Publications associées à Shapes From Echoes: Uniqueness From Point-to-Plane Distance Matrices

Blind as a bat: spatial perception without sight

Among our five senses, we rely mostly on audition and vision to perceive an environment. Our ears are able to detect stimuli from all directions, especially from obstructed and far-away objects. Even in smoke, harsh weather conditions, or at night â situ ...

EPFL2021

Coordinate Difference Matrices

Martin Vetterli, Gilles Baechler, Golnooshsadat Elhami, Miranda Krekovic

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

Point, Plane, Set, Match! Winning the Echo Grand SLAM

Miranda Krekovic

Some of the most important and challenging problems in science are inverse problems. They allow us to understand phenomena that cannot be measured directly. Inverse problems might not always have a unique or stable solution, or might not have any solution ...

EPFL2020

Distinct distances between points and lines

Frank de Zeeuw, Adrian Claudiu Valculescu, Shakhar Smorodinsky

We show that for m points and n lines in R-2, the number of distinct distances between the points and the lines is Omega(m(1/5)n(3/5)), as long as m(1/2)

Elsevier Science Bv2018

Bayesian adaptation of chaos representations using variational inference and sampling on geodesics

Panagiotis Tsilifis

A novel approach is presented for constructing polynomial chaos representations of scalar quantities of interest (QoI) that extends previously developed methods for adaptation in Homogeneous Chaos spaces. In this work, we develop a Bayesian formulation of ...

ROYAL SOC2018

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

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

From Tarski's Plank Problem to Simultaneous Approximation

János Pach, Andrei Kupavskii

A slab (or plank) is the part of the d-dimensional Euclidean space that lies between two parallel hyperplanes. The distance between the these hyperplanes is called the width of the slab. It is conjectured that the members of any infinite family of slabs wi ...

Mathematical Assoc Amer2017

Concept and Applications of Extents in Chemical Reaction Systems

Michael Amrhein, Dominique Bonvin, Julien Léo Billeter, Sriniketh Srinivasan, Diogo Filipe Mateus Rodrigues

Models of chemical reaction systems can be quite complex as they typically include information regarding the reactions, the various transfers of heat and mass, as well as the effects of the inlet and outlet flows. It is well known that a linear transformat ...

2017

Algebraic and topological methods in combinatorics

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The present thesis deals with problems arising from discrete mathematics, whose proofs make use of tools from algebraic geometry and topology. The thesis is based on four papers that I have co-authored, three of which have been published in journals, and o ...

EPFL2017

Shape Projectors for Landmark-Based Spline Curves

Michaël Unser, Daniel Andreas Schmitter

We present a generic method to construct orthogonal projectors for two-dimensional landmark-based parametric spline curves. We construct vector spaces that define a geometric transformation (e.g., affine, similarity, and scaling) that is applied to a refer ...

IEEE Institute of Electrical and Electronics Engineers2017

Combine and conquer: Relating BIP and Reo

Simon Bliudze

Coordination languages simplify design and development of concurrent systems. Particularly, exogenous coordination languages, like BIP and Reo, enable system designers to express the interactions among components in a system explicitly. A formal relation b ...

Elsevier Science Inc2017

Distinct Distances on Algebraic Curves in the Plane

János Pach, Frank de Zeeuw

Let S be a set of n points in R-2 contained in an algebraic curve C of degree d. We prove that the number of distinct distances determined by S is at least c(d)n(4/3), unless C contains a line or a circle. We also prove the lower bound c(d)' min{m(2/3)n(2/ ...

Cambridge Univ Press2017

A block algorithm for computing antitriangular factorizations of symmetric matrices

Daniel Kressner, Zvonimir Bujanovic

Any symmetric matrix can be reduced to antitriangular form in finitely many steps by orthogonal similarity transformations. This form reveals the inertia of the matrix and has found applications in, e.g., model predictive control and constraint preconditio ...

Springer2016

Approximation algorithms for geometric dispersion

Alfonso Bolívar Cevallos Manzano

The most basic form of the max-sum dispersion problem (MSD) is as follows: given n points in R^q and an integer k, select a set of k points such that the sum of the pairwise distances within the set is maximal. This is a prominent diversity problem, with w ...

EPFL2016

Projective transformations of structural equilibrium

Corentin Jean Dominique Fivet

Direct methods that transform the geometry of a structure and conserve its static equilibrium are of particular interest for designers. They allow the exploration of alternative solutions at minimum computational cost. While parallel transformations (stret ...

2016

Distinct Values Of Bilinear Forms On Algebraic Curves

Frank de Zeeuw, Adrian Claudiu Valculescu

Let B-M : C x C -> C be a bilinear form B-M(p, q) - p(T)Mq, with an invertible matrix M is an element of C-2x2. We prove that any finite set S contained in an irreducible algebraic curve C of degree d in C determines Omega(d)(vertical bar S vertical bar(4/ ...

Univ Calgary, Dept Math & Statistics2016

Poincaré, Scale and Conformal Symmetries : Gauge Perspective and Cosmological Ramifications

Georgios Karananas

Symmetries are omnipresent and play a fundamental role in the description of Nature. Thanks to them, we have at our disposal nontrivial selection rules that dictate how a theory should be constructed. This thesis, which is naturally divided into two parts, ...

EPFL2016

Local Geometric Transformations in Image Analysis

Zsuzsanna Püspöki

The characterization of images by geometric features facilitates the precise analysis of the structures found in biological micrographs such as cells, proteins, or tissues. In this thesis, we study image representations that are adapted to local geometric ...

EPFL2016

Euclidean Distance Matrices: Essential Theory, Algorithms and Applications

Martin Vetterli, Reza Parhizkar, Juri Ranieri, Ivan Dokmanic

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