Related papers: Secure pseudorandom bit generators and point sets …
It is well understood that if one is given a set $X \subset [0,1]$ of $n$ independent uniformly distributed random variables, then $$ \sup_{0 \leq x \leq 1} \left| \frac{\# X \cap [0,x]}{\# X} - x \right| \lesssim \frac{\sqrt{\log{n}}}{…
In this paper we study the geometric discrepancy of explicit constructions of uniformly distributed points on the two-dimensional unit sphere. We show that the spherical cap discrepancy of random point sets, of spherical digital nets and of…
Security of information transmitted through the Internet, against passive or active attacks is an international concern. The use of a chaos-based pseudo-random bit sequence to make it unrecognizable by an intruder, is a field of research in…
For a probability measure $\mu$ on $[0,1]$ without discrete component, the best possible order of approximation by a finite point set in terms of the star-discrepancy is $\frac{1}{2N}$ as has been proven relatively recently. However, if…
The dispersion of a point set $P\subset[0,1]^d$ is the volume of the largest box with sides parallel to the coordinate axes, which does not intersect $P$. Here, we show a construction of low-dispersion point sets, which can be deduced from…
The optimizations of the track fittings require complex simulations of silicon strip detectors to be compliant with the fundamental properties of the hit heteroscedasticity. Many different generations of random numbers must be available…
We introduce a collection of primarily centrally star-forming galaxies that are selected by disk color to have truncated disk star formation. We show that common explanations for centrally-concentrated star formation -- low stellar mass,…
We present results of extensive bit level tests on some pseudorandom number generators which are commonly used in physics applications. The generators have first been tested with an extended version of the $d$-tuple test. Second, we have…
We establish sharp non-asymptotic probabilistic bounds for the star discrepancy of double-infinite random matrices -- a canonical model for sequences of random point sets in high dimensions. By integrating the recently proved…
In this paper we study uniform distribution properties of digital sequences over a finite field of prime order. In 1998 it was shown by Larcher that for almost all $s$-dimensional digital sequences the star discrepancy $D_N^\ast$ satisfies…
Generating secure random numbers is a central problem in cryptography that needs a reliable source of enough computing entropy. Without enough entropy available - meaning no good source of secure random numbers - a device is susceptible to…
Internet communication systems involving cryptography and data hiding often require billions of random numbers. In addition to the speed of the algorithm, the quality of the pseudo-random number generator and the ease of its implementation…
We propose and demonstrate a technique for quantum random number generation based on the random population of the output spatial modes of a beam splitter when both inputs are simultaneously fed with indistinguishable weak coherent states.…
We develop a method for generating pseudorandom binary sequences using the Bernoulli map on cubic algebraic integers. The distinguishing characteristic of our generator is that it generates chaotic true orbits of the Bernoulli map by exact…
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…
With the dramatic growth in the number of application domains that generate probabilistic, noisy and uncertain data, there has been an increasing interest in designing algorithms for geometric or combinatorial optimization problems over…
Generation of pseudorandom numbers from different probability distributions has been studied extensively in the Monte Carlo simulation literature. Two standard generation techniques are the acceptance-rejection and inverse transformation…
There is much debate on how high-mass star formation varies with environment, and whether the sparsest star-forming environments are capable of forming massive stars. To address this issue, we have observed eight apparently isolated OB…
A random number generator is proposed based on a theorem about existence of chaos in fixed point iteration of x= cot2(x). Digital computer simulation of this function iteration exhibits random behavior. A method is proposed to extract…
Pseudo-random number generators are widely used in many branches of science, mainly in applications related to Monte Carlo methods, although they are deterministic in design and, therefore, unsuitable for tackling fundamental problems in…