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

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Blind as a bat: spatial perception without sight

Frederike Dümbgen

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

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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

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

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

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

Algebraic and topological methods in combinatorics

Adrian Claudiu Valculescu

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

Concept and Applications of Extents in Chemical Reaction Systems

Dominique Bonvin, Julien Léo Billeter, Michael Amrhein, 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

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

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