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2009. 10. 12. 22:24 @GSMC/이재준: Media Aesthetics
Aesthetic Computing, MIT Press

Chapter 3
A Forty-Year Perspective on Aesthetic Computing in the Leonardo Journal
Roger F. Malina





notes

1. Leonardo/ISAST is a professional organization that seeks to document and promote the work of
artists whose work involves contemporary science and technology, and to stimulate collaboration
among artists, scientists, and engineers. The Leonardo publications can be accessed at http://www.leonardo.info. These publications include the Leonardo journal, Leonardo Music Journal, the Leonardo
Book Series, and the electronic publications LEA and Leonardo On Line.

2. See, for example, the New Media Dictionary project, at http://www.comm.uqam.ca/GRAM/
Accueil.html. A number of researchers have been documenting the rapid mutation of terminology.
No good comprehensive cross-linguistic thesauruses exist.

3. See http://portal.unesco.org/digiarts. The UNESCO DIGIARTS program supports a number of
regional initiatives, as well as work in schools, through the young digital creators program.

4. See Intel Art and Entertainment Research Committee at http://www.intel.com/research/
university/aim/arts.htm.



references

Ascott, R. 1968. ‘‘The Cybernetic Stance: My Process and Purpose.’’ Leonardo 1(2): 105–12.

Ascott, R., and Loeffler, C. 1991. ‘‘Connectivity: Art and Interactive Telecommunications.’’ Leonardo 24(2): 1–85.

Bolter, J., and Gromala, D. 2003. Windows and Mirrors. Cambridge, MA: MIT Press.

Fishwick, P., et al. 2003. ‘‘Aesthetic Computing Manifesto.’’ Leonardo 36(4): 255.

Galloway, A. 2004. Protocol. Cambridge, MA: MIT Press.

Goldberg, K. 2000. The Robot in the Garden: Telerobotics and Telepistemology in the Age of the Internet. Cambridge, MA: MIT Press.

Harris, C., ed. 1999. Art and Innovation. Cambridge, MA: MIT Press.

Malina, F., ed. 1979. Visual Art, Mathematics and Computers: Selections from the Journal Leonardo. Oxford, UK: Pergamon Press.

Mallary, R. 1969. ‘‘Notes on Jack Burnham’s Concepts of a Software Exhibition.’’ Leonardo 3(2):
189–90.

Malloy, J. 2003. Women, Art and Technology. Cambridge, MA: MIT Press.

Manovich, L. 2001. The Language of New Media. Cambridge, MA: MIT Press.

Mitchell, W., ed. 2003. Beyond Productivity: Information Technology, Innovation and Creativity. Washington, DC: National Academy Press.

Naimark, M. 2003. Truth, Beauty, Freedom, and Money: Technology-Based Art and the Dynamics
of Sustainability. Accessed at http://www.artslab.net.

Rabinowitz, S., and Galloway, E. 1984. Cafe´ Manifesto. Accessed at http://main.ecafe.com.

Reichardt, J., ed. 1968. ‘‘Cybernetic Serendipity: The Computer and the Arts.’’ Studio International
special issue. London: Studio International.

Rheingold, H. 2002. Smart Mobs: The Next Social Revolution. Cambridge, MA: Perseus Publishing.

Snow, C. P. 1993. The Two Cultures. Cambridge: Cambridge University Press.

Wilson, S. 2002. Information Arts: Intersections of Art, Science, and Technology. Cambridge, MA: MIT
Press.


posted by maetel
2009. 10. 7. 20:42

보호되어 있는 글입니다.
내용을 보시려면 비밀번호를 입력하세요.

2009. 10. 7. 16:24

보호되어 있는 글입니다.
내용을 보시려면 비밀번호를 입력하세요.

2009. 10. 7. 16:21

보호되어 있는 글입니다.
내용을 보시려면 비밀번호를 입력하세요.

2009. 10. 7. 16:19

보호되어 있는 글입니다.
내용을 보시려면 비밀번호를 입력하세요.

Paul Fishwick <Aesthetic Computing>
: I Philosophy and Representation
: 1 an introduction to aesthetic computing, Paul Fishwick

전문 번역:




http://www.cise.ufl.edu/~fishwick/aescomputing/


in the context of related fields that combine art, mathematics, and computing
예술, 수학, 컴퓨팅이 결합되는 관련 분야들의 맥락에서

the impact and effect of aesthetics on the field of computing
미학이 컴퓨팅 분야에 미치는 파급 효과

the relationship between aesthetics and art ; "aesthetics being the philosophy of art"
미학과 예술의 관계 - "예술에 대한 철학으로서의 미학"

on the notion that aesthetics and art could play a role in computing disciplines
미학과 예술이 컴퓨팅 분야에서 모종의 역할을 할 수 있다는 전제로


Roger Malina
http://www.leonardo.info/rolodex/malina.roger.html
http://www.linkedin.com/in/rmalina

Christa Sommerer
http://www.interface.ufg.ac.at/christa-laurent/index.html
http://www.linkedin.com/pub/christa-sommerer/8/7a8/881

Paul Fishwick
http://www.cise.ufl.edu/~fishwick/

Univ. of Florida's cap 6402:Aesthetic Computing tutorial
- aesthetics to structures

source: Florida Uni. cap 6402:Aesthetic Computing tutorial


> Framework for creative exploration
1. Identification
2. Graph
3. Ontology
4. Map
5. Representation
(6. Assessment)

eg. Aesthetic Computing Student Models - 3d models
http://www.cise.ufl.edu/~fishwick/rube/studentmodels/3dPhysicalModels.html

The Art of Modeling - "The medium is the model"
"미디어는 모델이다"

Dagstuhl Seminar (Aesthetic Computing) 02291. 2002
http://www.dagstuhl.de/de/programm/kalender/semhp/?semnr=02291



Aesthetics

aesthetic computing
Aesthetic computing is the application of aesthetics to computing, which will be defined broadly as the area of computer science, and mathematics, the formal foundations for computing.
심미적 컴퓨팅은 미학을 컴퓨팅, 보다 넓게는 컴퓨터 과학, 그리고 컴퓨팅의 형식적 기반인 수학에 적용한 것(application)

beyond classic concepts such as symmetry and invariance to making art
대칭성이나 불변성과 같은 고전적 관점을 넘어 '예술을 만드는 것'과 관련된 통상적인 미학적 정의와 범주까지


aesthetics의 정의
어원
<- [그리스어] aisthitiki (aisyhtikh´)
<- aisthesis (i.e., perceived by the senses) 감각적으로 지각된
-> Plato’s aesthetics -> his 'forms' '형식'
-> Greek society's mimesis (i.e., imitation, mimicry) 모방, 흉내

의미 변환 - 예술과의 상관성
Baumgarten (1750)의 the 'science of the beautiful' 등 이전에는 예술과 미학을 별개로 취급함
Kant가 Critique (1790) 란 논문에서 감성을 논리적인 측면과 지각적인 측면 양쪽으로 확장시킴

현대적 해석
Oxford English Dictionary (2003): (1) the science that treats the conditions of sensuous perception; and (2) the philosophy or theory of taste, or of the perception of the beautiful in nature and art.
1) 감각적 지각 (sensuous perception)의 조건을 다루는 과학 2) 자연과 예술 작품에 담긴 아름다움에 대한 지각, 즉 취향에 관한 철학 또는 이론

Kelly (the Encyclopedia of Aesthetics, 1998): Aesthetics is the philosophical analysis of the beliefs, concepts, and theories implicit in the creation, experience, interpretation, or critique of art.
예술의 창작, 경험, 해석, 비평에 내재되어 있는 신념과 개념 그리고 이론을 철학적으로 분석하는 것
-> 미학의 철학적 역할과 문화적 역할을 통합하고자 미학의 계보를 추적
-> 예술의 정의의 확장: 논리적 측면과 물질적 측면, 즉 컴퓨팅과 예술을 결합 -> 대칭, 조화, Dali 등의 초현실주의

Bredin and Santoro-Brienza (2000) and Osborne (1970) : Aesthetics provides a philosophical foundation for art in theory and practice.
미학은 예술의 이론과 경험에 대한 철학적 기반이 된다.

http://en.wikipedia.org/wiki/Theory_of_Forms


art의 정의
Dorn (1999)
사상, 형식 또는 언어로서의 철학적 정의 + 하향식(top-down) 그리고 상향식(bottom-up)의 심리적 개념

Adams (1996) and Freeland (2001) - 특정 역사와 문화의 맥락에서 보는 관점
Adams - formalism, iconography, Marxism, feminism, biography, semiotics, and psychoanalysis
형식주의, 도상학, 막시즘, 페미니즘, 생물학, 기호학, 정신분석학 등을 동원한 현대적 해석

Wilson (2002)
수많은 영역, 실례, 당대의 쟁점이 예술가에게 영향을 미친다고 주장

Edwards (1986) and Edmonds and Candy (2002)
창작이란 과정에 자리한 예술의 실용주의적 역할을 조명



Computing

> computing의 정의
: 컴퓨터 과학, 컴퓨터 정보 과학, 컴퓨터 공학 등의 총칭 ( an assortment of names such as computer science, computer and information science, and computer engineering)

> computer science 컴퓨터 과학의 하위 영역
: 수학, 컴퓨팅 이론, 프로그래밍 언어, 데이터 구조, 인공 지능, CHI or HCI (computer-human or human-computer interaction), 운영 체제, 컴퓨터 그래픽스, 컴퓨터 시뮬레이션, 컴퓨터 비전.
 
Denning (2003)

(source: Denning 2003)


Levels of action in computing practices. (source: Denning 2003)



수학
discrete mathematics  이산수학 (離散數學)
: 컴퓨터 과학(computer science)의 기초 핵심 이론이며 automata 이론에서 대수학적으로 확장됨

formal  grammar, language notation, geometry, and topology
형식 문법, 언어 표기, 기하학, 위상학

"Mathematics establishes the formal infrastructure in which mathematical concepts and abstractions can be related to basic computing concepts."
수학적 개념과 추상화가 컴퓨팅의 기초 개념으로 이어짐으로써, 수학은 컴퓨팅의 형식적 하부 구조를 정립하게 된다.

http://en.wikipedia.org/wiki/Discrete_mathematics

http://en.wikipedia.org/wiki/Automata_theory
automaton (plural: automata or automatons) :  "자가 운영 기계 (self-operating machine)"

http://en.wikipedia.org/wiki/Topology

source: wikipedia, "topology"




Aesthetic Computing: An Overview

> aesthetic computing의 정의
: "the application of the theory and practice of art to the field of computing"
예술의 이론과 실천을 컴퓨팅에 적용한 것

> aesthetic computing의 실례(實例)
(1) representing programs and data structures with customized, culturally specific notations; (2) incorporating artistic methods in typically computing intensive activities, such as scientific visualization; (3) improving the emotional and cultural level of interaction with the computer
(1) 문화적으로 특별한 의미를 가진 맞춤화한 표기법을 가지고 프로그램과 데이터 구조를 재현하는 것
(2) 과학적 시각화와 같이 전형적으로 컴퓨팅이 집약된 활동에 예술적 방법을 적용하는 것
(3) 컴퓨터와의 상호작용을 감정적이고 문화적 차원으로 증진하는 것

> aesthetic applications 미학적 응용의 두 형태 : 분석 (analysis)과 종합 (synthesis)
- 분석적 응용:  컴퓨팅과 수학의 산물을 모방 (mimesis), 대칭 (symmetry), 최적화 (parsimony), 아름다움 (beauty)과 같은 미학적 '질 (qualities)'이라는 고전적인 관점에서 평가한다.  
- 종합적 응용: 미학을 컴퓨팅과 수학의 산물을 '재현'하는 수단으로 활용한다. (표현이 인터랙션과 인터페이스의 개념을 포함하는 것으로 확장됨)

my eg.
http://www.theyrule.net/
인터랙티브 태양계 시스템, 월간지 Newton
상대 체온 알림 메신저


plurality (Goodman 1978) -> aesthetic diversity (Fishwick 2002a) 미학적 다양성
육체와 마음, 물질과 정신을 아우르는 '다원성' -> 미학적 개념의 확장 -> 수학과 컴퓨팅에서의 미학을 예술 전반에 대한 미학의 일부로 규정 (예) 미니멀리즘, 대칭, 황금 비율)

multiperspectivism 다중조망주의

"Art has the potential to create new ways of looking, listening, and touching things that are relevant to computing: interfaces, programs, data, and models."
예술은 컴퓨팅과 관련한 것들 (인터페이스, 프로그램, 데이터, 모델)을 보고 듣고 만지는 새로운 방법들을 창조할 잠재력을 가지고 있다.

Aesthetic computing process architecture

미학적 컴퓨팅 과정의 구조 (source: Fishwick 2008: 7p)

위쪽의 컴퓨팅 영역에서 입자들이 떨어져 아래쪽의 미학적 컴퓨팅 영역으로 모래알처럼 쌓인다고 상상하자.

Subject/Medium filter 주제/매질 여과기
: using the computing discipline to provide a raw medium or the subject material for art
컴퓨팅을 예술의 (가공되지 않은) 원천 매개물 (raw medium) 또는 주제물 (subject material)로 만드는 여과기

http://en.wikipedia.org/wiki/Multiperspectivalism

my ref.
http://en.wikipedia.org/wiki/Edgar_Morin


물질성
Manovich 2001; Coyne 1999
materialism 유물론

embodiment (mind와 대조) 구현(具現)
Virtual reality, as discussed within the art literature (Grau 2003), is materialistic because it is consistent with embodiment and immersion in an enhanced sensory experience, regardless of whether this experience is real or illusory. Mental constructs, on the other hand, are nonsensory and so have no material existence. Continuing HCI and visualization research extends such materialistic qualities as presence, engagement, and immersion which facilitate human sensory connection to otherwise invisible information, or information that has minimal sensory qualities.

Grau 2003
가상 현실 (virtual reality)은 유물론적이다. 감각적 경험의 구현 (embodiment)과 몰입 (immerse)에 있어서 그 경험이 현실이든 환상이든 일치하기 때문이다. (한편, 정신적 구조는 비감각적이기 때문에 물질적 존재성이 없다.)

HCI와 시각화 연구
현전 (presence),  개입 (engagement), 몰입 (immersion)과 같이 인간의 감각을
비가시적 정보 (invisible information)와 연결해 주는 유물론적 특질을 확장한다.

http://en.wikipedia.org/wiki/Materialism


프로그램을 도구적 가치로만 사용하는 경우에는 컴퓨팅의 본질 (프로그램의 내용이나 데이터 구조 또는 수학적 기반)을 반영하지 않는다. 그러나, 재현 과정에 예술적 접근이나 방식이 들어가면 컴퓨팅의 요소들이 예술작품이 초점을 맞추는 주제물 (subject material)이 된다. (예) 소프트웨어 아트 (software art) : 프로그래밍을 매개로 하여 창조되는 예술)

사용성 (usability)이란 의미의 확장
좁은 의미의 performance-based interface usability (Nielsen 1993)에서 사용자의 정서에 기여할 필요성을 중시 (Picard 1997; Jordan 2000; Brave and Nass 2002; Norman 2004)

사용 (use)의 개념도 인간의 행위를 넘어서는 것으로 확장


> 사례

Diehl and Fishwick
컴퓨팅의 형식적 구조 (컴퓨터 프로그램이나 수학 모델)를 재현하는 데 미학을 적용

Prophet's Cell project (2003)

Löwgren
미래 인터페이스에 대한 미학적 요구 - 유연성 (pliability), 유창성 (fluency), 유혹성 (seductivity)

ARS Electronica Conference의 소프트웨어 아트 영역

Processing language (Fry and Reas)
http://processing.org/learning/basics/distance2d.html


Jonas Löwgren
http://webzone.k3.mah.se/k3jolo/
http://www.interaction-design.org/references/authors/jonas_lowgren.html


Emmer: "representing the solution space for mathematical structures (i.e., manifolds, surfaces, tessellations)"
수학적 구조를 심미적 필터를 거쳐 재현 (manifolds, surfaces, tessellations)

Fishwick (2002)


Leyton 2001 - group theory

Ferguson and Ferguson 1994 ‘‘stone and bronze’’

Lakoff and Nu´n˜ ez (2000)

Ferguson - Zero to Infinity in Nothing Flat



http://en.wikipedia.org/wiki/Mathematics_and_art
http://math-art.net/
http://mathartfun.com/

http://en.wikipedia.org/wiki/Tessellation


플라톤의 수학적 미학의 정의는 정리를 세우고 증명을 이끌어 내는 과정에서의 정신적 만족과 관련

Hadamard (1945) - 수학의 심리학적 본성

아인슈타인: "The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be ‘voluntarily’ reproduced and combined.’’

Emmer 1993 - 데카르트가 대수학과 기하학 그리고 현대적인 수학-예술 (math-art) 활동을 묶음

Petre and Blackwell (1999) - 프로그래머가 작업 중 수많은 시청각 효과를 상상한다고 보고

그러나 시각적 프로그래밍은 기술적 제한과 문화적 편견에 봉착한다. (디자인과 공학에 주어진 미결 문제)



Emmer (1993)
데카르트, 대수학 + 기하학 + 수학-예술 (math-art) 운동

Petre and Blackwell (1999)
visual programming

비문자 기반 표현은 항상 기술력에 제한을 받고, 새로운 인터페이스는 기존의 방식이 익숙하고 유효한 상황에서 문화적 반발을 산다.

http://en.wikipedia.org/wiki/Holodeck



Donald Knuth
프로그래밍의 문자적 부분은 기표(signifiers)를 지니며 예술이 추구하는 것과 같은 목표를 지향한다.

Nake (1974)
정보 처리 (information processing)

Gelernter (1998)
컴퓨팅에서의 미학의 당위성을 제시 - 매킨토시 컴퓨터 인터페이스



The Novelty of Aesthetic Computing


the Association for Computing Machinery (ACM)
the Institute for Electrical and Electronics, Engineers Computer Society (IEEE-CS)

심미적 컴퓨팅의 목적 중 하나는 미학을 촉매로 하여 컴퓨터 과학을 수정하는 것인 반면, 인공 생명에서는 인공 지능을 이용하여 새로운 형태를 만들기 위한 디자인이나 알고리즘을 창안하고자 하는 등 각 분야 별 입장 차이가 존재

시각화는 심미적 컴퓨팅이 발 디딜 수 있는 개인화나 맞춤화의 노력이 부족
(그러나 최근 디자인은 시각적으로 미니멀리즘을 띄는 경향이 있고, 사용자 생성 개념을 지향)

감성을 컴퓨팅한다는 것을 정의할 때 대칭이나 조화 같은 전통적 개념에 한정할 수 없고, 컴퓨팅의 형식적 구조 중에는 미학의 관점을 벗어나는 것들이 있음

Nadin 1991
미학적 알고리즘

심미적 알고리즘의 개념을 세우는 것이 디자인, 예술, 컴퓨팅 등 다른 분야를 보강하는 과정으로 진행되어야



Applying Aesthetics: The Artistic Influence


> 예술가들의 수학과 기술 사용
- 유클리드 기하학을 이용한 회화의 원근법
- Vermeer의  camera obscura의 사용
- Duchamp과 Escher 다차원 공간과 비유클리드 기하학의 적용
- 인공 생명, 생성 알고리즘, 카오스 이론

그런데 예술가들이 컴퓨팅에 실제로 영향을 주었다는 역사적 보고는 부재

미학을 컴퓨팅에 적용한다는 것의 의미를 살펴보기 위해 미학을 세 집단으로 나눔
- modality 양상 (樣相) : 사물과 상호접촉, 상호작용하는 방법 (아직은 HCI, 유비쿼터스 컴퓨팅, 증강현실, 가상현실, tangible computing 등의 분야는 컴퓨터 관련 기술력의 발전을 필요로 하므로 예술을 도입하기는 시기상조)
- culture : 다양한 예술 사조
XML:
<?xml version="1.0" encoding='UTF-8'?>
<painting>
<img src="madonna.jpg" alt='Foligno Madonna, by Raphael'/>
<caption>This is Raphael's "Foligno" Madonna, painted in
<date>1511</date>-<date>1512</date>.</caption>
</painting>
- quality : 칸트 이전의 일반적인 미학적 특질. 예술과 상응하는 것은 소수



Mathematical Modeling: Research at the University of Florida

심미적 여과기 (모델의 재현을 쉽게 변조하게 하는 소프트웨어 프레임웍)을 적용하여 미학을 컴퓨팅에 적용하는 데 종합적 접근을 취함

재현 단계에서 물질적 측면은 유효성, 사용성, 물질적 효율성을 가진 것에 기반을 둠

상태 (state)와 경계 (boundary)의 상징적 의미








references

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Fishwick, Paul. 1995. Simulation Model Design and Execution: Building Digital Worlds. Prentice Hall.

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Fishwick, Paul. 2003. ‘‘Aesthetic Computing Manifesto.’’ Leonardo 36(4): 255–56. MIT Press.

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Books.

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Knuth, Donald. 2003. Things a Computer Scientist Rarely Talks About. Stanford, CA: CSLI Publications.

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http://www.manovich.net/LNM/

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posted by maetel
LEONARDO
Roger F. Malina, series editor

The Visual Mind, edited by Michele Emmer, 1993

Leonardo Almanac, edited by Craig Harris, 1994

Designing Information Technology, Richard Coyne, 1995

Immersed in Technology: Art and Virtual Environments, edited by Mary Anne Moser with Douglas
MacLeod, 1996

Technoromanticism: Digital Narrative, Holism, and the Romance of the Real, Richard Coyne, 1999

Art and Innovation: The Xerox PARC Artist-in-Residence Program, edited by Craig Harris, 1999

The Digital Dialectic: New Essays on New Media, edited by Peter Lunenfeld, 1999

The Robot in the Garden: Telerobotics and Telepistemology in the Age of the Internet, edited by Ken Goldberg, 2000

The Language of New Media, Lev Manovich, 2001

Metal and Flesh: The Evolution of Man: Technology Takes Over, Ollivier Dyens, 2001

Uncanny Networks: Dialogues with the Virtual Intelligentsia, Geert Lovink, 2002

Information Arts: Intersections of Art, Science, and Technology, Stephen Wilson, 2002

Virtual Art: From Illusion to Immersion, Oliver Grau, 2003

Women, Art, and Technology, edited by Judy Malloy, 2003

Protocol: How Control Exists after Decentralization, Alexander R. Galloway, 2004

At a Distance: Precursors to Art and Activism on the Internet, edited by Annmarie Chandler and Norie
Neumark, 2005

The Visual Mind II, edited by Michele Emmer, 2005

CODE: Collaborative Ownership and the Digital Economy, edited by Rishab Aiyer Ghosh, 2005

The Global Genome: Biotechnology, Politics, and Culture, Eugene Thacker, 2005

Media Ecologies: Materialist Energies in Art and Technoculture, Matthew Fuller, 2005

From Technological to Virtual Art, Frank Popper, 2005

Art Beyond Biology, edited by Eduardo Kac, 2006

New Media Poetics: Contexts, Technotexts, and Theories, edited by Adalaide Morris and Thomas Swiss, 2006

Aesthetic Computing, edited by Paul A. Fishwick, 2006


posted by maetel
2009-09-09 수 @GA703


아름답다 <- 크다 <- 아름: 충만, 만족
미 = 그시 [일본]

미학
미학이란 인간의 감성적인 정신활동에서 나타나는 다양한 현상들을 철학적 반성 (질적 분석)과 과학적 분석 (양적 분석)을 통해 탐구하는 학문이다.


Platon
noesis (본질) - aesthesis (현상, 가상)

Aristoteles
poiesis (제작) - techne (행위)


sense 감관
sensation 감각
perception 지각
feeling (emotion) 감정
sensibility 감성

감성
인식론 - sensibility
인지과학 - sense, perception, emotion, affection
감성과학 - emotion and sensibility
미학 - the aesthetic property


Alexander Gottlieb Baumgarten (1714-1762)
<Aesthetica (미학)> 1 (1750), 2 (1758)

David Hume
Standard of Taste (취미기준론)

Immanuel Kant
Kritik der Urteilskraft (판단력 비판) (1790)


예술

Friedrich Wilhelm Joseph Schelling (1775-1854)
<Philosophie der Kunst (예술철학)> (1802-1805)

Georg Wilhelm Friedrich Hegel (1770-1831)
<Vorlesungen ueber die Aesthetik (미학강의)> (1817-1829)

Gustav Theodor Fechner (1801-1887)
Zur experimentalen Aesthetik (실험미학) (1871)
Vorschule der Aesthetik (1876)


미디어 미학

Walter Benjamin
Das Kunstwerk im Zeitalter seiner technischen Reproduzierbarkeit (1935)

M. McLuhan
Understanding Media
The Extensions of Man (1964)

W. Ong, Orality & Literacy
The Technologizing of the Word (1982)

J. D. Bolter, R. Grusin, Remediation
Understanding New Media
Cam. Mass., MIT Press (2000)

Welsch, Wolfgang (1993)
Deutsche Zeitschrift für Philosophie


뉴미디어

N. Wiener
Cybernetics: Orr the Control and Communication in the Animal and the Machine (1948)
The Human Beings (1950)

Bolter J. D. and Gromala, D
Windows and Mirrors (2008)
Interaction Design, Digital Art, and the Myth of Trasparency
Mass., MIT Press (2003)
진동: 오실레이션 (2008)

Nobert Bolz
Das Konstrollierte Chaos
Vom Humanismus zu Medienwirklichkeit, Econ Ullstein List Verlag GmbH & Co. KG (1995)
콘트롤된 카오스

S. Schmidt
Kognitive Autonomie und soziale Orientierung: Konstrucktivische Bemerkungen zum Zusammenhang von Kognition, Kommunikation, Medien und Kultur (1994)

N. Luhmann
System Theorie

N. Bolz
Medien Theorie

Maturana & F. Varela
Autopoiesis Theory


posted by maetel
Sahni
Data Structures, Algorithms and Applications in C++, 2nd ed.
: Chapter 16 Graphs

graph data structure

terminology:
vertex, edge, adjacent, incident, degree, cycle, path, connected component, and spanning tree

types:
undirected / directed / weighted

representation:
adjacent matrix / array adjacency lists /  linked adjacency lists

standard graph search methods:
breadth-first / depth-first search

algorithms:



16.1 Definitions

graph
: an ordered pair of finite sets of vertices (or nodes or points) and edges (or arcs or lines)

http://en.wikipedia.org/wiki/Graph_(data_structure)

loop
: self-edge

digraph
: directed graph

network
: weighted undirected graph or digraph


16.2 Applications and More Definitions

example 16.1: path problems

example 16.2: spanning trees

A graph is connected iff there is a path between every pair of vertices in the graph.

cycle
: simiple path with the same start and end vertex

tree
: a connected undirected graph that contains no cycles

spanning tree
: a subgraph of a graph that contains all the vertices of the graph and is a tree

example 16.3: interpreters

bipartite graphs


16.3 Properties

http://en.wikipedia.org/wiki/List_of_graph_theory_topics

in-degree
out-degree

complete digraph


16.4 The ADT graph
16.5 Representation of Unweighted Graphs

adjacency matrix
linked adjacency list
array adjacency list

http://en.wikipedia.org/wiki/Adjacency_matrix

http://en.wikipedia.org/wiki/Adjacency_list
16.6 Representation of Weighted Graphs


cost-adjacency-matrix


16.7 Class Implementations

 
16.8 Graph Search Methods

cp. level-order traversal of a binary tree
http://en.wikipedia.org/wiki/Binary_search_tree#Traversal

cp. pre-order traversal of a binary tree
 
 


 
posted by maetel
2009. 6. 11. 13:45

보호되어 있는 글입니다.
내용을 보시려면 비밀번호를 입력하세요.

2009. 6. 1. 01:51

보호되어 있는 글입니다.
내용을 보시려면 비밀번호를 입력하세요.

Yates & Goodman
Probability and Stochastic Process, 2nd ed.
Chapter 10 Stochastic Processes

http://en.wikipedia.org/wiki/Stochastic_process
One approach to stochastic processes treats them as functions of one or several deterministic arguments ("inputs", in most cases regarded as "time") whose values ("outputs") are random variables: non-deterministic (single) quantities which have certain probability distributions.


stochastic processes = random functions of time
-> time suquence of the events

time structure of a process vs. amplitude structure of a random variable
(autocorrelation function and autocovariance function vs. expected value and variance)

Poisson

Brownian

Gaussian

Wide sense stationary processes

cross-correlation



10.1 Definitions and Examples



NRZ 파형
http://en.wikipedia.org/wiki/Non-return-to-zero


posted by maetel
Yates & Goodman
Probability and Stochastic Process, 2nd ed.
Chapter 9 Estimation of a Random Variable

prediction
A predictor uses random variables produced in early subexperiments to estimate a random variable produced by a future subexperiment.


9.1 Optimum Estimation Given Another Random Variable


The estimate of X that produces the minimum mean square error is the expected value (or conditional expected value) of X calculated with the probability model that incorporates the available information.

Bind estimation of X

Estimation of X given an event

Minimum Mean Square Estimation of X given Y



9.2 Linear Estimation of X given Y


9.3 MAP and ML Estimation


9.4 Linear Estimation of Random Varaiables from Random Vectors




posted by maetel

Yates & Goodman
Probability and Stochastic Process, 2nd ed.
Chapter 8 Hypothesis Testing


statistical inference method
1) perform an experiment
2) observe an outcome
3) state a conclusion
 
http://en.wikipedia.org/wiki/Statistical_inference


8.1 Significance Testing

http://en.wikipedia.org/wiki/Significance_testing
In statistics, a result is called statistically significant if it is unlikely to have occurred by chance. "A statistically significant difference" simply means there is statistical evidence that there is a difference.  




http://en.wikipedia.org/wiki/Hypothesis_testing

8.2 Binary Hypothesis Testing

http://en.wikipedia.org/wiki/Binary_classification


Maximum A Posteriori Probability (MAP) Test

http://en.wikipedia.org/wiki/Maximum_a_posteriori_estimation

Minimum Cost Test

Neyman-Pearson Test

http://en.wikipedia.org/wiki/Neyman%E2%80%93Pearson_lemma

Maximum Likelihood Test

http://en.wikipedia.org/wiki/Maximum_likelihood


8.3 Multiple Hypothesis Test

posted by maetel
Yates and Goodman
Chapter 7 Parameter Estimation Using the Sample Mean

statistical inference

http://en.wikipedia.org/wiki/Statistical_inference
Statistical inference or statistical induction comprises the use of statistics and random sampling to make inferences concerning some unknown aspect of a population


7.1  Sample Mean: Expected Value and Variance

The sample mean converges to a constant as the number of repetitions of an experiment increases.

Althouth the result of a single experiment is unpredictable, predictable patterns emerge as we collect more and more data.


sample mean
= numerical average of the observations
: the sum of the sample values divided by the number of trials


7.2 Deviation of a Random Variable from the Expected Value

Markov Inequality
: an upper bound on thte probability that a sample value of a nonnegative random variable exceeds the expected value by any arbitrary factor

http://en.wikipedia.org/wiki/Markov_inequality


Chebyshev Inequality 
: The probability of a large deviation from the mean is inversely proportional to the square of the deviation

http://en.wikipedia.org/wiki/Chebyshev_inequality


7.3 Point Estimates of Model Parameters

http://en.wikipedia.org/wiki/Estimation_theory
estimating the values of parameters based on measured/empirical data. The parameters describe an underlying physical setting in such a way that the value of the parameters affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements.

http://en.wikipedia.org/wiki/Point_estimation
the use of sample data to calculate a single value (known as a statistic) which is to serve as a "best guess" for an unknown (fixed or random) population parameter


relative frequency (of an event)

point estimates :
bias
consistency
accuracy

consistent estimator
: sequence of estimates which converges in probability to a parameter of the probability model.



The sample mean is an unbiased, consistent estimator of the expected value of a random variable.

The sample variance is a biased estimate of the variance of a random variable.

mean square error
: expected squared difference between an estimate and the estimated parameter

 The standard error of the estimate of the expected value converges to zero as n grows without bound.

http://en.wikipedia.org/wiki/Law_of_large_numbers


7.4 Confidence Intervals

accuracy of estimate

confidence interval
: difference between a random variable and its expected value

confidence coefficient
: probability that a sample value of the random variable will be within the confidence interval

posted by maetel
central limit theorem
http://en.wikipedia.org/wiki/Central_limit_theorem


6.1 Expected Values of Sums

Theorem 6.1
The expected value of the sum equals the sum of the expected values whether or not each variables are independent.

Theorem 6.2
The variance of the sum is the sum of all the elements of the covariance matirx.


6.2 PDF of the Sum of Two Random Variables

Theorem 6.5
http://en.wikipedia.org/wiki/Convolution

linear system
http://en.wikipedia.org/wiki/Linear_system
 

6.3 Moment Generating Functions

In linear system theory, convolution in the time domain corresponds to multiplication in the frequency domain with time functions and frequency functions related by the Fourier transform.

In probability theory, we can use transform methods to replace the convolution of PDFs by multiplication of transforms.

moment generating function
: the transform of a PDF or a PMF

http://en.wikipedia.org/wiki/Moment_generating_function

http://en.wikipedia.org/wiki/Laplace_transform

region of convergence


6.4 MGF of the Sum of Independent Random Variables

Theorem 6.8
Moment generating functions provide a convenient way to study the properties of sums of independent finite discrete random variables.

Theorem 6.9
The sum of independent Poisson random variables is a Poisson random variable.

Theorem 6.10
The sum of independent Gaussian random variables is a Gaussian random variable.

In general, the sum of independent random variables in one family is a different kind of random variable.

Theorem 6.11
The Erlang random variable is the sum of n independent exponential random variables.


6.5 Random Sums of Independent Random Variables

random sum
: sum of iid random variables in which the number of terms in the sum is also a random variable

It is possible to express the probability model of R as a formula for the moment generating function.


The number of terms in the random sum cannot depend on the actual values of the terms in the sum.


6.6 Central Limit Theorem

Probability theory provides us with tools for interpreting observed data.

bell-shaped curve = normal distribution


So many practical phenomena produce data that can be modeled as Gaussian random variables.


http://en.wikipedia.org/wiki/Central_limit_theorem

Central Limit Theorem
The CDF of a sum of random variables more and more resembles a Gaussian CDF as the number of terms in the sum increases.
 
Central Limit Theorem Approximation = Gaussian approximation


6.7 Applications of the Central Limit Theorem

De Moivre-Laplace Formula

http://en.wikipedia.org/wiki/Theorem_of_de_Moivre%E2%80%93Laplace
normal approximation to the binomial distribution


6.8 The Chernoff Bound

Chernoff Bound

http://en.wikipedia.org/wiki/Chernoff_bound
exponentially decreasing bounds on tail distributions of sums of independent random variables


posted by maetel
By F. S. Hill, Jr., Francis S. Hill, Stephen M. Kelley, Stephen M. Kelley, Jr.
Edition: 3, illustrated, revised
Published by Prentice Hall, 2006
ISBN 0131496700, 9780131496705
posted by maetel

Sartaj Sahni
Data Structures, Algorithms, and Applications in C++

Chapter 8 Stacks



http://cplusplus.com/reference/stl/stack/

http://en.wikipedia.org/wiki/Stack_(data_structure)

http://www.sgi.com/tech/stl/stack.html

http://www.cppreference.com/wiki/stl/stack/start


stack = a linear list with a last-in-first-out (LIFO) structure

recursion stack

return address = location of the program instruction to execute once the invoked method completes


http://en.wikipedia.org/wiki/Abstract_data_type
An abstract data type (ADT) is a specification of a set of data and the set of operations that can be performed on the data. Such a data type is abstract in the sense that it is independent of various concrete implementations.

In software engineering, an abstract type is a type in a nominative type system which is declared by the programmer, and which has the property that it contains members which are also members of some declared subtype. In many object oriented programming languages, abstract types are known as abstract base classes, interfaces, traits, mixins, flavors, or roles.


http://cplusplus.com/reference/std/exception/exception/




posted by maetel
2009. 4. 2. 01:48

보호되어 있는 글입니다.
내용을 보시려면 비밀번호를 입력하세요.

Yates & Goodman
Probability and Stochastic Process, 2nd ed.

3.1 The Cumulative Distribution Function



3.2 Probability Density Function



3.3 Expected Values



3.4 Families of Continuous Random Variables

http://en.wikipedia.org/wiki/Uniform_distribution_(continuous)


http://en.wikipedia.org/wiki/Exponential_random_variable


http://en.wikipedia.org/wiki/Erlang_random_variable




3.5 Gaussian Random Variables

http://en.wikipedia.org/wiki/Gaussian_random_variable


3.6 Delta Functions, Mixed Random Variables


3.7 Probability Models of Derived Random Variables



3.8 Conditioning a Continuous Random Variable



3.9 MATLAB

http://en.wikipedia.org/wiki/Quantile_function











posted by maetel
2.1 Definitions


2.2 Probability Mass Function


2.3 Families of Discrete Random Variables

http://en.wikipedia.org/wiki/Bernoulli_random_variable



2.4 Cumulative Distribution Function (CDF)



2.5 Averages

http://www.amstat.org/publications/jse/v13n2/vonhippel.html



http://en.wikipedia.org/wiki/Mode_(statistics)




2.6 Functions of a Random Variable


2.7 Expected Value of a Derived Random Variable



2.8 Variance and Stand Deviation


2.9 Conditional Probaility Mass Function

posted by maetel
2009. 3. 13. 15:48

보호되어 있는 글입니다.
내용을 보시려면 비밀번호를 입력하세요.

sedumi

Kolman & Beck, Ch.1 Eg.1
: Activity Analysis or Product Mix

>> c = [-120; -100; 0; 0];
>> A = [ 2, 2, 1, 0; 5, 3, 0, 1];
>> b = [8, 15];
>> x= sedumi(A,b,c)
SeDuMi 1.1R3 by AdvOL, 2006 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
eqs m = 2, order n = 5, dim = 5, blocks = 1
nnz(A) = 6 + 0, nnz(ADA) = 4, nnz(L) = 3
 it :     b*y       gap    delta  rate   t/tP*  t/tD*   feas cg cg  prec
  0 :            4.18E-002 0.000
  1 : -5.02E+002 1.25E-002 0.000 0.2989 0.9000 0.9000   1.77  1  1  3.8E+000
  2 : -4.29E+002 3.65E-003 0.000 0.2927 0.9000 0.9000   2.52  1  1  6.4E-001
  3 : -4.29E+002 2.84E-004 0.000 0.0778 0.9900 0.9900   1.19  1  1  4.5E-002
  4 : -4.30E+002 9.99E-007 0.000 0.0035 0.9990 0.9990   1.03  1  1 
iter seconds digits       c*x               b*y
  4      0.2   Inf -4.3000000000e+002 -4.3000000000e+002
|Ax-b| =  2.3e-015, [Ay-c]_+ =  0.0E+000, |x|= 2.9e+000, |y|= 3.6e+001

Detailed timing (sec)
   Pre          IPM          Post
3.125E-002    1.563E-001    0.000E+000   
Max-norms: ||b||=15, ||c|| = 120,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 2.11427.
x =
   (1,1)       1.5000
   (2,1)       2.5000
>>








Kolman & Beck, Ch.1 Eg.3
: The Transportation Problem

>> c = [5; 7; 9; 6; 7; 10; 0; 0; 0; 0; 0];
>> A = [1,1,1,0,0,0,1,0,0,0,0; 0,0,0,1,1,1,0,1,0,0,0; 1,0,0,1,0,0,0,0,-1,0,0; 0,1,0,0,1,0,0,0,0,-1,0; 0,0,1,0,0,1,0,0,0,0,-1];
>> b = [120; 140; 100; 60; 80];
>> x = sedumi(A,b,c)
SeDuMi 1.1R3 by AdvOL, 2006 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
eqs m = 5, order n = 12, dim = 12, blocks = 1
nnz(A) = 17 + 0, nnz(ADA) = 17, nnz(L) = 12
 it :     b*y       gap    delta  rate   t/tP*  t/tD*   feas cg cg  prec
  0 :            3.24E+003 0.000
  1 :  1.16E+003 9.69E+002 0.000 0.2991 0.9000 0.9000   2.37  1  1  1.6E+000
  2 :  1.63E+003 2.05E+002 0.000 0.2114 0.9000 0.9000   1.34  1  1  3.0E-001
  3 :  1.69E+003 3.84E+001 0.000 0.1875 0.9000 0.9000   1.20  1  1  5.1E-002
  4 :  1.70E+003 1.08E+000 0.000 0.0282 0.9900 0.9900   1.03  1  1 
iter seconds digits       c*x               b*y
  4      0.5  15.9  1.7000000000e+003  1.7000000000e+003
|Ax-b| =  5.6e-014, [Ay-c]_+ =  7.6E-016, |x|= 1.1e+002, |y|= 1.4e+001

Detailed timing (sec)
   Pre          IPM          Post
3.125E-001    4.531E-001    1.250E-001   
Max-norms: ||b||=140, ||c|| = 10,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 1.
x =
   (1,1)      68.6083
   (3,1)      51.3917
   (4,1)      31.3917
   (5,1)      60.0000
   (6,1)      28.6083
   (8,1)      20.0000







posted by maetel
SeDuMi - Home
optimization package over symmetric cones

SeDuMi = Self-Dual-Minimization/ Optimization over self-dual homogeneous cones
: MatLab Toolbox developed by Jos F. Sturm


1) SeDuMi를 다운로드 받기 위해 홈페이지에 회원 등록
2) 메뉴의 Download에서 적당한 버전 다운로드
3) Matlab을 실행시키고, 메뉴에서 File > Set Path > Add Folder 클릭, SeDuMi가 들어 있는 폴더 지정 후 저장
4) command window에서 'help sedumi' 입력하여 toolbox 추가 확인


>> help sedumi
                                           [x,y,info] = sedumi(A,b,c,K,pars)
   
SEDUMI  Self-Dual-Minimization/ Optimization over self-dual homogeneous
          cones.
 
  >  X = SEDUMI(A,b,c) yields an optimal solution to the linear program
       MINIMIZE c'*x SUCH THAT A*x = b, x >= 0
       x is a vector of decision variables.
       If size(A,2)==length(b), then it solves the linear program
       MINIMIZE c'*x SUCH THAT A'*x = b, x >= 0
 
  >  [X,Y,INFO] = SEDUMI(A,b,c) also yields a vector of dual multipliers Y,
       and a structure INFO, with the fields INFO.pinf, INFO.dinf and
       INFO.numerr.
 
     (1) INFO.pinf=INFO.dinf=0: x is an optimal solution (as above)
       and y certifies optimality, viz.\ b'*y = c'*x and c - A'*y >= 0.
       Stated otherwise, y is an optimal solution to
       MAXIMIZE b'*y SUCH THAT c-A'*y >= 0.
       If size(A,2)==length(b), then y solves the linear program
       MAXIMIZE b'*y SUCH THAT c-A*y >= 0.
 
     (2) INFO.pinf=1: there cannot be x>=0 with A*x=b, and this is certified
       by y, viz. b'*y > 0 and A'*y <= 0. Thus y is a Farkas solution.
 
     (3) INFO.dinf=1: there cannot be y such that c-A'*y >= 0, and this is
       certified by x, viz. c'*x <0, A*x = 0, x >= 0. Thus x is a Farkas
       solution.
 
     (I)   INFO.numerr = 0: desired accuracy achieved (see PARS.eps).
     (II)  INFO.numerr = 1: numerical problems warning. Results are accurate
           merely to the level of PARS.bigeps.
     (III) INFO.numerr = 2: complete failure due to numerical problems.
 
     INFO.feasratio is the final value of the feasibility indicator. This
     indicator converges to 1 for problems with a complementary solution, and
     to -1 for strongly infeasible problems. If feasratio in somewhere in
     between, the problem may be nasty (e.g. the optimum is not attained),
     if the problem is NOT purely linear (see below). Otherwise, the reason
     must lie in numerical problems: try to rescale the problem.
 
  >  [X,Y,INFO] = SEDUMI(A,b,0) or SEDUMI(A,b) solves the feasibility problem
     FIND x>=0 such that A*x = b
 
  >  [X,Y,INFO] = SEDUMI(A,0,c) or SEDUMI(A,c) solves the feasibility problem
     FIND y such that A'*y <= c
 
  >  [X,Y,INFO] = SEDUMI(A,b,c,K) instead of the constraint "x>=0", this
       restricts x to a self-dual homogeneous cone that you describe in the
       structure K. Up to 5 fields can be used, called K.f, K.l, K.q, K.r and
       K.s, for Free, Linear, Quadratic, Rotated quadratic and Semi-definite.
       In addition, there are fields K.xcomplex, K.scomplex and K.ycomplex
       for complex-variables.
 
     (1) K.f is the number of FREE, i.e. UNRESTRICTED primal components.
       The dual components are restricted to be zero. E.g. if
       K.f = 2 then x(1:2) is unrestricted, and z(1:2)=0.
       These are ALWAYS the first components in x.
 
     (2) K.l is the number of NONNEGATIVE components. E.g. if K.f=2, K.l=8
       then x(3:10) >=0.
 
     (3) K.q lists the dimensions of LORENTZ (quadratic, second-order cone)
       constraints. E.g. if K.l=10 and K.q = [3 7] then
           x(11) >= norm(x(12:13)),
           x(14) >= norm(x(15:20)).
       These components ALWAYS immediately follow the K.l nonnegative ones.
       If the entries in A and/or c are COMPLEX, then the x-components in
       "norm(x(#,#))" take complex-values, whenever that is beneficial.
        Use K.ycomplex to impose constraints on the imaginary part of A*x.
 
     (4) K.r lists the dimensions of Rotated LORENTZ
       constraints. E.g. if K.l=10, K.q = [3 7] and K.r = [4 6], then
           2*x(21)x(22) >= norm(x(23:24))^2,
           2*x(25)x(26) >= norm(x(27:30))^2.
       These components ALWAYS immediately follow the K.q ones.
       Just as for the K.q-variables, the variables in "norm(x(#,#))" are
       allowed to be complex, if you provide complex data. Use K.ycomplex
       to impose constraints on the imaginary part of A*x.
 
     (5) K.s lists the dimensions of POSITIVE SEMI-DEFINITE (PSD) constraints
       E.g. if K.l=10, K.q = [3 7] and K.s = [4 3], then
           mat( x(21:36),4 ) is PSD,
           mat( x(37:45),3 ) is PSD.
       These components are ALWAYS the last entries in x.
 
     (a) K.xcomplex lists the components in f,l,q,r blocks that are allowed
      to have nonzero imaginary part in the primal. For f,l blocks, these
     (b) K.scomplex lists the PSD blocks that are Hermitian rather than
       real symmetric.
     (c) Use K.ycomplex to impose constraints on the imaginary part of A*x.
 
     The dual multipliers y have analogous meaning as in the "x>=0" case,
     except that instead of "c-A'*y>=0" resp. "-A'*y>=0", one should read that
     c-A'*y resp. -A'*y are in the cone that is described by K.l, K.q and K.s.
     In the above example, if z = c-A'*y and mat(z(21:36),4) is not symmetric/
     Hermitian, then positive semi-definiteness reflects the symmetric/
     Hermitian parts, i.e. Z + Z' is PSD.
 
     If the model contains COMPLEX data, then you may provide a list
     K.ycomplex, with the following meaning:
       y(i) is complex if ismember(i,K.ycomplex)
       y(i) is real otherwise
     The equality constraints in the primal are then as follows:
           A(i,:)*x = b(i)      if imag(b(i)) ~= 0 or ismember(i,K.ycomplex)
           real(A(i,:)*x) = b(i)  otherwise.
     Thus, equality constraints on both the real and imaginary part
     of A(i,:)*x should be listed in the field K.ycomplex.
 
     You may use EIGK(x,K) and EIGK(c-A'*y,K) to check that x and c-A'*y
     are in the cone K.
 
  >  [X,Y,INFO] = SEDUMI(A,b,c,K,pars) allows you to override the default
       parameter settings, using fields in the structure `pars'.
 
     (1) pars.fid     By default, fid=1. If fid=0, then SeDuMi runs quietly,
       i.e. no screen output. In general, output is written to a device or
       file whose handle is fid. Use fopen to assign a fid to a file.
 
     (2) pars.alg     By default, alg=2. If alg=0, then a first-order wide
       region algorithm is used, not recommended. If alg=1, then SeDuMi uses
       the centering-predictor-corrector algorithm with v-linearization.
       If alg=2, then xz-linearization is used in the corrector, similar
       to Mehrotra's algorithm. The wide-region centering-predictor-corrector
       algorithm was proposed in Chapter 7 of
         J.F. Sturm, Primal-Dual Interior Point Approach to Semidefinite Pro-
         gramming, TIR 156, Thesis Publishers Amsterdam, 1997.
 
     (3) pars.theta, pars.beta   By default, theta=0.25 and beta=0.5. These
       are the wide region and neighborhood parameters. Valid choices are
       0 < theta <= 1 and 0 < beta < 1. Setting theta=1 restricts the iterates
       to follow the central path in an N_2(beta)-neighborhood.
 
     (4) pars.stepdif, pars.w. By default, stepdif = 2 and w=[1 1].
        This implements an adaptive heuristic to control ste-differentiation.
        You can enable primal/dual step length differentiation by setting stepdif=1 or 0.
       If so, it weights the rel. primal, dual and gap residuals as
       w(1):w(2):1 in order to find the optimal step differentiation.
 
     (5) pars.eps     The desired accuracy. Setting pars.eps=0 lets SeDuMi run
       as long as it can make progress. By default eps=1e-8.
 
     (6) pars.bigeps  In case the desired accuracy pars.eps cannot be achieved,
      the solution is tagged as info.numerr=1 if it is accurate to pars.bigeps,
      otherwise it yields info.numerr=2.
 
     (7) pars.maxiter Maximum number of iterations, before termination.
 
     (8) pars.stopat  SeDuMi enters debugging mode at the iterations specified in this vector.
 
     (9) pars.cg      Various parameters for controling the Preconditioned conjugate
      gradient method (CG), which is only used if results from Cholesky are inaccurate.
     (a) cg.maxiter   Maximum number of CG-iterates (per solve). Theoretically needed
           is |add|+2*|skip|, the number of added and skipped pivots in Cholesky.
           (Default 49.)
     (b) cg.restol    Terminates if residual is a "cg.restol" fraction of duality gap.
           Should be smaller than 1 in order to make progress (default 5E-3).
     (c) cg.refine    Number of refinement loops that are allowed. The maximum number
           of actual CG-steps will thus be 1+(1+cg.refine)*cg.maxiter. (default 1)
     (d) cg.stagtol  Terminates if relative function progress less than stagtol (5E-14).
     (e) cg.qprec    Stores cg-iterates in quadruple precision if qprec=1 (default 0).
 
     (10) pars.chol   Various parameters for controling the Cholesky solve.
      Subfields of the structure pars.chol are:
     (a) chol.canceltol: Rel. tolerance for detecting cancelation during Cholesky (1E-12)
     (b) chol.maxu:   Adds to diagonal if max(abs(L(:,j))) > chol.maxu otherwise (5E5).
     (c) chol.abstol: Skips pivots falling below abstol (1e-20).
     (d) chol.maxuden: pivots in dense-column factorization so that these factors
       satisfy max(abs(Lk)) <= maxuden (default 5E2).
 
     (11) pars.vplot  If this field is 1, then SeDuMi produces a fancy
       v-plot, for research purposes. Default: vplot = 0.
 
     (12) pars.errors  If this field is 1 then SeDuMi outputs some error
     measures as defined in the Seventh DIMACS Challenge. For more details
     see the User Guide.
 
  Bug reports can be submitted at http://sedumi.mcmaster.ca.
 
  See also mat, vec, cellK, eyeK, eigK





posted by maetel

http://en.wikipedia.org/wiki/Linear_programming


1.1 The Linear Programming Problem



general  linear programming problem
- objective function
- constraints

standard form
canonical form

Every linear programming problem that has unconstrained variables can be solved by solving a corresponding linear programming problem in which all the variables are constrained to be nonnegative.

Every linear programming problem can be formulated as a corresponding standard linear programming problem or as a corresponding canonical linear programming problem.   (53p)


Minmization Problem as a Maximization Problem
: To minimize the objective function we could maximize its negative instead and then change the sign of the answer.

Reversing an Inequality

Changing an Equality to Inequality

Unconstrained Variables

Scaling
to make all coefficients in a linear programming problem approximately the same size



1.2 Matrix Notation


feasible solution
: a vector satisfying the constraints of a linear programming problem

optimal solution
: a feasible solution maximizing or minimizing the objective function of a linear programming



1.4




ref.
http://en.wikipedia.org/wiki/Convex_polyhedron
http://mathworld.wolfram.com/ConvexPolyhedron.html
http://en.wikipedia.org/wiki/Extreme_point
http://en.wikipedia.org/wiki/Krein%E2%80%93Milman_theorem
http://library.wolfram.com/infocenter/MathSource/440/
http://www.ifor.math.ethz.ch/~fukuda/fukuda.html



slack & surplus variable in the siimplex algorithm
http://www-fp.mcs.anl.gov/otc/Guide/CaseStudies/simplex/standard.html

posted by maetel