A multicurve can be decomposed into components. The ratios of the length each component to total give a hint shape multicurve. In this paper, we determine distribution these random with given topological type on closed hyperbolic surface, using methods Margulis’ thesis and Mirzakhani’s equidistribution theorem for horospheres. This admits polynomial density whose coefficients expressed explicit...

by Logan M. Axon Algorithmic randomness in the Cantor space, 2 ω , has recently become the subject of intense study. Originally defined in terms of the fair coin measure, algorithmic randomness has since been extended, for example in Reimann and Slaman [22, 23], to more general measures. Others have meanwhile developed definitions of algorithmic randomness for different spaces, for example the ...

State estimation entails the estimation of an unobserved random closed set from (partial) observation of an associated random set. Examples include edge effect correction, cluster detection, filtering and prediction. We focus on inference for random sets based on points sampled on its boundary. Such data are subject to mis-alignment and noise. First, we ignore mis-alignment and discuss maximum ...

In memory of J. Harrison Keywords: Image analysis Missing data Random closed set Spectral analysis a b s t r a c t We propose a spectral mean for closed sets described by sample points on their boundaries subject to mis-alignment and noise. We derive maximum likelihood estimators for the model and noise parameters in the Fourier domain. We estimate the unknown mean boundary curve by back-transf...

Lattice numerical simulations for planar closed random walks and their winding sectors are presented. The frontiers of the random walks and of their winding sectors have a Hausdorff dimension dH = 4/3. However, when properly defined by taking into account the inner 0-winding sectors, the frontiers of the random walks have a Hausdorff dimension dH ≈ 1.77.

In this paper, we discuss generating theorems of polyhedral quadrangulations closed surfaces. We prove that the set eight reductional operations {R1, …, R8} defined for is finitizable any surface F2, is, there exist finitely many minimal F2 using such R1, R7 and R8. Furthermore, show proper subset not torus.