最近オプション取引を学びながら以上の単語を見ました。 The Black-Scholes formula for option pricing is based on the assumption of geometric Brownian motion of stock returns. Stock returns are considered to be normally distributed about a mea…

最近オートマタ理論に関する本を読んでいます。What has captured my interest the most is the dependency relationship between four fundamental concepts of computer science: automata, grammars, languages, and computational complexity. The three…

最近Rの統計開発環境を使用してｌｍの関数を試しています。 I am confused about what exactly this function does. lm(y~x) supposedly computes a linear model in which y depends on x. Does this mean that a line through the data is computed. Outpu…

債権の基本の説明に戻って以前に読んで印象を書いた記事と比較しています。A forward rate for a bond is an given in slides I read (from a course at the University of Waterloo) to be the rate beginning at a future time period which is implied by…

現在Vasicekの論文を読んでいます。彼の導出に分からない事が多いです。 The objective of the paper seems to be to provide formulas to determine the present value of bonds and their term interest rates, given a maturity date. One point I do not…

I am uncertain as to how Einstein can justify the statement that the gravitational mass of a body is equivalent to its inertial mass. 重力場を磁場に比べます。 Just as a magnetic field causes action to take place on a piece of iron indirect…

最近アインシュタインの特例相対理論を読みながら４次元の空間を考えています。 Basically, I was wondering why the four-dimensional view of space and time is superior to the old one, that of a three-dimensional space and separate single dimensi…

時計と原子の比較に戻ります。 Let r' be the rate of a clock in K' and r be its rate in K. Then r = r'(1+phi/c**2). In the previous discussion, phi was related to angular velocity and the radius of rotation. Apparently, the vibrations of lig…

最近アインシュタインの相対性理論を再読しています。 Relativity basically involves the differences in our perception of temporal and spatial position depending on our frame of reference. In an appendix to his relativity treatise, Einstein di…

六件前に解説しようとした記事は先のアルゴリズムと関係がありそうです。 The recursion given by Kung was: a(ij)(1) = a(ij) a(ij)**(k+1) = a(ij)**(k)+l(ik)*(-u(kj)) l and u are elements in the lower triangular matrix L and upper triangular matr…

1. Note that, in the Doolittle algorithm, it is assumed that a(n,n) is non-zero for all n. Otherwise, the l(i,j)=-a(i,j)/a(n,n) term is undefined. 2. Proof that the inverse of a lower triangular. The proof is by contradiction. Let A be an …

アルゴリズムの詳細と証明を書きたいです。 In each iteration of the Doolittle algorithm, elements below the main diagonal in one of A's columns are eliminated. The result is an upper triangular matrix U, and the complexity is (2/3)n**3 (yet …

I have three objectives in examining LU factorization: 1. Consider the concepts and applications of this technique. 2. Examine at least one specific algorithm and possibly prove it works. 3. Compare the algorithm with the recurrence used b…

While I have worked on programs to infer numerical solutions to ordinary differential equations of a single variable, I have yet to complete any work involving partial differential equations. These are somewhat more complex, as the derivat…

In a recent programming competition, I wrote a program to execute a breadth first search through a state space of 9-character strings, in which each character was a distinct digit 1-9. The goal was, given a 3 by 3 matrix of digits 1-9, per…

I mentioned positive definite symmetric matrices in conjunction with LU factorization via systolic arrays in the previous post. A symmetric matrix is one which equals its transpose, e.g. 1 2 3 2 9 4 3 4 7 A positive definite matrix is one …

I recently perused a patent application by Professor Kung of Carnegie Mellon for a systolic array apparatus to be used in matrix computations. The arrays are multiple inner product step processors connected in a grid formation. Each proces…

今日コンピュータの歴史に関する記事を読みました。最初の電子計算機は微分方程式を解くために作成されました。 What I am wondering is why numerical differential equation solving is necessary. Couldn't the equations be solved analytically and the…

最近PRDCの利益を考えています。 These notes seem to involve an attempt by the investor to profit if the domestic currency (in this case yen) declines against the foreign currency (usually the dollar) and if the domestic interest rate either…

コンピュータサイエンスのシステム構成のひとつの課題は命令の順番を決める方法です。 An important topic for the past 25 years has been instruction level parallelism, which seems to be the ability for multiple instructions to be executed on one…

最近一行ずつガイウス・プリニウス・セクンドゥスの博物誌をラテン語から英語に翻訳しています。 全書は三十六冊ですけどまだ前書きを読んでいます。ところでウィキペディアによると三十七冊が含まっています。差の理由をまだ調べていません。 Pliny the Eld…

最近先物と派生証券の値計算に関してを読んで利率をたくさんな計算式に見ています。 It seems that the use of continuously compounded interest is critically important to valuation of futures, options, and other instruments. One area where compou…

最近情報取得に関する本を読んでいます。 検索エンジンの目的はユーザーが入力するクエリーに合う文書を調べる事です。 Issues involved in search engine architecture are: 1. Document tokenization 2. Index construction 3. Query parsing and index lo…

最近金融の計算方式を味わっています。数学が特に役に立つところが派生証券のリスク計算だと思います。 Matlab is used to automate computations, remember the results, and visualize output. It provides an interpreter and scripting front end to wha…

今回は二つの課題について書きます。一つはComputational complexity of computing Nash equilibriaです。もう一つは「将来の研究」です。 Traditional complexity theory studies tend to involve the notions of P and NP. P refers to a problem which ca…

最近目を通している論文はスタンフォード大学のラッフガーデン教授が書いた物です。 The objective of Algorithmic Game Theory seems to be the application of theoretical computer science concepts like quantitative computational models and proven …

無理だと判断する事が大変な将来になりそうですがどうやってこれを手に入れる事を考えると悩みます。 哲学か社会学に答えを探せばいいかも知れません。

微分方式の解答を見積もるために二つの絶対値の方法を比較します。 The way be which error in numerical approximations to the solutions of ordinary differential equations is measured involves convergence. Namely, as n goes to infinity, do measu…

複数のサッブキーを使う場合に一つの値を解き当ててほかのキーを計算する方法があるらしいです。 Another form of cryptanalysis is known as the "Meet in the Middle Attack". If equations for the cipher express the ciphertext in terms of the plaint…

コンピューターで物理的なシステムの模擬実験をする場合に微分方程式を計算しなければいけない時が多いと思います。この方程式は代数学的に解くと絶対値的に解く方法がある。機会にはほとんどの場合に代数学的な解答が無理です。 Concerns involved in solvi…