Related papers: Recursive Random Number Generator Using Prime Reci…

In this article, we propose a new three parameter distribution by compounding negative binomial with reciprocal inverse Gaussian model called negative binomial-reciprocal inverse Gaussian distribution. This model is tractable with some…

We introduce concepts of "recursive polynomial remainder sequence (PRS)" and "recursive subresultant," along with investigation of their properties. A recursive PRS is defined as, if there exists the GCD (greatest common divisor) of initial…

Pseudo-random number generators (PRNGs) are high-nonlinear processes, and they are key blocks in optimization of Large language models. Transformers excel at processing complex nonlinear relationships. Thus it is reasonable to generate…

Methods for specifying Moore type state machines (transducers) abstractly via primitive recursive functions and for defining parallel composition via simultaneous primitive recursion are discussed. The method is mostly of interest as a…

We study a new type of sequences whose elements are defined in terms of the position, sign and magnitude of another element of the sequence. The name ultra-recursive comes from the fact that these sequences possess terms that are generated…

We present a constant and a recursive relation to define a sequence $f_n$ such that the floor of $f_n$ is the $n$th prime. Therefore, this constant generates the complete sequence of primes. We also show this constant is irrational and…

Random numbers are important in many activities, including communication, encryption, science, gambling, finance, and decision-making. There is a strong demand for a hardware random number generator that could support cryptographic…

For the sequence defined by a(n) = a(n-1) + gcd(n, a(n-1)) with a(1) = 7 we prove that a(n) - a(n-1) takes on only 1s and primes, making this recurrence a rare "naturally occurring" generator of primes. Toward a generalization of this…

This paper proposes a type of pseudorandom number generator, Mersenne Twister for Graphic Processor (MTGP), for efficient generation on graphic processessing units (GPUs). MTGP supports large state sizes such as 11213 bits, and uses the…

I propose a class of non-positional numeral systems where numbers are represented by Dyck words, with the systems arising from a recursive extension of prime factorization. After describing two proper subsets of the Dyck language capable of…

We first present a simple recursive algorithm that generates cyclic rotation Gray codes for stamp foldings and semi-meanders, where consecutive strings differ by a stamp rotation. These are the first known Gray codes for stamp foldings and…

In PDE-constrained optimization, one aims to find design parameters that minimize some objective, subject to the satisfaction of a partial differential equation. A major challenges is computing gradients of the objective to the design…

Let G be the space of generating functions of a periodic infinite order linear recurrence. In this paper we provide an explicit procedure for computing a basis of G.

This paper presents an algorithm for generating pseudorandom numbers using quasigroups. Random numbers have several applications in the area of secure communication. The proposed algorithm uses a matrix of size n x n which is pre-generated…

Congruential pseudorandom number generators rely on good multipliers, that is, integers that have good performance with respect to the spectral test. We provide lists of multipliers with a good lattice structure up to dimension eight and up…

We describe a high-speed physical random number generator based on a hybrid Boolean network with autonomous and clocked logic gates, realized on a reconfigurable chip. The autonomous logic gates are arranged in a bidirectional ring topology…

This paper presents a regularized recursive identification algorithm with simultaneous on-line estimation of both the model parameters and the algorithms hyperparameters. A new kernel is proposed to facilitate the algorithm development. The…

Generating functions, which are widely used in combinatorics and probability theory, encode function values into the coefficients of a polynomial. In this paper, we explore their use as a tractable probabilistic model, and propose…

A random number generator for the Kappa velocity distribution in particle simulations is proposed. Approximating the cumulative distribution function with the q-exponential function, an inverse transform procedure is constructed. The…

We present results of an extensive test program of a group of pseudorandom number generators which are commonly used in the applications of physics, in particular in Monte Carlo simulations. The generators include public domain programs,…