'Method/Nature' 카테고리의 글 목록

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mathematical morphology (0)	2009.02.14
Jonathan Richard Shewchuk - An Introduction to the Conjugate Gradient Method Without the Agonizing Pain (0)	2008.11.05
MAT2110: 선형대수학 Linear Algebra (0)	2008.09.05
Linear Algebra resources (0)	2008.08.22
Superformula (0)	2007.07.20

Jonathan Richard Shewchuk - An Introduction to the Conjugate Gradient Method Without the Agonizing Pain

2008. 11. 5. 11:33 Method/Nature

An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
Edition 1+1/4
Jonathan Richard Shewchuk
August 4, 1994
School of Computer Science, Carnegie Mellon University

painless-conjugate-gradient.pdf

http://en.wikipedia.org/wiki/Residual_(numerical_analysis)

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

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posted by maetel

mathematical morphology (0)	2009.02.14
Jonathan Richard Shewchuk - An Introduction to the Conjugate Gradient Method Without the Agonizing Pain (0)	2008.11.05
Linear Algebra resources (0)	2008.08.22
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Peter A. Corning <Thermoeconomics Beyond the Second Law> (0)	2007.06.21

Jonathan Richard Shewchuk - An Introduction to the Conjugate Gradient Method Without the Agonizing Pain (0)	2008.11.05
MAT2110: 선형대수학 Linear Algebra (0)	2008.09.05
Superformula (0)	2007.07.20
Peter A. Corning <Thermoeconomics Beyond the Second Law> (0)	2007.06.21
Peter A. Corning <Thermodynamics, Information, and Life Revisited> (0)	2007.06.21

MAT2110: 선형대수학 Linear Algebra (0)	2008.09.05
Linear Algebra resources (0)	2008.08.22
Peter A. Corning <Thermoeconomics Beyond the Second Law> (0)	2007.06.21
Peter A. Corning <Thermodynamics, Information, and Life Revisited> (0)	2007.06.21
Emergence (0)	2007.06.21

Peter A. Corning <Thermoeconomics Beyond the Second Law>

2007. 6. 21. 17:26 Method/Nature

invalid-file

Thermoeconomics
Beyond the Second Law

Peter A. Corning, Ph.D.
Institute for the Study of Complex Systems
119 Bryant Street, Suite 212
Palo Alto, CA 94301 USA

Phone: (650) 325-5717
Fax: (650) 325-3775
Email: pacorning@complexsystems.org

In Press: JOURNAL OF BIOECONOMICS

"Horse manure does not explain a horse."

Stephen Jay Kline

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Graph theory (0)	2007.06.21

posted by maetel

Peter A. Corning <Thermodynamics, Information, and Life Revisited>

2007. 6. 21. 17:24 Method/Nature

Thermodynamics, Information, and Life Revisited
Part One -- "To Be Or Entropy"

Peter A. Corning, Ph.D.
Institute for the Study of Complex Systems
119 Bryant Street, Suite 212
Palo Alto, CA 94301 USA

Phone: (650) 325-5717
Fax: (650) 325-3775
Email: pacorning@complexsystems.org

and

Stephen Jay Kline
Woodard Professor of Science, Technology, and Society,
and of Mechanical Engineering, Emeritus
Stanford University, Stanford CA 94305 USA

"When I use a word, it means what I choose it to mean -- neither more nor less."

Humpty Dumpty (Lewis Carroll),
Through the Looking Glass

Thermodynamics, Information, and Life Revisited
Part Two -- "Thermoeconomics" and "Control Information"

Peter A. Corning, Ph.D.
Institute for the Study of Complex Systems
119 Bryant Street, Suite 212
Palo Alto, CA 94301 USA

Phone: (650) 325-5717
Fax: (650) 325-3775
Email: pacorning@complexsystems.org

and

Stephen Jay Kline
Woodard Professor of Science, Technology, and Society,
and of Mechanical Engineering, Emeritus
Stanford University, Stanford CA 94305 USA

"There is measure in everything."

Beatrice (W. Shakespeare),
Much Ado About Nothing

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del (0)	2007.06.19

posted by maetel

Emergence

2007. 6. 21. 17:05 Method/Nature

In philosophy, systems theory and the sciences, emergence refers to the way complex systems and patterns, such as those that form a hurricane, arise out of a multiplicity of relatively simple interactions. Like intelligence in the field of AI, or agents in distributed artificial intelligence, emergence is central to the physics of complex systems and yet very controversial.

"Perhaps the most elaborate recent definition of emergence was provided by Jeffrey Goldstein in the inaugural issue of Emergence.(Goldstein 1999) To Goldstein, emergence refers to "the arising of novel and coherent structures, patterns and properties during the process of self-organization in complex systems." The common characteristics are: (1) radical novelty (features not previously observed in systems); (2) coherence or correlation (meaning integrated wholes that maintain themselves over some period of time); (3) A global or macro "level" (i.e. there is some property of "wholeness"); (4) it is the product of a dynamical process (it evolves); and (5) it is "ostensive" - it can be perceived. For good measure, Goldstein throws in supervenience -- downward causation." (Corning 2002)

The term "emergent" was coined by the pioneer psychologist G. H. Lewes who wrote:
"Every resultant is either a sum or a difference of the co-operant forces; their sum, when their directions are the same -- their difference, when their directions are contrary. Further, every resultant is clearly traceable in its components, because these are homogeneous and commensurable. It is otherwise with emergents, when, instead of adding measurable motion to measurable motion, or things of one kind to other individuals of their kind, there is a co-operation of things of unlike kinds. The emergent is unlike its components insofar as these are incommensurable, and it cannot be reduced to their sum or their difference." (Lewes 1875, p. 412)(Blitz 1992)

However, the concept behind the term has been in use since at least the time of Aristotle.[1] John Stuart Mill[2] and Julian Huxley[3] are just some of the historic luminaries who have written on the concept.

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posted by maetel

Graph theory

2007. 6. 21. 15:02 Method/Nature

In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices and a collection of edges that connect pairs of vertices. A graph may be undirected, meaning that there is no distinction between the two vertices associated with each edge, or its edges may be directed from one vertex to another

*
The Seven Bridges of Königsberg is a famous solved mathematics problem inspired by an actual place and situation. The city of Königsberg, Prussia (now Kaliningrad, Russia) is set on the Pregel River, and included two large islands which were connected to each other and the mainland by seven bridges. The question is whether it is possible to walk with a route that crosses each bridge exactly once.
In 1736, Leonhard Euler proved that it was not possible. In proving the result, Euler formulated the problem in terms of graph theory, by abstracting the case of Königsberg

*
An Eulerian path, Eulerian trail or Euler walk in an undirected graph is a path that uses each edge exactly once. If such a path exists, the graph is called traversable.
An Eulerian cycle, Eulerian circuit or Euler tour in an undirected graph is a cycle that uses each edge exactly once. If such a cycle exists, the graph is called Eulerian or unicursal.

*
In algebraic topology, the Euler characteristic is a topological invariant, a number that describes one aspect of a topological space's shape or structure. It is commonly denoted by χ (Greek letter chi).

The Euler characteristic $χ$ was classically defined for polyhedra, according to the formula

$\chi=V-E+F, \,\!$

where V, E, and F are respectively the numbers of vertices (corners), edges and faces in the given polyhedron.

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posted by maetel

del

2007. 6. 19. 02:14 Method/Nature

Del is a vector differential operator.
Depending on the way del is applied, it can describe the gradient (slope), divergence (degree to which something converges or diverges) or curl (rotational motion at points in a fluid).

$The image “http://upload.wikimedia.org/math/8/f/a/8fa511fbbd1188d080aacab402d9f7ae.png” cannot be displayed, because it contains errors.$

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

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posted by maetel

Riemann Sum

2007. 4. 27. 18:48 Method/Nature

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

For all ε > 0, there exists δ > 0 such that for any tagged partition x_0,...,x_n and t_0,...,t_{n-1} whose mesh is less than δ

cp. epsilon-delta definition -> Cauchy definition (epsilon-delta)
cp. Continuous function (topology)

cf.
topology 위상수학

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posted by maetel

Bryson Bill [A Short History Of Nearly Everything]

2005. 4. 25. 01:10 Method/Nature

A Short History Of Nearly Everything

by Bryson Bill

invalid-file

wikipedia: A Short History of Nearly Everything
google Book

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