13 research outputs found
Fitting Voronoi Diagrams to Planar Tesselations
Given a tesselation of the plane, defined by a planar straight-line graph
, we want to find a minimal set of points in the plane, such that the
Voronoi diagram associated with "fits" \ . This is the Generalized
Inverse Voronoi Problem (GIVP), defined in \cite{Trin07} and rediscovered
recently in \cite{Baner12}. Here we give an algorithm that solves this problem
with a number of points that is linear in the size of , assuming that the
smallest angle in is constant.Comment: 14 pages, 8 figures, 1 table. Presented at IWOCA 2013 (Int. Workshop
on Combinatorial Algorithms), Rouen, France, July 201
Dragon-kings: mechanisms, statistical methods and empirical evidence
This introductory article presents the special Discussion and Debate volume
"From black swans to dragon-kings, is there life beyond power laws?" published
in Eur. Phys. J. Special Topics in May 2012. We summarize and put in
perspective the contributions into three main themes: (i) mechanisms for
dragon-kings, (ii) detection of dragon-kings and statistical tests and (iii)
empirical evidence in a large variety of natural and social systems. Overall,
we are pleased to witness significant advances both in the introduction and
clarification of underlying mechanisms and in the development of novel
efficient tests that demonstrate clear evidence for the presence of
dragon-kings in many systems. However, this positive view should be balanced by
the fact that this remains a very delicate and difficult field, if only due to
the scarcity of data as well as the extraordinary important implications with
respect to hazard assessment, risk control and predictability.Comment: 20 page
Testing separability in marked multidimensional point processes with covariates
Conditional intensity, Covariates, Marked point processes, Separability, Testing, Wildfires,
Using INLA to estimate a highly dimensional spatial model for forest fires in Portugal
Within the context of accessing the risk of forest fires, Amaral-Turkman
et al. [1] have proposed a spatio-temporal hierarchical approach which jointly models
the fire ignition probability and the fire’s size, in a Bayesian framework. This
is recovered and applied to Portuguese forest fires data, with some necessary modifications
in what concerns the format of the data (not available in a regular lattice
over the territory) and also because of the estimation complications that arise due the
high dimensionality of the neighbouring structure involved. To address the latter, as
it compromises the estimation via Markov Chain Monte Carlo (MCMC) methods,
and having the model be recognized as a latent Gaussian model, it was chosen to
do the Bayesian estimation also using an Integrated Nested Laplace Approximation
approach, with real computational advantages. Corresponding methodologies and
results are described and compared
Comparison of Pareto and tapered Pareto distributions for environmental phenomena
The Pareto distribution is often used to describe environmental phenomena such as the sizes of earthquakes or wildfires, or the interevent times or distances between such environmental disturbances. Because it is heavy-tailed, the Pareto distribution, or power-law distribution as it is occasionally called, suggests that a higher frequency of extremely large values occur compared to other, more familiar distributions such as the normal, exponential, or uniform. However, an alternative distribution called the tapered Pareto has been shown in some cases to fit as well or better to data than the Pareto distribution, and the tapered Pareto distribution is not heavy-tailed, suggesting a far lower frequency of extreme events. Even with rather large datasets, it is often quite difficult to distinguish which of these distributions is preferable, as they only differ markedly in the extreme upper tail where few, if any, observations are recorded. This article reviews the evidence and arguments related to these two competing distributions, especially in the context of earthquakes and wildfires
Hybrid kernel estimates of space–time earthquake occurrence rates using the epidemic-type aftershock sequence model
Bandwidths, Shape parameters, Cross-validation, ETAS models, Intensity function, Kernel estimates, Space–time point processes, Space–time ETAS model, Transformation of time,