Concept

Théorème

Publications associées (26)

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

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

Byzantine Machine Learning Made Easy By Resilient Averaging of Momentums

Rachid Guerraoui, John Stephan, Sadegh Farhadkhani, Nirupam Gupta, Rafaël Benjamin Pinot

Byzantine resilience emerged as a prominent topic within the distributed machine learning community. Essentially, the goal is to enhance distributed optimization algorithms, such as distributed SGD, in a way that guarantees convergence despite the presence ...

PMLR2022

A Determinantal Identity for the Permanent of a Rank 2 Matrix

Adam Wade Marcus

We prove an identity relating the permanent of a rank 2 matrix and the determinants of its Hadamard powers. When viewed in the right way, the resulting formula looks strikingly similar to an identity of Carlitz and Levine, suggesting the possibility that t ...

TAYLOR & FRANCIS INC2022

Direct FEM-Domain Decomposition Using Convex-to-Concave Spherical Ports for Space Applications

Juan Ramon Mosig, Javier Rubio, Pedro Robustillo Bayon

This letter proposes the application of a hybrid numerical technique to two cases of interest in the space business: the reallocation of radiators and scatters on satellite platforms; and the analysis of antennas for mobile communications. It is based on t ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

A Unifying Representer Theorem for Inverse Problems and Machine Learning

Michaël Unser

Regularization addresses the ill-posedness of the training problem in machine learning or the reconstruction of a signal from a limited number of measurements. The method is applicable whenever the problem is formulated as an optimization task. The standar ...

2021

Statistical Applications of Random Matrix Theory: Comparison of Two Populations

Rémy Mariétan

During the last twenty years, Random matrix theory (RMT) has produced numerous results that allow a better understanding of large random matrices. These advances have enabled interesting applications in the domain of communication. Although this theory can ...

EPFL2019

Real-Time State Estimation and Voltage Stability Assessment of Power Grids: From Theoretical Foundations to Practical Applications

Andreas Martin Kettner

The operators of power distribution systems strive to lower their operational costs and improve the quality of the power service provided to their customers. Furthermore, they are faced with the challenge of accommodating large numbers of Distributed Energ ...

EPFL2019

Sign-Changing Solutions for a Class of Zero Mass Nonlocal Schrodinger Equations

We consider the following class of fractional Schrodinger equations: (-Delta)(alpha)u + V(x)u = K(x)f(u) in R-N, where alpha is an element of (0, 1), N > 2 alpha, (-Delta)(alpha) is the fractional Laplacian, V and K are positive continuous functions which ...

2019

The unfolding argument: Why IIT and other causal structure theories cannot explain consciousness

Michael Herzog, Kathryn Hess Bellwald, Adrien Christophe Doerig, Aaron Schurger

How can we explain consciousness? This question has become a vibrant topic of neuroscience research in recent decades. A large body of empirical results has been accumulated, and many theories have been proposed. Certain theories suggest that consciousness ...

2019

The Myers-Steenrod Theorem For Finsler Manifolds Of Low Regularity

Marc Troyanov

We prove a version of Myers-Steenrod's theorem for Finsler manifolds under the minimal regularity hypothesis. In particular we show that an isometry between C-k,C-alpha-smooth (or partially smooth) Finsler metrics, with k + alpha > 0, k is an element of N ...

Amer Mathematical Soc2017

On some algebraic and extremal problems in discrete geometry

Seyed Hossein Nassajianmojarrad

In the present thesis, we delve into different extremal and algebraic problems arising from combinatorial geometry. Specifically, we consider the following problems. For any integer

n\ge 3

, we define

e(n)

to be the minimum positive integer such that an ...

EPFL2017

A Formally Verified NAT

George Candea, Solal Vincenzo Pirelli, Aikaterini Argyraki, Arseniy Zaostrovnykh, Luis David Figueiredo Mascarenhas Moreira Pedrosa

We present a Network Address Translator (NAT) written in C and proven to be semantically correct according to RFC 3022, as well as crash-free and memory-safe. There exists a lot of recent work on network verification, but it mostly assumes models of networ ...

Assoc Computing Machinery2017

Polynomials Vanishing On Cartesian Products: The Elekes-Szabo Theorem Revisited

Frank de Zeeuw

Let F 2 C[x; y; z] be a constant-degree polynomial, and let A; B; C subset of C be finite sets of size n. We show that F vanishes on at most O(n(11/6))points of the Cartesian product A X B X C, unless F has a special group-related form. This improves a the ...

Duke Univ Press2016

On the Zarankiewicz problem for intersection hypergraphs

János Pach

Let d and t be fixed positive integers, and let denote the complete d-partite hypergraph with t vertices in each of its parts, whose hyperedges are the d-tuples of the vertex set with precisely one element from each part. According to a fundamental theorem ...

Academic Press Inc Elsevier Science2016

Projection onto the Manifold of Elongated Structures for Accurate Extraction

Pascal Fua, Vincent Lepetit, Amos Sironi

Detection of elongated structures in 2D images and 3D image stacks is a critical prerequisite in many applications and Machine Learning-based approaches have recently been shown to deliver superior performance. However, these methods essentially classify i ...

2015

L-2-cohomology and complete Hamiltonian manifolds

Tudor Ratiu

A classical theorem of Frankel for compact Kahler manifolds states that a Kahler S-1-action is Hamiltonian if and only if it has fixed points. We prove a metatheorem which says that when the Hodge theory holds on non-compact manifolds, Frankel's theorem st ...

Elsevier2015

Hermitian Categories, Extension Of Scalars And Systems Of Sesquilinear Forms

Eva Bayer Fluckiger, Daniel Arnold Moldovan

We prove that the category of systems of sesquilinear forms over a given hermitian category is equivalent to the category of unimodular 1-hermitian forms over another hermitian category. The sesquilinear forms are not required to be unimodular or defined o ...

Pacific Journal Mathematics2014

Sesquilinear forms over rings with involution

Eva Bayer Fluckiger, Daniel Arnold Moldovan

Many classical results concerning quadratic forms have been extended to Hermitian forms over algebras with involution. However, not much is known in the case of sesquilinear forms without any symmetry property. The present paper will establish a Witt cance ...

Elsevier2014

Interface control domain decomposition methods for heterogeneous problems

Alfio Quarteroni, Marco Discacciati

This paper is concerned with the solution of heterogeneous problems by the interface control domain decomposition (ICDD) method, a strategy introduced for the solution of partial differential equations in computational domains partitioned into subdomains t ...

Wiley-Blackwell2014

Is there a common factor for vision?

Michael Herzog, Christine Mohr, Aaron Michael Clarke

In cognition, common factors play a crucial role. For example, different types of intelligence are highly correlated, pointing to a common factor, which is often called g. One might expect that a similar common factor would also exist for vision. Surprisin ...

Association for Research in Vision and Ophthalmology2014

Publications associées (26)

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

MDPI2023

Real-Time State Estimation and Voltage Stability Assessment of Power Grids: From Theoretical Foundations to Practical Applications

Andreas Martin Kettner

EPFL2019

n\ge 3

, we define

e(n)

to be the minimum positive integer such that an ...

EPFL2017