Related papers: Producing Quality Pseudorandomness with a Generali…
We study the dynamics of a family of continued fraction maps parametrized by the unit interval. This family contains as special instances the Gauss continued fraction map and the Fibonacci map. We determine the transfer operators of these…
The use of synthetic data in machine learning applications and research offers many benefits, including performance improvements through data augmentation, privacy preservation of original samples, and reliable method assessment with fully…
We introduce two families of generators (functions) $\mathcal{G}$ that consist of entire and meromorphic functions enjoying a certain periodicity property and contain the classical Gaussian and hyperbolic secant generators. Sharp results…
Quantum random number generator harnesses the power of quantum mechanics to generate true random numbers, making it valuable for various scientific applications. However, real-world devices often suffer from imperfections that can undermine…
Quantum pseudorandomness, also known as unitary designs, comprise a powerful resource for quantum computation and quantum engineering. While it is known in theory that pseudorandom unitary operators can be constructed efficiently, realizing…
Structure learning methods for covariance and concentration graphs are often validated on synthetic models, usually obtained by randomly generating: (i) an undirected graph, and (ii) a compatible symmetric positive definite (SPD) matrix. In…
The Mersenne Twister MT19937 pseudorandom number generator, introduced by the last two authors in 1998, is still widely used. It passes all existing statistical tests, except for the linear complexity test, which measures the ratio of the…
Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parameters affect the efficiency of pseudo-random…
Generating high-quality random numbers with a Gaussian probability distribution function is an important and resource consuming computational task for many applications in the fields of machine learning and Monte Carlo algorithms. Recently,…
Several machine learning problems arising in natural language processing can be modeled as a sequence labeling problem. We provide Gaussian process models based on pseudo-likelihood approximation to perform sequence labeling. Gaussian…
We prove that there exists a scrambled set for the Gauss map with full Hausdorff dimension. Meanwhile, we also investigate the topological properties of the sets of points with dense or non-dense orbits.
It is well-known that the quality of random number generators can often be improved by combining several generators, e.g. by summing or subtracting their results. In this paper we investigate the ratio of two random number generators as an…
Using quantum maps we study the accuracy of semiclassical trace formulas. The role of chaos in improving the semiclassical accuracy, in some systems, is demonstrated quantitatively. However, our study of the standard map cautions that this…
The regular logistic map was introduced in 1960s, served as an example of a complex system, and was used as an instrument to demonstrate and investigate the period doubling cascade of bifurcations scenario of transition to chaos. In this…
Quantum random number generators (QRNGs) promise perfectly unpredictable random numbers. However, the security certification of the random numbers in form of a stochastic model often introduces assumptions that are either hardly justified…
Variational autoencoders (VAE) often use Gaussian or category distribution to model the inference process. This puts a limit on variational learning because this simplified assumption does not match the true posterior distribution, which is…
We show that functions of type $X_n = P[Z^n]$, where $P[t]$ is a periodic function and $Z$ is a generic real number, can produce sequences such that any string of values $X_{s}, X_{s+1}, ...,X_{s+m}$ is deterministically independent of past…
Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact…
Pseudo-random number generators (PRNGs) are widely used in modern computing and are expected to exhibit excellent statistical performance and repeatability. This study evaluates and compares modern PRNGs used in high performance computing…
We consider a family $\{T_N:N \geq 1 \}$ of interval maps as generalizations of the Gauss transformation. For the continued fraction expansion arising from $T_N$, we solve its Gauss-Kuzmin-type problem by applying the theory of random…