Horizon 2020

H2020-MSCA-RISE-MIXMAX

   Action title:

Development and Implementation of new generation of Pseudo Random Number Generator MIXMAX
based on Anosov-Kolmogorov C-K systems

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sk´lodowska-Curie grant agreement No 644121.

   Summary:

The primary objective of the MIXMAX consortium was a systematic development of the state of the art new generation of Pseudo Random Number Generators based on Kolmogorov-Anosov K-systems, which demonstrates excellent statistical properties, into a multidisciplinary usable product. This innovative class of RNG was proposed earlier by the members of the network and relies on the fundamental discoveries and results of Ergodic theory. The MIXMAX generator has been implemented at CERN into the Geant4 software and Geant4/CLHEP software as default generator and became a part of the CMS Simulation   Software . The code of the MIXMAX generator has been implemented into PYTHIA software at PYTHIA 8 , which is widely used in high energy experiments at CERN. The MIXMAX generator is implemented into the the GSL - GNU Scientific Library, the Extensions/Applications. It is also available in the ROOT scientific library at CERN. A chapter devoted to the MIXMAX generator can be found in the book "Computational Physics" by K.Anagnostopulos.

   Participants:

1. NATIONAL CENTER FOR SCIENTIFIC RESEARCH "DEMOKRITOS"
2. EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
3. KOBENHAVNS UNIVERSITET
4. A.I.ALIKHANYAN NATIONAL SCIENCE LABORATORY
5. NANJING UNIVERSITY

   

   Meetings and Workshops:

      FIRST MIXMAX NETWORK MEETING and SUMMER RESEARCH WORKSHOP at CERN, July 3 - July 17, 2015

      SECOND MIXMAX NETWORK MEETING and SUMMER RESEARCH WORKSHOP at CERN, July 4 - July 18, 2016

      CONFERENCE and MIXMAX MTR NETWORK MEETING at NCSR "Demokritos", September 5, 2016,

      MIXMAX NETWORK MEETING: Overview of the ROOT and Geant4 Software at CERN at NCSR "Demokritos", May 3, 2017

       CONFERENCE and Workshop of the MIXMAX Consortium in Athens at NCSR "Demokritos", July 3-4, 2018

   The MIXMAX code in C and C++11 standard interface can be found here

   The MIXMAX code for GSL - GNU Scientific Library can be found here.

   The MIXMAX "thermodynamical" parameters: Dimension, Entropy, Decorrelation time, Relaxation time

   There is a rather detailed MIXMAX Manual and the demonstaration of the generated numbers in 2D planes

   The BigCrush testU01 of the MIXMAX generator of dimension N=256.

   The CAcert Research Lab test of the MIXMAX generator of dimension N=240.

   The BigCrush testU01 of various RNGs .

   Chapter on MIXMAX in the book: "using C++" .

   Publications:

  1. George Savvidy and Natalia Savvidy.
    On the Problem of Monte Carlo Modelling of Physical Systems
    EFI-865-16-86-YEREVAN, EFI-865(16)-86, Jan 1986. 13pp.
  2. George Savvidy and Natalia Savvidy
    On the Monte Carlo Simulation of Physical Systems.
    J.Comput.Phys. 97 (1991) 566
  3. Konstantin Savvidy,
    The MIXMAX random number generator
    Computer Physics Coomunications 196 (2015) 161
    e-print arXiv:1403.5355
  4. George Savvidy,
    Anosov C-systems and Random Number Generator
    Theor.Math.Phys. 188 (2016) 1155-1171; e-print arXiv:1507.06348
  5. Konstantin Savvidy and George Savvidy,
    Spectrum and Entropy of C-systems. MIXMAX random number generator.
    Chaos Fractals Solitons 91 (2016) 33; e-print arXiv:1510.06274
  6. Andrzej Görlich, Marios Kalomenopoulos, Konstantin Savvidy and George Savvidy,
    Distribution of periodic trajectories of C-K systems. MIXMAX pseudorandom number generator
    J.Mod.Phys. C28 (2016) 1750032; e-print arXiv:1608.03496
  7. Konstantin Savvidy and George Savvidy,
    Exponential decay of correlations functions in MIXMAX generator of pseudorandom numbers
    Chaos Fractals Solitons 107 (2018) 244-250 ; e-print arXiv:1702.03574
  8. Hasmik Poghosyan, Hrachya Babujian and George Savvidy,
    Artin Billiard Exponential Decay of Correlation Functions
    Theor.Math.Phys. (2018) ; e-print arXiv:1802.04543
  9. Hayk Poghosyan, Konstantin Savvidy and George Savvidy,
    Classical limit theorems and high entropy MIXMAX random number generator
    Chaotic Modeling and Simulation (CMSIM) 1 (2018) 79-89 ; e-print arXiv:1708.04129
  10. Narek Martirosyan, Konstantin Savvidy and George Savvidy,
    Spectral Test of the MIXMAX Random Number Generators
    e-print arXiv:1806.05243
  11. Hrachya Babujian, Rubik Poghossian and George Savvidy,
    Correlation Functions of Classical and Quantum Artin System defined on Labachevsky Plane and Scrambling Time
    e-print arXiv:1808.02132
  12. Talk at CERN on "PRNGs based on Anosov-Kolmogorov C-K-systems"
    George Savvidy (SFT Group Meeting, CERN, Switzerland, March 2014)
  13. Talk at CERN on "The MIXMAX Random Number Generator.
    Integration of the MIXMAX engine into the CERN Scientific Software ROOT and Geant4"
    George Savvidy (SFT Group Meeting, CERN, Switzerland, May 2017)
    https://indico.cern.ch/event/308953/
  14. MIXMAX in ROOT Release 6.04/06 on 2015-10-13,
  15. MIXMAX in CLHEP/GEANT4 Release 2.3.1.1 on 2015-11-10