Welcome

The MIXMAX Random Number Generator

• Georgios Savvidis (Nat. Cent. for Sci. Res. Demokritos)

The uniformly hyperbolic Anosov C-systems defined on a torus have exponential instability of their trajectories, and as such C-systems have mixing of all orders and nonzero Kolmogorov entropy. The mixing property of all orders means that all its correlation functions tend to zero. It was proven that the speed of decay in the C-systems is exponential, that is, the observables on the phase space become independent and uncorrelated exponentially fast. We have found that the upper bound on the exponential decay of the correlation functions universally depends on the value of a system entropy. A quintessence of the analyses is that local and homogeneous instability of the C-system phase space trajectories translated into the exponential decay of the correlation functions at the rate which is proportional to the Kolmogorov entropy, one of the fundamental characteristics of the Anosov automorphisms. This result allows to define the decorrrelation and relaxation times of the MIXMAX pseudorandom number generators.

Overview of ROOT, a software framework for data analysis of HEP data

• Lorenzo Moneta (CERN)

ROOT is a software framework written in C++ and used in High Energy Physics for the analysis of the experiment data and as a foundation library. This presentation will introduce the key features of ROOT, and why they are essential for the High Energy Physics community and possibly other field. ROOT provides also core mathematical and statistical libraries which are essen- tial for simulation, reconstruction and analysis of experiment data. These include pseusdo-random number generators used for simulation, Monte Carlo integration and statistical analysis. We will also show the new developments of ROOT in this area and in particular the new implementation of the MIXMAX random number generator.

Geant Particle Transport simulation: from pseudorandom sequences to applications in high energy physics, medical research and beyond.

• John Apostolakis (CERN)

Monte Carlo has been used for radiation and particle transport since the first gener- ation of digital computers. The Geant family is the mainstay of High Energy physics experiments over the last 30+ years; Geant4 is the backbone of the simulation of the LHC experiments at CERN, used to discover the Higgs Boson in 2012. It has been incorporated into innovative tools for medical research in imaging and radiotherapy, in the simulation of the effects of radiation on spacecraft and many other application areas. We give an overview of some of the underpinnings of Geant4, with emphasis on its use of pseudorandom number generators, including the recent advances including the inclusion of the MIXMAX generator, and the modeling of geometry in a common geometry engine, VecGeom. We also discuss the future of detector simulation, including the advanced require- ments for pseudo-random number generations the GeantV project, which seeks to use CPU’s caches and vector instructions (or accelerators including GPU and Xeon Phis) to obtain a large increase in computing performance. GeantV requires vec- torised implementation and improvements in geometry, physics processes and pseu- dorandom number generation. We discuss the additional requirements for PRNGs coming from the need to obtain the same simulated tracks even when the order in which particles are processed can change in a multi-threaded, fine-grain parallel pro- gram. The needs for very large periods, splitting and excellent statistical properties, which are driving forces for the continued development of MIXMAX are detailed.