Related papers: Randomness Evaluation with the Discrete Fourier Tr…
The problem of selecting a handful of truly relevant variables in supervised machine learning algorithms is a challenging problem in terms of untestable assumptions that must hold and unavailability of theoretical assurances that selection…
The distance transform (DT) and its many variations are ubiquitous tools for image processing and analysis. In many imaging scenarios, the images of interest are corrupted by noise. This has a strong negative impact on the accuracy of the…
Frequency estimation is a fundamental problem in many areas. The well-known A&M and its variant estimators have established an estimation framework by iteratively interpolating the discrete Fourier transform (DFT) coefficients. In general,…
Random number generators (RNG) are an important resource in many areas: cryptography (both quantum and classical), probabilistic computation (Monte Carlo methods), numerical simulations, industrial testing and labeling, hazard games,…
Distance correlation has gained much recent attention in the data science community: the sample statistic is straightforward to compute and asymptotically equals zero if and only if independence, making it an ideal choice to discover any…
Spectral interference, the frequency counterpart of the beating phenomenon in the time domain, can severely distort time-frequency representations (TFRs) in physical applications. We study this phenomenon for the short-time Fourier…
Two (so-called left and right) variants of N-centered ensemble density-functional theory (DFT) [Senjean and Fromager, Phys. Rev. A 98, 022513 (2018)] are presented. Unlike the original formulation of the theory, these variants allow for the…
We propose the density ratio permutation test, a hypothesis test that assesses whether the ratio between two densities is proportional to a known function based on independent samples from each distribution. The test uses an efficient…
A {\it pure significance test} (PST) tests a simple null hypothesis $H_f:Y\sim f$ {\it without specifying an alternative hypothesis} by rejecting $H_f$ for {\it small} values of $f(Y)$. When the sample space supports a proper uniform pmf…
We study distribution testing without direct access to a source of relevant data, but rather to one where only a tiny fraction is relevant. To enable this, we introduce the following verification query model. The goal is to perform a…
We introduce a rigorous and sensitive significance test for hyperuniformity that yields reliable results even from a single sample. Our approach is based on a detailed analysis of the empirical Fourier transform of a stationary point…
In this article, we develop comprehensive frequency domain methods for estimating and inferring the second-order structure of spatial point processes. The main element here is on utilizing the discrete Fourier transform (DFT) of the point…
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…
Quantum key distribution (QKD) is moving from research laboratories towards applications. As computing becomes more mobile, cashless as well as cardless payment solutions are introduced, and a need arises for incorporating QKD in a mobile…
We present a novel distribution-free approach, the data-driven threshold machine (DTM), for a fundamental problem at the core of many learning tasks: choose a threshold for a given pre-specified level that bounds the tail probability of the…
We present a nonparametric statistical framework for the quantification, analysis, and propagation of data uncertainty in direct volume rendering (DVR). The state-of-the-art statistical DVR framework allows for preserving the transfer…
Density Functional Theory (DFT) stands as a widely used and efficient approach for addressing the many-electron Schr\"odinger equation across various domains such as physics, chemistry, and biology. However, a core challenge that persists…
The Fast Fourier Transform (FFT) is the most efficiently known way to compute the Discrete Fourier Transform (DFT) of an arbitrary n-length signal, and has a computational complexity of O(n log n). If the DFT X of the signal x has only k…
We present the $U$-Statistic Permutation (USP) test of independence in the context of discrete data displayed in a contingency table. Either Pearson's chi-squared test of independence, or the $G$-test, are typically used for this task, but…
We propose a multi-dimensional (M-D) sparse Fourier transform inspired by the idea of the Fourier projection-slice theorem, called FPS-SFT. FPS-SFT extracts samples along lines (1-dimensional slices from an M-D data cube), which are…