#### 18000OA確率分布間の距離推定 : 機械学習分野における最新動向(サーベイ,<特集>機械学習研究部会)

vol.23, no.3, pp.439-452, 2013-09-25

#### 13000OAマーケットインパクト関数の非線形性について : 凸性・凹性に関する実証・シミュレーション分析と最適執行モデルの導出(応用,<特集>数理ファイナンス)

vol.24, no.3, pp.203-237, 2014-09-25

#### 10000OA情報幾何学

vol.2, no.1, pp.37-56, 1992-03-16

3

Information geometry is a new theoretical method to elucidate intrinsic geometrical structures underlying information systems. It is applicable to wide areas of information sciences including statistics, information theory, systems theory, etc. More concretely, information geometry studies the intrinsic geometrical structure of the manifold of probability distributions. It is found that the manifold of probability distributions leads us to a new and rich differential geometrical theory. Since most of information sciences are closely related to probability distributions, it gives a powerful method to study their intrinsic structures. A manifold consisting of a smooth family of probability distributions has a unique invariant Riemannian metric given by the Fisher information. It admits a one-parameter family of invariant affine connections, called the α-connection, where α and-α-connections are dually coupled with the Riemannian metric. The duality in affine connections is a new concept in differential geometry. When a manifold is dually flat, it admits an invariant divergence measure for which a generalized Pythagorian theorem and a projection theorem hold. The dual structure of such manifolds can be applied to statistical inference, multiterminal information theory, control systems theory, neural networks manifolds, etc. It has potential ability to be applied to general disciplines including physical and engineering sciences.

#### 6000OACourant-Friedrichs-Lewy条件についての注意(理論)

vol.24, no.1, pp.15-26, 2014-03-25

Courant-Friedrichs-Lewy条件(CFL条件)は双曲型偏微分方程式の差分近似の解析において,最も重要な条件の1つである.この条件は差分スキームの安定性と関連して論じられることが多いが,本来は差分解の収束に対する必要条件である.本論文においてはCFL条件の本来の意味を再確認し,この条件下においても計算機から出力される数値解は必ずしも"安定"ではないことを具体例を通して示すと伴に,丸め誤差の多様な挙動についても言及する.

#### 5000OA高速自動微分法(第2回年会特別講演)

vol.3, no.1, pp.58-66, 1993-03-15

#### 5000OAエラスティカを巡る数理 : ベルヌイ,オイラーから現代まで

vol.13, no.1, pp.48-60, 2003-03-25

1

In 1691, James Bernoulli proposed the following problem called elastica problem : "What shape of elastica, an ideal thin elastic rod in a plane, is allowed ?" Euler essentially solved the problem in 1744 by developing studies of variation problem and elliptic function theory. Their studies are regarded as prototypes of harmonic map theory, nonlinear differential theory, soliton theory, differential geometry, algebraic geometry, theory of moduil of elliptic curves and so on. In this article we mention their mathematical meaning with their historical background from viewpoint of pure and applied mathematics : Their studies started from concreteness to abstractand they applied constructed abstract theory to the concrete problem. We also introduce a current study of statistical mechanics of elasticas, which might be settled by knowledge of hyperelliptic function theory.

#### 5000OA高速道路交通流の数理・はじめに(<特集>交通流の数理)

vol.12, no.2, pp.104-108, 2002-06-15

6

As an introduction to the special topics section of traffic flow problem, a brief history of mathematical researches in this area is described. Some basic concepts, such as a q-k diagram, are introduced at the same time.

#### 4000OA自動微分とDE公式を用いた非整数階微分の数値計算

vol.16, no.1, pp.51-65, 2006-03-25

This paper proposes a new method of numerical calculation for fractional derivatives. Conventional methods using difference approximation have some defects such as rounding errors and computation time. In this paper, fractional derivatives are expressed as the combination of ordinary derivatives and integrals which are calculated using automatic differentiation and double exponential formula, respectively. Numerical examples show that the proposed method gives high-precision results with practical computational cost.

#### 4000OAいわゆる「蔵本モデル」について

vol.17, no.2, pp.175-177, 2007-06-26

#### 3000OA行列式とパフィアン(1)

vol.14, no.1, pp.62-66, 2004-03-25

1

#### 3000OA離散戸田方程式を用いた大規模疎行列の連立一次方程式, 行列式, 固有多項式の計算法(応用可積分系, <特集>平成17年研究部会連合発表会)

vol.15, no.3, pp.307-322, 2005-09-25

A new method for constructing the minimum polynomial for the symbolic computation in terms of the discrete Toda equation is proposed. For the sparse matrices, the proposed method is efficiently carried out on a finite field arithmetic avoiding the division by zero. As a consequence, this paper presents new methods for the symbolic computation of the solution of simultaneous equation, the determinant and the eigen polynomial of a large scaled sparse matrix.

#### 3000OAギンツブルグ・ランダウ方程式とボルテクス(<特集>パターンダイナミクス)

vol.11, no.2, pp.152-162, 2001-06-15

#### 3000OA非可換確率論における独立性概念

vol.13, no.2, pp.137-149, 2003-06-25

One of the main features of quantum probability(=noncommutative probability) is the diversity of notions of 'independence' for noncommutative random variables. Besides the three fundamental examples of universal independence (tensor, free and Boolean independence), there is another example called 'monotone independence' which was introduced and studied by the author. We give a brief review on 'monotone probability' which can be developed based on the notion of monotone independence. Especially we present the monotonic analogue of central limit theorem, law of small numbers, convolution, infinite divisibility and Levy-Hincin formula. Furthermore, we give a classification theorem for universal notions of independence.

#### 3000OA平安将棋の終盤戦の数理解析

vol.10, no.4, pp.327-334, 2000-12-15

It is supposed that HEIAN SHOGI is an ancient variant of the MODERN SHOGI (Japanese CHESS). When two experienced players play a game of HEIAN SHOGI, they often reach a 'King-and-Gold vs King'endgame. This paper presents the results of computer analyses of this 'King-and-Gold vs King'endgame to explore the evolutionary changes of the characteristics of games. The analyses were done in the various sizes of square board. The loop positions, that are included neither in the winning position of 'King-and-Gold'side nor in the obvious draw positions, appear in larger than 11×11 board, and these loop positions account for above 80% of all positions. And the number of steps of the longest position-to-mate approach to a certain value. These results mean that the characteristics of games radically change in the different size of the board. It is hoped that these results give us important suggestion to suppose why the ancient SHOGI variant changes to 9×9 board (MODERN SHOGI).

#### 3000OAScilab : 数値計算のためのフリーソフトウェア

ゴメス クロード 須田 礼仁

vol.19, no.1, pp.47-51, 2009-03-25

#### 2000OAヒット現象の数理 : 映画からAKB総選挙まで

vol.25, no.2, pp.50-58, 2015-06-25

We apply a mathematical theory for hit phenomenon for prediction of the "general election" of AKB48 which is very popular girls group in Japan.

#### 2000OA渋滞学のセルオートマトンモデル

vol.22, no.1, pp.2-14, 2012-03-27

Jamology is a new scientific and engineering research, which deals with flow and jam of every self-driven particle in the world. One of the most famous models used in Jamology is Cellular Automaton (CA), where time, space, and state are discrete. In this paper, we introduce the essence and the contribution of CA models in Jamology. Traffic CA models succeed to reproduce meta-stable state, which is an essential phenomenon in real traffic, and show some results which can be applied to ease congestion at junctions and weaving sections. Besides, collaboration of CA and Queueing theory creates a new queueing model which gives us mathematically-exact solution useful for application. Furthermore, two dimensional CA models for pedestrians are extended in many ways to study how the specific characteristics of pedestrians affect on their flow. In the last section of the paper, we also discuss the scope of application of CA models.

#### 2000OAエピソード記憶 : 海馬のカオスモデル

vol.18, no.3, pp.176-193, 2008-09-25

#### 2000OA東京大学生産技術研究所最先端数理モデル連携研究センター(ラボラトリーズ)

vol.20, no.4, pp.342-344, 2010-12-24

#### 2000OAデンマークの大学事情(海外情報)

vol.3, no.3, pp.242-246, 1993-09-16