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 $^{87}$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