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１．特　　論               ２．特別講義

2009

この講義は、人間が音を聞くということに関連した音響学とオーディオ技術の理解を深めることを目的としている。特に、音響学、信号処理、心理音響、空間音響、オーディオシステムといった５つの基本的なトピックについて、それらが人間とどのように関連するかに焦点を当てて紹介する。音響学では、人間の環境中で音がどのような振る舞いをするかについて、室内音響や騒音も含め説明する。信号処理では、ディジタルオーディオの基本ツールについて概観する。心理音響では、音の大きさの原理や他の心理音響パラメータについて紹介する。空間音響では、音像定位の原理や他の空間知覚について触れる。オーディオシステムでは、オーディオシステムの原理やその評価方法について述べる。７回の講義のうち、最後の２回では、これまでに学んできた原理をソニフィケーションにいかにして適応するかについて言及する（ソニフィケーションとは、音声ではない音信号によるデータの表現・提示方法のことである）。この講義は、特に、音、音響、オーディオシステムを人間へ応用する技術に興味がある学生には有用であろう。

Research in communication networking is about efficient sharing of network resources such as link bandwidth and router buffer space. The research problem can be formulated as an optimization problem to achieve optimal performance where the performance metric can be delay, throughput, fairness, etc. The complexity of solving the optimization depends on whether the problem is linear or non-linear, constrained or unconstrained, convex or non-convex, etc. In this lecture series, linear programming (LP) will first be introduced since many network optimization models actually are special types of linear programming problems. A remarkably efficient solution technique, the simplex method, will be described. The concept of duality and its many important ramifications in linear programming will also be discussed since the relationships between the dual problem and the original primal problem prove to be extremely useful in many situations. The second part of the lecture will introduce non-linear programming (NLP) since some network optimization problem is non-linear. The optimality conditions, known as the Karush-Kuhn-Tucker (KKT) conditions will be discussed and the concept of duality will also be introduced. Applications of LP and NLP with specific examples in network optimization will be illustrated. The first application is introduced through the network flow problem which is formulated as a linear programming problem. The third part of the lecture series will continue to discuss about applications specific to network optimization. The example will be drawn from the bandwidth sharing problem. The concept of fairness and Pareto efficiency will be introduced. The optimal bandwidth sharing problem will be formulated as a Network Utility Maximization (NUM) problem. Through the KKT conditions and the duality theory, a distributed method to obtain the optimal solution will be presented to illustrate the important application of duality theory. Students will have the opportunity throughout the course to use the optimization solver, Lingo, to solve some of problems discussed in the course.