Publications associées à Asymptotic Behavior of Solutions to the Helmholtz Equations with Sign Changing Coefficients

Publications associées (32)

Inverse Applications of the Generalized Littlewood Theorem Concerning Integrals of the Logarithm of Analytic Functions

Recently, we established and used the generalized Littlewood theorem concerning contour integrals of the logarithm of analytical function to obtain new criteria equivalent to the Riemann hypothesis. The same theorem was subsequently applied to calculate ce ...

2024

On the Sums over Inverse Powers of Zeros of the Hurwitz Zeta Function and Some Related Properties of These Zeros

Serguei Sekatski

Recently, we have applied the generalized Littlewood theorem concerning contour integrals of the logarithm of the analytical function to find the sums over inverse powers of zeros for the incomplete gamma and Riemann zeta functions, polygamma functions, an ...

MDPI2024

Stability: a search for structure

Wouter Jongeneel

In this thesis we study stability from several viewpoints. After covering the practical importance, the rich history and the ever-growing list of manifestations of stability, we study the following. (i) (Statistical identification of stable dynamical syste ...

EPFL2024

Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs

Fernando José Henriquez Barraza

We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recasting th ...

Springer Birkhauser2024

On the Use of the Generalized Littlewood Theorem Concerning Integrals of the Logarithm of Analytical Functions for the Calculation of Infinite Sums and the Analysis of Zeroes of Analytical Functions

Serguei Sekatski

Recently, we have established and used the generalized Littlewood theorem concerning contour integrals of the logarithm of an analytical function to obtain a few new criteria equivalent to the Riemann hypothesis. Here, the same theorem is applied to calcul ...

MDPI2023

Homogenization results for the generator of multiscale Langevin dynamics in weighted Sobolev spaces

Andrea Zanoni

We study the homogenization of the Poisson equation with a reaction term and of the eigenvalue problem associated to the generator of multiscale Langevin dynamics. Our analysis extends the theory of two-scale convergence to the case of weighted Sobolev spa ...

OXFORD UNIV PRESS2023

Asymmetric phase modulation of light with parity-symmetry broken metasurfaces

Karim Achouri

The design of wavefront-shaping devices is conventionally approached using real-frequency modeling. However, since these devices interact with light through radiative channels, they are by default non-Hermitian objects having complex eigenvalues (poles and ...

Optica Publishing Group2023

Mitochondrial respiratory chain dysfunction disrupts intracellular cholesterol homeostasis

Christopher Tadhg James Wall

Mitochondrial diseases are rare and severe conditions with debilitating symptoms. Biochemical defects in mitochondria however are common. The difference between these two frequencies is suspected to lie in the capability of the cells to adapt to the homeos ...

EPFL2022

Dipole polarizability of time-varying particles

Romain Christophe Rémy Fleury, Theodoros Koutserimpas, Mohammad Sajjad Mirmoosa

Invariance under time translation (or stationarity) is probably one of the most important assumptions made when investigating electromagnetic phenomena. Breaking this assumption is expected to open up novel possibilities and result in exceeding conventiona ...

2022

Localization errors of the stochastic heat equation

David Jean-Michel Candil

In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space

\R^d.

We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another ...

EPFL2022

Stochastic distributed learning with gradient quantization and double-variance reduction

Sebastian Urban Stich

We consider distributed optimization over several devices, each sending incremental model updates to a central server. This setting is considered, for instance, in federated learning. Various schemes have been designed to compress the model updates in orde ...

TAYLOR & FRANCIS LTD2022

Coarse graining and large-N behavior of the d-dimensional N-clock model

Matthias Benjamin Ruf

We study the asymptotic behavior of the N-clock model, a nearest neighbors ferromagnetic spin model on the d-dimensional cubic epsilon-lattice in which the spin field is constrained to take values in a discretization S-N of the unit circle S-1 consisting o ...

2021

Strictly Real Fundamental Theorem Of Algebra Using Polynomial Interlacing

Soham Basu

Without resorting to complex numbers or any advanced topological arguments, we show that any real polynomial of degree greater than two always has a real quadratic polynomial factor, which is equivalent to the fundamental theorem of algebra. The proof uses ...

CAMBRIDGE UNIV PRESS2021

On the asymptotic behavior of solutions to the Vlasov-Poisson system

Klaus Martin Widmayer

We prove small data modified scattering for the Vlasov-Poisson system in dimension

d=3

using a method inspired from dispersive analysis. In particular, we identify a simple asymptotic dynamic related to the scattering mass. ...

2022

From Polarizability to Effective Permittivity of Time-Varying Materials

Romain Christophe Rémy Fleury, Theodoros Koutserimpas, Mohammad Sajjad Mirmoosa

In this talk, we describe excitation of time-varying dipolar particles (time-modulated meta-atoms) by external time-varying fields from a nonstationary and causal perspective. For a time-harmonic excitation, we introduce a complex-valued function, called t ...

IEEE2020

Shear measurement bias: I. Dependencies on methods, simulation parameters, and measured parameters

Frédéric Courbin, Marc Gentile

We present a study of the dependencies of shear bias on simulation (input) and measured (output) parameters, noise, point-spread function anisotropy, pixel size, and the model bias coming from two different and independent galaxy shape estimators. We used ...

EDP SCIENCES S A2020

Interpolatory Rational Model Order Reduction of Parametric Problems Lacking Uniform Inf-Sup Stability

Davide Pradovera

We present a technique for the approximation of a class of Hilbert space--valued maps which arise within the framework of model order reduction (MOR) for parametric partial differential equations, whose solution map has a meromorphic structure. Our MOR str ...

2020

On the asymptotic behavior of the solutions to parabolic variational inequalities

Maria Colombo

We consider various versions of the obstacle and thin-obstacle problems, we interpret them as variational inequalities, with non-smooth constraint, and prove that they satisfy a new constrained Lojasiewicz inequality. The difficulty lies in the fact that, ...

2020

Graph Signal Processing for Machine Learning: A Review and New Perspectives

Pascal Frossard, Ntorina Thanou, Laura Toni, Xiaowen Dong, Michael Bronstein

The effective representation, processing, analysis, and visualization of large-scale structured data, especially those related to complex domains, such as networks and graphs, are one of the key questions in modern machine learning. Graph signal processing ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Ising Model and Field Theory: Lattice Local Fields and Massive Scaling Limit

Sung Chul Park

This thesis is devoted to the study of the local fields in the Ising model. The scaling limit of the critical Ising model is conjecturally described by Conformal Field Theory. The explicit predictions for the building blocks of the continuum theory (spin a ...

EPFL2019