505 research outputs found
State estimation for temporal point processes
This paper is concerned with combined inference for point processes on the
real line observed in a broken interval. For such processes, the classic
history-based approach cannot be used. Instead, we adapt tools from sequential
spatial point processes. For a range of models, the marginal and conditional
distributions are derived. We discuss likelihood based inference as well as
parameter estimation using the method of moments, conduct a simulation study
for the important special case of renewal processes and analyse a data set
collected by Diggle and Hawtin
Non-parametric indices of dependence between components for inhomogeneous multivariate random measures and marked sets
We propose new summary statistics to quantify the association between the
components in coverage-reweighted moment stationary multivariate random sets
and measures. They are defined in terms of the coverage-reweighted cumulant
densities and extend classic functional statistics for stationary random closed
sets. We study the relations between these statistics and evaluate them
explicitly for a range of models. Unbiased estimators are given for all
statistics and applied to simulated examples.Comment: Added examples in version
A spectral mean for point sampled closed curves
We propose a spectral mean for closed curves described by sample points on
its boundary subject to mis-alignment and noise. First, we ignore mis-alignment
and derive maximum likelihood estimators of the model and noise parameters in
the Fourier domain. We estimate the unknown curve by back-transformation and
derive the distribution of the integrated squared error. Then, we model
mis-alignment by means of a shifted parametric diffeomorphism and minimise a
suitable objective function simultaneously over the unknown curve and the
mis-alignment parameters. Finally, the method is illustrated on simulated data
as well as on photographs of Lake Tana taken by astronauts during a Shuttle
mission
A J-function for inhomogeneous spatio-temporal point processes
We propose a new summary statistic for inhomogeneous intensity-reweighted
moment stationary spatio-temporal point processes. The statistic is defined
through the n-point correlation functions of the point process and it
generalises the J-function when stationarity is assumed. We show that our
statistic can be represented in terms of the generating functional and that it
is related to the inhomogeneous K-function. We further discuss its explicit
form under some specific model assumptions and derive a ratio-unbiased
estimator. We finally illustrate the use of our statistic on simulated data
Summary statistics for inhomogeneous marked point processes
We propose new summary statistics for intensity-reweighted moment stationary
marked point processes with particular emphasis on discrete marks. The new
statistics are based on the n-point correlation functions and reduce to cross
J- and D-functions when stationarity holds. We explore the relationships
between the various functions and discuss their explicit forms under specific
model assumptions. We derive ratio-unbiased minus sampling estimators for our
statistics and illustrate their use on a data set of wildfires
Competing Claims in Public Space: The Construction of Frames in Different Relational Contexts
Contains fulltext :
151928.pdf (publisher's version ) (Open Access
Luminosity- and morphology-dependent clustering of galaxies
How does the clustering of galaxies depend on their inner properties like
morphological type and luminosity? We address this question in the mathematical
framework of marked point processes and clarify the notion of luminosity and
morphological segregation. A number of test quantities such as conditional
mark-weighted two-point correlation functions are introduced. These descriptors
allow for a scale-dependent analysis of luminosity and morphology segregation.
Moreover, they break the degeneracy between an inhomogeneous fractal point set
and actual present luminosity segregation. Using the Southern Sky Redshift
Survey~2 (da Costa et al. 1998, SSRS2) we find both luminosity and
morphological segregation at a high level of significance, confirming claims by
previous works using these data (Benoist et al. 1996, Willmer et al. 1998).
Specifically, the average luminosity and the fluctuations in the luminosity of
pairs of galaxies are enhanced out to separations of 15Mpc/h. On scales smaller
than 3Mpc/h the luminosities on galaxy pairs show a tight correlation. A
comparison with the random-field model indicates that galaxy luminosities
depend on the spatial distribution and galaxy-galaxy interactions. Early-type
galaxies are also more strongly correlated, indicating morphological
segregation. The galaxies in the PSCz catalog (Saunders et al. 2000) do not
show significant luminosity segregation. This again illustrates that mainly
early-type galaxies contribute to luminosity segregation. However, based on
several independent investigations we show that the observed luminosity
segregation can not be explained by the morphology-density relation alone.Comment: aastex, emulateapj5, 20 pages, 13 figures, several clarifying
comments added, ApJ accepte
Properties of commonly used calcium phosphate cements in trauma and orthopaedic surgery
Introduction
Half of the population sustains at least one fracture during their
lifetime, and the majority of these fractures heal successfully.
Successful fracture healing requires the following five elements; (i)
osteogenic cells (e.g., osteoblasts), (ii) osteoinductive stimuli (e.g.,
bone morphogenetic proteins); (iii) an osteoconductive matrix;
(iv) adequate blood and nutrient supply, and (v) sufficient
mechanical support. One or more elements can be compromised
due to the existence of a bone defect. Bone defects are
treated with bone grafts in order to avoid insufficient fracture
healing. Insufficient fracture healing is encountered in 5–10% of the
fractures, resulting in delayed union, malunion, or non-union
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