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

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Deliverables

Critical Indices and Loop Integrals (opens in new window)

The critical indices of random space-time manifolds, their Hausdorff dimensionality. The values of the scalar integrals representing quantum correction in decay branching ratios.

Statistical Data (opens in new window)

"The statistical data : comulative distribution functions; Kolmogorov-Smirnov test;""BigCrush"" suite of tests; Shapiro-Wilk test; Anderson-Darling test representing internal characteristics of the MIXMAX generator as a function of the dimensionality N=256,508,1260 of the generator and of the order of the Galois field p=2^61 -1."

Multi-thread Programmes (opens in new window)

An object-oriented software package designed and written in C++ ready to be used in ROOT and Geant4, together with on-line manual and validation tests to ensure its correctness.

MIXMAX generator (opens in new window)

Program of the MIXMAX generator with tuneable internal parameters of maximal dimensionality N=256,509,1260 and of the order of the Galois field p=2^61-1, embedded into a user friendly environment and with an on-line manual.

Publications

Бильярд Артина: экспоненциальный распад корреляционных функций (opens in new window)

Author(s): Хасмик Рубеновна Погосян, Hasmik Rubenovna Poghosyan, Г М Бабуджян, H M Babujian, Георгий Константинович Саввиди, Georgii Konstantinovich Savvidi
Published in: Теоретическая и математическая физика, Issue 197/2, 2018, Page(s) 230-251, ISSN 0564-6162
Publisher: Математический институт им. В.А. Стеклова Российской академии наук
DOI: 10.4213/tmf9549

Distribution of periodic trajectories of C-K systems MIXMAX pseudorandom number generator (opens in new window)

Author(s): Andrzej Görlich, Marios Kalomenopoulos, Konstantin Savvidy, George Savvidy
Published in: International Journal of Modern Physics C, Issue Vol. 28, No. 2 (2017) 1750032 (16 pages), 2016, Page(s) 1750032, ISSN 0129-1831
Publisher: World Scientific Publishing Co
DOI: 10.1142/S0129183117500322

Anosov C-systems and random number generators (opens in new window)

Author(s): G. K. Savvidy
Published in: Theoretical and Mathematical Physics, Issue 188/2, 2016, Page(s) 1155-1171, ISSN 0040-5779
Publisher: Maik Nauka/Interperiodica Publishing
DOI: 10.1134/S004057791608002X

Classical Limit Theorems and High Entropy MIXMAX random number generator

Author(s): Hayk Poghosyan, Konstantin Savvidy and George Savvidy
Published in: Chaotic Modeling and Simulation, Issue 1 (2018) 79–89, 2018, Page(s) 79-89, ISSN 2241-0503
Publisher: CMSIM

Spectral test of the MIXMAX random number generators (opens in new window)

Author(s): Narek Martirosyan, Konstantin Savvidy, George Savvidy
Published in: Chaos, Solitons & Fractals, Issue 118, 2019, Page(s) 242-248, ISSN 0960-0779
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.chaos.2018.11.024

Exponential decay of correlations functions in MIXMAX generator of pseudorandom numbers (opens in new window)

Author(s): George Savvidy, Konstantin Savvidy
Published in: Chaos, Solitons & Fractals, Issue 107, 2018, Page(s) 244-250, ISSN 0960-0779
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.chaos.2018.01.007

The MIXMAX random number generator (opens in new window)

Author(s): Konstantin G. Savvidy,
Published in: Computer Physics Communications, Issue Volume 196, November 2015,, 2015, Page(s) Pages 161–165, ISSN 0010-4655
Publisher: Elsevier BV
DOI: 10.1016/j.cpc.2015.06.003

Statistical Tests for MIXMAX Pseudorandom Number Generator

Author(s): Narek Martirosyan, Gevorg Karyan and Norayr Akopov
Published in: Mathematical Problems of Computer Science, Issue 47 (2017) 37-49, 2017, Page(s) 12 pages, ISSN 0131-4645
Publisher: """GITUTYUN"" PUBLISHING HOUSE OF NAS RA"

Spectrum and Entropy of C-systems. MIXMAX random number generator (opens in new window)

Author(s): Konstantin Savvidy and George Savvidy
Published in: Chaos Solitons and Fractals: the interdisciplinary journal of Nonlinear Science,, Issue 91 (2016) 33-38, 2016, ISSN 0960-0779
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.chaos.2016.05.003

Correlation Functions of Classical and Quantum Artin System defined on Labachevsky Plane and Scrambling Time

Author(s): Brachia Babujian, Rubik Poghossian and George Savvidy
Published in: https://arxiv.org/abs/1808.02132, 2018
Publisher: Cornell University

Quantum-Mechanical interpretation of Riemann zeta function zeros

Author(s): Konstantin Savvidy and George Savvidy
Published in: https://arxiv.org/abs/1809.09491, 2018
Publisher: Cornell University

Classical limit theorems and high entropy MIXMAX random number generator

Author(s): Hayk Poghosyan, Konstantin Savvidy and George Savvidy
Published in: Proceedings of the 10th Chaotic Modeling and Simulation International Conference, Issue Barcelona, Spain: 30 May-2 June, 2017, 2017, Page(s) pages: 661-675
Publisher: ISAST: International Society for the Advancement of Science and Technology.

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