Variational approximation for mixtures of linear mixed models

Mixtures of linear mixed models (MLMMs) are useful for clustering grouped data and can be estimated by likelihood maximization through the EM algorithm. The conventional approach to determining a suitable number of components is to compare different mixture models using penalized log-likelihood criteria such as BIC.We propose fitting MLMMs with variational methods which can perform parameter estimation and model selection simultaneously. A variational approximation is described where the variational lower bound and parameter updates are in closed form, allowing fast evaluation. A new variational greedy algorithm is developed for model selection and learning of the mixture components. This approach allows an automatic initialization of the algorithm and returns a plausible number of mixture components automatically. In cases of weak identifiability of certain model parameters, we use hierarchical centering to reparametrize the model and show empirically that there is a gain in efficiency by variational algorithms similar to that in MCMC algorithms. Related to this, we prove that the approximate rate of convergence of variational algorithms by Gaussian approximation is equal to that of the corresponding Gibbs sampler which suggests that reparametrizations can lead to improved convergence in variational algorithms as well.Comment: 36 pages, 5 figures, 2 tables, submitted to JCG

Towards the characterization of individual users through Web analytics

We perform an analysis of the way individual users navigate in the Web. We focus primarily in the temporal patterns of they return to a given page. The return probability as a function of time as well as the distribution of time intervals between consecutive visits are measured and found to be independent of the level of activity of single users. The results indicate a rich variety of individual behaviors and seem to preclude the possibility of defining a characteristic frequency for each user in his/her visits to a single site.Comment: 8 pages, 4 figures. To appear in Proceeding of Complex'0

Two-domains bulklike Fermi surface of Ag films deposited onto Si(111)-(7x7)

Thick metallic silver films have been deposited onto Si(111)-(7x7) substrates at room temperature. Their electronic properties have been studied by using angle resolved photoelectron spectroscopy (ARPES). In addition to the electronic band dispersion along the high-symmetry directions, the Fermi surface topology of the grown films has been investigated. Using ARPES, the spectral weight distribution at the Fermi level throughout large portions of the reciprocal space has been determined at particular perpendicular electron-momentum values. Systematically, the contours of the Fermi surface of these films reflected a sixfold symmetry instead of the threefold symmetry of Ag single crystal. This loss of symmetry has been attributed to the fact that these films appear to be composed by two sets of domains rotated 60$^o$ from each other. Extra, photoemission features at the Fermi level were also detected, which have been attributed to the presence of surface states and \textit{sp}-quantum states. The dimensionality of the Fermi surface of these films has been analyzed studying the dependence of the Fermi surface contours with the incident photon energy. The behavior of these contours measured at particular points along the Ag $\Gamma$L high-symmetry direction puts forward the three-dimensional character of the electronic structure of the films investigated.Comment: 10 pages, 12 figures, submitted to Physical Review

Geometric Phase: a Diagnostic Tool for Entanglement

Using a kinematic approach we show that the non-adiabatic, non-cyclic, geometric phase corresponding to the radiation emitted by a three level cascade system provides a sensitive diagnostic tool for determining the entanglement properties of the two modes of radiation. The nonunitary, noncyclic path in the state space may be realized through the same control parameters which control the purity/mixedness and entanglement. We show analytically that the geometric phase is related to concurrence in certain region of the parameter space. We further show that the rate of change of the geometric phase reveals its resilience to fluctuations only for pure Bell type states. Lastly, the derivative of the geometric phase carries information on both purity/mixedness and entanglement/separability.Comment: 13 pages 6 figure

Exploring morphological correlations among H2CO, 12CO, MSX and continuum mappings

There are relatively few H2CO mappings of large-area giant molecular cloud (GMCs). H2CO absorption lines are good tracers for low-temperature molecular clouds towards star formation regions. Thus, the aim of the study was to identify H2CO distributions in ambient molecular clouds. We investigated morphologic relations among 6-cm continuum brightness temperature (CBT) data and H2CO (111-110; Nanshan 25-m radio telescope), 12CO (1--0; 1.2-m CfA telescope) and midcourse space experiment (MSX) data, and considered the impact of background components on foreground clouds. We report simultaneous 6-cm H2CO absorption lines and H110\alpha radio recombination line observations and give several large-area mappings at 4.8 GHz toward W49 (50'\times50'), W3 (70'\times90'), DR21/W75 (60'\times90') and NGC2024/NGC2023 (50'\times100') GMCs. By superimposing H2CO and 12CO contours onto the MSX color map, we can compare correlations. The resolution for H2CO, 12CO and MSX data was about 10', 8' and 18.3", respectively. Comparison of H2CO and 12CO contours, 8.28-\mu m MSX colorscale and CBT data revealed great morphological correlation in the large area, although there are some discrepancies between 12CO and H2CO peaks in small areas. The NGC2024/NGC2023 GMC is a large area of HII regions with a high CBT, but a H2CO cloud to the north is possible against the cosmic microwave background. A statistical diagram shows that 85.21% of H2CO absorption lines are distributed in the intensity range from -1.0 to 0 Jy and the \Delta V range from 1.206 to 5 km/s.Comment: 18 pages, 22 figures, 5 tables. Accepted to be published in Astrophysics and Space Scienc

Negatively Charged Excitons and Photoluminescence in Asymmetric Quantum Well

We study photoluminescence (PL) of charged excitons ($X^-$) in narrow asymmetric quantum wells in high magnetic fields B. The binding of all $X^-$ states strongly depends on the separation $\delta$ of electron and hole layers. The most sensitive is the ``bright'' singlet, whose binding energy decreases quickly with increasing $\delta$ even at relatively small B. As a result, the value of B at which the singlet--triplet crossing occurs in the $X^-$ spectrum also depends on $\delta$ and decreases from 35 T in a symmetric 10 nm GaAs well to 16 T for $\delta=0.5$ nm. Since the critical values of $\delta$ at which different $X^-$ states unbind are surprisingly small compared to the well width, the observation of strongly bound $X^-$ states in an experimental PL spectrum implies virtually no layer displacement in the sample. This casts doubt on the interpretation of PL spectra of heterojunctions in terms of $X^-$ recombination

Hydrodynamic Synchronisation of Model Microswimmers

We define a model microswimmer with a variable cycle time, thus allowing the possibility of phase locking driven by hydrodynamic interactions between swimmers. We find that, for extensile or contractile swimmers, phase locking does occur, with the relative phase of the two swimmers being, in general, close to 0 or pi, depending on their relative position and orientation. We show that, as expected on grounds of symmetry, self T-dual swimmers, which are time-reversal covariant, do not phase-lock. We also discuss the phase behaviour of a line of tethered swimmers, or pumps. These show oscillations in their relative phases reminiscent of the metachronal waves of cilia.Comment: 17 pages, 8 figure

Number--conserving model for boson pairing

An independent pair ansatz is developed for the many body wavefunction of dilute Bose systems. The pair correlation is optimized by minimizing the expectation value of the full hamiltonian (rather than the truncated Bogoliubov one) providing a rigorous energy upper bound. In contrast with the Jastrow model, hypernetted chain theory provides closed-form exactly solvable equations for the optimized pair correlation. The model involves both condensate and coherent pairing with number conservation and kinetic energy sum rules satisfied exactly and the compressibility sum rule obeyed at low density. We compute, for bulk boson matter at a given density and zero temperature, (i) the two--body distribution function, (ii) the energy per particle, (iii) the sound velocity, (iv) the chemical potential, (v) the momentum distribution and its condensate fraction and (vi) the pairing function, which quantifies the ODLRO resulting from the structural properties of the two--particle density matrix. The connections with the low--density expansion and Bogoliubov theory are analyzed at different density values, including the density and scattering length regime of interest of trapped-atoms Bose--Einstein condensates. Comparison with the available Diffusion Monte Carlo results is also made.Comment: 21 pages, 12 figure

Electrical transport studies of quench condensed Bi films at the initial stage of film growth: Structural transition and the possible formation of electron droplets

The electrical transport properties of amorphous Bi films prepared by sequential quench deposition have been studied in situ. A superconductor-insulator (S-I) transition was observed as the film was made increasingly thicker, consistent with previous studies. Unexpected behavior was found at the initial stage of film growth, a regime not explored in detail prior to the present work. As the temperature was lowered, a positive temperature coefficient of resistance (dR/dT > 0) emerged, with the resistance reaching a minimum before the dR/dT became negative again. This behavior was accompanied by a non-linear and asymmetric I-V characteristic. As the film became thicker, conventional variable-range hopping (VRH) was recovered. We attribute the observed crossover in the electrical transport properties to an amorphous to granular structural transition. The positive dR/dT found in the amorphous phase of Bi formed at the initial stage of film growth was qualitatively explained by the formation of metallic droplets within the electron glass.Comment: 7 pages, 6 figure

Origin of strange metallic phase in cuprate superconductors

The origin of strange metallic phase is shown to exist due to these two conditions---(i) the electrons are strongly interacting such that there are no band and Mott-Hubbard gaps, and (ii) the electronic energy levels are crossed in such a way that there is an electronic energy gap between two energy levels associated to two different wave functions. The theory is also exploited to explain (i) the upward- and downward-shifts in the $T$-linear resistivity curves, and (ii) the spectral weight transfer observed in the soft X-ray absorption spectroscopic measurements of the La-Sr-Cu-O Mott insulator.Comment: To be published in J. Supercond. Nov. Mag