David B. Saakian is leading researcher of A. Alikhanyan National Science Laboratory (Yerevan physics institute) foundation, the PI of complex system statistical physics group.

E-mail: saakian@yerphi.am

The publications list is in:

https://scholar.google.com/citations?user=oK-Rr5AAAAAJ

I prepared my Phd thesis in FIAN (Lebedev Institute, Moscow), working with academicians Igor Sobelman, Boris Zeldovich, Yakov Zeldovich in 1980. The doctor of science thesis in 1993.

My groupIn my group currently works Edgar Vardanyan as a research assistant, I have also two other students Ruben Poghosyan and Sargis Jibilyan.

PhD Armen Allahverdyan (an independent researcher, got Armenian president’s prize as a best physicist in 2019) and PhD Narek Martirosyan are members of my research project team, project 18T-1C090Armenian State Science committee.

Current research grantsI am a PI of project “ An evolution on fluctuating landscapes and non-equlibrium statistical physics”, grant 18T-1C090, Armenian State Science committee and co-PI of the Evolution project of Russian Science Foundation, grant 19-11- 00008.

Former Phd StudentsI was a supervisor of 4 Phd theses, by Evgeny Prokhorenko, Armen Allahverdyan, Zara Kirakosyan, Tatiana Yakushkina, also a co-supervisor of Ronger Huang.

Former studentsAmong my former bachelor and master degree students are: Vahe Galstyan, Arax Martirosyan, Zhirayr Avetisyan, Boris Harutyunyan, Nickolay Ulyanov.

Main CollaboratorsEdgar Vardanyan, Tatiana Yakushkina, Eugene Koonin, Kanghao Cheong, Alexandr Bratus, Vladimir Redko.

Former collaborators:Chin-Kun Hu, Armen Allahverdyan, Hong Qian, Andreas KLumper .

My evolution conference in 2019In March 29-April 3 I organized an evolution conference (growing complexity) In Yerevan, with the participation of Eugene Koonin, Kunihiko Kaneko, Paulien Hogeweg and some other famous experts.

The President of Armenia Mr. Armen Sargsyan opened the conference:

Stories about my studentsI am working with the most talent students of different countries, laureates of the world Olympiads, Boris got gold medal of world chemistry Olympiad, Vahe and Zhirayr medals of the world Physics Olympiad, Edgar- gold and silver medals of the world physics Olympiad. My students in the age 18-20 solved a series of famous unsolved problems.

Zhirayr in 2010, phys. Rev. E, in 3 pages derived exact solution of evolution dynamics in case of recombination for many gene case.

Vahe in 2012, Phys. Rev. E found a method, how to solve the master equation, when it is strip of the 1-d chains of equations in the large system size limit. His method gives the solutions of Parrondo games, gene auto-regulation problem, mutator phenomenon, the evolution games with randomly changing payoffs.

In 2018 Ronger Huang suggested a method, how to calculate the finite size corrections for the model classes considered by Vahe.

Edgar in 2019 has done a really revolutionary work about finite population size problem in evolution.

All 4 works have been considered as very hard or almost unsolvable.

My main scientific results.In 1992 I proved exact mapping of Derrida’s REM to Shannon optimal coding found exact r any rate of information transition [1].

In 2005 I introduced the concept of reflections in complex systems [2], somehow resembling the Turchin’s theory of MST transitions.

In 2006 I calculated exactly the mean fitness of Eigen mode [3]l, in 2008-exact dynamics [4].

In 2009 found first exact mapping of REM to strings [5].

In 2011- exact solution of multi-fractal random walk model [6].

In 2017exact solution for the Parrondo games [7], in 2018-for the Brownian ratchets [8].

In 2017 I derived exact functional equation for the Hidden Markov models [9], in 2018- for the product of correlated random matrices [10].

My main conceptAll the advanced complex systems: evolution, markets, neuroscience, strings, turbulence should be described by the same models and methods, involving: REM, reflections and information thermodynamics.

I hope that the list of the target problems could be extended to include: high energy, 3-d critical models, the cosmology.

The list of my research interests:Exact solution of quasispecies models.

Evolution models on fluctuating fitness landscapes.

The evolution with multi-level selection with frustration, the relation of evolution models with Berry phase and analog of quantum anomalies.

When we have a “normal ” evolution with growth of complexity?

What versions of evolutionary dynamics give optimal development of social systems?

What version of reflections and evolutionary dynamics can give us a super Artificial Intelligence?

General theory of complex systems on the basis of REM, information thermodynamics and concept of reflections: multifractals, turbulence, strings, financial markets.

The sensing of chemicals by the cells, Parrondo games and Brownian ratchets.

The finite population size problem in evolution.

References- 1. D. Saakyan, Solution of the Derrida model with rare couplings and an asymmetric distribution of coupling constants; relationship with optimal coding, JETP Lett. 55, 192 (1993).
- 2.. D. B. Saakian, Error threshold in optimal coding, numerical criteria, and classes of universalities for complexity, Phys. Rev. E 71 (1), 016126 (2005).
- 3. 4. D. B. Saakian, C. K. Hu, Exact solution of the Eigen model, PNAS, 103 (13), 4935 (2006).
- 4. D. B. Saakian, O. Rozanova, A. Akmetzhanov, Dynamics of the Eigen and the Crow-Kimura models for molecular evolution, Physical Review E 78 (4), 041908 (2008)
- 5. D. B. Saakian, Phase structure of string theory and the Random Energy Model, Journal of Statistical Mechanics: Theory and Experiment (07), P07003 (2009).
- 6. D. B. Saakian, A Martirosyan, C. K. Hu, Z. R. Struzik, Exact probability distribution function for multifractal random walk models of stocks, EPL 95 (2), 28007 (2011).
- 7. R Zadourian, DB Saakian, A Klümper, Exact probability distribution functions for Parrondo's games Physical Review E 94 (6), 060102 (2017).
- 8. D. B. Saakian, A Klümper Exact solution of a ratchet with switching sawtooth potential. Physical Review E 97, 012153 (2018).,
- 9.DB Saakian, Physical Review E. Exact solution of the hidden Markov processes E 96, 052112 (2017)
- 10. D. B. Saakian, Semianalytical solution of the random-product problem of matrices and discrete-time random evolution, Physical Review E 98 (6), 062115 (2018).