Takafumi Matsuura

Refractory effects of chaotic neurodynamics for finding motifs from DNA sequences

To discover a common and conserved pattern, or motif, from DNA sequences is an important step to analyze DNA sequences because the patterns are acknowledged to reflect biological important information. However, it is difficult to discover unknown motifs from DNA sequences because of its huge number of combination. We have already proposed a new effective method to extract the motifs using a chaotic search, which combines a heuristic algorithm and a chaotic dynamics. To realize the chaotic search, we used a chaotic neural network. The chaotic search exhibits higher performance than conventional methods. Although we have indicated that the refractory effects realized by the chaotic neural network have an essential role, we did not clarify why the refractory effects are important to search optimal solutions. In this paper, we further investigate this issue and reveal the validity of the refractory effects of the chaotic dynamics using surrogate refractory effects. As a result, we discovered that it is important for searching optimal solutions to increase strength of the refractory effects after a firing of neurons.

Chaotic Search for Traveling Salesman Problems by Using 2-opt and Or-opt Algorithms

The traveling salesman problem (TSP) is one of the widely studied combinatorial optimization problems. Because, the TSP belongs to a class of

The Lin-Kernighan Algorithm Driven by Chaotic Neurodynamics for Large Scale Traveling Salesman Problems

\mathcal{NP}

Theory and Applications of Chaotic Optimization Methods

-hard, it is almost impossible to obtain an optimal solution in a reasonable time frame. To find the near optimum solutions of TSPs, a method with chaotic neurodynamics has already been proposed. In this paper, we propose a new method to solve TSP introducing chaotic neurodynamics, which uses not only the 2-opt algorithm but also the Or-opt algorithm, which is one of the powerful local searches. Namely, in the proposed method, the 2-opt and the Or-opt algorithms are adaptively driven by the chaotic neurodynamics. Thus, the local minimum problem in these algorithms is resolved by controlling executions of these local searches. As a result, the proposed method shows higher performance than the previous chaotic search methods.

Chaotic Motif Sampler for Motif Discovery Using Statistical Values of Spike Time-Series

The traveling salesman problem (TSP) is one of the typical

Quadratic Assignment Problems for Chaotic Neural Networks with Dynamical Noise

{\cal NP}

Chaotic motif sampler: detecting motifs from biological sequences by using chaotic neurodynamics

-hard problems. Then, it is inevitable to develop an effective approximate algorithm. We have already proposed an effective algorithm which uses chaotic neurodynamics. The algorithm drives a local search method, such as the 2-opt algorithm and the adaptive k -opt algorithm, to escape from undesirable local minima. In this paper, we propose a new chaotic search method using the Lin-Kernighan algorithm. The Lin-Kernighan algorithm is one of the most effective algorithms for solving TSP. Moreover, to diversify searching states, we introduce the double bridge algorithm. As a result, the proposed method exhibits higher performance than the conventional algorithms. We validate the applicability of the proposed method for very large scale instances, such as 105 order TSPs.

Soft Tabu Search for Solving Quadratic Assignment Problems

In our society, various combinatorial optimization problems exist and we must often solve them, for e.g. scheduling, delivery planning, circuit design, and computer wiring. Then, one of the important issues in science and engineering is how to develop effective algorithms for solving these combinatorial problems.

AD-Truck Routing Problem and Solution Methods

One of the most important issues in bioinformatics is to discover a common and conserved pattern, which is called a motif, from biological sequences. We have already proposed a motif extraction method called Chaotic Motif Sampler (CMS) by using chaotic dynamics. Exploring a searching space with avoiding undesirable local minima, the CMS discovers the motifs very effectively. During a searching process, chaotic neurons generate very complicated spike time-series. In the present paper, we analyzed the complexity of the spike time-series observed from each chaotic neuron by using a statistical measure, such as a coefficient of variation and a local variation of interspike intervals, which are frequently used in the field of neuroscience. As a result, if a motif is embedded in a sequence, corresponding spike time-series show characteristic behavior. If we use these characteristics, multiple motifs can be identified.

How to Decide Solutions of Quadratic Assignment Problem from Chaotic Neural Network

The quadratic assignment problem (QAP) is one of the combinatorial optimization problems which belong to a class of NP-hard. To solve QAP, various algorithms for finding near optimal solutions have already been proposed. Among them, the Hopfield-Tank neural network approach is very attractive from a viewpoint of an application of neural dynamics to combinatorial optimization, this approach is not so effective because of local minimum problem. To overcome this problem, a method which uses chaotic dynamics has already been proposed. On the other hand, to avoid undesirable local minima, dynamical noise is often used. In this paper, we combine these two approaches---chaotic dynamics and dynamical noise---to realize an effective approach for solving combinatorial optimization problems: we add dynamical noise to chaotic neural network for solving QAP. The results show that when the small amount of dynamical noise is added, the solving performance is much improved. We also analyze the influence of dynamical noise to the chaotic dynamics, and show that dynamical noise diversifies the searching states to explore much better solutions.