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On conway’s thrackle conjecture
 Proc. 11th ACM Symp. on Computational Geometry
, 1995
"... A thrackle is a graph drawn in the plane so that its edges are represented by Jordan arcs and any two distinct arcs either meet at exactly one common vertex or cross at exactly one point interior to both arcs. About forty years ago, J. H. Conway conjectured that the number of edges of a thrackle can ..."
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Cited by 19 (2 self)
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A thrackle is a graph drawn in the plane so that its edges are represented by Jordan arcs and any two distinct arcs either meet at exactly one common vertex or cross at exactly one point interior to both arcs. About forty years ago, J. H. Conway conjectured that the number of edges of a thrackle
Abstract A Study of Conway’s Thrackle Conjecture
"... A thrackle is a drawing of a simple graph on the plane, where each edge is drawn as a smooth arc with distinct endpoints, and every two arcs have exactly one common point, at which they have distinct tangents. Conway, who coined the term thrackle, conjectured that there is no thrackle with more edg ..."
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edges than vertices – a question which is still unsolved. A full thrackle is one with n vertices and n edges, and it is called nonextensible, if it cannot be a subthrackle of a counterexample to Conway’s conjecture on n vertices. We define the notion of incidence type for a thrackle, which
A Reduction of Conway’s Thrackle Conjecture
"... Abstract. A thrackle is a drawing of a simple graph on the plane, where each edge is drawn as a smooth arc with distinct endpoints, and every two arcs have exactly one common point, at which they have distinct tangents. Conway, who coined the term thrackle, conjectured that there is no thrackle wit ..."
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with more edges than vertices – a question which is still unsolved. A full thrackle is one with n vertices and n edges, and it is called nonextensible if it cannot be a subthrackle of a counterexample to Conway’s conjecture on n vertices. We define the notion of incidence type for a thrackle, which
Tangled Thrackles
"... A tangle is a graph drawn in the plane so that any pair of edges have precisely one point in common, and this point is either an endpoint or a point of tangency. If we allow a third option: the common point may be a proper crossing between the two edges, then the graph is called a tangled thrackle ..."
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thrackle. We establish the following analogues of Conway’s thrackle conjecture: The number of edges of a tangle cannot exceed its number of vertices, n. We also prove that the number of edges of an xmonotone tangled thrackle with n vertices is at most n+1. Both results are tight for n> 3
Gauss Codes and Thrackles  On Characterizations of Closed Curves in the Plane with an Application to the Thrackle Conjecture
, 2006
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Powerlaw distributions in empirical data
 ISSN 00361445. doi: 10.1137/ 070710111. URL http://dx.doi.org/10.1137/070710111
, 2009
"... Powerlaw distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and manmade phenomena. Unfortunately, the empirical detection and characterization of power laws is made difficult by the large fluctuations that occur in the t ..."
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Cited by 589 (7 self)
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demonstrate these methods by applying them to twentyfour realworld data sets from a range of different disciplines. Each of the data sets has been conjectured previously to follow a powerlaw distribution. In some cases we find these conjectures to be consistent with the data while in others the power law
The large N limit of superconformal field theories and supergravity
, 1998
"... We show that the large N limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of AntideSitter spacetimes, spheres and other compact manifolds. This is shown by taking some branes in the full M/string theory and ..."
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Cited by 5673 (21 self)
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in the superconformal group (as opposed to just the superPoincare group). The ’t Hooft limit of 3+1 N = 4 superYangMills at the conformal point is shown to contain strings: they are IIB strings. We conjecture that compactifications of M/string theory on various AntideSitter spacetimes is dual to various conformal
Good News and Bad News: Representation Theorems and Applications
 Bell Journal of Economics
"... prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtai ..."
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Cited by 684 (3 self)
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prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
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