Related papers: Close to Uniform Prime Number Generation With Fewe…
In this article, we study a non-uniform distribution on permutations biased by their number of records that we call \emph{record-biased permutations}. We give several generative processes for record-biased permutations, explaining also how…
An approach to quantum random number generation based on unambiguous quantum state discrimination (USD) is developed. We consider a prepare-and-measure protocol, where two non-orthogonal quantum states can be prepared, and a measurement…
Quantum random number generation exploits inherent randomness of quantum mechanical processes and measurements. Real-time generation rate of quantum random numbers is usually limited by electronic bandwidth and data processing rates. Here…
This paper considers some random processes of the form X_{n+1}=TX_n+B_n (mod p) where B_n and X_n are random variables over (Z/pZ)^d and T is a fixed d x d integer matrix which is invertible over the complex numbers. For a particular…
The generation of random bits is of enormous importance in modern information science. Cryptographic security is based on random numbers which require a physical process for their generation. This is commonly performed by hardware random…
Let $P = \{p(i)\}$ be a measure of strictly positive probabilities on the set of nonnegative integers. Although the countable number of inputs prevents usage of the Huffman algorithm, there are nontrivial $P$ for which known methods find a…
The initial state creation is a starting point of many quantum algorithms and usually is considered as a separate subroutine not included into the algorithm itself. There are many algorithms aimed on creation of special class of states. Our…
We present the realization of a physical quantum random number generator based on the process of splitting a beam of photons on a beam splitter, a quantum mechanical source of true randomness. By utilizing either a beam splitter or a…
The prototype quantum random number (random bit) generators (QRNG) consists of one photon at a time falling on a $50:50$ beam splitter followed by random detection in one or the other other output beams due to the irreducible probabilistic…
Quantum random number generators are becoming mandatory in a demanding technology world of high performing learning algorithms and security guidelines. Our implementation based on principles of quantum mechanics enable us to achieve the…
Gaussian random number generators attract a widespread interest due to their applications in several fields. Important requirements include easy implementation, tail accuracy, and, finally, a flat spectrum. In this work, we study the…
To improve accuracy and speed of regressions and classifications, we present a data-based prediction method, Random Bits Regression (RBR). This method first generates a large number of random binary intermediate/derived features based on…
Inspired by [4] we present a new algorithm for uniformly random generation of ordered trees in which all occuring outdegrees can be specified by a given sequence of numbers. The method can be used for random generation of binary or n-ary…
An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in…
Probabilistic computing has been introduced to operate functional networks using a probabilistic bit (p-bit), generating 0 or 1 probabilistically from its electrical input. In contrast to quantum computers, probabilistic computing enables…
We describe a deterministic algorithm for finding a generating element of the multiplicative group of the finite field $\mathbb{F}_{p^n}$ where $p$ is a prime. In time polynomial in $p$ and $n$, the algorithm either outputs an element that…
We present an iterative approach to constructing pseudorandom generators, based on the repeated application of mild pseudorandom restrictions. We use this template to construct pseudorandom generators for combinatorial rectangles and…
We describe random processes (with binary alphabet) whose entropy is less than 1 (per letter), but they mimic true random process, i.e., by definition, generated sequence can be interpreted as the result of the flips of a fair coin with…
This article applies the principle of Occam's Razor to non-parametric model building of statistical data, by finding a model with the minimal number of bits, leading to an exceptionally effective regularization method for probability…
We provide an efficient algorithm to generate random samples from the bounded kth order statistic in a sample of independent, but not necessarily identically distributed, random variables. The bounds can be upper or lower bounds and need…