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UID:6891@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20191203T110000
DTEND;TZID=Europe/Paris:20191203T120000
DTSTAMP:20241120T202618Z
URL:https://www.i2m.univ-amu.fr/evenements/asaki-saito-pseudorandom-number
 -generator-based-on-the-bernoulli-map-on-cubic-algebraic-integers/
SUMMARY:Asaki Saito (Future University Hakodate\, Japon): Pseudorandom numb
 er generator based on the Bernoulli map on cubic algebraic integers
DESCRIPTION:Asaki Saito: Pseudorandom sequences with high (dimensional) uni
 formity and quasirandom sequences are known to be very useful for Monte Ca
 rlo computation. It is\, however\, still an interesting question how we ca
 n generate a {pseudorandom sequence in the original sense}\, i.e.\, a comp
 uter-generated sequence of numbers that appear similar to a typical sample
  of independently identically distributed random variables.\nAccording to 
 ergodic theory\, one of the simplest chaotic maps on the unit interval\, n
 amely the Bernoulli map {x} ↦ 2{x} mod 1\, can generate ideal random bin
 ary sequences. However\, its use as a pseudorandom number generator has be
 en difficult due to the drawbacks of conventional simulation methods\, suc
 h as those using double-precision binary floating-point numbers or arbitra
 ry-precision rational numbers.\nIn this talk\, we present a pseudorandom b
 it generator that exactly computes chaotic true orbits of the Bernoulli ma
 p on real cubic algebraic integers having complex conjugates. In particula
 r\, we clarify a seed selection method that can select initial points (i.e
 .\, seeds) without bias and can make the pseudorandom sequences derived fr
 om them be very different from each other.\nMoreover\, in order to evaluat
 e the memory usage of our generator\, we give upper bounds concerning the 
 growth of the representation of points on a true orbit. We also report res
 ults of a large variety of tests indicating that the generated pseudorando
 m sequences have good statistical properties as well as an advantage over 
 what is probably the most popular generator\, the Mersenne Twister MT19937
 . In the end\, we discuss the use of Newton's method to approximate the tr
 ue orbit generator.\n\nThis is a joint work with Akihiro Yamaguchi\n\n\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Asaki_Saito.jpg
CATEGORIES:Séminaire,Ernest
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