Levenberg–Marquardt algorithm

Extreme physical information (EPI) is a principle, first described and formulated in 1998 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, biology, the biophysics of cancer growth,chemistry, and economics. 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:

$\mathcal{ℐ}-\mathcal{𝒥}=\mathrm{E}\mathrm{x}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{m}\mathrm{u}\mathrm{m}$

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

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