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A Mathematical Approach to Research Problems of Science and Technology

Part of the Mathematics for Industry Book Series (volume 5)

Editors: Nishii, Ryuei; Ei, Shin-ichiro; Koiso, Miyuki; Ochiai, Hiroyuki; Okada, Kanzo; Saito, Shingo; Shirai, Tomoyuki

DOI: 10.1007/978-4-431-55060-0

ISBN: 978-4-431-55059-4

Publisher: Springer Japan - Springer Journals

Jul 15, 2014

21 - 30 of 36 Chapters

LitStream

An Introduction to the Minimum Description Length Principle

Takeuchi, Jun’ichi

Pages: 279 –296

[We give a brief introduction to the minimum description length (MDL) principle. The MDL principle is a mathematical formulation of Occam’s razor. It says ‘simple explanations of a given phenomenon are to be preferred over complex ones.’ This is recognized as one of basic stances of scientists,...
LitStream

An Introduction to Ergodic Theory

Trinh, Khanh Duy

Pages: 297 –309

[Ergodic theory concerns with the study of the long-time behavior of a dynamical system. An interesting result known as Birkhoff’s ergodic theorem states that under certain conditions, the time average exists and is equal to the space average. The applications of ergodic theory are the main...
LitStream

Discrete Optimization: Network Flows and Matchings

Kamiyama, Naoyuki

Pages: 313 –323

[In this paper, we give a brief introduction to network flow problems and matching problems that are representative problems in discrete optimization. Network flow problems are used for modeling, e.g., car traffic and evacuation. Matching problems are used when we allocate jobs to workers and...
LitStream

Strict Feasibility of Conic Optimization Problems

Waki, Hayato

Pages: 325 –335

[A conic optimization problem (COP) is the problem of minimizing a given linear objective function over the intersection of an affine space and a closed convex cone. Conic optimization problem is often used for solving nonconvex optimization problems. The strict feasibility of COP is important...
LitStream

Theory of Automata, Abstraction and Applications

Mizoguchi, Yoshihiro

Pages: 337 –348

[We introduce computational models, such as sequential machines and automata, using the category theory. In particular, we introduce a generalized theorem which states the existence of the most efficient finite state automaton, called the minimal realization. First, we introduce set theoretical...
LitStream

Markov Chain Monte Carlo Algorithms

Maruyama, Osamu

Pages: 349 –363

[Markov chain Monte Carlo (MCMC) methods are a general framework of algorithms for generating samples from a specified probability distribution. They are useful when direct sampling from the distribution is unknown. This article describes theory of MCMC, presents two typical MCMC algorithms...
LitStream

Modeling of Fluid Flows by Nonlinear Schrödinger Equation

Fukumoto, Yasuhide

Pages: 365 –378

[Fluid flows exhibit diverse ways of their behavior, from ordered to chaotic and turbulent motion. The Navier-Stokes or Euler equations governing such motion are formidable as they are, and even the highest performance computers have difficulty in producing accurate and therefore useful...
LitStream

Financial Applications of Quasi-Monte Carlo Methods

Tezuka, Shu

Pages: 379 –392

[This article overviews major developments in the last two decades on the applications of quasi-Monte Carlo methods to financial computations.]
LitStream

Pure Mathematics and Applied Mathematics are Inseparably Intertwined: Observation of the Early Analysis of the Infinity

Takase, Masahito

Pages: 393 –399

[In this work I consider the connection between pure mathematics and applied mathematics from a historian’s point of view and I conclude that pure mathematics and applied mathematics are inseparably intertwined.]
LitStream

High Performance Computing for Mathematical Optimization Problem

Fujisawa, Katsuki

Pages: 401 –421

[The semidefinite programming (SDP) problem is one of the central problems in mathematical optimization. The primal-dual interior-point method (PDIPM) is one of the most powerful algorithms for solving SDP problems, and many research groups have employed it for developing software packages....

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