Inhomogeneous Fermi and quantum spin systems on lattices

We study the thermodynamic properties of a certain type of space-inhomogeneous Fermi and quantum spin systems on lattices. We are particularly interested in the case where the space scale of the inhomogeneities stays macroscopic, but very small as compared to the side-length of the box containing fermions or spins. The present study is however not restricted to "macroscopic inhomogeneities" and also includes the (periodic) microscopic and mesoscopic cases. We prove that - as in the homogeneous case - the pressure is, up to a minus sign, the conservative value of a two-person zero-sum game, named here thermodynamic game. Because of the absence of space symmetries in such inhomogeneous systems, it is not clear from the beginning what kind of object equilibrium states should be in the thermodynamic limit. However, we give rigorous statements on correlations functions for large boxes. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4763465]

Mating system parameters at hierarchical levels of fruits, individuals and populations in the Brazilian insect-pollinated tropical tree, Tabebuia roseo-alba (Bignoniaceae)

For many tree species, mating system analyses have indicated potential variations in the selfing rate and paternity correlation among fruits within individuals, among individuals within populations, among populations, and from one flowering event to another. In this study, we used eight microsatellite markers to investigate mating systems at two hierarchical levels (fruits within individuals and individuals within populations) for the insect pollinated Neotropical tree Tabebuia roseo-alba. We found that T. roseo-alba has a mixed mating system with predominantly outcrossed mating. The outcrossing rates at the population level were similar across two T. roseo-alba populations; however, the rates varied considerably among individuals within populations. The correlated paternity results at different hierarchical levels showed that there is a high probability of shared paternal parentage when comparing seeds within fruits and among fruits within plants and full-sibs occur in much higher proportion within fruits than among fruits. Significant levels of fixation index were found in both populations and biparental inbreeding is believed to be the main cause of the observed inbreeding. The number of pollen donors contributing to mating was low. Furthermore, open-pollinated seeds varied according to relatedness, including half-sibs, full-sibs, self-sibs and self- half-sibs. In both populations, the effective population size within a family (seed-tree and its offspring) was lower than expected for panmictic populations. Thus, seeds for ex situ conservation genetics, progeny tests and reforestation must be collected from a large number of seed-trees to guarantee an adequate effective population in the sample.

Symmetry insights for design of supercomputer network topologies: roots and weights lattices

We present a family of networks whose local interconnection topologies are generated by the root vectors of a semi-simple complex Lie algebra. Cartan classification theorem of those algebras ensures those families of interconnection topologies to be exhaustive. The global arrangement of the network is defined in terms of integer or half-integer weight lattices. The mesh or torus topologies that network millions of processing cores, such as those in the IBM BlueGene series, are the simplest member of that category. The symmetries of the root systems of an algebra, manifested by their Weyl group, lends great convenience for the design and analysis of hardware architecture, algorithms and programs.

Parameter recovery for a skew-normal IRT model under a Bayesian approach: hierarchical framework, prior and kernel sensitivity and sample size

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is an interest in studying latent variables (or latent traits). Usually such latent traits are assumed to be random variables and a convenient distribution is assigned to them. A very common choice for such a distribution has been the standard normal. Recently, Azevedo et al. [Bayesian inference for a skew-normal IRT model under the centred parameterization, Comput. Stat. Data Anal. 55 (2011), pp. 353-365] proposed a skew-normal distribution under the centred parameterization (SNCP) as had been studied in [R. B. Arellano-Valle and A. Azzalini, The centred parametrization for the multivariate skew-normal distribution, J. Multivariate Anal. 99(7) (2008), pp. 1362-1382], to model the latent trait distribution. This approach allows one to represent any asymmetric behaviour concerning the latent trait distribution. Also, they developed a Metropolis-Hastings within the Gibbs sampling (MHWGS) algorithm based on the density of the SNCP. They showed that the algorithm recovers all parameters properly. Their results indicated that, in the presence of asymmetry, the proposed model and the estimation algorithm perform better than the usual model and estimation methods. Our main goal in this paper is to propose another type of MHWGS algorithm based on a stochastic representation (hierarchical structure) of the SNCP studied in [N. Henze, A probabilistic representation of the skew-normal distribution, Scand. J. Statist. 13 (1986), pp. 271-275]. Our algorithm has only one Metropolis-Hastings step, in opposition to the algorithm developed by Azevedo et al., which has two such steps. This not only makes the implementation easier but also reduces the number of proposal densities to be used, which can be a problem in the implementation of MHWGS algorithms, as can be seen in [R.J. Patz and B.W. Junker, A straightforward approach to Markov Chain Monte Carlo methods for item response models, J. Educ. Behav. Stat. 24(2) (1999), pp. 146-178; R. J. Patz and B. W. Junker, The applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses, J. Educ. Behav. Stat. 24(4) (1999), pp. 342-366; A. Gelman, G.O. Roberts, and W.R. Gilks, Efficient Metropolis jumping rules, Bayesian Stat. 5 (1996), pp. 599-607]. Moreover, we consider a modified beta prior (which generalizes the one considered in [3]) and a Jeffreys prior for the asymmetry parameter. Furthermore, we study the sensitivity of such priors as well as the use of different kernel densities for this parameter. Finally, we assess the impact of the number of examinees, number of items and the asymmetry level on the parameter recovery. Results of the simulation study indicated that our approach performed equally as well as that in [3], in terms of parameter recovery, mainly using the Jeffreys prior. Also, they indicated that the asymmetry level has the highest impact on parameter recovery, even though it is relatively small. A real data analysis is considered jointly with the development of model fitting assessment tools. The results are compared with the ones obtained by Azevedo et al. The results indicate that using the hierarchical approach allows us to implement MCMC algorithms more easily, it facilitates diagnosis of the convergence and also it can be very useful to fit more complex skew IRT models.

A decaying factor accounts for contained activity in neuronal networks with no need of hierarchical or modular organization

The mechanisms responsible for containing activity in systems represented by networks are crucial in various phenomena, for example, in diseases such as epilepsy that affect the neuronal networks and for information dissemination in social networks. The first models to account for contained activity included triggering and inhibition processes, but they cannot be applied to social networks where inhibition is clearly absent. A recent model showed that contained activity can be achieved with no need of inhibition processes provided that the network is subdivided into modules (communities). In this paper, we introduce a new concept inspired in the Hebbian theory, through which containment of activity is achieved by incorporating a dynamics based on a decaying activity in a random walk mechanism preferential to the node activity. Upon selecting the decay coefficient within a proper range, we observed sustained activity in all the networks tested, namely, random, Barabasi-Albert and geographical networks. The generality of this finding was confirmed by showing that modularity is no longer needed if the dynamics based on the integrate-and-fire dynamics incorporated the decay factor. Taken together, these results provide a proof of principle that persistent, restrained network activation might occur in the absence of any particular topological structure. This may be the reason why neuronal activity does not spread out to the entire neuronal network, even when no special topological organization exists.

Three-dimensional solitons in cross-combined linear and nonlinear optical lattices

The existence and stability of three-dimensional (3D) solitons, in cross-combined linear and nonlinear optical lattices, are investigated. In particular, with a starting optical lattice (OL) configuration such that it is linear in the x-direction and nonlinear in the y-direction, we consider the z-direction either unconstrained (quasi-2D OL case) or with another linear OL (full 3D case). We perform this study both analytically and numerically: analytically by a variational approach based on a Gaussian ansatz for the soliton wavefunction and numerically by relaxation methods and direct integrations of the corresponding Gross-Pitaevskii equation. We conclude that, while 3D solitons in the quasi-2D OL case are always unstable, the addition of another linear OL in the z-direction allows us to stabilize 3D solitons both for attractive and repulsive mean interactions. From our results, we suggest the possible use of spatial modulations of the nonlinearity in one of the directions as a tool for the management of stable 3D solitons.

Spin-glass behaviour on random lattices

The ground-state phase diagram of an Ising spin-glass model on a random graph with an arbitrary fraction w of ferromagnetic interactions is analysed in the presence of an external field. Using the replica method, and performing an analysis of stability of the replica-symmetric solution, it is shown that w = 1/2, corresponding to an unbiased spin glass, is a singular point in the phase diagram, separating a region with a spin-glass phase (w < 1/2) from a region with spin-glass, ferromagnetic, mixed and paramagnetic phases (w > 1/2).

Why Are Women With Cervical Cancer Not Being Diagnosed in Preinvasive Phase? An Analysis of Risk Factors Using a Hierarchical Model

Objective: To assess the risk factors for delayed diagnosis of uterine cervical lesions. Materials and Methods: This is a case-control study that recruited 178 women at 2 Brazilian hospitals. The cases (n = 74) were composed of women with a late diagnosis of a lesion in the uterine cervix (invasive carcinoma in any stage). The controls (n = 104) were composed of women with cervical lesions diagnosed early on (low-or high-grade intraepithelial lesions). The analysis was performed by means of logistic regression model using a hierarchical model. The socioeconomic and demographic variables were included at level I (distal). Level II (intermediate) included the personal and family antecedents and knowledge about the Papanicolaou test and human papillomavirus. Level III (proximal) encompassed the variables relating to individuals' care for their own health, gynecologic symptoms, and variables relating to access to the health care system. Results: The risk factors for late diagnosis of uterine cervical lesions were age older than 40 years (odds ratio [OR] = 10.4; 95% confidence interval [CI], 2.3-48.4), not knowing the difference between the Papanicolaou test and gynecological pelvic examinations (OR, = 2.5; 95% CI, 1.3-4.9), not thinking that the Papanicolaou test was important (odds ratio [OR], 4.2; 95% CI, 1.3-13.4), and abnormal vaginal bleeding (OR, 15.0; 95% CI, 6.5-35.0). Previous treatment for sexually transmissible disease was a protective factor (OR, 0.3; 95% CI, 0.1-0.8) for delayed diagnosis. Conclusions: Deficiencies in cervical cancer prevention programs in developing countries are not simply a matter of better provision and coverage of Papanicolaou tests. The misconception about the Papanicolaou test is a serious educational problem, as demonstrated by the present study.

Annealed Ising model on hierarchical structures: a transfer matrix approach.

Spin systems in the presence of disorder are described by two sets of degrees of freedom, associated with orientational (spin) and disorder variables, which may be characterized by two distinct relaxation times. Disordered spin models have been mostly investigated in the quenched regime, which is the usual situation in solid state physics, and in which the relaxation time of the disorder variables is much larger than the typical measurement times. In this quenched regime, disorder variables are fixed, and only the orientational variables are duly thermalized. Recent studies in the context of lattice statistical models for the phase diagrams of nematic liquid-crystalline systems have stimulated the interest of going beyond the quenched regime. The phase diagrams predicted by these calculations for a simple Maier-Saupe model turn out to be qualitative different from the quenched case if the two sets of degrees of freedom are allowed to reach thermal equilibrium during the experimental time, which is known as the fully annealed regime. In this work, we develop a transfer matrix formalism to investigate annealed disordered Ising models on two hierarchical structures, the diamond hierarchical lattice (DHL) and the Apollonian network (AN). The calculations follow the same steps used for the analysis of simple uniform systems, which amounts to deriving proper recurrence maps for the thermodynamic and magnetic variables in terms of the generations of the construction of the hierarchical structures. In this context, we may consider different kinds of disorder, and different types of ferromagnetic and anti-ferromagnetic interactions. In the present work, we analyze the effects of dilution, which are produced by the removal of some magnetic ions. The system is treated in a “grand canonical" ensemble. The introduction of two extra fields, related to the concentration of two different types of particles, leads to higher-rank transfer matrices as compared with the formalism for the usual uniform models. Preliminary calculations on a DHL indicate that there is a phase transition for a wide range of dilution concentrations. Ising spin systems on the AN are known to be ferromagnetically ordered at all temperatures; in the presence of dilution, however, there are indications of a disordered (paramagnetic) phase at low concentrations of magnetic ions.

Hierarchical multi-label classification using local neural networks

Hierarchical multi-label classification is a complex classification task where the classes involved in the problem are hierarchically structured and each example may simultaneously belong to more than one class in each hierarchical level. In this paper, we extend our previous works, where we investigated a new local-based classification method that incrementally trains a multi-layer perceptron for each level of the classification hierarchy. Predictions made by a neural network in a given level are used as inputs to the neural network responsible for the prediction in the next level. We compare the proposed method with one state-of-the-art decision-tree induction method and two decision-tree induction methods, using several hierarchical multi-label classification datasets. We perform a thorough experimental analysis, showing that our method obtains competitive results to a robust global method regarding both precision and recall evaluation measures.

Experimental Investigation of Three-Dimensional Single and Double optical Lattices

A complete laser cooling setup was built, with focus on threedimensional near-resonant optical lattices for cesium. These consist of regularly ordered micropotentials, created by the interference of four laser beams. One key feature of optical lattices is an inherent ”Sisyphus cooling” process. It efficiently extracts kinetic energy from the atoms, leading to equilibrium temperatures of a few µK. The corresponding kinetic energy is lower than the depth of the potential wells, so that atoms can be trapped. We performed detailed studies of the cooling processes in optical lattices by using the time-of-flight and absorption-imaging techniques. We investigated the dependence of the equilibrium temperature on the optical lattice parameters, such as detuning, optical potential and lattice geometry. The presence of neighbouring transitions in the cesium hyperfine level structure was used to break symmetries in order to identify, which role “red” and “blue” transitions play in the cooling. We also examined the limits for the cooling process in optical lattices, and the possible difference in steady-state velocity distributions for different directions. Moreover, in collaboration with ´Ecole Normale Sup´erieure in Paris, numerical simulations were performed in order to get more insight in the cooling dynamics of optical lattices. Optical lattices can keep atoms almost perfectly isolated from the environment and have therefore been suggested as a platform for a host of possible experiments aimed at coherent quantum manipulations, such as spin-squeezing and the implementation of quantum logic-gates. We developed a novel way to trap two different cesium ground states in two distinct, interpenetrating optical lattices, and to change the distance between sites of one lattice relative to sites of the other lattice. This is a first step towards the implementation of quantum simulation schemes in optical lattices.

A simple strategy for defining polynomial spline spaces over hierarchical T-meses

[EN]We present a new strategy for constructing spline spaces over hierarchical T-meshes with quad- and octree subdivision scheme. The proposed technique includes some simple rules for inferring local knot vectors to define C 2 -continuous cubic tensor product spline blending functions. Our conjecture is that these rules allow to obtain, for a given T-mesh, a set of linearly independent spline functions with the property that spaces spanned by nested T-meshes are also nested, and therefore, the functions can reproduce cubic polynomials. In order to span spaces with these properties applying the proposed rules, the T-mesh should fulfill the only requirement of being a 0- balanced mesh...

Stellar Relics of the hierarchical assembly of the Galaxy

This PhD Thesis is part of a long-term wide research project, carried out by the "Osservatorio Astronomico di Bologna (INAF-OABO)", that has as primary goal the comprehension and reconstruction of formation mechanism of galaxies and their evolution history. There is now substantial evidence, both from theoretical and observational point of view, in favor of the hypothesis that the halo of our Galaxy has been at least partially, built up by the progressive accretion of small fragments, similar in nature to the present day dwarf galaxies of the Local Group. In this context, the photometric and spectroscopic study of systems which populate the halo of our Galaxy (i.e. dwarf spheroidal galaxy, tidal streams, massive globular cluster, etc) permits to discover, not only the origin and behaviour of these systems, but also the structure of our Galactic halo, combined with its formation history. In fact, the study of the population of these objects and also of their chemical compositions, age, metallicities and velocity dispersion, permit us not only an improvement in the understanding of the mechanisms that govern the Galactic formation, but also a valid indirect test for cosmological model itself. Specifically, in this Thesis we provided a complete characterization of the tidal Stream of the Sagittarius dwarf spheroidal galaxy, that is the most striking example of the process of tidal disruption and accretion of a dwarf satellite in to our Galaxy. Using Red Clump stars, extracted from the catalogue of the Sloan Digital Sky Survey (SDSS) we obtained an estimate of the distance, the depth along the line of sight and of the number density for each detected portion of the Stream (and more in general for each detected structure along our line of sight). Moreover comparing the relative number (i.e. the ratio) of Blue Horizontal Branch stars and Red Clump stars (the two features are tracers of different age/different metallicity populations) in the main body of the galaxy and in the Stream, in order to verify the presence of an age-metallicity gradient along the Stream. We also report the detection of a population of Red Clump stars probably associated with the recently discovered Bootes III stellar system. Finally, we also present the results of a survey of radial velocities over a wide region, extending from r ~ 10' out to r ~ 80' within the massive star cluster Omega Centauri. The survey was performed with FLAMES@VLT, to study the velocity dispersion profile in the outer regions of this stellar system. All the results presented in this Thesis, have already been published in refeered journals.

Constructing correlated spin states with neutral atoms in optical lattices

This thesis reports on the experimental investigation of controlled spin dependent interactions in a sample of ultracold Rubidium atoms trapped in a periodic optical potential. In such a situation, the most basic interaction between only two atoms at one common potential well, forming a micro laboratory for this atom pair, can be investigated. Spin dependent interactions between the atoms can lead to an intriguing time evolution of the system. In this work, we present two examples of such spin interaction induced dynamics. First, we have been able to observe and control a coherent spin changing interaction. Second, we have achieved to examine and manipulate an interaction induced time evolution of the relative phase of a spin 1/2-system, both in the case of particle pairs and in the more general case of N interacting particles. The first part of this thesis elucidates the spin-changing interaction mechanism underlying many fascinating effects resulting from interacting spins at ultracold temperatures. This process changes the spin states of two colliding particles, while preserving total magnetization. If initial and final states have almost equal energy, this process is resonant and leads to large amplitude oscillations between different spin states. The measured coupling parameters of such a process allow to precisely infer atomic scattering length differences, that e.g. determine the nature of the magnetic ground state of the hyperfine states in Rubidium. Moreover, a method to tune the spin oscillations at will based on the AC-Zeeman effect has been implemented. This allowed us to use resonant spin changing collisions as a quantitative and non-destructive particle pair probe in the optical lattice. This led to a series of experiments shedding light on the Bosonic superfluid to Mott insulator transition. In a second series of experiments we have been able to coherently manipulate the interaction induced time evolution of the relative phase in an ensemble of spin 1/2-systems. For two particles, interactions can lead to an entanglement oscillation of the particle pair. For the general case of N interacting particles, the ideal time evolution leads to the creation of spin squeezed states and even Schrödinger cat states. In the experiment we have been able to control the underlying interactions by a Feshbach resonance. For particle pairs we could directly observe the entanglement oscillations. For the many particle case we have been able to observe and reverse the interaction induced dispersion of the relative phase. The presented results demonstrate how correlated spin states can be engineered through control of atomic interactions. Moreover, the results point towards the possibility to simulate quantum magnetism phenomena with ultracold atoms in optical traps, and to realize and analyze many novel quantum spin states which have not been experimentally realized so far.

Probing strongly correlated states of ultracold atoms in optical lattices

This thesis describes experiments which investigate ultracold atom ensembles in an optical lattice. Such quantum gases are powerful models for solid state physics. Several novel methods are demonstrated that probe the special properties of strongly correlated states in lattice potentials. Of these, quantum noise spectroscopy reveals spatial correlations in such states, which are hidden when using the usual methods of probing atomic gases. Another spectroscopic technique makes it possible to demonstrate the existence of a shell structure of regions with constant densities. Such coexisting phases separated by sharp boundaries had been theoretically predicted for the Mott insulating state. The tunneling processes in the optical lattice in the strongly correlated regime are probed by preparing the ensemble in an optical superlattice potential. This allows the time-resolved observation of the tunneling dynamics, and makes it possible to directly identify correlated tunneling processes.