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Previously, we built up a set of photon-free quantum random number generator(QRNG) with InGaAs single photon avalanche diodes. We exploited the stochastic property of quantum tunneling effect. Here, we utilized tunneling signals in Si…
Pulsars exhibit signals with precise inter-arrival times that are on the order of milliseconds to seconds, depending on the individual pulsar. There are subtle variations in the timing of pulsar signals. We show that these variations can…
It is shown that from two strings that are partially random and independent (in the sense of Kolmogorov complexity) it is possible to effectively construct polynomially many strings that are random and pairwise independent. If the two…
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…
Given a stochastic structure with a filtration $\mathbb{F}$, the class of all random times whose conditional distribution functions are differentiable with respect to some $\mathbb{F}$ adapted non decreasing processes is considered. The…
Random numbers are a fundamental and useful resource in science and engineering with important applications in simulation, machine learning and cyber-security. Quantum systems can produce true random numbers because of the inherent…
It is a classical problem to compute a minimal set of invariant polynomial generating the invariant ring of a finite group as an algebra. We present here an algorithm for the computation of minimal generating sets in the non-modular case.…
We present a practical high-speed quantum random number generator, where the timing of single-photon detection relative to an external time reference is measured as the raw data. The bias of the raw data can be substantially reduced…
In a recent work, O'Donnell, Servedio and Tan (STOC 2019) gave explicit pseudorandom generators (PRGs) for arbitrary $m$-facet polytopes in $n$ variables with seed length poly-logarithmic in $m,n$, concluding a sequence of works in the last…
Data can be assumed to be continuous functions defined on an infinite-dimensional space for many phenomena. However, the infinite-dimensional data might be driven by a small number of latent variables. Hence, factor models are relevant for…
Let $G$ be a finite simple group. In this paper we consider the existence of small subsets $A$ of $G$ with the property that, if $y \in G$ is chosen uniformly at random, then with high probability $y$ invariably generates $G$ together with…
Existing image generator networks rely heavily on spatial convolutions and, optionally, self-attention blocks in order to gradually synthesize images in a coarse-to-fine manner. Here, we present a new architecture for image generators,…
Random numbers are a fundamental resource in science and technology. Among the different approaches to generating them, random numbers created by exploiting the laws of quantum mechanics have proven to be reliable and can be produced at…
Random numbers are an essential resource to many applications, including cryptography and Monte Carlo simulations. Quantum random number generators (QRNGs) represent the ultimate source of randomness, as the numbers are obtained by sampling…
Quantum theory allows for randomness generation in a device-independent setting, where no detailed description of the experimental device is required. Here we derive a general upper bound on the amount of randomness that can be generated in…
We count the number of irreducible polynomials in several variables of a given degree over a finite field. The results are expressed in terms of a generating series, an exact formula and an asymptotic approximation. We also consider the…
A compiler approach for generating low-level computer code from high-level input for discontinuous Galerkin finite element forms is presented. The input language mirrors conventional mathematical notation, and the compiler generates…
Let $K/k$ be a finite extension of a global field. Such an extension can be generated over $k$ by a single element. The aim of this article is to prove the existence of a "small" generator in the function field case. This answers the…
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…
Instances generation is crucial for linear programming algorithms, which is necessary either to find the optimal pivot rules by training learning method or to evaluate and verify corresponding algorithms. This study proposes a general…