2,006 research outputs found
Estimating the probability law of the codelength as a function of the approximation error in image compression
International audienceAfter a recollection on compression through a projection onto a polyhedral set (which generalizes the compression by coordinates quantization), we express, in this framework, the probability that an image is coded with coefficients as an explicit function of the approximation error
Classification of alternating knots with tunnel number one
This paper gives a complete classification of all alternating knots with
tunnel number one, and all their unknotting tunnels. We prove that the only
such knots are two-bridge knots and certain Montesinos knots.Comment: 38 pages, 26 figures; to appear in Communications in Analysis and
Geometr
Hyperbolic semi-adequate links
We provide a diagrammatic criterion for semi-adequate links to be hyperbolic.
We also give a conjectural description of the satellite structures of
semi-adequate links. One application of our result is that the closures of
sufficiently complicated positive braids are hyperbolic links.Comment: 25 pages, 9 figure
Bounds for the genus of a normal surface
This paper gives sharp linear bounds on the genus of a normal surface in a
triangulated compact, orientable 3--manifold in terms of the quadrilaterals in
its cell decomposition---different bounds arise from varying hypotheses on the
surface or triangulation. Two applications of these bounds are given. First,
the minimal triangulations of the product of a closed surface and the closed
interval are determined. Second, an alternative approach to the realisation
problem using normal surface theory is shown to be less powerful than its dual
method using subcomplexes of polytopes.Comment: 38 pages, 25 figure
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