VI

Chapter VI

Evidences and arguments of the probabilistic model of the universe

The application of the theory of probabilities and of the law of the large numbers to the phenomena of the various scales of nature is naturally found in the scientific fields which study them. It is naturally in " hard " sciences that indeterminism most obviously appears : physics, astrophysics, cosmology, etc… but also, as it low will be seen, in innumerable probabilistic models in the multiple disciplines of biological sciences, in mathematics, and, much less apparent, in social and human sciences.

The physical or biological phenomena, , where the process of economy or optimization appears, i.e. where the movement, the energy or the action are optimal or minimal, raise, as we saw it previously, from the theory of probabilities. Their mathematical chances or their probabilities of occurring being raised, they occur.

Physics :

1. The interpretation of quantum mechanics and, more largely, of quantum physics is difficult and discussed. It rests on a certain number of indemonstrable postulates but whose validity is operational. The probabilistic wave equation of Schrödinger and the relations of uncertainty or indeterminism of Heisenberg constitute the major paradigms of them. The quantum of minimal action of Planck is the angular stone of all the microscopic physical phenomena. The concept of minimal fundamental level of energy ( no excited state of the atom ) also plays a significant role.

2. The interpretation of quantum physics, which one finds in his most significant aspects, is probabilistic.

3. According to the theory of General Relativity, a particle of test describes an optimal or minimal trajectory ( geodesic ) in a four-dimensional space (space-time) curved by the presence of matter-energy. That the space-time or that the trajectory in the space-time is curved by matter-energy, this trajectory is minimal. The shorter distance or geodesic from General Relativity is, as we saw it previously, in last analysis, an anthropic concept of optimization which is, the anthropic translation, of the ananthropic concept of dominant or preponderant probability.

4. Like the geodesic one in General Relativity, the Second Principle of the Thermodynamics which minimizes, by the probability, the evolution of the order in a closed system out of balance is a concept of optimization i.e. of dominating probability (Poincaré).

5. In the statistical mechanics of Boltzmann, who is at the base of the kinetic theory of gases, the third fundamental hypothesis indicates that " the state of gas in balance is that which corresponds to the maximum probability ".

6. The principle of least action of Maupertuis, fundamental in all traditional physics states that the action is minimal in all the physical phenomena. This principle was applied by Feynman to quantum physics. Hildebrandt, in the same way, stated a principle of the least action quantum. Theses principles of the least action are, as we saw it previously, the anthropic translation of the ananthropic concept of dominant or preponderant probability

7. In optics, according to the principle of Fermat, the way taken by the light to go from one point to another is that for which the time of course is minimum. One can also state it by saying that the length between these 2 points is minimum. These minima constitute, also, the anthropic translation of the ananthropic concept of dominant or preponderant probability

Planetology :

The current ratio 3 / 2 rotation /orbit of the planet Mars corresponds to a probability of stability to this resonance of 55 % (A. Correia and J.Laskar, Nature 2004).

Spheres: the major part of stars or planets is made up of spheres. It is known that the sphere is the geometrical form which minimizes the surface of an object of a given volume.

Biological sciences :

As we indicate it higher, the advanced researchs in current biological sciences privilege more and more probabilistic models with the detriment of the strictly deterministic models.

1. Laws of Mendel: in these laws, which gave rise to the modern genetics, in the sexual cells, the two components of male origin and of female origin, of each character, dissociate and, in fecundation, the components of each origin are linked randomly, i.e. in a probabilistic way, for each character.

2. Genetics: The mutations of genes, the supports of the biological evolution, occur in a probabilistic way.

3. Cycle of Kreps: Let us point out the maximum effectiveness of the cycle of Kreps in the energy production in the aerobic cells: By glycolysis and the fermentative way, the anaerobic cells manufacture, starting from glucose, 2 molecules of A.T.P., whereas the same reaction, continuing with breathing in the aerobic cells, produces 32 molecules of A.T.P. (oxidative phosphorylation of the cycle of Krebs) that is to say 16 times more energy ( Mason 1992, Robert J.Huskey 1998 ).

4. The author proposes a probabilistic model of the biological evolution which integrates the Darwinian theory with a new interpretation which respects the ananthropic character of nature: A probabilistic model of the biological evolution < http://site.voila.fr/dinosaurs >. This model proposes 3 probabilistic examples of the biological evolution: 1) 5 mass extinctions ( with the causes of the death of the Dinosaurs at border K / T), 2) the hominization 3) the increase of the PO2 P.A.L..

5) The expression of genes has been presented like a deterministic process for a long time. Today, this deterministic paradigm is cancelled by many experimental arguments in favour of a probabilistic mechanism of the expression of genes. The cellular data are reinforced by a number growing of studies carried out at the molecular level. The life of a cell would be founded on probabilistic mechanisms due to non-specific molecular interactions where the Brownian chance plays a dominating role (Jean-Jacques Kupiec 2005 - Paldi - 2003).

6) In all the fields of biological research, the probabilistic models are essential, today, with the probabilistic tools, bayesian methods, hidden of Markov Models, laws of the great numbers, Monte-Carlo method. Some examples extracted from the innumerable current probabilistic models:

Probabilities and biology:

Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids (with hidden Markov Models) (Richard Durbin, Cambridge University Press 1999-07-01) Probabilistic modeling of biological data (Pierre Baldi ICS 277B - A unified Bayesian probabilistic framework for modeling and mining biological data...)

Statistical Methods in Bioinformatics (probability and statistics in the bioinformatics context - Warren J Ewens, Gregory R. Grant - Springer April 20, 2001)

The analysis of the biological sequences by hidden Chains of Markov (HMM), (Bernard Prum 1999)

Learning Probabilistic Relational Models - Nir Friedman (with Bayesian networks BNs) (Koller and Pfeffer - Stanford University 1998)

Brain:

Brain, chance and chaos (Henri Korn - University of all the knowledges 21.10.2002)

Probabilistic causal networks on a large scale: a new formalism for the modeling of the cerebral data processing (Vincent Labatut - Inserm u455 - 2 Mars 2004).

OMEGA: probabilistic calculation of models of the electric activity of the neurons (Denis Talay - INRIA - 2005)

Probabilistic brain atlases (Paul Thompson - UCLA Medical Center)

A probabilistic Framework for Region-Specific Remodeling of Dendrites in Three-Dimensional Neuronal Reconstructions (Narayanan - Narayan - Chattarji - National Centre for Biological Sciences - Bangalore - India - Neural Computation 2005)

Genome:

Regulation of Genome Expression (probabilistic models of genome regulatory networks - Richard A. Young - MIT)

Expression of genes and cancer: a question of probability ? (Jean-Jacques Kupiec - INSERM - 2005)

Bayes Networks and Graphical Models in Molecular Biology (MIT - Boston University Biocomputing Research - Graphical models at Kevin' s site at MIT: Protein Modeling (Hidden Markov Models); System Biology, Functional Genomics, Gene Expression Analysis, Protein Protein Interaction (Bayes Networks); Gene Expression (Microarray) Analysis, Networks, Pathways (Bayesian Network); Biological Dated Integration (Bayesian Framework); Protein Protein Interaction and Functional Annotation (Markov Random Field Approaches); DNA Sequence Analysis (Bayes Networks); Genetics, Phylogeny Linkage Analysis (hidden Markov phylogeny)

Probabilistic Models in Computational Molecular Biology (Stanford University, Stanford, CA - 2000)

Rich probabilistic models for genomic data (Eran Segal - August 2004)

A probabilist theory for cell differenciation (J-j Kupiec - 1986)

Probabilistic discovery of overlapping cellular processes and to their regulation (Annual conference on Research in Computation Molecular Biology - Alexis Battle, Eran Segal, Daphne Koller - Stanford University, Stanford, CA)

Probabilistic models of Proteins and Nucleic Acids (HMMs - Durbin-Cambridge, Eddy-Washington University, Krogh-Lyngby-Denmark, Mitchison - 1998)

Probabilistic code for DNA recognition by proteins of the EGR family (Benos, Lapedes, Stormo - J Mol Biol. Nov. 2002 1)

Recognizing complex, asymmetric functional sites in protein structures using a bayesian scoring function (Wei, Altman – Journal of Bioinformatics and Computational Biology) A probabilistic view of gene function (Fraser, Marcotte - Nature Genetics - 27 May 2004) Differential Proteomics via Probabilistic Peptide Identification Scores (Colinge, Chiappe, Lagache, Moniatte, Bougueleret - Anal. Chem. 2005)

A probabilistic functional network of yeast genes (Lee, Date, Adai, Marcotte - Science Nov. 2004 26)

Chemistry - Biochemistry:

Amazing cellular biochemistry in terms of molecular networks (computational approaches within has Bayesian formalism - Xia, Yu, Jansen, Seringhaus, Baxter, Greebaum, Zhao, Gerstein - Annual Review of Biochemistry - July 2004)

A Thermodynamic-Probabilistic Analysis of Diverse Homogenous Stoichiometric Chemical Reactions (Garfinckle - J Physical Chemistry 2002)

Populations:

Theory of Probability (Chance plays a major role in the dynamics of a population - Joe Romano - Biomathematics 2005)

Stochastic models for biological populations - Genealogies and spatial structures (Birkner and all. - Dutch-German Bilateral Research Group "Mathematics of random spatial models from physics and biology)

Various:

John Gosline (1984) proved that it was a stochastic arrangement of the amorphous protein chains which gives to the silk of spiders its unrivalled properties (4 times more solid than steel)

Biased random walk (biochemistry) enables bacteria to search for food and flee for harm (Wikipedia)

Active perception of the 3 D forms within the framework of a bayesian model (Jacques Droulez - CNRS - College of France - December 8, 2004)

A Probabilistic Approach to Large-Scale Association Scans: A Semi-Bayesian Method to Detect Disease-Predisposing Alleles (Steven J Schrodi - Statistical Applications in Genetics and Molecular Biology - November 1, 2005)

Understanding the LDL receptor Structure through Probabilistic Models (using HMMs of the LDL receptor - MIT Computational Biophysics Laboratory - October 2005)

A Web-Based System for Public-Private Sector Collaborative Ecosystem Management (construction of probabilistic models of ecosystems processes - Timothy C Haas - University of Wisconsin-Milwaukee)

Probabilistic Basecalling (Speed, Li, Nelson, Cawley - University of California, Berkeley - January 1999)

A probabilistic analysis of a greedy algorithm arising from computational biology (Daniel G Brown - Cornel University)

A probabilistic model of mosaicism based one thee histological analysis of chimaeric rat liver (Iannaccone, Weinberg, Berkwits - Northwestern University Medical School, Chicago II)

Mathematics:

The chance does not miss of this "pure" branch of scientific research:

"These concepts of chance and impredictibility, which are fundamental in traditional physics and quantum physics, are also in the heart of pure mathematics" (Chaitin – La Recherche December 2004 N° 381)"...

It seems well that the decimals of µ (pi) appear in a random way: those which sought regularities in the distribution of the decimals found anything, even with very thorough statistical tests "(Simon Plouffe – La Recherche - December 2005 - N° 392)

Social and human sciences :

Insurances: To envisage the evolutions of many data, interest rates, growth of the GDP, evolution of the rate of fruitfulness, etc… or to establish the amount of the premiums, according to the various risks (fire, life, various), the actuaries apply the theory of probabilities.

The increasing use, in many fields, of statistics, reveals the importance attached by the researchers to the theory of probabilities and the law of the large numbers.

Next : VII Conclusions

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