Publications related to On the Richter-Thomassen Conjecture about Pairwise Intersecting Closed Curves

Medial axis transformation as a solid modeling representation method for computer aided design software

Paul Xirouchakis, Mihai-Bogdan Lazar, Ian Anthony Stroud, Florian Barras, Guillaume Goualard

A method for achieving a representation of an object within a data structure for a Computer Aided Design system employing a Medial Axis Transformation (MAT), the representation of the object comprising a set of adjacent bounded surface elements called MAT ...

2016

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

Robert Granger

For any positive integers

n\geq 3, r\geq 1

we present formulae for the number of irreducible polynomials of degree

n

over the finite field

\mathbb{F}_{2^r}

where the coefficients of

x^{n-1}

,

x^{n-2}

and

x^{n-3}

are zero. Our proofs involve coun ...

Elsevier2016

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

Lower bounds for Pythagoras numbers of function fields

David Maximilian Grimm

We show that the transcendence degree of a real function field over an arbitrary real base field is a strict lower bound for its Pythagoras number and a weak lower bound for all its higher Pythagoras numbers. ...

European Mathematical Soc2015

Elliptic equations with general singular lower order term and measure data

Linda Maria De Cave

In this paper we study a nonlinear elliptic boundary value problem with a general singular lower order term, whose model is {-Delta u = H(u)mu, in Omega, u = 0 on partial derivative Omega, u > 0 on Omega, where Omega is an open bounded subset of R-N, mu is ...

Pergamon-Elsevier Science Ltd2015

Empty Triangles in Complete Topological Graphs

Andres Jacinto Ruiz Vargas

A simple topological graph is a graph drawn in the plane so that its edges are represented by continuous arcs with the property that any two of them meet at most once. Let be a complete simple topological graph on vertices. The three edges induced by any t ...

Springer2015

Constructing reparameterization invariant metrics on spaces of plane curves

Martins Bruveris, Martin Bauer

Metrics on shape spaces are used to describe deformations that take one shape to another, and to define a distance between shapes. We study a family of metrics on the space of curves, which includes several recently proposed metrics, for which the metrics ...

Elsevier2014

Decentralized Self-Selection of Swarm Trajectories: From Dynamical Systems to Robotic Implementation

Francesco Mondada, Max-Olivier Hongler, Guillaume Adrien Sartoretti, Marcelo Elias de Oliveira

In this paper, we present a distributed control strategy, enabling agents to converge onto and travel along a consensually selected curve among a class of closed planar curves. Individual agents identify the number of neighbors within a finite circular sen ...

Springer Verlag2014

Sampling Curves with Finite Rate of Innovation

Thierry Blu, Hanjie Pan, Pier Luigi Dragotti

In this paper, we extend the theory of sampling signals with finite rate of innovation (FRI) to a specific class of two-dimensional curves, which are defined implicitly as the zeros of a mask function. Here the mask function has a parametric representation ...

Institute of Electrical and Electronics Engineers2014

Modular Functions and Special Cycles

Maryna Viazovska

In this thesis we study algebraic cycles on Shimura varieties of orthogonal type. Such varieties are a higher dimensional generalization of modular curves and their important feature is that they have natural families of algebraic cycles in all codimesions ...

Rheinische Friedrich-Wilhelms-Universität Bonn2013

On the Richter-Thomassen Conjecture about Pairwise Intersecting Closed Curves

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Medial axis transformation as a solid modeling representation method for computer aided design software

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

Similarity-Based Shape Priors for 2D Spline Snakes

Lower bounds for Pythagoras numbers of function fields

Elliptic equations with general singular lower order term and measure data

Empty Triangles in Complete Topological Graphs

Constructing reparameterization invariant metrics on spaces of plane curves

Decentralized Self-Selection of Swarm Trajectories: From Dynamical Systems to Robotic Implementation

Sampling Curves with Finite Rate of Innovation

Modular Functions and Special Cycles

Empty Triangles in Complete Topological Graphs

Sampling Curves with Finite Rate of Innovation

Lower bounds for Pythagoras numbers of function fields

Decentralized Self-Selection of Swarm Trajectories: From Dynamical Systems to Robotic Implementation

Modular Functions and Special Cycles

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

Similarity-Based Shape Priors for 2D Spline Snakes

Medial axis transformation as a solid modeling representation method for computer aided design software

Constructing reparameterization invariant metrics on spaces of plane curves

Elliptic equations with general singular lower order term and measure data