Santa Fe Institute Events Wiki - User contributions [en]

The Many Roots of Complexity Science

2007-06-25T03:46:33Z

Ashp:

== Post Your Favorite Roots in Chronological Order if you can [See explanation of project at end] ==

'''1937 - Landau''' published '' On the Theory of Phase Transitions... [Landau1937]''
The history of the theory of critical phenomena and phase transitions starts with Landau's works of 1937, where he introduced fundamental notions of spontaneous symmetry violation and the order parameter as a measure of this violation. It is impossible to exaggerate the impact which this idea had on practically all branches of physics and non-linear mechanics. Due to the concept of the order parameter, phase transition theory became a cross-disciplinary branch of science, much like the theory of oscillations. Landau gave simple prescriptions, how to describe order in terms of irreducible representations of the symmetry group. Around 1960 Landau formulated the general problem of fluctuation-driven phase transitions via a calculation of the path integral over all configurations of the order parameter.
[Landau1937] L.D. Landau, ZhETF 7, 19 (1937); Phys. Zs. Sowjet. 11, 26 (1937).

'''1941 - Kolmogorov''' proposed a scaling approach for hydrodynamic turbulence.
[Kolmogorov1941] A.N. Kolmogorov, DAN SSSR, 30, 299; Ib. 31, 99 (1941).

'''1944 - Onsager''' published an exact solution of the 2-d Ising model [Onsager1944], a truly exceptional (even singular) accomplishment. As of 2007, despite numerous attempts, 3D Ising model has eluded exact solution. It is even conjectured that the exact solution is in general not possible.
[Onsager1944] L. Onsager, Phys, Rev. 65, 117 (1944);

'''1948 - Norbert Weiner''' published '' Cybernetics ''

He used the newly formed fields of statistical Information and Control Theory to establish the role of feedback and nonlinearity in engineering design and biology. [Cybernetics]'' (Contibuted by J. DeRosa)''

'''1950 - Norbert Weiner''' published '' The Human Use of Human Beings ''

In this companion book to Cybernetics, Weiner expounded on the principles of Cybernetics with no equations and warned of the dangers of scientific research that did not consider the social implications of the technology and research. [Cybernetics]'' (Contibuted by J. DeRosa)''

'''1959 - ''' It is realized [Levanyuk1959],[Ginsburg1960] that mean field theory neglects fluctuations which grow rapidly near the phase transition point. Thus, mean field theory works well outside a small vicinity of the transition point and is invalidated by fluctuations within it. In this way the necessity to include fluctuations in phase transition theory was first recognized. Simultaneously Fisher [Fisher1959] approached the problem by attempting to generalize Onsager's results to non-exactly-solvable problems. By introducing critical exponents he made the decisive step to scaling.
[Levanyuk1959] A.I. Levanyuk, ZhETF 36, 810 (1959); [Fisher1959] M.E. Fisher, Physica 25, 521 (1959); [Ginsburg1960] V.L. Ginsburg, Fizika Tverdogo Tela (Solid State Physics, in Russian) 2, 2034 (1960).

'''1958 - Norbert Weiner''' published '' Nonlinear Problems in Random Theory ''

This book is decidedly mathematical and lays out the framework for the general functional analysis of nonlinear systems. For a clear exposition of the mathematics see the book written by one of his students M. Schetzen ''The Volterra and Wiener Theory of Nonlinear Sy''stems [System Theory]'' (Contibuted by J. DeRosa)''

'''1964 - Patashinskii and Pokrovskii''' in Russia formulated the field theory equations and conjectured correctly that the correlation functions of any order should obey scaling laws [Patashin1964]. Soon thereafter, they introduced the theory of scaling [Patashin1966], first presented at the International Symposium on Phase Transitions in Dubna, May 1965. The physical picture was that, for critical fluctuations the distribution of the order parameter remains invariant with temperature if the length scale and other observables are adjusted properly. The theory was physically equivalent to Kadanoff's formulation, which was published 4 months later[Kadanoff1966]. In addition, in his work Kadanoff first formulated a program of elimination of short-range degrees of freedom by decimation of spin blocks, an embryo of the Wilson Renormalization Group, though still not a practical tool for calculations.
[Patashin1964] A.Z. Patashinskii and V.L. Pokrovskii, ZhETF, 50, 439 (1964) [Sov. Phys. JETP 19, 677 (1964)]; [Patashin1966] A.Z. Patashinskii and V.L. Pokrovskii, ZhETF 50, 439 (1966) [Sov. Phys. JETP 23, 292 (1966)]; [Kadanoff1966] L.P. Kadanoff, Physics 2, 263 (1966).

'''1968 - Polyakov and Migdal''' used such physical requirements as causality and unitarity, which permitted, in principle, numerical calculations of the critical exponents [Pol1968], [Mig1968]. Unfortunately, the equations were too complicated to solve using computers of that time.
[Pol1968] A.M. Polyakov, ZhETF 55, 1026 (1968) [Sov. Phys. JETP 28, 533 (1969)].
[Mig1968] A.A. Migdal, ZhETF 55, 1964 (1968) [Sov. Phys. JETP 28, 1036 (1969)].

'''1971 - Kadanoff and Wegner''' proved the universality hypothesis.
[Kadanoff1971] L.P. Kadanoff and F.J. Wegner, Phys. Rev. B4, 3989 (1971).
According to this hypothesis, the critical behavior is determined by symmetry and how it is violated. All phase transitions may be divided into universality classes.

'''1972 - Wilson''' introduced renormalization group approach, which elucidated the structure of the theory to the extent that standard methods could be employed. This effectively marks the birth of the theory of phase transitions, scaling and renormalization group as we know it today. Kenneth Wilson went on to recieve a Nobel Prize in Physics, 1982.
[Wilson1972] K.G. Wilson, Phys, Rev. Lett. 28, 548 (1972).

'''1977 - Ilya Prigogine ''' wins the ''Nobel Prize in Chemistry ''

For his groundbraking work in non-equilibrium thermodynamics-especially non-dissipative structures. [Chemistry]'' (Contibuted by J. DeRosa)''

'''1984 - Ilya Prigogine and Isabelle Stengers''' publish ''Order out of Chaos: Man's New Dialogue with Nature''

A brilliant account of the journey from Newtonian science to complex dynamical systems. An emphasis on thermodynamics and dissipative struvtures. One of the works that triggered the study of complexity science. [Chemistry]'' (Contibuted by J. DeRosa)''

'''1999 - Gary William Flake''' published the '''The Computational Beauty of Nature'''. Computer explorations of fractals, chaos, complex systems and adaptation. (Contributed by --[[User:Luciano Oviedo|Luciano Oviedo]] 19:03, 24 June 2007 (MDT))

== Use This Simple Template: (or refine it)==
'''Date - Name(s) of Person(s) ''' followed by '' Milestone ''

Description and significance (short text)
[Source Discipline(s)]
''(Contributed by your name)'' [so we can backtrack to update]

== Team Members and Contributors== (Hopefully many will contribute)
#Joe DeRosa
#
#
== Explanation of Project ==
'''The Roots of Rock and Roll''' go deep into Gospel, Rythmn and Blues, Folk and Bluegrass - even the familiar I-IV-I-V-IV-I chord progressions can be found in Bach and Beethoven. When Elvis Presley and the Beatles appeared on the Ed Sullivan Show in 1956 and 1964, it was significant because huge audiences tuned in every Sunday night at 8:00. Rock and Roll became a legitimate part of the culture. When the Rolling stones hit the concert circuit in 1969, it was significant because they were billed as the greatest rock and roll band in the world, but also because they became drugs-sex-rock-and-roll cultural icons of the new social norms.

Here we all sit in '''the Rock and Roll of Complexity Science'''. Our roots are in physics, biology, sociology, etc. Collectively we know the “who, what and why” of the key milestones in our fields that led us here: '''The Roots of Complexity Science'''. This is a project for all those who wish to participate from the CSSS Class of 07. Who knows where the trajectory will lead?

The Many Roots of Complexity Science

2007-06-25T03:43:47Z

Ashp:

== Post Your Favorite Roots in Chronological Order if you can [See explanation of project at end] ==

'''1937 - Landau''' published '' On the Theory of Phase Transitions... [Landau1937]''
The history of the theory of critical phenomena and phase transitions starts with Landau's works of 1937, where he introduced fundamental notions of spontaneous symmetry violation and the order parameter as a measure of this violation. It is impossible to exaggerate the impact which this idea had on practically all branches of physics and non-linear mechanics. Due to the concept of the order parameter, phase transition theory became a cross-disciplinary branch of science, much like the theory of oscillations. Landau gave simple prescriptions, how to describe order in terms of irreducible representations of the symmetry group. Around 1960 Landau formulated the general problem of fluctuation-driven phase transitions via a calculation of the path integral over all configurations of the order parameter.
[Landau1937] L.D. Landau, ZhETF 7, 19 (1937); Phys. Zs. Sowjet. 11, 26 (1937).

'''1941 - Kolmogorov''' proposed a scaling approach for hydrodynamic turbulence.
[Kolmogorov1941] A.N. Kolmogorov, DAN SSSR, 30, 299; Ib. 31, 99 (1941).

'''1944 - Onsager''' published an exact solution of the 2-d Ising model [Onsager1944], a truly exceptional (even singular) accomplishment. As of 2007, despite numerous attempts, 3D Ising model has eluded exact solution. It is even conjectured that the exact solution is in general not possible.
[Onsager1944] L. Onsager, Phys, Rev. 65, 117 (1944);

'''1948 - Norbert Weiner''' published '' Cybernetics ''

He used the newly formed fields of statistical Information and Control Theory to establish the role of feedback and nonlinearity in engineering design and biology. [Cybernetics]'' (Contibuted by J. DeRosa)''

'''1950 - Norbert Weiner''' published '' The Human Use of Human Beings ''

In this companion book to Cybernetics, Weiner expounded on the principles of Cybernetics with no equations and warned of the dangers of scientific research that did not consider the social implications of the technology and research. [Cybernetics]'' (Contibuted by J. DeRosa)''

'''1959 - ''' It is realized [Levanyuk1959],[Ginsburg1960] that mean field theory neglects fluctuations which grow rapidly near the phase transition point. Thus, mean field theory works well outside a small vicinity of the transition point and is invalidated by fluctuations within it. In this way the necessity to include fluctuations in phase transition theory was first recognized. Simultaneously Fisher [Fisher1959] approached the problem by attempting to generalize Onsager's results to non-exactly-solvable problems. By introducing critical exponents he made the decisive step to scaling.
[Levanyuk1959] A.I. Levanyuk, ZhETF 36, 810 (1959); [Fisher1959] M.E. Fisher, Physica 25, 521 (1959); [Ginsburg1960] V.L. Ginsburg, Fizika Tverdogo Tela (Solid State Physics, in Russian) 2, 2034 (1960).

'''1958 - Norbert Weiner''' published '' Nonlinear Problems in Random Theory ''

This book is decidedly mathematical and lays out the framework for the general functional analysis of nonlinear systems. For a clear exposition of the mathematics see the book written by one of his students M. Schetzen ''The Volterra and Wiener Theory of Nonlinear Sy''stems [System Theory]'' (Contibuted by J. DeRosa)''

'''1964 - Patashinskii and Pokrovskii[Patashin1964]''' in Russia formulated the field theory equations and conjectured correctly that the correlation functions of any order should obey scaling laws. Soon thereafter, they introduced the theory of scaling [Patashin1966], first presented at the International Symposium on Phase Transitions in Dubna, May 1965. The physical picture was that, for critical fluctuations the distribution of the order parameter remains invariant with temperature if the length scale and other observables are adjusted properly. The theory was physically equivalent to Kadanoff's formulation, which was published 4 months later[Kadanoff1966]. In addition, in his work Kadanoff first formulated a program of elimination of short-range degrees of freedom by decimation of spin blocks, an embryo of the Wilson Renormalization Group, though still not a practical tool for calculations.
[Patashin1964] A.Z. Patashinskii and V.L. Pokrovskii, ZhETF, 50, 439 (1964) [Sov. Phys. JETP 19, 677 (1964)]; [Patashin1966] A.Z. Patashinskii and V.L. Pokrovskii, ZhETF 50, 439 (1966) [Sov. Phys. JETP 23, 292 (1966)]; [Kadanoff1966] L.P. Kadanoff, Physics 2, 263 (1966).

'''1968 - Polyakov [Pol1968] and Migdal [Mig1968]''' used such physical requirements as causality and unitarity, which permitted, in principle, numerical calculations of the critical exponents. Unfortunately, the equations were too complicated to solve using computers of that time.
[Pol1968] A.M. Polyakov, ZhETF 55, 1026 (1968) [Sov. Phys. JETP 28, 533 (1969)].
[Mig1968] A.A. Migdal, ZhETF 55, 1964 (1968) [Sov. Phys. JETP 28, 1036 (1969)].

'''1971 - Kadanoff and Wegner''' proved the universality hypothesis.
[Kadanoff1971] L.P. Kadanoff and F.J. Wegner, Phys. Rev. B4, 3989 (1971).
According to this hypothesis, the critical behavior is determined by symmetry and how it is violated. All phase transitions may be divided into universality classes.

'''1972 - K. Wilson''' introduced renormalization group approach, which elucidated the structure of the theory to the extent that standard methods could be employed. This effectively marks the completion of the theory of phase transitions, scaling and renormalization group as we know it today. Kenneth Wilson went on to recieve a Nobel Prize in Physics, 1982.
[Wilson1972] K.G. Wilson, Phys, Rev. Lett. 28, 548 (1972).

'''1977 - Ilya Prigogine ''' wins the ''Nobel Prize in Chemistry ''

For his groundbraking work in non-equilibrium thermodynamics-especially non-dissipative structures. [Chemistry]'' (Contibuted by J. DeRosa)''

'''1984 - Ilya Prigogine and Isabelle Stengers''' publish ''Order out of Chaos: Man's New Dialogue with Nature''

A brilliant account of the journey from Newtonian science to complex dynamical systems. An emphasis on thermodynamics and dissipative struvtures. One of the works that triggered the study of complexity science. [Chemistry]'' (Contibuted by J. DeRosa)''

'''1999 - Gary William Flake''' published the '''The Computational Beauty of Nature'''. Computer explorations of fractals, chaos, complex systems and adaptation. (Contributed by --[[User:Luciano Oviedo|Luciano Oviedo]] 19:03, 24 June 2007 (MDT))

== Use This Simple Template: (or refine it)==
'''Date - Name(s) of Person(s) ''' followed by '' Milestone ''

Description and significance (short text)
[Source Discipline(s)]
''(Contributed by your name)'' [so we can backtrack to update]

== Team Members and Contributors== (Hopefully many will contribute)
#Joe DeRosa
#
#
== Explanation of Project ==
'''The Roots of Rock and Roll''' go deep into Gospel, Rythmn and Blues, Folk and Bluegrass - even the familiar I-IV-I-V-IV-I chord progressions can be found in Bach and Beethoven. When Elvis Presley and the Beatles appeared on the Ed Sullivan Show in 1956 and 1964, it was significant because huge audiences tuned in every Sunday night at 8:00. Rock and Roll became a legitimate part of the culture. When the Rolling stones hit the concert circuit in 1969, it was significant because they were billed as the greatest rock and roll band in the world, but also because they became drugs-sex-rock-and-roll cultural icons of the new social norms.

Here we all sit in '''the Rock and Roll of Complexity Science'''. Our roots are in physics, biology, sociology, etc. Collectively we know the “who, what and why” of the key milestones in our fields that led us here: '''The Roots of Complexity Science'''. This is a project for all those who wish to participate from the CSSS Class of 07. Who knows where the trajectory will lead?

Applications of non-commutative harmonic analysis

2007-06-11T17:59:55Z

Ashp:

This would be a shortened version of the 4-hour tutorial I am preparing for a conference [http://www.cs.columbia.edu/~risi/ICMLtutorial/index.html (topics)]. Let me know if you are interested.

Non-commutative harmonic analysis is based on group representation theory, but I do not expect people to have prior knowledge about that. Only familiarity with linear algebra is assumed.

The tutorial will answer the following questions:

1. What is the natural generalization of Fourier analysis to groups?

2. What does the Fourier spectrum of functions on permutations look like and what is the interpretation of the individual components?

3. How do non-commutative FFTs work?

4. How can we use all this stuff for multi-object tracking?

5. What is the bispectrum and why do we love it so much?

6. How can we construct simultaneously translation and rotation invariant features for images?

7. How can we tell in polynomial time whether two graphs are the same or not? (OK, still working on that one)

Risi.

I'd definitely be interested if my head hasn't exploded by then. --James

yup - john

i'm in for sure - mike

I'm in. -Kristen

yeah cool! Will L.

I would really like to participate, but I can't do it Friday June 15. Can we perhaps switch to any other day? Thanks a lot -Alex Shpunt

Friday 3:00 Lab Signup

2007-06-07T05:03:25Z

Ashp:

{{CSSS 2007 Santa Fe}}

# Vikas Shah <br>
# Kristen Fortney <br>
# Jose Delgado
# Joe DeRosa
# Amir Goldberg
# Heather Beil
# Joseph Lizier
# Mike Wojnowicz
# James Battin
# Alex Healing
# Saleha Habibullah
# Alexander Shpunt

Alexander Shpunt

2007-04-02T06:02:24Z

Ashp:

Hi All!

My name is Alex. I am PhD candidate in Physics at MIT.

I have BSc in Physics/CS and MSc in EE
(Combinatorics and Topology of Information Processing).

My current interests

• Structure and dynamics/scaling/walks in Complex Networks
• Rigorous results in Random Graphs/Probabilistic Method with applications
• Complex systems; Nonlinear Dynamics and Chaos; Biophysics
• Error correction in biological/nanometer scale processes
• Percolation theory applied to questions of structural stability
• Scaling laws and statistical mechanics
• Application of the insights of Theoretical Physics to help solve important problems (e.g. energy sources, global warming, pollution dynamics, bio-sphere sustainability)
• Physical Aspects of Information
• Fundamental questions in Physics, fundamental limitations imposed by the physical law and solutions when the technological advance hits these limits.

Looking forward to an exciting CSSS 2007!

Alex

Alexander Shpunt

2007-04-02T05:58:44Z

Ashp: Introduction

Hi,

My name is Alex. I am PhD candidate in Physics at MIT,
currently on a special named fellowship from MIT Physics Dept.

I have BSc in Physics/CS and MSc in EE
(Combinatorics and Topology of Information Processing).

My current interests

• Structure and dynamics/scaling/walks in Complex Networks
• Rigorous results in Random Graphs/Probabilistic Method with applications
• Complex systems; Nonlinear Dynamics and Chaos; Biophysics
• Error correction in biological/nanometer scale processes
• Percolation theory applied to questions of structural stability
• Scaling laws and statistical mechanics
• Application of the insights of Theoretical Physics to help solve important problems (e.g. energy sources, global warming, pollution dynamics, bio-sphere sustainability)
• Physical Aspects of Information
• Fundamental questions in Physics, fundamental limitations imposed by the physical law and solutions when the technological advance hits these limits.

Looking forward to an exciting CSSS 2007!

Alex

Alexander Shpunt

2007-04-02T05:48:11Z

Ashp:

howdy