Related papers: Pseudorandom number generation by p-adic ergodic t…

By abstracting a connection between gauge symmetry and gauge identity on a noncommutative space, we analyse star (deformed) gauge transformations with usual Leibnitz rule as well as undeformed gauge transformations with a twisted Leibnitz…

Designing a pseudorandom number generator (PRNG) is a difficult and complex task. Many recent works have considered chaotic functions as the basis of built PRNGs: the quality of the output would indeed be an obvious consequence of some…

We construct a pseudorandom generator which fools read-$k$ oblivious branching programs and, more generally, any linear length oblivious branching program, assuming that the sequence according to which the bits are read is known in advance.…

Let $\Lambda$ be an artin algebra with representation dimension equal to three and $M$ an Auslander generator of $\Lambda$. We show how, under certain assumptions, we can mutate $M$ to get a new Auslander generator whose endomorphism ring…

We consider stochastic and open quantum systems with a finite number of states, where a stochastic transition between two specific states is monitored by a detector. The long-time counting statistics of the observed realizations of the…

The ring of invariant polynomials ${\mathbb C}[V]^G$ over a given finite dimensional representation space $V$ of a complex reductive group $G$ is known, by a famous theorem of Hilbert, to be finitely generated. The general proof being…

A characterization of finitely generated shift-invariant subspaces is given when generators are g-minimal. An algorithm is given for the determination of the coefficients in the well known representation of the Fourier transform of an…

Sequences are often conveniently encoded in the form of a generating function depending on a formal variable. This note presents two observations that allow one to draw conclusions about the generated sequence from the generating function.…

We establish mean convergence for multiple ergodic averages with iterates given by distinct fractional powers of primes and related multiple recurrence results. A consequence of our main result is that every set of integers with positive…

Generalizing Krieger's finite generation theorem, we give conditions for an ergodic system to be generated by a pair of partitions, each required to be measurable with respect to a given sub-algebra, and also required to have a fixed size.

We extend a previous conjecture [cond-mat/0407477] relating the Perron-Frobenius eigenvector of the monodromy matrix of the O(1) loop model to refined numbers of alternating sign matrices. By considering the O(1) loop model on a…

We study almost symmetric semigroups generated by odd integers. If the embedding dimension is four, we characterize when a symmetric semigroup that is not complete intersection or a pseudo-symmetric semigroup is generated by odd integers.…

We give a new practical method for computing subvarieties of projective hypersurfaces. By computing the periods of a given hypersurface X, we find algebraic cohomology cycles on X. On well picked algebraic cycles, we can then recover the…

We introduce new families of enhanced chaotic number generators in order to compute very fast long series of pseudorandom numbers. The key feature of these generators being the use of chaotic numbers themselves for sampling chaotic…

Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…

We conjecture that bounded generalised polynomial functions cannot be generated by finite automata, except for the trivial case when they are ultimately periodic. Using methods from ergodic theory, we are able to partially resolve this…

In this paper, a new chaotic pseudo-random number generator (PRNG) is proposed. It combines the well-known ISAAC and XORshift generators with chaotic iterations. This PRNG possesses important properties of topological chaos and can…

Invariants are a set of properties over program attributes that are expected to be true during the execution of a program. Since developing those invariants manually can be costly and challenging, there are a myriad of approaches that…

We analyze the structure of the periodic trajectories of the K-system generator of pseudorandom numbers on rational sublattice which coincides with the Galois field. The period of the trajectories increases as a function of lattice size and…

This work considers the deployment of pseudo-random number generators (PRNGs) on graphics processing units (GPUs), developing an approach based on the xorgens generator to rapidly produce pseudo-random numbers of high statistical quality.…