310 research outputs found
Bayesian psychometric scaling
In educational and psychological studies, psychometric methods are involved in the measurement of constructs, and in constructing and validating measurement instruments. Assessment results are typically used to measure student proficiency levels and test characteristics. Recently, Bayesian item response models received considerable attention to analyze test data and to measure latent variables. Bayesian psychometric modeling allows to include prior information about the assessment in addition to information available in the observed response data. An introduction is given to Bayesian psychometric modeling, and it is shown that this approach is very flexible, provides direct estimates of student proficiencies, and depends less on asymptotic results. Various Bayesian item response models are discussed to provide insight in Bayesian psychometric scaling and the Bayesian way of making psychometric inferences. This is done according to a general multilevel modeling approach, where observations are nested in students and items, and students are nested in schools. Different examples are given to illustrate the influence of prior information, the effects of clustered response data following a PISA study, and Bayesian methods for scale construction
Bogoliubov sound speed in periodically modulated Bose-Einstein condensates
We study the Bogoliubov excitations of a Bose-condensed gas in an optical
lattice. Of primary interest is the long wavelength phonon dispersion for both
current-free and current-carrying condensates. We obtain the dispersion
relation by carrying out a systematic expansion of the Bogoliubov equations in
powers of the phonon wave vector. Our result for the current-carrying case
agrees with the one recently obtained by means of a hydrodynamic theory.Comment: 16 pages, no figure
Modulated Amplitude Waves in Bose-Einstein Condensates
We analyze spatio-temporal structures in the Gross-Pitaevskii equation to
study the dynamics of quasi-one-dimensional Bose-Einstein condensates (BECs)
with mean-field interactions. A coherent structure ansatz yields a
parametrically forced nonlinear oscillator, to which we apply Lindstedt's
method and multiple-scale perturbation theory to determine the dependence of
the intensity of periodic orbits (``modulated amplitude waves'') on their wave
number. We explore BEC band structure in detail using Hamiltonian perturbation
theory and supporting numerical simulations.Comment: 5 pages, 4 figs, revtex, final form of paper, to appear in PRE
(forgot to include \bibliography command in last update, so this is a
correction of that; the bibliography is hence present again
Probing the energy bands of a Bose-Einstein condensate in an optical lattice
We simulate three experimental methods which could be realized in the
laboratory to probe the band excitation energies and the momentum distribution
of a Bose-Einstein condensate inside an optical lattice. The values of the
excitation energies obtained in these different methods agree within the
accuracy of the simulation. The meaning of the results in terms of density and
phase deformations is tested by studying the relaxation of a phase-modulated
condensate towards the ground state.Comment: 5 pages, 5 figure
Dynamic splitting of a Bose-Einstein Condensate
We study the dynamic process of splitting a condensate by raising a potential
barrier in the center of a harmonic trap. We use a two-mode model to describe
the phase coherence between the two halves of the condensate. Furthermore, we
explicitly consider the spatial dependence of the mode funtions, which varies
depending on the potential barrier. This allows to get the tunneling coupling
between the two wells and the on-site energy as a function of the barrier
height. Moreover we can get some insight on the collective modes which are
excited by raising the barrier. We describe the internal and external degrees
of freedom by variational ansatz. We distinguish the possible regimes as a
function of the characteristic parameters of the problem and identify the
adiabaticity conditions.Comment: 17 pages, 8 figure
Stability of Repulsive Bose-Einstein Condensates in a Periodic Potential
The cubic nonlinear Schr\"odinger equation with repulsive nonlinearity and an
elliptic function potential models a quasi-one-dimensional repulsive dilute gas
Bose-Einstein condensate trapped in a standing light wave. New families of
stationary solutions are presented. Some of these solutions have neither an
analog in the linear Schr\"odinger equation nor in the integrable nonlinear
Schr\"odinger equation. Their stability is examined using analytic and
numerical methods. All trivial-phase stable solutions are deformations of the
ground state of the linear Schr\"odinger equation. Our results show that a
large number of condensed atoms is sufficient to form a stable, periodic
condensate. Physically, this implies stability of states near the Thomas-Fermi
limit.Comment: 12 pages, 17 figure
Optimization of evaporative cooling towards a large number of Bose-Einstein condensed atoms
We study the optimization of evaporative cooling in trapped bosonic atoms on
the basis of quantum kinetic theory of a Bose gas. The optimized cooling
trajectory for Rb atoms indicates that the acceleration of evaporative
cooling around the transition point of Bose-Einstein condensation is very
effective against loss of trapped atoms caused by three-body recombination. The
number of condensed atoms is largely enhanced by the optimization, more than
two orders of magnitude in our present calculation using relevant experimental
parameters, as compared with the typical value given by the conventional
evaporative cooling where the frequency of radio-frequency magnetic field is
swept exponentially. In addition to this optimized cooling, it is also shown
that highly efficient evaporative cooling can be achieved by an initial
exponential and then a rapid linear sweep of frequency.Comment: 7 pages, REVTeX, 5 eps figures, Phys. Rev A in press (01 Feburuary
2003
Bose-Einstein Condensates in Optical Lattices: Band-Gap Structure and Solitons
We analyze the existence and stability of spatially extended (Bloch-type) and
localized states of a Bose-Einstein condensate loaded into an optical lattice.
In the framework of the Gross-Pitaevskii equation with a periodic potential, we
study the band-gap structure of the matter-wave spectrum in both the linear and
nonlinear regimes. We demonstrate the existence of families of spatially
localized matter-wave gap solitons, and analyze their stability in different
band gaps, for both repulsive and attractive atomic interactions
Nonlinear atom optics and bright gap soliton generation in finite optical lattices
We theoretically investigate the transmission dynamics of coherent matter
wave pulses across finite optical lattices in both the linear and the nonlinear
regimes. The shape and the intensity of the transmitted pulse are found to
strongly depend on the parameters of the incident pulse, in particular its
velocity and density: a clear physical picture for the main features observed
in the numerical simulations is given in terms of the atomic band dispersion in
the periodic potential of the optical lattice. Signatures of nonlinear effects
due the atom-atom interaction are discussed in detail, such as atom optical
limiting and atom optical bistability. For positive scattering lengths, matter
waves propagating close to the top of the valence band are shown to be subject
to modulational instability. A new scheme for the experimental generation of
narrow bright gap solitons from a wide Bose-Einstein condensate is proposed:
the modulational instability is seeded in a controlled way starting from the
strongly modulated density profile of a standing matter wave and the solitonic
nature of the generated pulses is checked from their shape and their
collisional properties
An Integrated TCGA Pan-Cancer Clinical Data Resource to Drive High-Quality Survival Outcome Analytics
For a decade, The Cancer Genome Atlas (TCGA) program collected clinicopathologic annotation data along with multi-platform molecular profiles of more than 11,000 human tumors across 33 different cancer types. TCGA clinical data contain key features representing the democratized nature of the data collection process. To ensure proper use of this large clinical dataset associated with genomic features, we developed a standardized dataset named the TCGA Pan-Cancer Clinical Data Resource (TCGA-CDR), which includes four major clinical outcome endpoints. In addition to detailing major challenges and statistical limitations encountered during the effort of integrating the acquired clinical data, we present a summary that includes endpoint usage recommendations for each cancer type. These TCGA-CDR findings appear to be consistent with cancer genomics studies independent of the TCGA effort and provide opportunities for investigating cancer biology using clinical correlates at an unprecedented scale. Analysis of clinicopathologic annotations for over 11,000 cancer patients in the TCGA program leads to the generation of TCGA Clinical Data Resource, which provides recommendations of clinical outcome endpoint usage for 33 cancer types
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