In the field of pattern recognition or outlier detection, it is often necessary to estimate the region where data of a particular class are generated. In other words, it is required to accurately estimate the support of the distribution that generates the data. Considering the 1-dimensional distribution whose support is a finite interval, the data region is estimated effectively by the maximum value and the minimum value in the samples. Limiting distributions of these values have been studied in the extreme-value theory in statistics. In this research, we propose a method to estimate the data region using the maximum value and the minimum value in the samples. We show the average loss of the estimator and derive the optimally improved estimators for given loss functions. The method can be extended to estimate the higher dimensional input space.

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Building on results of E. Barletta et al., [4], we give several applications of discrete Fourier calculus and the convolution product of functions defined on binary codes and generalize a result by R.P. Stanley, [17], on the vertex-switching reconstruction problem.

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NTRUSign is a lattice-based digital signature scheme proposed by Hoffstein et al. NTRUSign is quite different from many other signature schemes in a sense that its security depends on neither the integer factorization problem nor the discrete logarithm problem but on a geometric problem called the close vector searching problem. However, it is known that there is some vulnerability in NTRUSign, namely there is an attack called the transcript attack. In this paper, we propose a countermeasure for protecting NTRUSign against the transcript attack, and give an improved NTRUSign algorithm.

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The Backward Induction Method, which is the most basic algorithm used for game tree searches, has two weak points. First, the move selected by this method is assured to be the best move as far as the search depth of the game tree is concerned, but is not necessarily the best move towards the end of the game. Secondly, the values evaluated for the leaf nodes do not necessarily give the best advantage at the end of the game.
In a previous paper, we proposed a new algorithm, the Probability Method, which is useful for games finishing at the constant moves such as Othello.
In this paper we compare the Probability Method with the Backward Induction and Bayesian Methods using Othello.
Moreover we propose a pruning procedure for the Probability Method and compare it with the alpha-beta pruning procedure used in the Backward Induction Method.
We show that the Probability Method is more effective than both of the Backward Induction and Bayesian Methods and that the pruning procedure for the Probability Method is more advantageous than alpha-beta pruning in the Backward Induction Method for some phases.

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We carry out an econometric analysis of the Chinese regional system using Chinese economic data, constructing Chinese national and regional production and investment models by sector, in order to discover the causes of and remedies for interregional disparity, and to investigate the relation between the regional systems and the national economy in China. It is shown that regional production technology is a minor factor causing Chinese interregional disparity, and that regional investment level is the most important factor.

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P2P (Peer to Peer) has a great potential to handle highly-distributed computing resources and is expected to be a key technology to realize ubiquitous computing environments over the Internet. However, P2P systems tend to waste the network bandwidth for resource acquisition because of their decentralized resource management. This paper presents an efficient control mechanism for self-organizing overlay networks of large-scale P2P systems, and evaluate its performance in detail. The overlay network is configured by making local clusters reflect current interests of individual peers and connecting them together based on their similarity. As a result, the overlay network provides the resource exploitation space for some specific interests. In addition, the overlay network can dynamically be reconfigured based on the change in the interests of individual peers across time so that more useful peers at that time can be reconnected closer to their client peers. Therefore, multicasting of resource requesting messages can be carried out only over peers with similar interests that are dynamically connected through the overlay network, resulting in a remarkable decrease in both messages for resource acquisition and hops a resource requesting query travels to reach the peer that satisfies the request. Experimental results indicate that the proposed mechanism can realize effective self-organization of the overlay network in which useful peers are dynamically relocated around client peers. In addition, the adaptive allocation of links to peers according to their capability works well to keep the higher performance and fault-tolerance of the self-organizing overlay network.

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This paper deals with a new conception “dual Bézier triangle” and we develop a method for drawing a rational tensor product Bézier surface with two rational Bézier triangles. We also give a method for drawing a rational Bézier triangle with a rational tensor product Bézier surface.

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As is well known in neuroscience, simple cells of the mammalian’s striate cortex possess both orientation and spatial-frequency selectivity, and are similar to the Gabor filters or Gaussian derivative filters in shape. The purpose of this paper is to propose a method of designing perfect reconstruction 2D filterbanks which act on finite dimensional linear spaces consisting of 2D signals of a certain size, and have several analogous features to simple cells: (1) the filterbanks consist of several spatial-frequency channels with orientation selectivity, (2) the filterbanks have shift-invariant multiresolution (multiscale) structures, (3) filters contained in them are FIR, and are similar in appearance to not only Gaussian derivatives of 1st and 2nd order, but also ones of higher order. Moreover, they are constructed by finite linear combinations of separable filters. As is described in the text, by virtue of these properties, our 2D filterbanks can become bases of constructing computational nonlinear models of visual information processing. In this paper we construct the 2D filterbanks, and discuss them from the viewpoint of vision science. For example we disclose a possible role of “Gaussian-derivative-like” filters of higher order in our filterbanks. Practical applications of our 2D filterbanks to vision science and image processing will be given in our subsequent papers.

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