白田 由香利

学生にとって難解と思われているブラック＝ショールズ方程式であるが，視覚的にグラフィクス表現することで，理解が容易になる。本稿では，その確率的ブラウン運動を含む確立微分方程式に関するシミュレーション実験結果と代数学的に求められる理論的結果を3次元グラフィクスにより示す。確率的現象をコンピュータ上に再現することで，確率的ブラウン運動の理解が容易になり，同時に理論的に求められる正規分布を示し両者を比較することで，理論的事柄の理解を深める。また，オプションの期待値の導出過程における，期待値計算の積分計算範囲を，正規分布に伴う確率変数と対数正規分布に従う確率変数に関して，両者同時にグラフィクスで視覚的に示す。本稿のグラフィクスの特長は，変数間の関係をスライダー操作によるモーションとして表現した点である。スライダーで変数を動かすことにより，複雑な関係式における他の変数への影響の理解が容易になる。

本稿では，経営学科の学生に固有値の概念を理解させる教授法として，対角行列で表わされる線型変換を初めに与える方法を提案する。そこでは，始めに，固有値とはその拡大操作による各軸方向の拡大率である，という比喩を用いて説明する。ついで，この拡大操作を複数の非直交座標系に対して行う際，基底変換が必要である，と説明する。伝えるべきことは，直感的解釈として，この対角行列で表される拡大マシンの，各軸方向への倍率が固有値であり，2次元の場合，拡大操作行列の2つの列ベクトルを作る面積が行列式であり，その両者の値は基底を変えても不変，ということである。この教授法を使って，主成分分析を比喩的に説明した。主成分分析とは，その分散共分散行列の固有値を求め，固有値を固有ベクトル方向のデータの分散の度合いと解釈する分析法である。固有ベクトル方向に拡大した様子を分析することが，主成分分析の目的である，と説明する。

Web:How2SolveIt is a website provided for Gakushuin University to help students understand maths concepts,mainly in the areas of Economics and Business.The site offers a practical collection of quality study material,with useful videos.\ The site has been evaluated by "walking through" the student interface,applying some typical user cases,which are typical usage stories of student users.We recommend a few changes to the site,which would help students to find what they need easily, making it more attractive for students and for academics who contribute their materials.For example,the Home Page should give more useful context information and a text-entry search box should always be visible,with which students can navigate the collection of teaching resources.\ An attractive feature of the site is the hand-written question sheets,which explain or amplify important teaching points.Some changes to the presentation of the sheets and the videos would make them easier for students to follow.\ A usability study,where a small number of volunteers from the target demographic are observed while carrying out typical tasks,would quickly and cheaply give valuable insight into the way that real users respond to the site.\ Directions for possible future development of the site include:\ Adding further explanations,videos,notes and formulae to cover further topics in Business Maths\ Adding further content from other lecturers\ Offering the site to other students outside the Economics Faculty\ Offering the site to High School Students\ Developing a bi-lingual version of the site for teaching through the medium of English as well as Japanese\ These future directions would involve varying degrees of additional effort and investment.

Once a disaster occurs, people discuss various topics in social media such as electronic bulletin boards, SNSs and video services, and their decision-making tends to be affected by discussions in social media. Under the circumstance, a mechanism to detect topics in social media has become important. This paper targets the East Japan Great Earthquake, and proposes a time series topic detection method based on modularity measure which shows the quality of a division of a network into modules or communities. Our proposed method clarifies emerging topics from social media messages by computing the modularity and analyzing them over time, and visualizes topic structures. An experimental result by actual social media data about the East Japan Great Earthquake is also shown.

In many companies of the province of Tohoku (North-East Japan), stock prices were declining just after the East-Japan earthquake. However, on the other hand, some companies' stock prices rose in Tohoku. We have analyzed the reasons using text mining technologies on web data. In our studies, a combination of a stock price analysis and the text mining of the company can weave unexpected facts like a word associative game. First we surveyed stock prices of all listed companies that were headquartered in the damaged three prefectures in Tohoku. Then, we found the remarkable growth of YAMAYA which was an alcohol wholesaler and retailer company. The headquarters are located in Sendai-city, the capital and biggest city of Miyagi prefecture. On the other hand, we found YAMAZAWA's growth which was the same kind of an alcohol retailer company as YAMAYA. Although stock prices of almost all super markets in Tohoku intensely grew just after the disaster, the growth of YAMAYA and YAMAZAWA was distinguished. Therefore we conducted text mining to seek the reason of the company's stock price increase. As a result, we thought the alcohol consumption in Sendai-city caused the rapid stock price rises. In addition, from the comparison, we found that the recovery of YAMAZAWA's was quicker than that of YAMAYA's. We think that the reason for the YAMAYA's delay is that the earthquake damage in Sendai-city was larger than that in Yamagata. YAMAWA is headquartered in Sendai-city and YAMAZAWA is headquartered in Yamagata prefecture. The difference about locations would make the delay in the stock price recoveries. From the analysis, we inferred that an increase of alcohol consumption was one of the triggers for the economic reconstruction in Sendai-city. The paper discusses the economic reconstruction processes through increases of stock prices in the Tohoku province. © 2013 IEEE.

After the East Japan Great Earthquake occurred in Japan on 11th March 2011, many messages related to the earthquake were posted to social media. Especially, in Asian countries, a lot of messages about the earthquake were posted, so that different topics such as concerning about damages by the earthquake, afflicted people were observed, etc. observed. These topics can be recognized as reactions to the earthquake. Therefore, exploring topics related to the earthquake on social media in Asian countries gains a rich insight into the Asian social context. The goal of our research is to analyze Asian people reactions to the East Japan Great Earthquake on social media using data mining technique. As the first step, this paper targets Thai language and conducts the preliminary approximation to investigate topics on Thai social media. We analyze how Thai people reacted to the earthquake and compare with reactions in Japan. © 2013 IEEE.

Social media, which enable people to easily communicate and effectively share the information through the web, are rapidly spreading recently. In such media, effective topic extraction technique from messages has been significant so that trend topics and their reputation can be recognised. However, since messages contain redundancy and topic boundaries are ambiguous, it is difficult to extract appropriate topics. As the first step for topic extraction, this paper proposes an effective measure to automatic determination of appropriate number of topics based on the intra-cluster distance and the inter-cluster distance among topic clusters. We present our experimental results to show the effectiveness of our proposed approach. Copyright © 2012 Inderscience Enterprises Ltd.

This paper presents a concept model for solving bond mathematics problems; it is the manner in which our knowledge concerning bond mathematics is organized into a cognitive architecture. We build a concept model for bond mathematics to achieve good organization and to integrate the knowledge for bond mathematics. The ultimate goal is to enable many students to understand the solution process without difficulty. Our concept model comprises entity-relationship diagrams, and using our concept models, students can integrate financial theories and mathematical formulas. This paper illustrates concept models for bond mathematics by showing concrete examples of word mathematics problems. It also describes our principles in developing the concept model and the descriptive power of our model.

This paper proposes a method to discover consumer behavior from buzz marketing sites. For example, in 2009, the super-flu virus spawned significant effects on various product marketing domains around the globe. Using text mining technology, we found a relationship between the flu pandemic and the reluctance of consumers to buy digital single-lens reflex camera. We could easily expect more air purifiers to be sold due to flu pandemic. However, the reluctance to buy digital single-lens reflex cameras because of the flu is not something we would have expected. This paper applies text mining techniques to analyze expected and unexpected consumer behavior caused by a current topic like the flu. The unforeseen relationship between a current topic and products is modeled and visualized using a directed graph that shows implicit knowledge. Consumer behavior is further analyzed based on the time series variation of directed graph structures.

我々は，経営数学教育における推論の重要性を感じ，講義においても，演繹過程を解法プラングラフとして学生に提示し，推論力養成を目標としてきた。本稿では，経営数学の問題解法において，どのような推論が行われているかを，事例を挙げながら論じる。我々は，その推論は，未知数から始まり，与えられたデータの方向に向かっている，つまり逆向きに推論がなされていると考えた。また，その過程において，学習者はアブダクションにより部分目標を設定していると考えた。この考えに基づき，学習支援システムにおいて，そうした特徴をもつ学習者の推論を支援する機能をどのように実現していくかを論じる。

我々は2011年3月の東日本大震災によって引き起こされた経済活動における事象の記録,震災という未曽有の経済的混乱の状況下での被害状況および復興のようすを,若い世代に伝えたいと考える.そのためにはビジュアルな表現が有効であるが,単に客観的データをグラフ化するだけではなく,テキストマイニングで得た時事情報などを経済指標データに付加し,時系列にデータが変化するようすを可視化していきたい.まず,webから入手可能な経済の指標の時系列データを保存する.そして,それらの経済事象間の関連を多層的に解釈分析し,スライダーバーの付加,3次元表現などにより,分かりやすいデータの可視化を行う.若い世代に伝えることを目的とした場合,経済分析結果を論文として発表するだけでは効果が薄いので,初めから,若い世代むけ教材作成を研究目標とする.経済分析の方針としては,奥村の提唱する,リアルタイムとイグノランスを取り入れた構造分析の方針をとる.これにより,震災という不確実性の内在する状況下において各経済主体がどのような行動をとったかを,リアルタイムにストーリーをもって伝えることができる.

When the student is not able to solve a given problem, a plausible deductive reasoning process should be offered to him/her. Our final goal is a development of an e-Learning system which could help students not too much and not too little so that they can acquire as much deductive experience of independent work as possible. In the paper, we illustrate a solution plan graph which is a plausible deductive reasoning material with a concrete word problem. Our guiding principle for conducting the deduction is the thinking method of "working backwards" from the unknown. The paper also illustrates the details of the working backwards method.

金融工学数学のためのグラフィクス教材のデータベースのWEB サイトを立ち上げたので報告する。金融工学数学は難しいと言われるが，数学を理解させるために，グラフィクスの利用は有効であり，その利用により学生の理解度を高めることが可能である。我々は，大学および高校の数学授業において，グラフィクス教材をもっと多く活用してもらうためにこのサイトを開いた。そのため，数式処理ソフトウェアとしては，国内でも普及しているフリーソフトであるMAXIMA（マキシマ）を使った。本稿の目的は，グラフィクス教材作成に際して，ユーザー自身が，パラメータ値を自由に変更でき，ユーザー独自の金融工学数学グラフィクス教材を作成できるようにすることである。教材の内容としては，グラフィクスが効果的に生かせるテーマをとして，ポートフォリオの効率的フロンティア及びイミュニゼーションのテイラー展開描画，住宅ローン，年金の増加関数と減少関数の描画，債券価格の３次元的描画などを選んだ。本稿では，我々が研究中である，債券数学の学習支援システム構想にもふれ，このグラフィクス教材データベースが，その一部であることを説明する。

筆者の経営数学の講義では，学生に推論エンジンをシミュレーションさせる教授法「推論エンジンシミュレーション法（Inference Engine Simulating Method）」を行っている。本方法においては、学生にまず2 種類のルール・データベースを頭の中に構築してもらう。ひとつは数学公式をルールとする，数学ルール・データベースである。もうひとつは，経済・経営に関するルール・データベースであり，経済・経営に関するセオリーがルールとして蓄積されている。経営に関する文章題が与えられた場合，推論エンジンシミュレーション法では，第一に，文中の重要キーワードを探し，そのキーワードを使って，2 種類のルール・データベースを検索し，関連するルールを収集する。そして，そのルールの集合に対して,演繹推論を行い，文章題で与えられたデータと,未知数との間の関係を求めていく。本稿では,筆者の経営数学1 の講義においてこの推論エンジンシミュレーション法を用いた結果，学生の学習効果がどれほど向上したかをアンケートにより調査する。In my business mathematics class, I conduct my original heuristics titled "Inference Engine Simulating Method" so that students can solve mathematics problems by simulating the inference engine system. In the method, the students in advance have to construct two kinds of rule databases in their heads; one is a mathematics rule database where mathematics formulas are stored and another is an economics rule database where economics theories are stored. Given a mathematics word problem, the students will firstly find the most important keyword among the words. Then with the keyword, they will retrieve the rule databases to collect the related rules. Secondly, the students conduct the deductive reasoning on the rules to find the relationship between the given data in the problem words and the unknown. In my business mathematics lectures, I have used this Inference Engine Based Instruction Method. To analyze the effects of this method, I conducted the questionnaires in my class. The results will be shown in the paper.