112,086 research outputs found
Density matrix interpretation of solutions of Lie-Nambu equations
The spectrum of a density matrix is conserved by a Lie-Nambu
dynamics if is a self-adjoint and Hilbert-Schmidt solution of a
nonlinear triple-bracket equation. This generalizes to arbitrary separable
(positive- and indefinite-metric) Hilbert spaces the previous result which was
valid for finite-dimensional Hilbert spaces.Comment: final version, to be published in Phys. Lett. A 239 No. 6, pp.
353-358 (16 March 1998
Clustering student skill set profiles in a unit hypercube using mixtures of multivariate betas
<br>This paper presents a finite mixture of multivariate betas as a new model-based clustering method tailored to applications where the feature space is constrained to the unit hypercube. The mixture component densities are taken to be conditionally independent, univariate unimodal beta densities (from the subclass of reparameterized beta densities given by Bagnato and Punzo 2013). The EM algorithm used to fit this mixture is discussed in detail, and results from both this beta mixture model and the more standard Gaussian model-based clustering are presented for simulated skill mastery data from a common cognitive diagnosis model and for real data from the Assistment System online mathematics tutor (Feng et al 2009). The multivariate beta mixture appears to outperform the standard Gaussian model-based clustering approach, as would be expected on the constrained space. Fewer components are selected (by BIC-ICL) in the beta mixture than in the Gaussian mixture, and the resulting clusters seem more reasonable and interpretable.</br>
<br>This article is in technical report form, the final publication is available at http://www.springerlink.com/openurl.asp?genre=article &id=doi:10.1007/s11634-013-0149-z</br>
Hamiltonian Coupling of Electromagnetic Field and Matter
Reversible part of evolution equations of physical systems is often generated
by a Poisson bracket. We discuss geometric means of construction of Poisson
brackets and their mutual coupling (direct, semidirect and matched-pair
products) as well as projections of Poisson brackets to less detailed Poisson
brackets. This way the Hamiltonian coupling between transport of mixtures and
electrodynamics is elucidated
A robust method for cluster analysis
Let there be given a contaminated list of n R^d-valued observations coming
from g different, normally distributed populations with a common covariance
matrix. We compute the ML-estimator with respect to a certain statistical model
with n-r outliers for the parameters of the g populations; it detects outliers
and simultaneously partitions their complement into g clusters. It turns out
that the estimator unites both the minimum-covariance-determinant rejection
method and the well-known pooled determinant criterion of cluster analysis. We
also propose an efficient algorithm for approximating this estimator and study
its breakdown points for mean values and pooled SSP matrix.Comment: Published at http://dx.doi.org/10.1214/009053604000000940 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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