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Distinct Distances on Algebraic Curves in the Plane

Related publications (43)

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Sur la méthode de Buser-Silhol pour l'uniformisation des surfaces de Riemann hyperelliptiques

Grégoire Aubry

The Uniformization Theorem due to Koebe and Poincaré implies that every compact Riemann surface of genus greater or equal to 2 can be endowed with a metric of constant curvature – 1. On the other hand, a compact Riemann surface is a complex algebraic curve ...

EPFL2010

Ideal knots and other packing problems of tubes

Henryk Gerlach

This thesis concerns optimal packing problems of tubes, or thick curves, where thickness is defined as follows. Three points on a closed space curve define a circle. Taking the infimum over all radii of pairwise-distinct point triples defines the thickness ...

EPFL2010

Conformational analysis of nucleic acids revisited: Curves

John Maddocks, Daiva Petkeviciute

We describe Curves+, a new nucleic acid conformational analysis program which is applicable to a wide range of nucleic acid structures, including those with up to four strands and with either canonical or modified bases and backbones. The program is algori ...

Oxford University Press2009

A geometric characterization of orient at ion-reversing involutions

Hugo Parlier

We give a geometric characterization of compact Riemann surfaces admitting orientation-reversing involutions with fixed points. Such surfaces are generally called real surfaces and can be represented by real algebraic curves with non-empty real part. We sh ...

2008

Direct measurement of drainage curves in infiltration of SiC particle preforms

Andreas Mortensen, Ludger Weber, Maryam Bahraini Hasani

Drainage curves (plots of the non-wetting fluid saturation versus applied pressure) for infiltration of SiC particle preforms with Al and Al-12.2 at.% Si are measured at 1023 K (750 degrees C) with a pressure infiltration apparatus adapted for direct track ...

2008

Ate Pairing on Hyperelliptic Curves

Robert Granger

In this paper we show that the Ate pairing, originally defined for elliptic curves, generalises to hyperelliptic curves and in fact to arbitrary algebraic curves. It has the following surprising properties: The loop length in Miller’s algorithm can be up t ...

Springer-Verlag Berlin Heidelberg2007

Some remarks on the uniformizing function in genus 2

Robert Silhol

The authors propose a numerical method for the uniformization of Riemann surfaces and algebraic curves in genus two with highly accurate results. Let

G

be a Fuchsian group acting on the unit disk

Bbb D

, and let

S = Bbb D / G

. It is well known that $S ...

Kluwer Academic Publishers, Springer2005

Global radii of curvature, and the biarc approximation of space curves

Jana Smutny

The distance from self-intersection of a (smooth and either closed or infinite) curve q in three dimensions can be characterised via the global radius of curvature at q(s), which is defined as the smallest possible radius amongst all circles passing throug ...

EPFL2004

Non-linear subdivision using local spherical coordinates

Touradj Ebrahimi, Pierre Vandergheynst, Nicolas Aspert

In this paper, we present an original non-linear subdivision scheme suitable for univariate data, plane curves and discrete triangulated surfaces, while keeping the complexity acceptable. The proposed technique is compared to linear subdivision methods hav ...

2003

On the learning mechanism of adaptive filters

Ali H. Sayed

This paper highlights, both analytically and by simulations, some interesting phenomena regarding the behavior of ensemble-average learning curves of adaptive filters that may have gone unnoticed. Among other results, the paper shows that even ensemble-ave ...

IEEE2000