Recently, due to the fundamental nature, the coding problem of interference channels in multi-user information theory, is vigorously tackled by many communication theorists. Especially, in order to understand the essential character, the situation with two couples of sender and receiver has been well studied. Among a lot of results, the achievable region, so-called the HK region, given by Han and Kobayashi in 1981 continues to be the best single-letter expression for the general interference channel up to today. In this survey paper, we elucidate the details of the HK region, the study to simplify the expression of HK region, and give the explanation on subclasses of interference channels for which the capacity problem has been already fixed. Further, we explain the result by Etkin, Tse, Wang. They showed the asymptotic optimality for Gaussian interference channels by using a simple case of the HK scheme when SNR and INR tend to very large. Moreover, quite recently, by demonstrating the existence of an achievable rate pair outside the HK region, Nair, et.al., show that the optimality of HK region now breaks. Thus, we are now faced with a historical turning point in the study on the interference channel.

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The　discovery and the following investigation of the Motion Induced Blindness (MIB) are reviewed. The physiological mechanisms and functional organization of MIB are of most interest as a peculiar example of visual blindness. The natural Blind Spot (BS) has the perfect Filling-In (FI) functions. MIB could be identified with an Artificial blind Spot (AS). Recent research results by the authors are explained. Investigating the blindness, we could approach to our visual awareness issue which are of interest in physiology, psychology, cognitive science, and even in philosophy.

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I have studied maintenance theory for about half a century and published three books(1)~(3), that summarize my research results up to 2010. It is necessary to study stochastic processes to understand reliability theory. My fourth book(4) was rewritten as an elementary textbook on stochastic processes in which all the examples are based on reliability models. Recently, systems have been randomized as they have become increasingly complex and large-scale. My fifth book(5) shows how to form stochastic random models, to analyze them theoretically, and to derive a variety of optimal maintenance policies. Classic maintenance theory was established by the book(6) written by Barlow and Proschan fifty years ago. In this report, replacement problems are roughly divided into three periods: the past, present, and future: In the past period, I introduce the standard replacement policy in Barlow and prosvhan's book and its modifications and extensions, in the present period, I discuss some parts of my fifth book, and in the future period, I propose new reliability problems and replacement policies that are currently being studied, and explain simply them as an examples of cumulative damage models. I use the word ‘replacement' in this report, which may be used interchangeably with ‘preventive maintenance's.

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This article sheds light on principles of human-human communication such as everyday conversation. Traditional views of communication generally have the following four principles in common: communication is (i) based on information transfer, (ii) the participants’ intentions, (iii) co-presence among participants, and (iv) actions. These principles, however, actually often obfuscate various phenomena and distort their descriptions and explanations. This article shows this concretely through an observation of modern spoken Japanese. Then, a more useful view of communication is elicited that captures communication as a part of participants’ lives based on a consciousness that states, “My co-presence with others is mutually acknowledged by others.”

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This exposition summarizes our papers on adaptive algorithms published over about twenty years. According to the results presented in them, adaptive algorithms can be classified by the type of approximation method used for the non-diagonal elements of the autocorrelation matrix. Among these methods, the arithmetic mean method has the lowest degree of approximation, followed by the coefficient reuse method, the normalized least mean square (NLMS) algorithm, and the individually normalized least mean square (INLMS) algorithm, with the sub-recursive least square (sub-RLS) algorithm having the highest degree of approximation. The adaptive algorithms are generally introduced in the order of the Wiener-Hopf solution, the least square (LS) method, the steepest descent method, the LMS algorithm, and the NLMS algorithm where the first two require the operation of the inverse matrix. In this exposition, we show that the reuse of the estimated coefficients makes this operation unnecessary. This coefficient reuse method can be assumed to be the source of steepest descent method type adaptive algorithms, from which various algorithms can be derived. Finally, we clarify the role of each element composing, the NLMS algorithm.

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Petri nets, which are a mathematical modeling language, have been investigated from theoretical and practical viewpoints since they were first introduced by Dr. Carl Adam Petri in his Ph.D thesis in 1962. Petri nets are suitable for treating scheduling problems since they can model not only system event dynamics but also the quantitative characteristics of events if we use time Petri nets. This paper summarizes Petri-net-based approaches to scheduling problems such as parallel machine scheduling, flow-shop scheduling, and job-shop scheduling problems. As an example of an application in agriculture, a case study of Petri-net-based scheduling for sugarcane production is reported.

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