1,078 research outputs found
Generalizations of Ripley's K-function with Application to Space Curves
The intensity function and Ripley's K-function have been used extensively in
the literature to describe the first and second moment structure of spatial
point sets. This has many applications including describing the statistical
structure of synaptic vesicles. Some attempts have been made to extend Ripley's
K-function to curve pieces. Such an extension can be used to describe the
statistical structure of muscle fibers and brain fiber tracks. In this paper,
we take a computational perspective and construct new and very general variants
of Ripley's K-function for curves pieces, surface patches etc. We discuss the
method from [Chiu, Stoyan, Kendall, & Mecke 2013] and compare it with our
generalizations theoretically, and we give examples demonstrating the
difference in their ability to separate sets of curve pieces.Comment: 9 pages & 8 figure
Creation and characterization of vortex clusters in atomic Bose-Einstein condensates
We show that a moving obstacle, in the form of an elongated paddle, can
create vortices that are dispersed, or induce clusters of like-signed vortices
in 2D Bose-Einstein condensates. We propose new statistical measures of
clustering based on Ripley's K-function which are suitable to the small size
and small number of vortices in atomic condensates, which lack the huge number
of length scales excited in larger classical and quantum turbulent fluid
systems. The evolution and decay of clustering is analyzed using these
measures. Experimentally it should prove possible to create such an obstacle by
a laser beam and a moving optical mask. The theoretical techniques we present
are accessible to experimentalists and extend the current methods available to
induce 2D quantum turbulence in Bose-Einstein condensates.Comment: 9 pages, 9 figure
Simulation of truncated normal variables
We provide in this paper simulation algorithms for one-sided and two-sided
truncated normal distributions. These algorithms are then used to simulate
multivariate normal variables with restricted parameter space for any
covariance structure.Comment: This 1992 paper appeared in 1995 in Statistics and Computing and the
gist of it is contained in Monte Carlo Statistical Methods (2004), but I
receive weekly requests for reprints so here it is
Topological Homogeneity for Electron Microscopy Images
In this paper, the concept of homogeneity is defined, from a
topological perspective, in order to analyze how uniform is the material
composition in 2D electron microscopy images. Topological multiresolution
parameters are taken into account to obtain better results than
classical techniques.Ministerio de EconomÃa y Competitividad MTM2016-81030-PMinisterio de EconomÃa y Competitividad TEC2012-37868-C04-0
Extracting galactic binary signals from the first round of Mock LISA Data Challenges
We report on the performance of an end-to-end Bayesian analysis pipeline for
detecting and characterizing galactic binary signals in simulated LISA data.
Our principal analysis tool is the Blocked-Annealed Metropolis Hasting (BAM)
algorithm, which has been optimized to search for tens of thousands of
overlapping signals across the LISA band. The BAM algorithm employs Bayesian
model selection to determine the number of resolvable sources, and provides
posterior distribution functions for all the model parameters. The BAM
algorithm performed almost flawlessly on all the Round 1 Mock LISA Data
Challenge data sets, including those with many highly overlapping sources. The
only misses were later traced to a coding error that affected high frequency
sources. In addition to the BAM algorithm we also successfully tested a Genetic
Algorithm (GA), but only on data sets with isolated signals as the GA has yet
to be optimized to handle large numbers of overlapping signals.Comment: 13 pages, 4 figures, submitted to Proceedings of GWDAW-11 (Berlin,
Dec. '06
Markov basis and Groebner basis of Segre-Veronese configuration for testing independence in group-wise selections
We consider testing independence in group-wise selections with some
restrictions on combinations of choices. We present models for frequency data
of selections for which it is easy to perform conditional tests by Markov chain
Monte Carlo (MCMC) methods. When the restrictions on the combinations can be
described in terms of a Segre-Veronese configuration, an explicit form of a
Gr\"obner basis consisting of moves of degree two is readily available for
performing a Markov chain. We illustrate our setting with the National Center
Test for university entrance examinations in Japan. We also apply our method to
testing independence hypotheses involving genotypes at more than one locus or
haplotypes of alleles on the same chromosome.Comment: 25 pages, 5 figure
Longitudinal Peer Network Data in Higher Education
This chapter employs a longitudinal social network approach to research small group teaching in higher education. Longitudinal social network analyses can provide in-depth understanding of the social dynamics in small groups. Specifically, it is possible to investigate and disentangle the processes by which students make or break social connections with peers and are influenced by them, as well as how those processes relate to group compositions and personal attributes, such as achievement level. With advanced methods for modelling longitudinal social networks, researchers can identify social processes affecting small group teaching and learning
Using Markov chain Monte Carlo methods for estimating parameters with gravitational radiation data
We present a Bayesian approach to the problem of determining parameters for
coalescing binary systems observed with laser interferometric detectors. By
applying a Markov Chain Monte Carlo (MCMC) algorithm, specifically the Gibbs
sampler, we demonstrate the potential that MCMC techniques may hold for the
computation of posterior distributions of parameters of the binary system that
created the gravity radiation signal. We describe the use of the Gibbs sampler
method, and present examples whereby signals are detected and analyzed from
within noisy data.Comment: 21 pages, 10 figure
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