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Concept

Complete lattice

Publications associées (28)

Some Mordell-Weil lattices and applications to sphere packings

Gauthier Leterrier

We provide new explicit examples of lattice sphere packings in dimensions 54, 55, 162, 163, 486 and 487 that are the densest known so far, using Kummer families of elliptic curves over global function fields. In some cases, these families of elliptic curve ...

EPFL2024

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

Nihar Prakash Gargava

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

Geometric Considerations in Lattice Programming

Moritz Andreas Venzin

We provide faster algorithms and fine-grained reductions for lattice problems in general norms. ...

EPFL2023

Correspondence functors and duality

Jacques Thévenaz, Serge Bouc

A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. By means of a suitably defined duality, new correspondence functors are constructed, having remarkable p ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2023

On the Mordell-Weil lattice of y(2) = x(3) + bx plus t(3n+1) in characteristic 3

Gauthier Leterrier

We study the elliptic curves given by y(2) = x(3) + bx + t(3n+1) over global function fields of characteristic 3 ; in particular we perform an explicit computation of the L-function by relating it to the zeta function of a certain superelliptic curve u(3) ...

SPRINGER INT PUBL AG2022

The concept of axial weak twins

Cyril Cayron

It is generally assumed that the parent-twin interface is a fully invariant plane. The calculations of the rational interfaces of the type I twins and irrational interfaces of the type II twins are based on this hypothesis. Recently, some asymmetric facets ...

PERGAMON-ELSEVIER SCIENCE LTD2022

BLOOM: Bimodal Lattice One-out-of-Many Proofs and Applications

Ngoc Khanh Karol Nguyen

We give a construction of an efficient one-out-of-many proof system, in which a prover shows that he knows the pre-image for one element in a set, based on the hardness of lattice problems. The construction employs the recent zero-knowledge framework of Ly ...

SPRINGER INTERNATIONAL PUBLISHING AG2022

Efficient protocols for oblivious linear function evaluation from ring-LWE

Juan Ramón Troncoso-Pastoriza

An oblivious linear function evaluation protocol, or OLE, is a two-party protocol for the function f (x) = ax + b, where a sender inputs the field elements a, b, and a receiver inputs x and learns f (x). OLE can be used to build secret-shared multiplicatio ...

IOS PRESS2022

The Completion Of Covariance Kernels

Victor Panaretos, Kartik Waghmare

We consider the problem of positive-semidefinite continuation: extending a partially specified covariance kernel from a subdomain Omega of a rectangular domain I x I to a covariance kernel on the entire domain I x I. For a broad class of domains Omega call ...

INST MATHEMATICAL STATISTICS-IMS2022

Formula Normalizations in Verification

Viktor Kuncak, Simon Guilloud, Dragana Milovancevic, Mario Bucev

We propose a new approach for normalization and simplification of logical formulas. Our approach is based on algorithms for lattice-like structures. Specifically, we present two efficient algorithms for computing a normal form and deciding the word problem ...

2023

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

Idempotents in the endomorphism algebra of a finite lattice

Jacques Thévenaz, Serge Bouc

We give a direct construction of a specific central idempotent in the endomorphism algebra of a finite lattice T. This idempotent is associated with all possible sublattices of T which are totally ordered. A generalization is considered in a conjectural fa ...

2022

Forward-reflected-backward method with variance reduction

Volkan Cevher, Ahmet Alacaoglu

We propose a variance reduced algorithm for solving monotone variational inequalities. Without assuming strong monotonicity, cocoercivity, or boundedness of the domain, we prove almost sure convergence of the iterates generated by the algorithm to a soluti ...

2021

Positive moments for scattering amplitudes

Riccardo Rattazzi, Francesco Riva, Brando Bellazzini, Marc Riembau Saperas

We find the complete set of conditions satisfied by the forward 2 -> 2 scattering amplitude in unitary and causal theories. These are based on an infinite set of energy dependent quantities (the arcs) which are dispersively expressed as moments of a positi ...

American Physical Society2021

The algebra of Boolean matrices, correspondence functors, and simplicity

Jacques Thévenaz, Serge Bouc

We determine the dimension of every simple module for the algebra of the monoid of all relations on a finite set (i.e. Boolean matrices). This is in fact the same question as the determination of the dimension of every evaluation of a simple correspondence ...

2020

Recursive evaluation and iterative contraction of N-body equivariant features

Michele Ceriotti, Jigyasa Nigam, Sergey Pozdnyakov

Mapping an atomistic configuration to a symmetrized N-point correlation of a field associated with the atomic positions (e.g., an atomic density) has emerged as an elegant and effective solution to represent structures as the input of machine-learning algo ...

2020

Correspondence functors and lattices

Jacques Thévenaz, Serge Bouc

A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. A main tool for this study is the construction of a correspondence functor associated to any finite latt ...

2019

Complete coordination of robotic fiber positioners for massive spectroscopic surveys

Denis Gillet, Jean-Paul Richard Kneib, Matin Macktoobian

Robotic fiber positioners play a vital role in the generation of massive spectroscopic surveys. The more complete a positioners set is coordinated, the more information its corresponding spectrograph receives during an observation. The complete coordinatio ...

2019

Suitably graded THB-spline refinement and coarsening: Towards an adaptive isogeometric analysis of additive manufacturing processes

Rafael Vazquez Hernandez

In the present work we introduce a complete set of algorithms to efficiently perform adaptive refinement and coarsening by exploiting truncated hierarchical B-splines (THB-splines) defined on suitably graded isogeometric meshes, that are called admissible ...

ELSEVIER SCIENCE SA2019

Quasiconvexity and Relaxation in Optimal Transportation of Closed Differential Forms

Bernard Dacorogna

This manuscript extends the relaxation theory from nonlinear elasticity to electromagnetism and to actions defined on paths of differential forms. The introduction of a gauge allows for a reformulation of the notion of quasiconvexity in Bandyopadhyay et al ...

SPRINGER2019