Levenberg–Marquardt algorithm: Difference between revisions

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Extreme physical information (EPI) is a principle, first described and formulated in 1998^[1] by B. Roy Frieden, Emeritus Professor of Optical Sciences at the University of Arizona, that states, the precipitation of scientific laws can be derived through Fisher information, taking the form of differential equations and probability distribution functions.

Introduction

Physicist John Archibald Wheeler stated that: 36 year-old Diving Instructor (Open water ) Vancamp from Kuujjuaq, spends time with pursuits for instance gardening, public listed property developers in singapore developers in singapore and cigar smoking. Of late took some time to go China Danxia. By using Fisher information, in particular its loss I - J incurred during observation, the EPI principle provides a powerful new approach for deriving laws governing many aspects of nature and human society. EPI can be seen as an extension of information theory that encompasses much theoretical physics and chemistry. Examples include the Schrödinger wave equation and the Maxwell-Boltzmann distribution law. EPI has been used to derive a number of fundamental laws of physics,^[2]^[3] biology,^[4] the biophysics of cancer growth,^[5]chemistry,^[5] and economics.^[6] EPI can also be seen as a game against nature, first proposed by Charles Sanders Peirce. The approach does require prior knowledge of an appropriate invariance principle or data.

EPI principle

The EPI principle builds on the well known idea that the observation of a "source" phenomenon is never completely accurate. That is, information present in the source is inevitably lost when observing the source. Moreover, the random errors that contaminate the observations are presumed to define the probability distribution function of the source phenomenon. That is, "the physics lies in the fluctuations." The information loss is postulated to be an extreme value. Thus, if the Fisher information in the data is ${\mathcal {I}}$ , and the Fisher information in the source is ${\mathcal {J}}$ , the EPI principle states that:

{\mathcal {I}}-{\mathcal {J}}=\mathrm {Extremum}

The extremum for most situations is a minimum, meaning that there is a comforting tendency for any observation to describe its source faithfully. The EPI principle was recently derived, based on the mathematical axioms of L. Hardy that underlie all known physics (see 2013 paper cited below by Frieden and Gatenby).

Books

Frieden, B. Roy - Physics from Fisher Information: A Unification , 1st Ed. Cambridge University Press, ISBN 0-521-63167-X, pp328, 1998
Frieden, B. Roy - Science from Fisher Information: A Unification , 2nd Ed. Cambridge University Press, ISBN 0-521-00911-1, pp502, 2004
Frieden, B.R. & Gatenby, R.A. eds. - Exploratory Data Analysis Using Fisher Information, Springer-Verlag (in press), pp358, 2006

Recent papers using EPI

Frieden, B. Roy & Gatenby, Robert A - "Principle of maximum Fisher information from Hardy's axioms applied to statistical systems", Phys. Rev. E 88, 042144,1-6, 2013

http://link.aps.org/doi/10.1103/PhysRevE.88.042144

Gatenby, Robert A. & Frieden, B. Roy - "Application of Information Theory and Extreme Physical Information to Carcinogenesis", :Cancer Research 62, 3675-3684, July 1, 2002

http://cancerres.aacrjournals.org/cgi/content/full/62/13/3675

Chimento,L.P. & Pennini, F. & Plastino, A. - "Naudts-like duality and the Extreme Fisher information principle",

Phys. Rev. E 62, 7462-7465, 2000

http://prola.aps.org/abstract/PRE/v62/i5/p7462_1subj: statistical mechanics

Nagy, A. - "Fisher information in density functional theory,", J. Chem. Phys. 119, 9401-9405, 2003

http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JCPSA6000119000018009401000001&idtype=cvips&gifs=yes

Subj: The Euler equation of density functional theory is derived using EPI.

Anton, M. & Weisen, H. & Dutch, M.J. - "X-ray tomography on the TCV tokamak",

Plasma Phys. Control. Fusion 38, 1849-1878, 1996

http://ej.iop.org/links/q80/fVFo+Bx3KRlwd6qcdU2Saw/p61101.pdf

Mlynar, J. & Bertalot, L. - "Neutron spectra unfolding with minimum Fisher regularization"

http://pos.sissa.it/archive/conferences/025/063/FNDA2006_063.pdf

Subj: Diagnosis of plasma shape within the tokamak fusion machine using reconstructions based upon EPI.

Venkatesan, Ravi. - "Information encryption using a Fisher-Schrödinger Model",

Presented at 6th International Conference on Complex Systems (ICCS) June, 2006

Boston, MA Full paper is in Frieden and Gatenby, 2006

http://necsi.edu/community/wiki/index.php/ICCS06/235

Subj: Encryption, secure transmission using EPI, in particular game aspect.

Fath B.D. & Cabezas, H. & CW Pawlowski - "Exergy and Fisher information as ecological indices",

Ecological Modeling 174, 25-35, 2004 - CW 2003

http://zp9vv3zm2k.scholar.serialssolutions.com/sid=google&auinit=BD&aulast=Fath&atitle=Exergy+and+Fisher+Information+as+ecological+indices&id=doi:10.1016/j.ecolmodel.2003.12.045

Subj: monitoring of the environment for species diversity

Yolles. M.I. - "Knowledge Cybernetics: A New Metaphor for Social Collectives", 2005

http://isce.edu/ISCE_Group_Site/web-content/ISCE_Events/Christchurch_2005/Papers/Yolles.pdf

Subj: Information-based approaches to knowledge management.

Venkatesan, R.C. - "Invariant Extreme Physical Information and Fuzzy Clustering", Proc. SPIE Symposium on Defense & Security,

Intelligent Computing: Theory and Applications II, Priddy, K. L. ed, Volume 5421, pp. 48-57, Orlando, FL, 2004

http://spiedl.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PSISDG005421000001000048000001&idtype=cvips&prog=normal

Ménard, Michel. & Eboueya, Michel. - "Extreme physical information and objective function in fuzzy clustering",

Fuzzy Sets and Systems 128(3): 285-303, 2002

http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V05-45SR1TJ-1-1&_cdi=5637&_user=56761&_orig=na&_coverDate=06%2F162F2002&_sk=998719996&view=c&wchp=dGLbVlz-zSkWb&md5=4280259595b947a7b560f634f47de5c4&ie=/sdarticle.pdf

Ménard,Michel. & Dardignac, Pierre-André. & Chibelushi, Claude C. - "Non-extensive thermostatistics and

extreme physical information for fuzzy clustering (invited paper)", IJCC, 2 (4): 1-63, 2004

http://www.yangsky.us/ijcc/pdf/ijcc241.pdf

Notes

↑ Frieden, B. Roy Physics from Fisher Information: A Unification , 1st Ed. Cambridge University Press, ISBN 0-521-63167-X, pp328, 1998 ([ref name="Frieden6"] shows 2nd Ed.)
↑ Frieden, B.R. & Hughes, R.J., Spectral 1/f noise derived from extremized physical information, Phys. Rev. E 49, 2644, 1994
↑ Frieden, B.R. & Soffer, B.H., Lagrangians of physics and the game of Fisher-information transfer, Phys. Rev. E 52, 2274, 1995
↑ Frieden, B.R., & Plastino, A. & Soffer, B.H., Population genetics from an information perspective, J. Theor. Biol. 208, 49-64, 2001
↑ ^5.0 ^5.1 Frieden, B.R. & Gatenby, R.A. - Information dynamics in carcinogenesis and tumor growth, Mutat. Res. 568, 259, 2004
↑ Hawkins, R.J. & Frieden, B.R. & D'Anna, J.L. - Ab initio yield curve dynamics, Phys. Lett. A 344, 317, 2005

References

Frieden, B.R. - Fisher information as the basis for the Schrödinger wave equation, Am. J. Physics 57, 1004-1008, 1989
Frieden, B.R. - Fisher information, disorder, and the equilibrium distributions of physics, Phys. Rev. A 41, 4265-4276, 1990
Frieden, B.R. - Estimation of distribution laws, and physical laws, by a principle of extremized physical information, Physica A 198, 262-338, 1993
Frieden, B.R. - Physics from Fisher Information, Mathematics Today 37, 115-119, 2001
Frieden, B.R. & Gatenby, R.A. - Power laws of complex systems from extreme physical information, Phys. Rev. E 72, 036101, 2005
Frieden, B.R. & Soffer, B.H. - Information-theoretic significance of the Wigner distribution, Phys. Rev. A, to be published 2006

External links

B. Roy Frieden, "Fisher Information, a New Paradigm for Science: Introduction, Uncertainty principles, Wave equations, Ideas of Escher, Kant, Plato and Wheeler." This essay is continually revised in the light of ongoing research using EPI.
The Bactra Review A critical review of the first edition of Science from Fisher Information (2nd ed. listed above), and on EPI in general.
Unexpected Union - Physics and Fisher Information: An uncritical review of the same book and an introduction to EPI from SIAM News Vol 33 #6; July 17, 2000

[Frienden3-1] Frieden, B. Roy Physics from Fisher Information: A Unification , 1st Ed. Cambridge University Press, ISBN 0-521-63167-X, pp328, 1998 ([ref name="Frieden6"] shows 2nd Ed.)

[Frieden1-2] Frieden, B.R. & Hughes, R.J., Spectral 1/f noise derived from extremized physical information, Phys. Rev. E 49, 2644, 1994

[Frieden2-3] Frieden, B.R. & Soffer, B.H., Lagrangians of physics and the game of Fisher-information transfer, Phys. Rev. E 52, 2274, 1995

[Frieden4-4] Frieden, B.R., & Plastino, A. & Soffer, B.H., Population genetics from an information perspective, J. Theor. Biol. 208, 49-64, 2001

[Frieden5-5] 5.0 ^5.1 Frieden, B.R. & Gatenby, R.A. - Information dynamics in carcinogenesis and tumor growth, Mutat. Res. 568, 259, 2004

[Frieden7-6] Hawkins, R.J. & Frieden, B.R. & D'Anna, J.L. - Ab initio yield curve dynamics, Phys. Lett. A 344, 317, 2005

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+'''Extreme physical information''' ('''EPI''') is a principle, first described and formulated in 1998<ref name="Frienden3">Frieden, B. Roy ''Physics from Fisher Information: A Unification '', 1st Ed. Cambridge University Press, ISBN 0-521-63167-X, pp328, 1998 ([ref name="Frieden6"] shows 2nd Ed.)</ref> by [[B. Roy Frieden]], Emeritus Professor of Optical Sciences at the [[University of Arizona]], that states, the precipitation of scientific laws can be derived through [[Fisher information]], taking the form of [[differential equation]]s and [[probability distribution function]]s.
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+== Introduction ==
+Physicist [[John Archibald Wheeler]] stated that:
+{{Quotation|All things physical are information-theoretic in origin and this is a participatory universe... Observer participancy gives rise to information; and information gives rise to physics.}}
+By using [[Fisher information]], in particular its loss ''I'' - ''J'' incurred during observation, the EPI principle provides a powerful new approach for deriving laws governing many aspects of nature and human society. EPI can be seen as an extension of [[information theory]] that encompasses much theoretical [[physics]] and [[chemistry]]. Examples include the [[Schrödinger wave equation]] and the [[Maxwell-Boltzmann distribution]] law. EPI has been used to derive a number of fundamental laws of [[physics]],<ref name="Frieden1">Frieden, B.R. & Hughes, R.J., ''Spectral [[1/f noise]] derived from extremized physical information'', ''Phys. Rev. E'' '''49,''' 2644, 1994</ref><ref name="Frieden2">Frieden, B.R. & Soffer, B.H., ''Lagrangians of physics and the game of Fisher-information transfer'', ''Phys. Rev. E'' '''52,''' 2274, 1995</ref> [[biology]],<ref name="Frieden4">Frieden, B.R., & Plastino, A. & Soffer, B.H., ''Population genetics from an information perspective'', ''J. Theor. Biol.'' '''208,''' 49-64, 2001</ref> the [[biophysics]] of [[cancer]] growth,<ref name="Frieden5">Frieden, B.R. & Gatenby, R.A. - ''Information dynamics in carcinogenesis and tumor growth'', ''Mutat. Res.'' '''568,''' 259, 2004</ref>[[chemistry]],<ref name="Frieden5" /> and [[economics]].<ref name="Frieden7">Hawkins, R.J. & Frieden, B.R. & D'Anna, J.L. - ''Ab initio yield curve dynamics'', ''Phys. Lett. A'' '''344,''' 317, 2005</ref> EPI can also be seen as a [[game theory|game]] against nature, first proposed by [[Charles Sanders Peirce]].   The approach does require prior knowledge of an appropriate invariance principle or data.
+== EPI principle ==
+The EPI principle builds on the well known idea that the observation of a "source" phenomenon is never completely accurate. That is, information present in the source is inevitably lost when observing the source. Moreover, the random errors that contaminate the observations are presumed to define the probability distribution function of the source phenomenon. That is, "the physics lies in the fluctuations."  The information loss is postulated to be an extreme value. Thus, if the [[Fisher information]] in the data is <math>\mathcal{I}</math>, and the Fisher information in the source is <math>\mathcal{J}</math>, the EPI principle states that:
+:<math>
+\mathcal{I}
+-
+\mathcal{J}
+=
+\mathrm {Extremum}
+</math>
+The extremum for most situations is a minimum, meaning that there is a comforting tendency for any observation to describe its source faithfully. The EPI principle was recently derived, based on the mathematical axioms of L. Hardy that underlie all known physics (see 2013 paper cited below by Frieden and Gatenby).
+== Books ==
+*Frieden, B. Roy - ''Physics from Fisher Information: A Unification '', 1st Ed. Cambridge University Press, ISBN 0-521-63167-X, pp328, 1998
+*Frieden, B. Roy - ''Science from Fisher Information: A Unification '', 2nd Ed. Cambridge University Press, ISBN 0-521-00911-1, pp502, 2004
+*Frieden, B.R. & Gatenby, R.A. eds. - ''Exploratory Data Analysis Using Fisher Information'', Springer-Verlag (in press), pp358, 2006
+== Recent papers using EPI ==
+*Frieden, B. Roy & Gatenby, Robert A - "Principle of maximum Fisher information from Hardy's axioms applied to statistical systems", Phys. Rev. E 88, 042144,1-6, 2013
+:http://link.aps.org/doi/10.1103/PhysRevE.88.042144
+*Gatenby, Robert A. & Frieden, B. Roy - "Application of Information Theory and Extreme Physical Information to Carcinogenesis", :Cancer Research 62, 3675-3684, July 1, 2002
+:http://cancerres.aacrjournals.org/cgi/content/full/62/13/3675
+*Chimento,L.P. & Pennini, F. & Plastino, A. - "Naudts-like duality and the Extreme Fisher information principle",
+:Phys. Rev. E 62, 7462-7465, 2000
+:http://prola.aps.org/abstract/PRE/v62/i5/p7462_1subj: statistical mechanics
+*Nagy, A. - "Fisher information in density functional theory,", J. Chem. Phys. 119, 9401-9405, 2003
+:http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JCPSA6000119000018009401000001&idtype=cvips&gifs=yes
+:Subj: The Euler equation of density functional theory is derived using EPI.
+*Anton, M. & Weisen, H. & Dutch, M.J. - "X-ray tomography on the TCV tokamak",
+:Plasma Phys. Control. Fusion 38, 1849-1878, 1996
+:http://ej.iop.org/links/q80/fVFo+Bx3KRlwd6qcdU2Saw/p61101.pdf
+*Mlynar, J. & Bertalot, L. - "Neutron spectra unfolding with minimum Fisher regularization"
+:http://pos.sissa.it/archive/conferences/025/063/FNDA2006_063.pdf
+:Subj: Diagnosis of plasma shape within the tokamak fusion machine using reconstructions based upon EPI.
+*Venkatesan, Ravi. - "Information encryption using a Fisher-Schrödinger Model",
+:Presented at 6th International Conference on Complex Systems (ICCS) June, 2006
+:Boston, MA Full paper is in Frieden and Gatenby, 2006
+:http://necsi.edu/community/wiki/index.php/ICCS06/235
+:Subj: Encryption, secure transmission using EPI, in particular game aspect.
+*Fath B.D. & Cabezas, H. & CW Pawlowski - "Exergy and Fisher information as ecological indices",
+:Ecological Modeling 174, 25-35, 2004 - CW 2003
+:http://zp9vv3zm2k.scholar.serialssolutions.com/sid=google&auinit=BD&aulast=Fath&atitle=Exergy+and+Fisher+Information+as+ecological+indices&id=doi:10.1016/j.ecolmodel.2003.12.045
+:Subj: monitoring of the environment for species diversity
+*Yolles. M.I. - "Knowledge Cybernetics: A New Metaphor for Social Collectives", 2005
+:http://isce.edu/ISCE_Group_Site/web-content/ISCE_Events/Christchurch_2005/Papers/Yolles.pdf
+:Subj: Information-based approaches to knowledge management.
+*Venkatesan, R.C. - "Invariant Extreme Physical Information and Fuzzy Clustering", Proc. SPIE Symposium on Defense & Security,
+:Intelligent Computing: Theory and Applications II, Priddy, K. L. ed, Volume 5421, pp. 48-57, Orlando, FL, 2004
+:http://spiedl.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PSISDG005421000001000048000001&idtype=cvips&prog=normal
+*Ménard, Michel. & Eboueya, Michel. - "Extreme physical information and objective function in fuzzy clustering",
+:Fuzzy Sets and Systems 128(3): 285-303, 2002
+:http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V05-45SR1TJ-1-1&_cdi=5637&_user=56761&_orig=na&_coverDate=06%2F162F2002&_sk=998719996&view=c&wchp=dGLbVlz-zSkWb&md5=4280259595b947a7b560f634f47de5c4&ie=/sdarticle.pdf
+*Ménard,Michel. & Dardignac, Pierre-André. & Chibelushi, Claude C. - "Non-extensive thermostatistics and
+:extreme physical information for fuzzy clustering (invited paper)", IJCC, 2 (4): 1-63, 2004
+:http://www.yangsky.us/ijcc/pdf/ijcc241.pdf
+==See also==
+*[[Digital physics]]
+*[[Physical information]]
+*[[Information geometry]]
+==Notes==
+<references/>
+==References==
+*Frieden, B.R. - ''Fisher information as the basis for the Schrödinger wave equation'', Am. J. Physics '''57''', 1004-1008, 1989
+*Frieden, B.R. - ''Fisher information, disorder, and the equilibrium distributions of physics'', Phys. Rev. A '''41''', 4265-4276, 1990
+*Frieden, B.R. - ''Estimation of distribution laws, and physical laws, by a principle of extremized physical information'', Physica A '''198''', 262-338, 1993
+*Frieden, B.R. - ''Physics from Fisher Information'', Mathematics Today '''37''', 115-119, 2001
+*Frieden, B.R. & Gatenby, R.A. - ''Power laws of complex systems from extreme physical information'', ''Phys. Rev. E'' '''72,''' 036101, 2005
+*Frieden, B.R. & Soffer, B.H. - ''Information-theoretic significance of the Wigner distribution'', ''Phys. Rev. A'', to be published 2006
+==External links==
+*[[B. Roy Frieden]], "[http://www.optics.arizona.edu/Frieden/Fisher_Information.htm Fisher Information, a New Paradigm for Science: Introduction, Uncertainty principles, Wave equations, Ideas of Escher, Kant, Plato and Wheeler.]" This essay is continually revised in the light of ongoing research using EPI.
+*[http://www.cscs.umich.edu/~crshalizi/reviews/physics-from-fisher-info/ The Bactra Review] A critical review of the first edition of ''Science from Fisher Information'' (2nd ed. listed above), and on EPI in general.
+*[http://www.siam.org/pdf/news/659.pdf Unexpected Union - Physics and Fisher Information]: An uncritical review of the same book and an introduction to EPI from [http://www.siam.org/news/news.php?issue=0033.06 SIAM News Vol 33 #6; July 17, 2000]
+[[Category:Information theory]]