Concept

Isolated point

Related publications (22)

Laser-based manufacturing of freeform glass micro-optics through topological transformation

Glass has been the material of choice for making optical elements, in large part due to its intrinsic properties: a temperature-dependent viscosity, which enables shaping the material into a broad variety of functional and artistic glassware. Silica glass ...

EPFL2024

From SU(2)5 to SU(2)3 Wess-Zumino-Witten transitions in a frustrated spin-52 chain

Frédéric Mila, Natalia Chepiga

We investigate the properties of a frustrated spin-5/2 chain with next-nearest-neighbor two- and three-site interactions, with two questions in mind: the nature of the transition into the dimerized phase induced by the three-site interaction, and the possi ...

2022

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

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

Wulfram Gerstner, Clément Hongler, Johanni Michael Brea, Francesco Spadaro, Berfin Simsek, Arthur Jacot

We study how permutation symmetries in overparameterized multi-layer neural networks generate `symmetry-induced' critical points. Assuming a network with

L

layers of minimal widths

r_1^*, \ldots, r_{L-1}^*

reaches a zero-loss minimum at $ r_1^*! \c ...

2021

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

Separation with restricted families of sets

János Pach, Gábor Tardos, Márton Naszódi, Zsolt Langi

Given a finite n-element set X, a family of subsets F subset of 2(X) is said to separate X if any two elements of X are separated by at least one member of F. It is shown that if vertical bar F vertical bar > 2(n-1), then one can select vertical bar log n ...

Academic Press Inc Elsevier Science2016

Bisector Energy and Few Distinct Distances

Frank de Zeeuw

We define the bisector energy E(P) of a set P in R-2 to be the number of quadruples (a, b, c, d) is an element of P-4 such that a, b determine the same perpendicular bisector as c, d. Equivalently, E(P) is the number of isosceles trapezoids determined by P ...

Springer2016

Few distinct distances implies no heavy lines or circles

Frank de Zeeuw

We study the structure of planar point sets that determine a small number of distinct distances. Specifically, we show that if a set of n points determines o(n) distinct distances, then no line contains Omega(n (7/8)) points of and no circle contains Omega ...

Springer Heidelberg2016

Similarity-Based Shape Priors for 2D Spline Snakes

Michaël Unser, Daniel Andreas Schmitter

We present a new formulation of a shape space containing all continuously defined 2D spline curves up to a similarity transform of a reference shape. We are able to measure a distance between an arbitrary curve and the shape space itself. Our contribution ...

IEEE2015

The visible perimeter of an arrangement of disks

János Pach, Gabriel Nivasch, Gábor Tardos

Given a collection of n opaque unit disks in the plane, we want to find a stacking order for them that maximizes their visible perimeter, the total length of all pieces of their boundaries visible from above. We prove that if the centers of the disks form ...

Elsevier Science Bv2014

Density of rational points on del Pezzo surfaces of degree one

We state conditions under which the set S(k) of k-rational points on a del Pezzo surface S of degree 1 over an infinite field k of characteristic not equal to 2 or 3 is Zariski dense. For example, it suffices to require that the elliptic fibration S -> P-1 ...

Academic Press Inc Elsevier Science2014

The flux-coordinate independent approach applied to X-point geometries

A Flux-Coordinate Independent (FCI) approach for anisotropic systems, not based on magnetic flux coordinates, has been introduced in Hariri and Ottaviani [Comput. Phys. Commun. 184, 2419 (2013)]. In this paper, we show that the approach can tackle magnetic ...

Amer Inst Physics2014

The Visible Perimeter of an Arrangement of Disks

János Pach, Gabriel Nivasch, Gábor Tardos

Springer2013

An alternate point-wise scheme for Electric Field Integral Equations

Juan Ramon Mosig, Gabriele Rosati

A point-wise approach that can be used efficiently in the numerical solution of Electric Field Integral Equations is introduced. The algorithm is based on the so-called magic distance concept, which defines exactly the point-to-point equivalent of a four-d ...

Wiley-Blackwell2013

Meta Morphic Particle Swarm Optimization

Auke Ijspeert, Soha Pouya, Jesse van den Kieboom

Particle Swarm Optimization is a simple and elegant optimization algorithm used to solve a large variety of different real-valued problems. When it comes to solving combinations of continuous and discrete problems however, PSO by itself is not very well su ...

Springer2013

Two and a half billion years of distance research

János Pach, Filip Moric

In a seminal paper published in 1946, Erd ̋os initiated the investigation of the distribution of distances generated by point sets in metric spaces. In spite of some spectacular par- tial successes and persistent attacks by generations of mathe- maticians, ...

2013

A Model Predictive Control Scheme with Additional Performance Index for Transient Behavior

Colin Neil Jones, Andrea Alessandretti, António Pedro Rodrigues de Aguiar

This paper presents a Model Predictive Control (MPC) scheme for nonlinear continuous time systems where an extra performance index, which is not a measure of the distance to the set point, is introduced to influence the transient behavior of the controlled ...

2013

Plenoptic Spherical Sampling

Pascal Frossard, Pierre Vandergheynst, Luigi Bagnato

We present a novel plenoptic sampling scheme that permits an efficient representation of the full light ray field in a space limited by a convex closed surface. We show that a convenient way to sample the light ray field around an observer consists in usin ...

2012

Order Types of Convex Bodies

We prove a Hadwiger transversal-type result, characterizing convex position on a family of non-crossing convex bodies in the plane. This theorem suggests a definition for the order type of a family of convex bodies, generalizing the usual definition of ord ...

2011

Delaunay Graphs of Point Sets in the Plane With Respect to Axis-Parallel Rectangles

János Pach, Gábor Tardos

Given a point set P in the plane, the Delaunay graph with respect to axis-parallel rectangles is a graph defined on the vertex set P, whose two points p, q is an element of P are connected by an edge if and only if there is a rectangle parallel to the coor ...

Wiley-Blackwell2009