Publications related to Squaring the circle

On the Volume of the John-Lowner Ellipsoid

We find an optimal upper bound on the volume of the John ellipsoid of a k-dimensional section of the n-dimensional cube, and an optimal lower bound on the volume of the Lowner ellipsoid of a projection of the n-dimensional cross-polytope onto a k-dimension ...

SPRINGER2020

On Sets Defining Few Ordinary Circles

Frank de Zeeuw

An ordinary circle of a set P of n points in the plane is defined as a circle that contains exactly three points of P. We show that if P is not contained in a line or a circle, then P spans at least ordinary circles. Moreover, we determine the exact minimu ...

Springer2018

Discontinuous Galerkin scheme for the spherical shallow water equations with applications to tsunami modeling and prediction

Jan Sickmann Hesthaven, Boris Bonev

We present a novel high-order discontinuous Galerkin discretization for the spherical shallow water equations, able to handle wetting/drying and non-conforming, curved meshes in a well-balanced manner. This requires a well-balanced discretization, that can ...

2018

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

An Inner-Product Calculus for Periodic Functions and Curves

Michaël Unser, Daniel Andreas Schmitter, Anaïs Laure Marie-Thérèse Badoual

Our motivation is the design of efficient algorithms to process closed curves represented by basis functions or wavelets. To that end, we introduce an inner-product calculus to evaluate correlations and

L _{ 2 }

distances between such curves. In partic ...

IEEE Institute of Electrical and Electronics Engineers2016

Obligatory averaging in mean size perception

Aire Raidvee

The perception of ensemble characteristics is often regarded as an antidote to an established bottleneck in focused attention and working memory, both of which appear to be limited in capacity to a few objects only. In order to test the associative law of ...

Elsevier2014

Calibration in Circular Ultrasound Tomography Devices

Martin Vetterli, Amin Karbasi, Reza Parhizkar

We consider the position calibration problem in circular tomography devices, where sensors deviate from a perfect circle. We introduce a new method of calibration based on the time-of-flight measurements between sensors when the enclosed medium is homogene ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2011

Phase extraction in speckle interferometry by a circle fitting procedure in the complex plane

Pierre Jacquot, Sébastien Equis

In speckle interferometry (SI), temporal signals are amplitude- and frequency-modulated signals and exhibit a fluctuating background. Prior to phase computation, this background intensity must be eliminated. Here our approach is to build a complex signal f ...

Optical Society of America2011

Classroom orchestration : The third circle of usability

Pierre Dillenbourg, Frédéric Kaplan, Patrick Jermann, Guillaume Zufferey, Sébastien Cuendet, Quentin Bonnard, Hamed Seiied Alavi, Lenh Hung Son Do

We analyze classroom orchestration as a question of usability in which the classroom is the user. Our experiments revealed design features that reduce the global orchestration load. According to our studies in vocational schools, paper-based interfaces hav ...

International Society of the Learning Sciences2011

Square Trisection

János Pach, Christian Blanvillain

A square trisection is a problem of assembling three identical squares from a larger square, using a minimal number of pieces. This paper presents an historical overview of the square trisection problem starting with its origins in the third century. We de ...

2010

Integrable Evolution Equations on Spaces of Tensor Densities and Their Peakon Solutions

Feride Tiglay

We study a family of equations defined on the space of tensor densities of weight lambda on the circle and introduce two integrable PDE. One of the equations turns out to be closely related to the inviscid Burgers equation while the other has not been iden ...

Springer Verlag2010

Perceived speed differences explain apparent compression in slit viewing

Michael Herzog

When a figure moves behind a stationary narrow slit, observers often report seeing the figure as an integrated whole, a phenomenon known as slit viewing or anorthoscopic perception. Interestingly, in slit viewing, the figure is perceived compressed along t ...

Elsevier2008