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.     

An annealed chaotic maximum neural network for bipartite subgraph problem

In this paper, based on maximum neural network, we propose a new parallel algorithm that can help the maximum neural network escape from local minima by including a transient chaotic neurodynamics for bipartite subgraph problem. The goal of the bipartite subgraph problem, which is an NP- complete problem, is to remove the minimum number of edges in a given graph such that the remaining graph is a bipartite graph. Lee et al. presented a parallel algorithm using the maximum neural model (winner-take-all neuron model) for this NP- complete problem. The maximum neural model always guarantees a valid solution and greatly reduces the search space without a burden on the parameter-tuning. However, the model has a tendency to converge to a local minimum easily because it is based on the steepest descent method. By adding a negative self-feedback to the maximum neural network, we proposed a new parallel algorithm that introduces richer and more flexible chaotic dynamics and can prevent the network from getting stuck at local minima. After the chaotic dynamics vanishes, the proposed algorithm is then fundamentally reined by the gradient descent dynamics and usually converges to a stable equilibrium point. The proposed algorithm has the advantages of both the maximum neural network and the chaotic neurodynamics. A large number of instances have been simulated to verify the proposed algorithm. The simulation results show that our algorithm finds the optimum or near-optimum solution for the bipartite subgraph problem superior to that of the best existing parallel algorithms.     

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.     

A novel efficient learning algorithm for self-generating fuzzy neural network with applications

In this paper, a novel efficient learning algorithm towards self-generating fuzzy neural network (SGFNN) is proposed based on ellipsoidal basis function (EBF) and is functionally equivalent to a Takagi-Sugeno-Kang (TSK) fuzzy system. The proposed algorithm is simple and efficient and is able to generate a fuzzy neural network with high accuracy and compact structure. The structure learning algorithm of the proposed SGFNN combines criteria of fuzzy-rule generation with a pruning technology. The Kalman filter (KF) algorithm is used to adjust the consequent parameters of the SGFNN. The SGFNN is employed in a wide range of applications ranging from function approximation and nonlinear system identification to chaotic time-series prediction problem and real-world fuel consumption prediction problem. Simulation results and comparative studies with other algorithms demonstrate that a more compact architecture with high performance can be obtained by the proposed algorithm. In particular, this paper presents an adaptive modeling and control scheme for drug delivery system based on the proposed SGFNN. Simulation study demonstrates the ability of the proposed approach for estimating the drug's effect and regulating blood pressure at a prescribed level.     

Equilibrium Distributions of Populations of Biological Species on Networks of Social Sites

ABSTRACT

We investigate the problem of how a population of biological species would distribute over a given network of social sites so that their social contacts through the connected sites can be maximized (or minimized). This problem has applications in modelling the behaviours of social (or solitary) species such as the development of social groups in human society and the spread of solitary animals in distant habitats. We show that this problem can be formulated as an evolutionary game, with the equilibrium state of the game corresponding to a strategy for choosing the residing sites, each with a certain probability, or equivalently, to a distribution of the population on these sites. The game has a symmetric payoff matrix, and can therefore be analyzed via the solution of a corresponding quadratic programme: An equilibrium strategy of the game is a KKT point of the quadratic programme, which may be a local maximizer, local minimizer, or saddle point, but it is evolutionarily stable if and only if it is a strict local maximizer. In general, with a goal to maximize the social contacts, the species tend to spread on network sites where there are dense connections such as a complete subnetwork or in other words, a network clique. We show that at equilibrium, the population may or may not distribute on a network clique, but the stability of the equilibrium state does depend on the structure of the selected subnetwork. In particular, we show that the distribution of the population on a maximal network clique is evolutionarily stable unless the clique is ‘attached’ to another clique of the same or larger size, when the population may be able to switch or expand to the neighbouring clique to increase or at least maintain its total amount of contacts. However, the distribution of the population on a non-clique subnetwork is always evolutionarily unstable or weakly evolutionarily stable at the very best, for the population can always move away from its current distribution without decreasing its total amount of contacts. We conclude that the strategies to spread on maximal network cliques are not only equilibrium strategies but also evolutionarily more stable than those on non-clique subnetworks, thus theoretically reaffirming the evolutionary advantages of joining social cliques in social networks for social species.     

Vertical decomposition with Genetic Algorithm for Multiple Sequence Alignment

Background

Mapping protein primary sequences to their three dimensional folds referred to as the 'second genetic code' remains an unsolved scientific problem. A crucial part of the problem concerns the geometrical specificity in side chain association leading to densely packed protein cores, a hallmark of correctly folded native structures. Thus, any model of packing within proteins should constitute an indispensable component of protein folding and design.

Results

In this study an attempt has been made to find, characterize and classify recurring patterns in the packing of side chain atoms within a protein which sustains its native fold. The interaction of side chain atoms within the protein core has been represented as a contact network based on the surface complementarity and overlap between associating side chain surfaces. Some network topologies definitely appear to be preferred and they have been termed 'packing motifs', analogous to super secondary structures in proteins. Study of the distribution of these motifs reveals the ubiquitous presence of typical smaller graphs, which appear to get linked or coalesce to give larger graphs, reminiscent of the nucleation-condensation model in protein folding. One such frequently occurring motif, also envisaged as the unit of clustering, the three residue clique was invariably found in regions of dense packing. Finally, topological measures based on surface contact networks appeared to be effective in discriminating sequences native to a specific fold amongst a set of decoys.

Conclusions

Out of innumerable topological possibilities, only a finite number of specific packing motifs are actually realized in proteins. This small number of motifs could serve as a basis set in the construction of larger networks. Of these, the triplet clique exhibits distinct preference both in terms of composition and geometry.     

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.     

Application of chaotic dynamics in a recurrent neural network to control: hardware implementation into a novel autonomous roving robot

Originating from a viewpoint that complex/chaotic dynamics would play an important role in biological system including brains, chaotic dynamics introduced in a recurrent neural network was applied to control. The results of computer experiment was successfully implemented into a novel autonomous roving robot, which can only catch rough target information with uncertainty by a few sensors. It was employed to solve practical two-dimensional mazes using adaptive neural dynamics generated by the recurrent neural network in which four prototype simple motions are embedded. Adaptive switching of a system parameter in the neural network results in stationary motion or chaotic motion depending on dynamical situations. The results of hardware implementation and practical experiment using it show that, in given two-dimensional mazes, the robot can successfully avoid obstacles and reach the target. Therefore, we believe that chaotic dynamics has novel potential capability in controlling, and could be utilized to practical engineering application.     

A chaotic neural network mimicking an olfactory system and its application on image recognition

1 Introduction A biological neural system is complicated and ef-ficient. People have tried for years to simulate it to per-form complex signal processing functions. For example,the artificial neural network is a kind of model derivedfrom a biological neural system. Most artificial neuralnetworks simulate some important features such as thethreshold behaviour and plasticity of synapses. However,they are primary simulations and still much simpler incomparison with specific biological neural…     

Modelling and prediction for chaotic fir laser attractor using rational function neural network

Many real-world systems such as irregular ECG signal, volatility of currency exchange rate and heated fluid reaction exhibit highly complex nonlinear characteristic known as chaos. These chaotic systems cannot be retreated satisfactorily using linear system theory due to its high dimensionality and irregularity. This research focuses on prediction and modelling of chaotic FIR (Far InfraRed) laser system for which the underlying equations are not given. This paper proposed a method for prediction and modelling a chaotic FIR laser time series using rational function neural network. Three network architectures, TDNN (Time Delayed Neural Network), RBF (radial basis function) network and the RF (rational function) network, are also presented. Comparisons between these networks performance show the improvements introduced by the RF network in terms of a decrement in network complexity and better ability of predictability.     

嗅觉系统神经网络模型的模拟与动力学特性分析

在哺乳动物嗅觉系统的拓扑结构及生理实验的基础上建立了一套非线性动力学神经网络模型．此模型在模拟嗅觉神经系统方面有着突出的优点,同时在信号处理以及模式识别中表现出了奇异的混沌特性．着重描述了K系列模型的非线性动力学特性,并通过数值模拟进行分析．     

Hierarchical genetic algorithm for near optimal feedforward neural network design

In this paper, we propose a genetic algorithm based design procedure for a multi layer feed forward neural network. A hierarchical genetic algorithm is used to evolve both the neural networks topology and weighting parameters. Compared with traditional genetic algorithm based designs for neural networks, the hierarchical approach addresses several deficiencies, including a feasibility check highlighted in literature. A multi objective cost function is used herein to optimize the performance and topology of the evolved neural network simultaneously. In the prediction of Mackey Glass chaotic time series, the networks designed by the proposed approach prove to be competitive, or even superior, to traditional learning algorithms for the multi layer Perceptron networks and radial basis function networks. Based upon the chosen cost function, a linear weight combination decision making approach has been applied to derive an approximated Pareto optimal solution set. Therefore, designing a set of neural networks can be considered as solving a two objective optimization problem.     

Study of a Bionic Pattern Classifier Based on Olfactory Neural System

Simulating biological olfactory neural system, KIII network, which is a high-dimensional chaotic neural network, is designed in this paper. Different from conventional artificial neural network, the KⅢ network works in its chaotic trajectory. It can simulate not only the output EEG waveform observed in electrophysiological experiments, but also the biological intelligence for pattern classification. The simulation analysis and application to the recognition of handwriting numerals are presented here. The classification performance of the KⅢ network at different noise levels was also investigated.     

Self-organizing fuzzy graphs for structure-based comparison of protein pockets

Patterns of receptor-ligand interaction can be conserved in functionally equivalent proteins even in the absence of sequence homology. Therefore, structural comparison of ligand-binding pockets and their pharmacophoric features allow for the characterization of so-called "orphan" proteins with known three-dimensional structure but unknown function, and predict ligand promiscuity of binding pockets. We present an algorithm for rapid pocket comparison (PoLiMorph), in which protein pockets are represented by self-organizing graphs that fill the volume of the cavity. Vertices in these three-dimensional frameworks contain information about the local ligand-receptor interaction potential coded by fuzzy property labels. For framework matching, we developed a fast heuristic based on the maximum dispersion problem, as an alternative to techniques utilizing clique detection or geometric hashing algorithms. A sophisticated scoring function was applied that incorporates knowledge about property distributions and ligand-receptor interaction patterns. In an all-against-all virtual screening experiment with 207 pocket frameworks extracted from a subset of PDBbind, PoLiMorph correctly assigned 81% of 69 distinct structural classes and demonstrated sustained ability to group pockets accommodating the same ligand chemotype. We determined a score threshold that indicates "true" pocket similarity with high reliability, which not only supports structure-based drug design but also allows for sequence-independent studies of the proteome.     

混沌理论及其在建立神经网络模型中的应用

随着许多学科的相互紧密交叉以及混沌理论的日益深入的研究,人们从生物现象中提出了许多与混沌有关的神经网络模型,本文对混沌理论的基本原理做了简要概述,并着重介绍了四种有代表性的混沌神经网络模型及其应用．同时指出这一研究方向无论在理论还是在应用方面都具有十分诱人的前景．     

Neural network modeling in optimisation of continuous fermentation processes

The capability of self-recurrent neural networks in dynamic modeling of continuous fermentation is investigated in this simulation study. In the past, feedforward neural networks have been successfully used as one-step-ahead predictors. However, in steady-state optimisation of continuous fermentations the neural network model has to be iterated to predict many time steps ahead into the future in order to get steady-state values of the variables involved in objective cost function, and this iteration may result in increasing errors. Therefore, as an alternative to classical feedforward neural network trained by using backpropagation method, self-recurrent multilayer neural net trained by backpropagation through time method was chosen in order to improve accuracy of long-term predictions. Prediction capabilities of the resulting neural network model is tested by implementing this into the Integrated System Optimisation and Parameter Estimation (ISOPE) optimisation algorithm. Maximisation of cellular productivity of the baker's yeast continuous fermentation was used as the goal of the proposed optimising control problem. The training and prediction results of proposed neural network and performances of resulting optimisation structure are demonstrated.     

Full-state tracking control of a mobile robot using neural networks

In this paper a nonholonomic mobile robot with completely unknown dynamics is discussed. A mathematical model has been considered and an efficient neural network is developed, which ensures guaranteed tracking performance leading to stability of the system. The neural network assumes a single layer structure, by taking advantage of the robot regressor dynamics that expresses the highly nonlinear robot dynamics in a linear form in terms of the known and unknown robot dynamic parameters. No assumptions relating to the boundedness is placed on the unmodeled disturbances. It is capable of generating real-time smooth and continuous velocity control signals that drive the mobile robot to follow the desired trajectories. The proposed approach resolves speed jump problem existing in some previous tracking controllers. Further, this neural network does not require offline training procedures. Lyapunov theory has been used to prove system stability. The practicality and effectiveness of the proposed tracking controller are demonstrated by simulation and comparison results.     

A clique-based method for the edit distance between unordered trees and its application to analysis of glycan structures

Background

Measuring similarities between tree structured data is important for analysis of RNA secondary structures, phylogenetic trees, glycan structures, and vascular trees. The edit distance is one of the most widely used measures for comparison of tree structured data. However, it is known that computation of the edit distance for rooted unordered trees is NP-hard. Furthermore, there is almost no available software tool that can compute the exact edit distance for unordered trees.

Results

In this paper, we present a practical method for computing the edit distance between rooted unordered trees. In this method, the edit distance problem for unordered trees is transformed into the maximum clique problem and then efficient solvers for the maximum clique problem are applied. We applied the proposed method to similar structure search for glycan structures. The result suggests that our proposed method can efficiently compute the edit distance for moderate size unordered trees. It also suggests that the proposed method has the accuracy comparative to those by the edit distance for ordered trees and by an existing method for glycan search.

Conclusions

The proposed method is simple but useful for computation of the edit distance between unordered trees. The object code is available upon request.

     

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.     

A Spike-Timing Pattern Based Neural Network Model for the Study of Memory Dynamics

It is well accepted that the brain''s computation relies on spatiotemporal activity of neural networks. In particular, there is growing evidence of the importance of continuously and precisely timed spiking activity. Therefore, it is important to characterize memory states in terms of spike-timing patterns that give both reliable memory of firing activities and precise memory of firing timings. The relationship between memory states and spike-timing patterns has been studied empirically with large-scale recording of neuron population in recent years. Here, by using a recurrent neural network model with dynamics at two time scales, we construct a dynamical memory network model which embeds both fast neural and synaptic variation and slow learning dynamics. A state vector is proposed to describe memory states in terms of spike-timing patterns of neural population, and a distance measure of state vector is defined to study several important phenomena of memory dynamics: partial memory recall, learning efficiency, learning with correlated stimuli. We show that the distance measure can capture the timing difference of memory states. In addition, we examine the influence of network topology on learning ability, and show that local connections can increase the network''s ability to embed more memory states. Together theses results suggest that the proposed system based on spike-timing patterns gives a productive model for the study of detailed learning and memory dynamics.