Publications related to Analytic number theory

Mean value theorems for collections of lattices with a prescribed group of symmetries

Euclidean lattices are mathematical objects of increasing interest in the fields of cryptography and error-correcting codes. This doctoral thesis is a study on high-dimensional lattices with the motivation to understand how efficient they are in terms of b ...

EPFL2024

On the Double Descent of Random Features Models Trained with SGD

Volkan Cevher, Fanghui Liu

We study generalization properties of random features (RF) regression in high dimensions optimized by stochastic gradient descent (SGD) in under-/overparameterized regime. In this work, we derive precise non-asymptotic error bounds of RF regression under b ...

2022

High energy barriers for edge dislocation motion in body-centered cubic high entropy alloys

William Curtin, Recep Ekin Kubilay, Francesco Maresca, Alireza Ghafarollahi

Recent theory proposes that edge dislocations in random body-centered cubic (BCC) high entropy alloys have high barriers for motion, conveying high strengths up to high temperatures. Here, the energy barriers for edge motion are computed for two model allo ...

NATURE RESEARCH2021

Demography of galactic technosignatures

Claudio Grimaldi

Probabilistic arguments about the existence of technological life beyond Earth traditionally refer to the Drake equation to draw possible estimates of the number of technologically advanced civilizations releasing, either intentionally or not, electromagne ...

OXFORD UNIV PRESS2021

Rate of change of frequency under line contingencies in high voltage electric power networks with uncertainties

Philippe René Joseph Jacquod, Melvyn Sandy Tyloo, Robin Delabays

In modern electric power networks with fast evolving operational conditions, assessing the impact of contingencies is becoming more and more crucial. Contingencies of interest can be roughly classified into nodal power disturbances and line faults. Despite ...

American Institute of Physics2019

Improved Credit Bounds for the Credit-Based Shaper in Time-Sensitive Networking

Jean-Yves Le Boudec, Eleni Stai, Ehsan Mohammadpour

In Time-Sensitive Networking (TSN), it is important to formally prove per-flow latency and backlog bounds. To this end, recent works have applied network calculus and obtained latency bounds from service curves. The latency component of such service curves ...

2019

Approximate analytic expressions using Stokes model for tokamak polarimetry and their range of validity

Olivier Sauter, Ambrogio Fasoli, Basil Duval, Stefano Coda, Martinus Gijs, Jonathan Graves, Yves Martin, Duccio Testa, Patrick Blanchard, Bruno Emanuel Ferreira De Sousa Correia, Alessandro Pau, Pierre-Thomas Paul Brun, Cristian Sommariva, Henri Weisen, Richard Pitts, Sun Hee Kim, Yann Camenen, Jan Horacek, Javier García Hernández, Marco Wischmeier, Mikhail Maslov, Nicola Vianello, Miguel Fernández Ruiz, Federico Nespoli, Antonio José Pereira de Figueiredo, Liang Yao, Yao Zhou, David Pfefferlé, Dalziel Joseph Wilson, Robin Humphry-Baker, Davide Galassi, José Pedro Rebelo Ferreira Marques, Ana Francisca Leal Silva Soares, Jonathan Marc Philippe Faustin, Daniel Scott Alessi, Arnout Lodewijk M Beckers, Julio Rodriguez, Hamish William Patten, Jonnathan Cesar Hidalgo Acosta, , , , , , , , ,

Distributed Learning over Networks under Subspace Constraints

Ali H. Sayed, Stefan Vlaski, Roula Nassif

This work presents and studies a distributed algorithm for solving optimization problems over networks where agents have individual costs to minimize subject to subspace constraints that require the minimizers across the network to lie in a low-dimensional ...

IEEE2019

Multi-Scale Electrolyte Transport Simulations for Lithium Ion Batteries

Max David Veit

Establishing a link between atomistic processes and battery cell behavior is a major challenge for lithium ion batteries. Focusing on liquid electrolytes, we describe parameter-free molecular dynamics predictions of their mass and charge transport properti ...

2019

Optimal Number of Paths with Multipath Routing in Hybrid Networks

Patrick Thiran, Sébastien Christophe Henri

In recent years, multipath routing, i.e., employing several paths simultaneously, has emerged as an efficient way to provide significant throughput gains in local networks. This has been observed both with technologies that are not subject to interference, ...

2018

Optimal Number of Paths with Multipath Routing in Hybrid Networks

Patrick Thiran, Sébastien Christophe Henri

In recent years, multipath routing, i.e., employing several paths simultaneously, has emerged as an efficient way to provide significant throughput gains in local networks. This has been observed both with technologies that are not subject to interference, ...

IEEE2018

Chebyshev Inequalities for Products of Random Variables

Daniel Kuhn, Napat Rujeerapaiboon, Wolfram Wiesemann

We derive sharp probability bounds on the tails of a product of symmetric non-negative random variables using only information about their first two moments. If the covariance matrix of the random variables is known exactly, these bounds can be computed nu ...

2018

Swimming with a cage: low-Reynolds-number locomotion inside a droplet

François Gallaire, Lailai Zhu

Inspired by recent experiments using synthetic microswimmers to manipulate droplets, we investigate the low-Reynolds-number locomotion of a model swimmer (a spherical squirmer) encapsulated inside a droplet of a comparable size in another viscous fluid. Me ...

Royal Society of Chemistry2017

A study in sums of products

Philippe Michel

We give a general version of cancellation in exponential sums that arise as sums of products of trace functions satisfying a suitable independence condition related to the Goursat-Kolchin-Ribet criterion, in a form that is easily applicable in analytic num ...

Royal Society, The2015

Resting-brain functional connectivity predicted by analytic measures of network communication

Jean-Philippe Thiran, Alessandra Griffa, Patric Hagmann, Olaf Sporns

6 The complex relationship between structural and functional connectivity, as measured by noninvasive imaging of the human brain, poses many unresolved challenges and open questions. Here, we apply analytic measures of network communication to the structur ...

National Academy of Sciences2014

Wireless Network Simplification: The Gaussian N-Relay Diamond Network

Christina Fragouli

We consider the Gaussian N-relay diamond network, where a source wants to communicate to destination node through a layer of N-relay nodes. We investigate the following question: what fraction of the capacity can we maintain using only k out of the N avail ...

Institute of Electrical and Electronics Engineers2014

The flux-coordinate independent approach applied to X-point geometries

A Flux-Coordinate Independent (FCI) approach for anisotropic systems, not based on magnetic flux coordinates, has been introduced in Hariri and Ottaviani [Comput. Phys. Commun. 184, 2419 (2013)]. In this paper, we show that the approach can tackle magnetic ...

Amer Inst Physics2014

The Contact of Elastic Regular Wavy Surfaces Revisited

Jean-François Molinari, Guillaume Anciaux, Vladislav Yastrebov

We revisit the classic problem of an elastic solid with a two-dimensional wavy surface squeezed against an elastic flat half-space from infinitesimal to full contact. Through extensive numerical calculations and analytic derivations, we discover previously ...

Springer/Plenum Publishers2014

On the size of Satake parameters for unitary cuspidal automorphic representations for GL(4)

Nahid Walji

Let Pi be a cuspidal automorphic representation for GL(4) over a number field F. We obtain unconditional lower bounds on the number of places at which the Satake parameters are not "too large". In the case of self-dual Pi with non-trivial central character ...

Academic Press Inc Elsevier Science2013

Soft control of swarms: Analytical approach

Max-Olivier Hongler, Guillaume Adrien Sartoretti

We analytically study the collective dynamics of mutually interacting heterogeneous agents evolving in a random environment. Our formal framework consists of a collection of JV scalar drifted Brownian motions (BM) diffusing on R. The mutual interactions ar ...

2013