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Asymptotics of visibility in the hyperbolic plane
Boolean model hyperbolic geometry visibility Poincar´ e disc
2011/2/25
At each point of a Poisson point process of intensity in the hyperbolic place, center a ball of bounded random radius. Consider the probability Pr that from a fixed point, there is some direction in...
Unsolved Problems in Visibility Graphs of Points, Segments and Polygons
Unsolved Problems Visibility Graphs of Points Segments Polygons
2011/3/3
In this survey paper, we present open problems and conjectures on visibility graphs of points, segments and polygons along with necessary backgrounds for understanding them.
Horizontal visibility graphs transformed from fractional Brownian motions: Topological properties versus Hurst index
Horizontal visibility graphs transformed fractional Brownian motions Topological properties versus Hurst index
2010/12/28
Nonlinear time series analysis aims at understanding the dynamics of stochastic or chaotic processes.In recent years, quite a few methods have been proposed to transform a single time series to a comp...
Description of stochastic and chaotic series using visibility graphs
Data Analysis, Statistics and Probability (physics.data-an) Chaotic Dynamics (nlin.CD)
2010/11/10
Nonlinear time series analysis is an active field of research that studies the structure of complex signals in order to derive information of the process that generated those series, for understanding...
Horizontal visibility graphs: exact results for random time series
Horizontal visibility graphs random time series
2010/4/2
The visibility algorithm has been recently introduced as a mapping between time series and complex networks. This procedure allows to apply methods of complex network theory for characterizing time se...
Solutions of some visibility and contour problems in the visualisation of surfaces
Computer graphics visualisation visibility and contour problems
2009/1/4
We give a short survey of the main principles of our software
for the visualisation and animation in mathematics and study the visibility
and contour problems in the representation of surfaces, whic...