45,056 research outputs found
Optimal Calibration of PET Crystal Position Maps Using Gaussian Mixture Models
A method is developed for estimating optimal PET gamma-ray detector crystal position maps, for arbitrary crystal configurations, based on a binomial distribution model for scintillation photon arrival. The approach is based on maximum likelihood estimation of Gaussian mixture model parameters using crystal position histogram data, with determination of the position map taken from the posterior probability boundaries between mixtures. This leads to minimum probability of error crystal identification under the assumed model
Nonlinear stability and ergodicity of ensemble based Kalman filters
The ensemble Kalman filter (EnKF) and ensemble square root filter (ESRF) are
data assimilation methods used to combine high dimensional, nonlinear dynamical
models with observed data. Despite their widespread usage in climate science
and oil reservoir simulation, very little is known about the long-time behavior
of these methods and why they are effective when applied with modest ensemble
sizes in large dimensional turbulent dynamical systems. By following the basic
principles of energy dissipation and controllability of filters, this paper
establishes a simple, systematic and rigorous framework for the nonlinear
analysis of EnKF and ESRF with arbitrary ensemble size, focusing on the
dynamical properties of boundedness and geometric ergodicity. The time uniform
boundedness guarantees that the filter estimate will not diverge to machine
infinity in finite time, which is a potential threat for EnKF and ESQF known as
the catastrophic filter divergence. Geometric ergodicity ensures in addition
that the filter has a unique invariant measure and that initialization errors
will dissipate exponentially in time. We establish these results by introducing
a natural notion of observable energy dissipation. The time uniform bound is
achieved through a simple Lyapunov function argument, this result applies to
systems with complete observations and strong kinetic energy dissipation, but
also to concrete examples with incomplete observations. With the Lyapunov
function argument established, the geometric ergodicity is obtained by
verifying the controllability of the filter processes; in particular, such
analysis for ESQF relies on a careful multivariate perturbation analysis of the
covariance eigen-structure.Comment: 38 page
Thermal and cryogenic design study for space infrared telescope facility (SIRTF)
A study was conducted to determine the ability of an all superfluid helium design to meet the performance requirements of background limited to 200 micrometer, and a two year lifetime for a one meter class free flying infrared observatory. Both a 98 deg and 28.5 deg inclination orbits were examined, and aperture shade designs were developed for both orbits. A unique forebaffle cooling design significantly reduces the sensitivity to aperture heat loads. With certain restrictions on observing modes, the study determined that an all superfluid helium Dewar will meet the temperature and lifetime requirements. A dual cryogen SFHe/SH2 system was also investigated for the 28.5 deg orbit and found to provide a more constant forebaffle temperature but with only a slight improvement in lifetime
Büchwald-Hartwig reaction applied to synthesis of new luminescent liquid crystal triarylamines derived from isoxazoles
© 2015 Taylor & Francis Group, LLC. The present work describes the synthesis and characterization of novel series of triarylamines isoxazoles (TAA) addressed to the organic photovoltaic materials. Diarylisoxazoles were synthesized by sequential [3+2] 1,3-dipolar cycloaddition reaction between arylnitrile oxides and selected arylalkenes followed by MnO2-oxidation. Isoxazoles were coupled to diarylamines by Büchwald-Hartwig reaction to afford desired compounds 6a-k. Some TAA display liquid-crystalline behaviour and UV-Vis absorption and fluorescence emission were analysed for all samples of TAA 6a-k
Well-Posedness And Accuracy Of The Ensemble Kalman Filter In Discrete And Continuous Time
The ensemble Kalman filter (EnKF) is a method for combining a dynamical model
with data in a sequential fashion. Despite its widespread use, there has been
little analysis of its theoretical properties. Many of the algorithmic
innovations associated with the filter, which are required to make a useable
algorithm in practice, are derived in an ad hoc fashion. The aim of this paper
is to initiate the development of a systematic analysis of the EnKF, in
particular to do so in the small ensemble size limit. The perspective is to
view the method as a state estimator, and not as an algorithm which
approximates the true filtering distribution. The perturbed observation version
of the algorithm is studied, without and with variance inflation. Without
variance inflation well-posedness of the filter is established; with variance
inflation accuracy of the filter, with resepct to the true signal underlying
the data, is established. The algorithm is considered in discrete time, and
also for a continuous time limit arising when observations are frequent and
subject to large noise. The underlying dynamical model, and assumptions about
it, is sufficiently general to include the Lorenz '63 and '96 models, together
with the incompressible Navier-Stokes equation on a two-dimensional torus. The
analysis is limited to the case of complete observation of the signal with
additive white noise. Numerical results are presented for the Navier-Stokes
equation on a two-dimensional torus for both complete and partial observations
of the signal with additive white noise
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