4,022 research outputs found
A Block Minorization--Maximization Algorithm for Heteroscedastic Regression
The computation of the maximum likelihood (ML) estimator for heteroscedastic
regression models is considered. The traditional Newton algorithms for the
problem require matrix multiplications and inversions, which are bottlenecks in
modern Big Data contexts. A new Big Data-appropriate minorization--maximization
(MM) algorithm is considered for the computation of the ML estimator. The MM
algorithm is proved to generate monotonically increasing sequences of
likelihood values and to be convergent to a stationary point of the
log-likelihood function. A distributed and parallel implementation of the MM
algorithm is presented and the MM algorithm is shown to have differing time
complexity to the Newton algorithm. Simulation studies demonstrate that the MM
algorithm improves upon the computation time of the Newton algorithm in some
practical scenarios where the number of observations is large
Quantum Statistical Calculations and Symplectic Corrector Algorithms
The quantum partition function at finite temperature requires computing the
trace of the imaginary time propagator. For numerical and Monte Carlo
calculations, the propagator is usually split into its kinetic and potential
parts. A higher order splitting will result in a higher order convergent
algorithm. At imaginary time, the kinetic energy propagator is usually the
diffusion Greens function. Since diffusion cannot be simulated backward in
time, the splitting must maintain the positivity of all intermediate time
steps. However, since the trace is invariant under similarity transformations
of the propagator, one can use this freedom to "correct" the split propagator
to higher order. This use of similarity transforms classically give rises to
symplectic corrector algorithms. The split propagator is the symplectic kernel
and the similarity transformation is the corrector. This work proves a
generalization of the Sheng-Suzuki theorem: no positive time step propagators
with only kinetic and potential operators can be corrected beyond second order.
Second order forward propagators can have fourth order traces only with the
inclusion of an additional commutator. We give detailed derivations of four
forward correctable second order propagators and their minimal correctors.Comment: 9 pages, no figure, corrected typos, mostly missing right bracket
Any-order propagation of the nonlinear Schroedinger equation
We derive an exact propagation scheme for nonlinear Schroedinger equations.
This scheme is entirely analogous to the propagation of linear Schroedinger
equations. We accomplish this by defining a special operator whose algebraic
properties ensure the correct propagation. As applications, we provide a simple
proof of a recent conjecture regarding higher-order integrators for the
Gross-Pitaevskii equation, extend it to multi-component equations, and to a new
class of integrators.Comment: 10 pages, no figures, submitted to Phys. Rev.
Spontaneous radiative decay of translational levels of an atom near a dielectric surface
We study spontaneous radiative decay of translational levels of an atom in
the vicinity of a semi-infinite dielectric. We systematically derive the
microscopic dynamical equations for the spontaneous decay process. We calculate
analytically and numerically the radiative linewidths and the spontaneous
transition rates for the translational levels. The roles of the interference
between the emitted and reflected fields and of the transmission into the
evanescent modes are clearly identified. Our numerical calculations for the
silica--cesium interaction show that the radiative linewidths of the bound
excited levels with large enough but not too large vibrational quantum numbers
are moderately enhanced by the emission into the evanescent modes and those for
the deep bound levels are substantially reduced by the surface-induced red
shift of the transition frequency
Calibration of the Ames Anechoic Facility. Phase 1: Short range plan
A calibration was made of the acoustic and aerodynamic characteristics of a small, open-jet wind tunnel in an anechoic room. The jet nozzle was 102 mm diameter and was operated subsonically. The anechoic-room dimensions were 7.6 m by 5.5 m by 3.4 m high (wedge tip to wedge tip). Noise contours in the chamber were determined by various jet speeds and exhaust collector positions. The optimum nozzle/collector separation from an acoustic standpoint was 2.1 m. Jet velocity profiles and turbulence levels were measured using pressure probes and hot wires. The jet was found to be symmetric, with no unusual characteristics. The turbulence measurements were hampered by oil mist contamination of the airflow
Infrasonic backpulsed membrane cleaning micro-and ultrafiltration membranes fouled with alumina and yeast
Membrane fouling is universally considered to be one of the most critical problems in the wider application of membrane filtration. In this research microfiltration membranes were fouled during a cross-flow filtration process, using yeast and alumina suspensions in a flat cell. Infrasonic backpulsing directly into the permeate space was then used to clean the membrane, using both permeate water and soap solutions. Ultrasonic time domain reflectometry (UTDR) was used to detect and measure the growth of fouling on membrane surfaces, during the filtration and cleaning processes. The objective of this work was to examine the efficiency of back-pulse cleaning, using different combinations of membrane materials and foulants, in flat cells. The results show that a flux value of between 60% and 95% of the clean water value can be recovered after cleaning, by using a sequence of three 6.7 Hz backpulses, each pulse being 35 s long with a peak amplitude of about 140 kPa
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