Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives

We generalise the construction of fuzzy CP^N in a manner that allows us to access all noncommutative equivariant complex vector bundles over this space. We give a simplified construction of polarization tensors on S^2 that generalizes to complex projective space, identify Laplacians and natural noncommutative covariant derivative operators that map between the modules that describe noncommuative sections. In the process we find a natural generalization of the Schwinger-Jordan construction to su(n) and identify composite oscillators that obey a Heisenberg algebra on an appropriate Fock space.Comment: 34 pages, v2 contains minor corrections to the published versio

How should a spatial-coverage sample design for a geostatistical soil survey be supplemented to support estimation of spatial covariance parameters?

We use an expression for the error variance of geostatistical predictions, which includes the effect of uncertainty in the spatial covariance parameters, to examine the performance of sample designs in which a proportion of the total number of observations are distributed according to a spatial coverage design, and the remaining observations are added at supplementary close locations. This expression has been used in previous studies on numerical optimization of spatial sampling, the objective of this study was to use it to discover simple rules of thumb for practical geostatistical sampling. Results for a range of sample sizes and contrasting properties of the underlying random variables show that there is an improvement on adding just a few sample points and close pairs, and a rather slower increase in the prediction error variance as the proportion of sample points allocated in this way is increased above 10 to 20% of the total sample size. One may therefore propose a rule of thumb that, for a fixed sample size, 90% of sample sites are distributed according to a spatial coverage design, and 10% are then added at short distances from sites in the larger subset to support estimation of spatial covariance parameters

Fuzzy Scalar Field Theory as a Multitrace Matrix Model

We develop an analytical approach to scalar field theory on the fuzzy sphere based on considering a perturbative expansion of the kinetic term. This expansion allows us to integrate out the angular degrees of freedom in the hermitian matrices encoding the scalar field. The remaining model depends only on the eigenvalues of the matrices and corresponds to a multitrace hermitian matrix model. Such a model can be solved by standard techniques as e.g. the saddle-point approximation. We evaluate the perturbative expansion up to second order and present the one-cut solution of the saddle-point approximation in the large N limit. We apply our approach to a model which has been proposed as an appropriate regularization of scalar field theory on the plane within the framework of fuzzy geometry.Comment: 1+25 pages, replaced with published version, minor improvement

Determination of perchlorate in infant formula by isotope dilution ion chromatography/tandem mass spectrometry

A sensitive and selective isotope dilution ion chromatography/tandem mass spectrometry (ID IC-MS/MS) method was developed and validated for the determination of perchlorate in infant formula. The perchlorate was extracted from infant formula by using 20 ml of methanol and 5 ml of 1% acetic acid. All samples were spiked with 18O4 isotope-labelled perchlorate internal standard prior to extraction. After purification on a graphitised carbon solid-phase extraction column, the extracts were injected into an ion chromatography system equipped with an Ionpac AS20 column for separation of perchlorate from other anions. The presence of perchlorate in samples was quantified by isotope dilution mass spectrometry. Analysis of both perchlorate and its isotope-labelled internal standard was carried out on a Waters Quattro Ultima triple quadrupole mass spectrometer operating in a multiple reaction monitoring (MRM) negative ionisation mode. The method was validated for linearity and range, accuracy, precision, sensitivity, and matrix effects. The limit of quantification (LOQ) was 0.4 μg 1−1 for liquid infant formula and 0.95 μg kg−1 for powdered infant formula. The recovery ranged from 94% to 110% with an average of 98%. This method was used to analyse 39 infant formula, and perchlorate concentrations ranging from <LOQ to 13.5 μg 1−1

Hierarchical Gaussian process mixtures for regression

As a result of their good performance in practice and their desirable analytical properties, Gaussian process regression models are becoming increasingly of interest in statistics, engineering and other fields. However, two major problems arise when the model is applied to a large data-set with repeated measurements. One stems from the systematic heterogeneity among the different replications, and the other is the requirement to invert a covariance matrix which is involved in the implementation of the model. The dimension of this matrix equals the sample size of the training data-set. In this paper, a Gaussian process mixture model for regression is proposed for dealing with the above two problems, and a hybrid Markov chain Monte Carlo (MCMC) algorithm is used for its implementation. Application to a real data-set is reported

Numerical simulations of a non-commutative theory: the scalar model on the fuzzy sphere

We address a detailed non-perturbative numerical study of the scalar theory on the fuzzy sphere. We use a novel algorithm which strongly reduces the correlation problems in the matrix update process, and allows the investigation of different regimes of the model in a precise and reliable way. We study the modes associated to different momenta and the role they play in the ``striped phase'', pointing out a consistent interpretation which is corroborated by our data, and which sheds further light on the results obtained in some previous works. Next, we test a quantitative, non-trivial theoretical prediction for this model, which has been formulated in the literature: The existence of an eigenvalue sector characterised by a precise probability density, and the emergence of the phase transition associated with the opening of a gap around the origin in the eigenvalue distribution. The theoretical predictions are confirmed by our numerical results. Finally, we propose a possible method to detect numerically the non-commutative anomaly predicted in a one-loop perturbative analysis of the model, which is expected to induce a distortion of the dispersion relation on the fuzzy sphere.Comment: 1+36 pages, 18 figures; v2: 1+55 pages, 38 figures: added the study of the eigenvalue distribution, added figures, tables and references, typos corrected; v3: 1+20 pages, 10 eps figures, new results, plots and references added, technical details about the tests at small matrix size skipped, version published in JHE

Anomalous diffusion with absorption: Exact time-dependent solutions

Recently, analytical solutions of a nonlinear Fokker-Planck equation describing anomalous diffusion with an external linear force were found using a non extensive thermostatistical Ansatz. We have extended these solutions to the case when an homogeneous absorption process is also present. Some peculiar aspects of the interrelation between the deterministic force, the nonlinear diffusion and the absorption process are discussed.Comment: RevTex, 16 pgs, 4 figures. Accepted in Physical Review

Vortices and dynamics in trapped Bose-Einstein condensates

I review the basic physics of ultracold dilute trapped atomic gases, with emphasis on Bose-Einstein condensation and quantized vortices. The hydrodynamic form of the Gross-Pitaevskii equation (a nonlinear Schr{\"o}dinger equation) illuminates the role of the density and the quantum-mechanical phase. One unique feature of these experimental systems is the opportunity to study the dynamics of vortices in real time, in contrast to typical experiments on superfluid $^4$He. I discuss three specific examples (precession of single vortices, motion of vortex dipoles, and Tkachenko oscillations of a vortex array). Other unusual features include the study of quantum turbulence and the behavior for rapid rotation, when the vortices form dense regular arrays. Ultimately, the system is predicted to make a quantum phase transition to various highly correlated many-body states (analogous to bosonic quantum Hall states) that are not superfluid and do not have condensate wave functions. At present, this transition remains elusive. Conceivably, laser-induced synthetic vector potentials can serve to reach this intriguing phase transition.Comment: Accepted for publication in Journal of Low Temperature Physics, conference proceedings: Symposia on Superfluids under Rotation (Lammi, Finland, April 2010

The incidence of psychotic disorders among migrants and minority ethnic groups in Europe: Findings from the multinational EU-GEI study

BackgroundIn Europe, the incidence of psychotic disorder is high in certain migrant and minority ethnic groups (hence: 'minorities'). However, it is unknown how the incidence pattern for these groups varies within this continent. Our objective was to compare, across sites in France, Italy, Spain, the UK and the Netherlands, the incidence rates for minorities and the incidence rate ratios (IRRs, minorities v. the local reference population).MethodsThe European Network of National Schizophrenia Networks Studying Gene-Environment Interactions (EU-GEI) study was conducted between 2010 and 2015. We analyzed data on incident cases of non-organic psychosis (International Classification of Diseases, 10th edition, codes F20-F33) from 13 sites.ResultsThe standardized incidence rates for minorities, combined into one category, varied from 12.2 in Valencia to 82.5 per 100 000 in Paris. These rates were generally high at sites with high rates for the reference population, and low at sites with low rates for the reference population. IRRs for minorities (combined into one category) varied from 0.70 (95% CI 0.32-1.53) in Valencia to 2.47 (95% CI 1.66-3.69) in Paris (test for interaction: p = 0.031). At most sites, IRRs were higher for persons from non-Western countries than for those from Western countries, with the highest IRRs for individuals from sub-Saharan Africa (adjusted IRR = 3.23, 95% CI 2.66-3.93).ConclusionsIncidence rates vary by region of origin, region of destination and their combination. This suggests that they are strongly influenced by the social context

Social disadvantage, linguistic distance, ethnic minority status and first-episode psychosis: Results from the EU-GEI case-control study

BackgroundEthnic minority groups in Western countries face an increased risk of psychotic disorders. Causes of this long-standing public health inequality remain poorly understood. We investigated whether social disadvantage, linguistic distance and discrimination contributed to these patterns.MethodsWe used case-control data from the EUropean network of national schizophrenia networks studying Gene-Environment Interactions (EU-GEI) study, carried out in 16 centres in six countries. We recruited 1130 cases and 1497 population-based controls. Our main outcome measure was first-episode ICD-10 psychotic disorder (F20-F33), and exposures were ethnicity (white majority, black, mixed, Asian, North-African, white minority and other), generational status, social disadvantage, linguistic distance and discrimination. Age, sex, paternal age, cannabis use, childhood trauma and parental history of psychosis were included as a priori confounders. Exposures and confounders were added sequentially to multivariable logistic models, following multiple imputation for missing data.ResultsParticipants from any ethnic minority background had crude excess odds of psychosis [odds ratio (OR) 2.03, 95% confidence interval (CI) 1.69-2.43], which remained after adjustment for confounders (OR 1.61, 95% CI 1.31-1.98). This was progressively attenuated following further adjustment for social disadvantage (OR 1.52, 95% CI 1.22-1.89) and linguistic distance (OR 1.22, 95% CI 0.95-1.57), a pattern mirrored in several specific ethnic groups. Linguistic distance and social disadvantage had stronger effects for first- A nd later-generation groups, respectively.ConclusionSocial disadvantage and linguistic distance, two potential markers of sociocultural exclusion, were associated with increased odds of psychotic disorder, and adjusting for these led to equivocal risk between several ethnic minority groups and the white majority