Quantum fluctuations of one-dimensional free fermions and Fisher-Hartwig formula for Toeplitz determinants

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Statistical limits of dictionary learning: Random matrix theory and the spectral replica method

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We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast with most existin ...

AMER PHYSICAL SOC2022

Distribution-on-distribution regression via optimal transport maps

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We present a framework for performing regression when both covariate and response are probability distributions on a compact interval. Our regression model is based on the theory of optimal transportation, and links the conditional Frechet mean of the resp ...

OXFORD UNIV PRESS2022

Assessment of the Lightning Performance of overhead distribution lines based on Lightning Location Systems data

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This article presents the Lightning Performance (LP) assessment of a realistic portion of the Italian distribution network with the use of probability distributions for lightning parameters inferred from local data recorded by a Lightning Location System ( ...

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The Lang-Trotter conjecture for products of non-CM elliptic curves

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Inspired by the work of Lang-Trotter on the densities of primes with fixed Frobenius traces for elliptic curves defined over Q and by the subsequent generalization of Cojocaru-Davis-Silverberg-Stange to generic abelian varieties, we study the analogous que ...

SPRINGER2022

Principles of checkpoint override

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Why biological quality-control systems fail is often mysterious. Specifically, checkpoints such as the DNA damage checkpoint or the spindle assembly checkpoint are overriden after prolonged arrests allowing cells to continue dividing despite the continued ...

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Bootstrapping for Approximate Homomorphic Encryption with Negligible Failure-Probability by Using Sparse-Secret Encapsulation

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Bootstrapping parameters for the approximate homomorphic-encryption scheme of Cheon et al., CKKS (Asiacrypt 17), are usually instantiated using sparse secrets to be efficient. However, using sparse secrets constrains the range of practical parameters withi ...

SPRINGER INTERNATIONAL PUBLISHING AG2022

Removing Algorithmic Discrimination (With Minimal Individual Error)

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We address for the first time the problem of correcting group discriminations within a score function, while minimizing the individual error. Each group is described by a probability density function on the set of profiles. We first solve the problem analy ...

2022

On rationally connected varieties over C1 fields of characteristic 0

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We use birational geometry to show that the existence of rational points on proper rationally connected varieties over fields of characteristic 0 is a consequence of the existence of rational points on terminal Fano varieties. We discuss several consequenc ...

MATHEMATICAL SCIENCE PUBL2022

Investigation and Validation of Unstructured Mesh Methodologies for Modeling Experimental Reactors

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MDPI2022

Discrete Optimal Transport with Independent Marginals is #P-Hard

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We study the computational complexity of the optimal transport problem that evaluates the Wasser- stein distance between the distributions of two K-dimensional discrete random vectors. The best known algorithms for this problem run in polynomial time in th ...

SIAM Publications2023