Publications associées à An extremal problem on crossing vectors

Additive and geometric transversality of fractal sets in the integers

By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we in ...

2024

Toroidal families and averages of L-functions, I

Philippe Michel

We initiate the study of certain families of L-functions attached to characters of subgroups of higher-rank tori, and of their average at the central point. In particular, we evaluate the average of the values L( 2 1 , chi a )L( 21 , chi b ) for arbitrary ...

Polish Acad Sciences Inst Mathematics-Impan2024

Diversity of radial spin textures in chiral materials

Oleg Yazyev, Alberto Crepaldi, Daniel Gosalbez Martinez

We introduce a classification of the radial spin textures in momentum space that emerge at the high-symmetry points in crystals characterized by nonpolar chiral point groups (D2, D3, D4, D6, T, O). Based on the symmetry constraints imposed by these point g ...

Amer Physical Soc2023

Get the Best of Both Worlds: Improving Accuracy and Transferability by Grassmann Class Representation

Zhigang Li, Haoqi Wang

We generalize the class vectors found in neural networks to linear subspaces (i.e., points in the Grassmann manifold) and show that the Grassmann Class Representation (GCR) enables simultaneous improvement in accuracy and feature transferability. In GCR, e ...

Ieee Computer Soc2023

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

Fourier non-uniqueness sets from totally real number fields

Martin Peter Stoller

Let K be a totally real number field of degree n >= 2. The inverse different of K gives rise to a lattice in Rn. We prove that the space of Schwartz Fourier eigenfunctions on R-n which vanish on the "component-wise square root" of this lattice, is infinite ...

EUROPEAN MATHEMATICAL SOC-EMS2022

The exploration process of critical Boltzmann planar maps decorated by a triangular O(n) loop model

Aleksandra Korzhenkova

In this paper we investigate pointed (q, g, n)-Boltzmann loop-decorated maps with loops traversing only inner triangular faces. Using peeling exploration Budd (2018) modified to this setting we show that its law in the non-generic critical phase can be cod ...

IMPA2022

Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning

Tommaso Vanzan

Iterative substructuring Domain Decomposition (DD) methods have been extensively studied, and they are usually associated with nonoverlapping decompositions. It is less known that classical overlapping DD methods can also be formulated in substructured for ...

2022

Further results on latent discourse models and word embeddings

Youssef Allouah

We discuss some properties of generative models for word embeddings. Namely, (Arora et al., 2016) proposed a latent discourse model implying the concentration of the partition function of the word vectors. This concentration phenomenon led to an asymptotic ...

Microtome Publishing2021

Collaborative Learning in the Jungle (Decentralized, Byzantine, Heterogeneous, Asynchronous and Nonconvex Learning)

Rachid Guerraoui, El Mahdi El Mhamdi, Le Nguyen Hoang, Sébastien Louis Alexandre Rouault, Arsany Hany Abdelmessih Guirguis, Sadegh Farhadkhani

We study Byzantine collaborative learning, where n nodes seek to collectively learn from each others' local data. The data distribution may vary from one node to another. No node is trusted, and f < n nodes can behave arbitrarily. We prove that collaborati ...

2021

Proximity Results and Faster Algorithms for Integer Programming Using the Steinitz Lemma

Friedrich Eisenbrand

We consider integer programming problems in standard form max{c(T)x : Ax = b, x >= 0, x is an element of Z(n)} where A is an element of Z(mxn), b is an element of Z(m), and c is an element of Z(n). We show that such an integer program can be solved in time ...

ASSOC COMPUTING MACHINERY2020

Minimal graphs for 2-factor extension

Dominique de Werra

Let G = (V, E) be a simple loopless finite undirected graph. We say that G is (2-factor) expandable if for any non-edge uv, G + uv has a 2-factor F that contains uv. We are interested in the following: Given a positive integer n = vertical bar V vertical b ...

ELSEVIER2020

A simple proof for a forbidden subposet problem

Abhishek Methuku

The poset Y-k,Y-2 consists of k + 2 distinct elements x(1), x(2), ..., x(k), y(1), y(2), such that x(1)

ELECTRONIC JOURNAL OF COMBINATORICS2020

Packing the Boolean lattice with copies of a poset

Istvan Tomon

The Boolean lattice (2[n],subset of) is the family of all subsets of [n]={1,MIDLINE HORIZONTAL ELLIPSIS,n}, ordered by inclusion. Let P be a partially ordered set. We prove that if n is sufficiently large, then there exists a packing P of copies of P in (2 ...

WILEY2020

Locally supported tangential vector, n-vector, and tensor fields

Christopher Brandt

We introduce a construction of subspaces of the spaces of tangential vector, n-vector, and tensor fields on surfaces. The resulting subspaces can be used as the basis of fast approximation algorithms for design and processing problems that involve tangenti ...

2020

Code Integration, Data Verification, and Models Validation Using the ITER Integrated Modeling and Analysis System (IMAS) in EUROfusion

Olivier Sauter, José Pedro Rebelo Ferreira Marques, Antoine Pierre Emmanuel Alexis Merle, Giovanni Tardini

The ITER Integrated Modelling and Analysis System (IMAS) has been adopted by the EUROfusion Consortium as a platform to facilitate the analysis and verification of data from multiple tokamaks for the integration of physics codes and the validation of physi ...

2020

Forbidden induced subposets of given height

Istvan Tomon

Let P be a partially ordered set. The function La* (n, P) denotes the size of the largest family F subset of 2([n]) that does not contain an induced copy of P. It was proved by Methuku and Palvolgyi that there exists a constant C-P (depending only on P) su ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2019

The Bounded Cohomology of SL2 Over Local Fields and S-Integers

Nicolas Monod

It is proved that the continuous bounded cohomology of SL2(k) vanishes in all positive degrees whenever k is a non-Archimedean local field. This holds more generally for boundary-transitive groups of tree automorphisms and implies low degree vanishing for ...

OXFORD UNIV PRESS2019

Observation of tau(-) -> pi(-)nu(tau)e(+)e(-) and search for tau(-) -> pi(-)nu(tau)mu(+)mu(-)

Olivier Schneider, Sun Hee Kim, Tagir Aushev, Mingkui Wang, Chao Wang, Ke Huang, Donghyun Kim, Lei Li, Yiming Li

We present the first measurements of branching fractions of rare tau-lepton decays, tau(-) -> pi(-)nu(tau)l(+)l(-) (l = e or mu), using a data sample corresponding to 562 fb(-1) collected at a center-of-mass energy of 10.58 GeV with the Belle detector at t ...

American Physical Society2019

Role of higher order plasmonic modes in one-dimensional nanogratings

Foziyeh Sohrabi, Ershad Mohammadi

By theoretically investigating the optical behavior of one-dimensional gold nanogratings using Fourier Modal Method, we have shown that both integer and non-integer multiples of surface plasmon polariton wavelengths should be taken into consideration in sp ...

SPRINGER2019