification.     

Chaotic neural network applied to two-dimensional motion control

Chaotic dynamics generated in a chaotic neural network model are applied to 2-dimensional (2-D) motion control. The change of position of a moving object in each control time step is determined by a motion function which is calculated from the firing activity of the chaotic neural network. Prototype attractors which correspond to simple motions of the object toward four directions in 2-D space are embedded in the neural network model by designing synaptic connection strengths. Chaotic dynamics introduced by changing system parameters sample intermediate points in the high-dimensional state space between the embedded attractors, resulting in motion in various directions. By means of adaptive switching of the system parameters between a chaotic regime and an attractor regime, the object is able to reach a target in a 2-D maze. In computer experiments, the success rate of this method over many trials not only shows better performance than that of stochastic random pattern generators but also shows that chaotic dynamics can be useful for realizing robust, adaptive and complex control function with simple rules.