Related papers: Secure pseudorandom bit generators and point sets …
Our ability to trust that a random number is truly random is essential for fields as diverse as cryptography and fundamental tests of quantum mechanics. Existing solutions both come with drawbacks -- device-independent quantum random number…
We prove that if $(\mathcal{M},d)$ is an $n$-point metric space that embeds quasisymmetrically into a Hilbert space, then for every $\tau>0$ there is a random subset $\mathcal{Z}$ of $\mathcal{M}$ such that for any pair of points $x,y\in…
Stochasticity of bright stars introduces uncertainty and bias into derived structural parameters of star clusters. We have simulated a grid of cluster $V$-band images, observed with Subaru Suprime-Cam with age, mass, and size representing a…
Datasets in high-dimension do not typically form clusters in their original space; the issue is worse when the number of points in the dataset is small. We propose a low-computation method to find statistically significant clustering…
Following a result of D.~Bylik and M.T.~Lacey from 2008 it is known that there exists an absolute constant $\eta>0$ such that the (unnormalized) $L^{\infty}$-norm of the three-dimensional discrepancy function, i.e, the (unnormalized) star…
Given a numerical semigroup $S$ and a positive integer $d$, the fraction $\frac{S}{d}=\{ x \in \mathbb{N} \ | \ dx \in S\}$ is again a numerical semigroup. In this paper we determine a generating set for $\frac{S}{d}$ in terms of the…
We introduce a class of $\gamma$-negatively dependent random samples. We prove that this class includes, apart from Monte Carlo samples, in particular Latin hypercube samples and Latin hypercube samples padded by Monte Carlo. For a…
We study the problem of approximating the quality of a disperser. A bipartite graph $G$ on $([N],[M])$ is a $(\rho N,(1-\delta)M)$-disperser if for any subset $S\subseteq [N]$ of size $\rho N$, the neighbor set $\Gamma(S)$ contains at least…
The construction of confidence intervals for the mean of a bounded random variable is a classical problem in statistics with numerous applications in machine learning and virtually all scientific fields. In particular, obtaining the…
Camera calibration is fundamental to 3D vision, and the choice of calibration pattern greatly affects the accuracy. To address aberration issue, star-shaped pattern has been proposed as alternatives to traditional checkerboard. However,…
We investigate the stability of a Sequential Monte Carlo (SMC) method applied to the problem of sampling from a target distribution on $\mathbb{R}^d$ for large $d$. It is well known that using a single importance sampling step one produces…
Multiple sets of synthetic spectra of OB-binary stars are used to test the suitability of disentangling for deriving accurate spectroscopic orbits. Given a set of spectra with broad phase coverage and sufficient total integration time…
We study the problem of robustly estimating the mean or location parameter without moment assumptions. We show that for a large class of symmetric distributions, the same error as in the Gaussian setting can be achieved efficiently. The…
We prove that with high probability, a uniform sample of $n$ points in a convex domain in $\mathbb{R}^d$ can be rounded to points on a grid of step size proportional to $1/n^{d+1+\epsilon}$ without changing the underlying chirotope…
In this paper we give explicit constructions of point sets in the $s$ dimensional unit cube yielding quasi-Monte Carlo algorithms which achieve the optimal rate of convergence of the worst-case error for numerically integrating high…
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…
An operating system kernel uses cryptographically secure pseudorandom number generator for creating address space localization randomization offsets to protect memory addresses to processes from exploration, storing users' password securely…
Star formation by gravitational instabilities, sequential triggering, and turbulence triggering are briefly reviewed in order to compare the various mechanisms that are observed in main galaxy disks with those in the inner kiloparsec…
Given a point set $P\subset \mathbb{R}^d$, the kernel density estimate of $P$ is defined as \[ \overline{\mathcal{G}}_P(x) = \frac{1}{\left|P\right|}\sum_{p\in P}e^{-\left\lVert x-p \right\rVert^2} \] for any $x\in\mathbb{R}^d$. We study…
Small and bright stellar disks with scale lengths of few tens of parsec are known to reside in the center of galaxies. They are believed to have formed in a dissipational process as the end result of star formation in gas either accreted in…