Related papers: Improving the pseudo-randomness properties of chao…

We show that the probability distribution function that best fits the distribution of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space deviates from the exponential statistics by a…

The finest state space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation the neighborhoods of deterministic periodic orbits can be computed as distributions…

Recently, a general data driven numerical framework has been developed for learning and modeling of unknown dynamical systems using fully- or partially-observed data. The method utilizes deep neural networks (DNNs) to construct a model for…

We present here a new method which applies well ordered symbolic dynamics to find unstable periodic and non-periodic orbits in a chaotic system. The method is simple and efficient and has been successfully applied to a number of different…

This paper targets to search so-called \emph{good} generators by doing a brief survey over the generators developed in the history of pseudo-random number generators (PRNGs), verify their claims and rank them based on strong empirical tests…

Even if the output of a Random Number Generator (RNG) is perfectly uniformly distributed, it may be correlated to pre-existing information and therefore be predictable. Statistical tests are thus not sufficient to guarantee that an RNG is…

We develop a computationally efficient and robust algorithm for generating pseudo-random samples from a broad class of smooth probability distributions in one and two dimensions. The algorithm is based on inverse transform sampling with a…

This paper describes a revision of the classic Lazy Probabilistic Roadmaps algorithm (Lazy PRM), that results from pairing PRM and a novel Branch-and-Cut (BC) algorithm. Cuts are dynamically generated constraints that are imposed on minimum…

Surveillance and exploration of large environments is a tedious task. In spaces with limited environmental cues, random-like search is an effective approach as it allows the robot to perform online coverage of environments using simple…

We uncover and characterize different chaotic transport scenarios on perfect periodic surfaces by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect. After identifying…

Quality randomness is fundamental to cryptographic operations but on embedded systems good sources are (seemingly) hard to find. Rather than use expensive custom hardware, our ERHARD-RNG Pseudo-Random Number Generator (PRNG) utilizes…

For generic Hamiltonian systems we derive predictions for dynamical tunneling from regular to chaotic phase-space regions. In contrast to previous approaches, we account for the resonance-assisted enhancement of regular-to-chaotic tunneling…

The use of artificial neural networks as models of chaotic dynamics has been rapidly expanding. Still, a theoretical understanding of how neural networks learn chaos is lacking. Here, we employ a geometric perspective to show that neural…

Many Random Number Generators (RNG) are available nowadays; they are divided in two categories, hardware RNG, that provide "true" random numbers, and algorithmic RNG, that generate pseudo random numbers (PRNG). Both types usually generate…

A central approach to algorithmic derandomization is to construct probability distributions with small support that "fool" randomized algorithms, often enabling efficient parallel (NC) implementations. An abstraction of this idea is fooling…

We investigate the boundary separating regular and chaotic dynamics in the generalized Chirikov map, an extension of the standard map with phase-shifted secondary kicks. Lyapunov maps were computed across the parameter space (K, K{\alpha},…

Chaotic behavior arises from very simple non-linear dynamical equation of logistic map which makes it was used often in designing chaotic image encryption schemes. However, some properties of chaotic maps can also facilitate cryptanalysis…

An algorithm for detecting periodic orbits in chaotic systems [Phys. Rev. E, 60 (1999), pp.~6172--6175], which combines the set of stabilising transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78 (1997), pp.~4733--4736]…

Xorshift128+ is a newly proposed pseudorandom number generator (PRNG), which is now the standard PRNG on a number of platforms. We demonstrate that three-dimensional plots of the random points generated by the generator have visible…

Recently patterns were found in the least significant digits in the logistic map orbits in the chaotic regime. However, the dynamic of these digits was not explored in deep. We propose a new interpretation of the patterns found in the least…