Publications associées à Euclidean plane isometry

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

Unlikely intersections on the p-adic formal ball

Vlad Serban

We investigate generalizations along the lines of the Mordell-Lang conjecture of the author's p-adic formal Manin-Mumford results for n-dimensional p-divisible formal groups F. In particular, given a finitely generated subgroup (sic) of F(Q(p)) and a close ...

SPRINGER INT PUBL AG2023

Shapes From Echoes: Uniqueness From Point-to-Plane Distance Matrices

Martin Vetterli, Ivan Dokmanic, Miranda Krekovic

We study the problem of localizing a configuration of points and planes from the collection of point-to-plane distances. This problem models simultaneous localization and mapping from acoustic echoes as well as the & x201C;structure from sound & x201D; app ...

2020

UCLID-Net: Single View Reconstruction in Object Space

Pascal Fua, Benoît Alain René Guillard, Edoardo Remelli

Most state-of-the-art deep geometric learning single-view reconstruction approaches rely on encoder-decoder architectures that output either shape parametrizations or implicit representations. However, these representations rarely preserve the Euclidean st ...

2020

Experimental studies of the equilibrium and out-of-equilibrium electronic structure of non-symmorphic topological materials

Gianmarco Gatti

Symmetry and topology are fundamental properties of nature. Mathematics provides us with a general framework to understand these concepts. On one side, symmetry describes the invariance properties of an object for specific transformations. On the other sid ...

EPFL2020

Coordinate Difference Matrices

Martin Vetterli, Gilles Baechler, Miranda Krekovic, Golnooshsadat Elhami

In many problems such as phase retrieval, molecular biology, source localization, and sensor array calibration, one can measure vector differences between pairs of points and attempt to recover the position of these points; this class of problems is called ...

SIAM PUBLICATIONS2020

A transmurally heterogeneous orthotropic activation model for ventricular contraction and its numerical validation

Alfio Quarteroni, Luca Dede', Simone Rossi, Luca Barbarotta

Models for cardiac mechanics require an activation mechanism properly representing the stress-strain relations in the contracting myocardium. In this paper, we propose a new activation model that accounts for the transmural heterogeneities observed in myoc ...

Wiley2018

Omnidirectional bats, point-to-plane distances, and the price of uniqueness

Martin Vetterli, Ivan Dokmanic, Miranda Krekovic

We study simultaneous localization and mapping with a device that uses reflections to measure its distance from walls. Such a device can be realized acoustically with a synchronized collocated source and receiver; it behaves like a bat with no capacity for ...

Ieee2017

Patching And Weak Approximation In Isometry Groups

Eva Bayer Fluckiger

Let R be a semilocal principal ideal domain. Two algebraic objects over R in which scalar extension makes sense (e.g. quadratic spaces) are said to be of the same genus if they become isomorphic after extending scalars to all completions of R and its fract ...

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

Atomistic simulations of dislocations in a model BCC multicomponent concentrated solid solution alloy

William Curtin, Céline Varvenne, Satish I Rao

Molecular statics and molecular dynamics simulations are presented for the structure and glide motion of a/2(111) dislocations in a randomly-distributed model-BCC Co16.67Fe36.67Ni16.67Ti30 alloy. Core structure variations along an individual dislocation li ...

Elsevier2017

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

Mechanism and energetics of < c plus a > dislocation cross-slip in hcp metals

William Curtin, Zhaoxuan Wu

Hexagonal close-packed (hcp) metals such as Mg, Ti, and Zr are lightweight and/or durable metals with critical structural applications in the automotive (Mg), aerospace (Ti), and nuclear (Zr) industries. The hcp structure, however, brings significant compl ...

National Academy of Sciences2016

Euclidean Distance Matrices: Essential Theory, Algorithms and Applications

Martin Vetterli, Ivan Dokmanic, Juri Ranieri, Reza Parhizkar

Euclidean distance matrices (EDMs) are matrices of the squared distances between points. The definition is deceivingly simple; thanks to their many useful properties, they have found applications in psychometrics, crystallography, machine learning, wireles ...

2015

An indiscrete Bieberbach theorem: from amenable CAT$(0)$ groups to Tits buildings

Nicolas Monod

Non-positively curved spaces admitting a cocompact isometric action of an amenable group are investigated. A classification is established under the assumption that there is no global fixed point at infinity under the full isometry group. The visual bounda ...

2015

Obstacle strength of binary junction due to dislocation dipole formation: An in-situ transmission electron microscopy study

Seyed Masood Hafez Haghighat

We report the experimental observation of the 1/2 < 111 > edge dislocation dipole formation and annihilation in ultra-high purity Fe using transmission electron microscopy (TEM) in-situ straining. The observation is confirmed by TEM image simulations. The ...

Elsevier Science Bv2015

Relax and Unfold: Microphone Localization with Euclidean Distance Matrices

Martin Vetterli, Ivan Dokmanic, Juri Ranieri

Recent methods for localization of microphones in a microphone array exploit sound sources at a priori unknown locations. This is convenient for ad-hoc arrays, as it requires little additional infrastructure. We propose a flexible localization algorithm by ...

2015

Bloch Theorem With Revised Boundary Conditions Applied To Glide Plane And Screw Axis Symmetric, Quasi-One-Dimensional Structures

Alessandro Spadoni, Florian Paul Robert Maurin

Bloch theorem provides a useful tool to analyze wave propagation in periodic systems. It has been widely used in physics to obtain the energy bands of various translationally-periodic cristals and with the advent of nanosciences like nanotubes, it has been ...

Int Center Numerical Methods Engineering2014

Scalar masses in general N=2 gauged supergravity theories

Claudio Scrucca, Paul Smyth, Francesca Catino

We readdress the question of whether any universal upper bound exists on the square mass m(2) of the lightest scalar around a supersymmetry breaking vacuum in generic N=2 gauged supergravity theories for a given gravitino mass m(3/2) and cosmological const ...

Springer Nature2014

Atomistic simulation of the a(0) < 1 0 0 > binary junction formation and its unzipping in body-centered cubic iron

Seyed Masood Hafez Haghighat

Molecular dynamics simulation is used to study the formation of the a(0) < 1 0 0 > binary dislocation junction in body-centered cubic Fe. Results show that under an applied strain two intersecting 1/2 a(0) < 1 1 1 > dislocations, one mobile edge and one im ...

Pergamon-Elsevier Science Ltd2014