This paper investigates the characteristics of the associative memories of Hopfield networks (HF) and cellular neural networks (CNN). In a Hopfield network, the memories which are to be stored correspond to the extrema of the energy function defined in the network, and in a CNN, they correspond to the asymptotically stable points of the differential equation of the CNN. The associative memory networks of Chinese characters are simulated on a 9×9 matrix network. And it is found that the memory capacity of a CNN is larger than that of an HF by numerical simulations. In a 3×3 matrix network, the characteristics of the associative memories of Hopfield networks and cellular neural networks are examined in details.

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A procedure to interpret principal component axes is proposed by making use of hypothesistesting procedure in the means of observed variables between the positive and negative sign groups which are defined by the observed principal component scores. It gives similar analytic properties as the usual procedure based on the eigen vectors of the covariance matrix, when the observed vector x conforms to a multivariate normal distribution. It is shown to work well by two examples from Mardia, Kent & Bibby (1979) and Tanaka, Tarumi & Wakimoto (1984).

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Redundancy analysis (RDA) was developed originally for descriptive data analysis of two sets of quantitative (continuous) variables, one set being dependent on the other. Israels (1984) generalized it to the case of qualitative (categorical) variables. In this paper we suggest a procedure (QRDA), extending RDA to deal with data described in terms of both qualitative and quantitative variables. For its evaluation, we give a Monte Carlo study to examine the stability of data analysis by QRDA, and demonstrate its validity. Further we discuss properties of QRDA in comparison with Israels' procedure on the point of eigenvalue problems, stating that the two procedures give the same eigenvector under a special condition on the data matrix. Then we show, on the basis of simulation study, that QRDA is more advantageous than Israels' procedure even in analyzing data in terms of qualitative variables only.

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The Internet is claimed to be very democratic medium. Every person can transmit and receive wide variety of information at the very low cost. But this causes the "flood" of problematic expression including pornography and hate speech as well. This article first sketches the various efforts to control these information by countries and an international organization including the United States, the European Union, France, Germany, the United Kingdom, Singapore and Japan. The United States has chosen to suppress "indecent" expression on line by law, namely "Communications Decency Act of 1996." The constitutionality of the Act was immediately challenged in courts. Two of the federal district courts ruled the law unconstitutional, and the Supreme Court is expected to reveal its opinion by this summer. In contrast Japanese Ministry of Telecommunications is planning to avoid legal restriction and to give private Internet-related organizations the primary responsibility for settling the complaints from the Internet users. In addition, the Ministry is encouraging to develop practical filtering software that screens content that is harmful to minors. It is afraid, however, that the government might exert substantial control over the problem in terms of providing "guidelines" that "lacks" any legal effect but has de facto binding power in a society like Japanese. The article concludes by pointing out the doctrinal issues underlying the content restriction in the cyberspace. (1) In a society where all of the effective communicative tools are virtually monopolized by the mass media, the Internet has superior constitutional value considering its highly democratic character. (2) The protection of minors provides good reason to restrict harmful content in theory, but this type of restriction usually turns out to be unconstitutionally overbroad constraint in practice. The legal protection of children may become unnecessary with installation of proper filtering mechanism. (3) As suggested above, "voluntary restraint" may have strong restrictive power due to the nature of the society, and warrants close constitutional analysis.

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