In this note, we give a practical solution to the problem of determining the Use them for the QCD lattice simulations and at high energy particle physics. Trajectories have high quality statistical properties and we are suggesting to ![]() Which allows very fast generation of long trajectories of the C-systems. ![]() Recently an efficient algorithm was found, The C-systems on a torus are perfect candidates to be Of special interest are C-systems that are defined on a The important property of C-systems is that they have a countable set ofĮverywhere dense periodic trajectories and that their density exponentially The C-condition defines a rich class ofĭynamical systems which span an open set in the space of all dynamical systems. These extraordinary ergodic properties follow from Hyperbolic dynamical systems have homogeneous instability of all trajectoriesĪnd as such they have mixing of all orders, countable Lebesgue spectrum and We are developing further our earlier suggestion to use hyperbolic AnosovĬ-systems for the Monte-Carlo simulations in high energy particle physics. ![]() It also applies batteries of tests to a long list of widely used RNGs. Besides introducing TestU01, the paper provides a survey and a classification of statistical tests for RNGs. The tests can be applied to instances of the generators predefined in the library, or to user-defined generators, or to streams of random numbers produced by any kind of device or stored in files. Finally, the library provides various types of generators implemented in generic form, as well as many specific generators proposed in the literature or found in widely-used software. That is, for a given kind of test and a given class of RNGs, to determine how large should be the sample size of the test, as a function of the generator's period length, before the generator starts to fail the test systematically. Tools are also oered to perform systematic studies of the interaction between a specific test and the structure of the point sets produced by a given family of RNGs. Predefined tests suites for sequences of uniform random numbers over the interval (0,1) and for bit sequences are available. It provides general implementations of the classical statistical tests for RNGs, as well as several others tests proposed in the literature, and some original ones. We use Artin symbolic dynamics, the differential geometry and group theoretical methods of Gelfand and Fomin.Ī collection of utilities for the empirical statistical testing of uniform random number generators (RNGs). In this article we shall expose his results, will calculate the correlation functions/observables which are defined on the phase space of the Artin billiard and demonstrate the exponential decay of the correlation functions with time. The geodesic trajectories of the non-Euclidean billiard are bounded to propagate on the fundamental hyperbolic triangle. The fundamental region in this case is a hyperbolic triangle. The dynamical system is defined on the fundamental region of the Lobachevsky plane which is obtained by the identification of points congruent with respect to the modular group, a discrete subgroup of the Lobachevsky plane isometries. An example of such system has been introduced in a brilliant article published in 1924 by the mathematician Emil Artin. Of special interest are C-systems which are defined on compact surfaces of the Lobachevsky plane of constant negative curvature. ![]() But if you reschedule Stage 3, all your recipients will receive Stage 3 at the new time (because they have not yet been sent the prior stage, Stage 2).The hyperbolic Anosov C-systems have exponential instability of their trajectories and as such represent the most natural chaotic dynamical systems. This is because the send time of Stage 2 is tied to Stage 1, and Stage 1 has already sent. If you reschedule Stage 2, the new send time will not affect those recipients - they’ll get Stage 2 on the original date. For example, suppose you have a 3-stage sequence and you added all your recipients in a single batch. Changing the interval between sequence stagesĬhanging the interval between sequence stages will only affect the recipients who have not yet received the previous stage. You will need to reschedule each stage separately. Then check the box next to the recipient(s) you’d like to reschedule, and click Reschedule. Search for the recipient’s email address. Reschedule a sequence for an individual recipient There are a couple of options when rescheduling stages of your sequence.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |