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Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…
A remarkable achievement of the realistic superstring standard--like models is the successful prediction of the top quark mass, assuming the Minimal Supersymmetric Standard Model spectrum below the string scale. Recently it was shown that…
Machine learning (ML) frameworks rely heavily on pseudorandom number generators (PRNGs) for tasks such as data shuffling, weight initialization, dropout, and optimization. Yet, the statistical quality and reproducibility of these…
Thermal jitter (phase noise) from a free-running ring oscillator is a common, easily implementable physical randomness source in True Random Number Generators (TRNGs). We show how to evaluate entropy, autocorrelation, and bit pattern…
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,…
A new converse bound is presented for the two-user multiple-access channel under the average probability of error constraint. This bound shows that for most channels of interest, the second-order coding rate -- that is, the difference…
We study the statistical limits of testing and estimation for a rank one deformation of a Gaussian random tensor. We compute the sharp thresholds for hypothesis testing and estimation by maximum likelihood and show that they are the same.…
This study investigates the application of machine learning predictors for min-entropy estimation in Random Number Generators (RNGs), a key component in cryptographic applications where accurate entropy assessment is essential for…
We propose methods for constructing high-quality pseudorandom number generators (RNGs) based on an ensemble of hyperbolic automorphisms of the unit two-dimensional torus (Sinai-Arnold map or cat map) while keeping a part of the information…
We explore a large class of correlation measures called the $\alpha-z$ R\'enyi mutual informations (RMIs). Unlike the commonly used notion of RMI involving linear combinations of R\'enyi entropies, the $\alpha-z$ RMIs are positive…
Three measures of pseudorandomness of finite binary sequences were introduced by Mauduit and S\'ark\"ozy in 1997 and have been studied extensively since then: the normality measure, the well-distribution measure, and the correlation measure…
Signal-to-noise ratio (SNR) detection statistic has wide-spread applications. A potential event is recorded when the SNR from a specific template exceeds a threshold set by a desired false positive rate. In template bank searches, the…
This paper introduces a unified framework for the detection of a source with a sensor array in the context where the noise variance and the channel between the source and the sensors are unknown at the receiver. The Generalized Maximum…
A TPM (trusted platform module) is a chip present mostly on newer motherboards, and its primary function is to create, store and work with cryptographic keys. This dedicated chip can serve to authenticate other devices or to protect…
Within the Guessing Random Additive Noise Decoding (GRAND) family, ordered reliability bits GRAND (ORBGRAND) has received considerable attention for its hardware-friendly exploitation of soft information. Existing information-theoretic…
In this article we consider the graph alignment problem from the perspective of high-dimensional statistics: we aim to estimate an unknown permutation $\pi^*$ from the observation of two correlated random adjacency matrices $A_1$, $A_2$. We…
The aim of this paper is to describe a way to improve the reliability of the measurement of the statistical parameters of the phase noise in a multi-ring oscillator-based TRNG. This is necessary to guarantee that the entropy rate is within…
We study one-sided and $\alpha$-correct sequential hypothesis testing for data generated by an ergodic Markov chain. The null hypothesis is that the unknown transition matrix belongs to a prescribed set $P$ of stochastic matrices, and the…
Affinity has proven to be a useful tool for quantifying the non-equilibrium character of time continuous Markov processes since it serves as a measure for the breaking of time reversal symmetry. It has recently been conjectured that the…
Previous results indicate that while chaos can lead to substantial entropy production, thereby maximizing dynamical entanglement, this still falls short of maximality. Random Matrix Theory (RMT) modeling of composite quantum systems,…