Application of Subordination Principle to Log-Harmonic alpha-spirallike Mappings

MSC 2010: 30C45, 30C55

Applications of Subordination Principle to Log-Harmonic Mappings

MSC 2010: 30C45, 30C55

An hr-adaptive discontinuous Galerkin method for advection-diffusion problems

We propose an adaptive mesh refinement strategy based on exploiting a combination of a pre-processing mesh re-distribution algorithm employing a harmonic mapping technique, and standard (isotropic) mesh subdivision for discontinuous Galerkin approximations of advection-diffusion problems. Numerical experiments indicate that the resulting adaptive strategy can efficiently reduce the computed discretization error by clustering the nodes in the computational mesh where the analytical solution undergoes rapid variation.

Effect of spatial inhomogeneity on the mapping between strongly interacting fermions and weakly interacting spins

A combined analytical and numerical study is performed of the mapping between strongly interacting fermions and weakly interacting spins, in the framework of the Hubbard, t-J, and Heisenberg models. While for spatially homogeneous models in the thermodynamic limit the mapping is thoroughly understood, we here focus on aspects that become relevant in spatially inhomogeneous situations, such as the effect of boundaries, impurities, superlattices, and interfaces. We consider parameter regimes that are relevant for traditional applications of these models, such as electrons in cuprates and manganites, and for more recent applications to atoms in optical lattices. The rate of the mapping as a function of the interaction strength is determined from the Bethe-Ansatz for infinite systems and from numerical diagonalization for finite systems. We show analytically that if translational symmetry is broken through the presence of impurities, the mapping persists and is, in a certain sense, as local as possible, provided the spin-spin interaction between two sites of the Heisenberg model is calculated from the harmonic mean of the onsite Coulomb interaction on adjacent sites of the Hubbard model. Numerical calculations corroborate these findings also in interfaces and superlattices, where analytical calculations are more complicated.

Mapping numbers onto space in preschool children and adults

Tese de Doutoramento em Psicologia - Especialidade em Psicologia Experimental e Ciências Cognitivas

Multi-ethnic fine-mapping of 14 central adiposity loci.

The Genetic Investigation of Anthropometric Traits (GIANT) consortium identified 14 loci in European Ancestry (EA) individuals associated with waist-to-hip ratio (WHR) adjusted for body mass index. These loci are wide and narrowing the signals remains necessary. Twelve of 14 loci identified in GIANT EA samples retained strong associations with WHR in our joint EA/individuals of African Ancestry (AA) analysis (log-Bayes factor >6.1). Trans-ethnic analyses at five loci (TBX15-WARS2, LYPLAL1, ADAMTS9, LY86 and ITPR2-SSPN) substantially narrowed the signals to smaller sets of variants, some of which are in regions that have evidence of regulatory activity. By leveraging varying linkage disequilibrium structures across different populations, single-nucleotide polymorphisms (SNPs) with strong signals and narrower credible sets from trans-ethnic meta-analysis of central obesity provide more precise localizations of potential functional variants and suggest a possible regulatory role. Meta-analysis results for WHR were obtained from 77 167 EA participants from GIANT and 23 564 AA participants from the African Ancestry Anthropometry Genetics Consortium. For fine mapping we interrogated SNPs within ± 250 kb flanking regions of 14 previously reported index SNPs from loci discovered in EA populations by performing trans-ethnic meta-analysis of results from the EA and AA meta-analyses. We applied a Bayesian approach that leverages allelic heterogeneity across populations to combine meta-analysis results and aids in fine-mapping shared variants at these locations. We annotated variants using information from the ENCODE Consortium and Roadmap Epigenomics Project to prioritize variants for possible functionality.

Predictive analysis and mapping of indoor radon concentrations in Switzerland

It is estimated that around 230 people die each year due to radon (222Rn) exposure in Switzerland. 222Rn occurs mainly in closed environments like buildings and originates primarily from the subjacent ground. Therefore it depends strongly on geology and shows substantial regional variations. Correct identification of these regional variations would lead to substantial reduction of 222Rn exposure of the population based on appropriate construction of new and mitigation of already existing buildings. Prediction of indoor 222Rn concentrations (IRC) and identification of 222Rn prone areas is however difficult since IRC depend on a variety of different variables like building characteristics, meteorology, geology and anthropogenic factors. The present work aims at the development of predictive models and the understanding of IRC in Switzerland, taking into account a maximum of information in order to minimize the prediction uncertainty. The predictive maps will be used as a decision-support tool for 222Rn risk management. The construction of these models is based on different data-driven statistical methods, in combination with geographical information systems (GIS). In a first phase we performed univariate analysis of IRC for different variables, namely the detector type, building category, foundation, year of construction, the average outdoor temperature during measurement, altitude and lithology. All variables showed significant associations to IRC. Buildings constructed after 1900 showed significantly lower IRC compared to earlier constructions. We observed a further drop of IRC after 1970. In addition to that, we found an association of IRC with altitude. With regard to lithology, we observed the lowest IRC in sedimentary rocks (excluding carbonates) and sediments and the highest IRC in the Jura carbonates and igneous rock. The IRC data was systematically analyzed for potential bias due to spatially unbalanced sampling of measurements. In order to facilitate the modeling and the interpretation of the influence of geology on IRC, we developed an algorithm based on k-medoids clustering which permits to define coherent geological classes in terms of IRC. We performed a soil gas 222Rn concentration (SRC) measurement campaign in order to determine the predictive power of SRC with respect to IRC. We found that the use of SRC is limited for IRC prediction. The second part of the project was dedicated to predictive mapping of IRC using models which take into account the multidimensionality of the process of 222Rn entry into buildings. We used kernel regression and ensemble regression tree for this purpose. We could explain up to 33% of the variance of the log transformed IRC all over Switzerland. This is a good performance compared to former attempts of IRC modeling in Switzerland. As predictor variables we considered geographical coordinates, altitude, outdoor temperature, building type, foundation, year of construction and detector type. Ensemble regression trees like random forests allow to determine the role of each IRC predictor in a multidimensional setting. We found spatial information like geology, altitude and coordinates to have stronger influences on IRC than building related variables like foundation type, building type and year of construction. Based on kernel estimation we developed an approach to determine the local probability of IRC to exceed 300 Bq/m3. In addition to that we developed a confidence index in order to provide an estimate of uncertainty of the map. All methods allow an easy creation of tailor-made maps for different building characteristics. Our work is an essential step towards a 222Rn risk assessment which accounts at the same time for different architectural situations as well as geological and geographical conditions. For the communication of 222Rn hazard to the population we recommend to make use of the probability map based on kernel estimation. The communication of 222Rn hazard could for example be implemented via a web interface where the users specify the characteristics and coordinates of their home in order to obtain the probability to be above a given IRC with a corresponding index of confidence. Taking into account the health effects of 222Rn, our results have the potential to substantially improve the estimation of the effective dose from 222Rn delivered to the Swiss population.

Linkage disequilibrium assessment via log-linear modeling of SNP haplotype frequencies

Analyses of high-density single-nucleotide polymorphism (SNP) data, such as genetic mapping and linkage disequilibrium (LD) studies, require phase-known haplotypes to allow for the correlation between tightly linked loci. However, current SNP genotyping technology cannot determine phase, which must be inferred statistically. In this paper, we present a new Bayesian Markov chain Monte Carlo (MCMC) algorithm for population haplotype frequency estimation, particulary in the context of LD assessment. The novel feature of the method is the incorporation of a log-linear prior model for population haplotype frequencies. We present simulations to suggest that 1) the log-linear prior model is more appropriate than the standard coalescent process in the presence of recombination (>0.02cM between adjacent loci), and 2) there is substantial inflation in measures of LD obtained by a "two-stage" approach to the analysis by treating the "best" haplotype configuration as correct, without regard to uncertainty in the recombination process. Genet Epidemiol 25:106-114, 2003. (C) 2003 Wiley-Liss, Inc.

Mapping antimalarial pharmacophores as a useful tool for the rapid discovery of drugs effective in vivo: design, construction, characterization, and pharmacology of metaquine

Resistant strains of Plasmodium falciparum and the unavailability of useful antimalarial vaccines reinforce the need to develop new efficacious antimalarials. This study details a pharmacophore model that has been used to identify a potent, soluble, orally bioavailable antimalarial bisquinoline, metaquine (N,N'-bis(7-chloroquinolin-4-yl)benzene-1,3-diamine) (dihydrochloride), which is active against Plasmodium berghei in vivo (oral ID50 of 25 mu mol/kg) and multidrug-resistant Plasmodium falciparum K1 in vitro (0.17 mu M). Metaquine shows strong affinity for the putative antimalarial receptor, heme at pH 7.4 in aqueous DMSO. Both crystallographic analyses and quantum mechanical calculations (HF/6-31+G*) reveal important regions of protonation and bonding thought to persist at parasitic vacuolar pH concordant with our receptor model. Formation of drug-heme adduct in solution was confirmed using high-resolution positive ion electrospray mass spectrometry. Metaquine showed strong binding with the receptor in a 1: 1 ratio (log K = 5.7 +/- 0.1) that was predicted by molecular mechanics calculations. This study illustrates a rational multidisciplinary approach for the development of new 4-aminoquinoline antimalarials, with efficacy superior to chloroquine, based on the use of a pharmacophore model.

Entanglement entropy in long-range harmonic oscillators

We study the Von Neumann and Renyi entanglement entropy of long-range harmonic oscillators (LRHO) by both theoretical and numerical means. We show that the entanglement entropy in massless harmonic oscillators increases logarithmically with the sub-system size as S - c(eff)/3 log l. Although the entanglement entropy of LRHO's shares some similarities with the entanglement entropy at conformal critical points we show that the Renyi entanglement entropy presents some deviations from the expected conformal behaviour. In the massive case we demonstrate that the behaviour of the entanglement entropy with respect to the correlation length is also logarithmic as the short-range case. Copyright (c) EPLA, 2012

Mapping Individual Variation in Male Mating Preference Space: Multiple Choice in a Color Polymorphic Cichlid Fish

Sexual selection theory largely rests on the assumption that populations contain individual variation in mating preferences and that individuals are consistent in their preferences. However, there are few empirical studies of within-population variation and even fewer have examined individual male mating preferences. Here, we studied a color polymorphic population of the Lake Victoria cichlid fish Neochromis omnicaeruleus, a species in which color morphs are associated with different sex-determining factors. Wild-caught males were tested in three-way choice trials with multiple combinations of different females belonging to the three color morphs. Compositional log-ratio techniques were applied to analyze individual male mating preferences. Large individual variation in consistency, strength, and direction of male mating preferences for female color morphs was found and hierarchical clustering of the compositional data revealed the presence of four distinct preference groups corresponding to the three color morphs in addition to a no-preference class. Consistency of individual male mating preferences was higher in males with strongest preferences. We discuss the implications of these findings for our understanding of the mechanisms underlying polymorphism in mating preferences.

The ionized gas in the CALIFA early-type galaxies I. Mapping two representative cases: NGC 6762 and NGC 5966

As part of the ongoing CALIFA survey, we have conducted a thorough bidimensional analysis of the ionized gas in two E/S0 galaxies, NGC 6762 and NGC 5966, aiming to shed light on the nature of their warm ionized ISM. Specifically, we present optical (3745–7300 Å) integral field spectroscopy obtained with the PMAS/PPAK integral field spectrophotometer. Its wide field-of-view (1′ × 1′) covers the entire optical extent of each galaxy down to faint continuum surface brightnesses. To recover the nebular lines, we modeled and subtracted the underlying stellar continuum from the observed spectra using the STARLIGHT spectral synthesis code. The pure emission-line spectra were used to investigate the gas properties and determine the possible sources of ionization. We show the advantages of IFU data in interpreting the complex nature of the ionized gas in NGC 6762 and NGC 5966. In NGC 6762, the ionized gas and stellar emission display similar morphologies, while the emission line morphology is elongated in NGC 5966, spanning ~6 kpc, and is oriented roughly orthogonal to the major axis of the stellar continuum ellipsoid. Whereas gas and stars are kinematically aligned in NGC 6762, the gas is kinematically decoupled from the stars in NGC 5966. A decoupled rotating disk or an “ionization cone” are two possible interpretations of the elongated ionized gas structure in NGC 5966. The latter would be the first “ionization cone” of such a dimension detected within a weak emission-line galaxy. Both galaxies have weak emission-lines relative to the continuum[EW(Hα) ≲ 3 Å] and have very low excitation, log([OIII]λ5007/Hβ) ≲ 0.5. Based on optical diagnostic ratios ([OIII]λ5007/Hβ, [NII]λ6584/Hα, [SII]λ6717, 6731/Hα, [OI]λ6300/Hα), both objects contain a LINER nucleus and an extended LINER-like gas emission. The emission line ratios do not vary significantly with radius or aperture, which indicates that the nebular properties are spatially homogeneous. The gas emission in NGC 6762 can be best explained by photoionization by pAGB stars without the need of invoking any other excitation mechanism. In the case of NGC 5966, the presence of a nuclear ionizing source seems to be required to shape the elongated gas emission feature in the “ionization cone” scenario, although ionization by pAGB stars cannot be ruled out. Further study of this object is needed to clarify the nature of its elongated gas structure.

A mathematical resolution to log transformations and the binning effect in applied processing of data in flow cytometry

This dissertation develops a new mathematical approach that overcomes the effect of a data processing phenomenon known as “histogram binning” inherent to flow cytometry data. A real-time procedure is introduced to prove the effectiveness and fast implementation of such an approach on real-world data. The histogram binning effect is a dilemma posed by two seemingly antagonistic developments: (1) flow cytometry data in its histogram form is extended in its dynamic range to improve its analysis and interpretation, and (2) the inevitable dynamic range extension introduces an unwelcome side effect, the binning effect, which skews the statistics of the data, undermining as a consequence the accuracy of the analysis and the eventual interpretation of the data. ^ Researchers in the field contended with such a dilemma for many years, resorting either to hardware approaches that are rather costly with inherent calibration and noise effects; or have developed software techniques based on filtering the binning effect but without successfully preserving the statistical content of the original data. ^ The mathematical approach introduced in this dissertation is so appealing that a patent application has been filed. The contribution of this dissertation is an incremental scientific innovation based on a mathematical framework that will allow researchers in the field of flow cytometry to improve the interpretation of data knowing that its statistical meaning has been faithfully preserved for its optimized analysis. Furthermore, with the same mathematical foundation, proof of the origin of such an inherent artifact is provided. ^ These results are unique in that new mathematical derivations are established to define and solve the critical problem of the binning effect faced at the experimental assessment level, providing a data platform that preserves its statistical content. ^ In addition, a novel method for accumulating the log-transformed data was developed. This new method uses the properties of the transformation of statistical distributions to accumulate the output histogram in a non-integer and multi-channel fashion. Although the mathematics of this new mapping technique seem intricate, the concise nature of the derivations allow for an implementation procedure that lends itself to a real-time implementation using lookup tables, a task that is also introduced in this dissertation. ^

A mathematical resolution to log transformations and the binning effect in applied processing of data in flow cytometry

This dissertation develops a new mathematical approach that overcomes the effect of a data processing phenomenon known as "histogram binning" inherent to flow cytometry data. A real-time procedure is introduced to prove the effectiveness and fast implementation of such an approach on real-world data. The histogram binning effect is a dilemma posed by two seemingly antagonistic developments: (1) flow cytometry data in its histogram form is extended in its dynamic range to improve its analysis and interpretation, and (2) the inevitable dynamic range extension introduces an unwelcome side effect, the binning effect, which skews the statistics of the data, undermining as a consequence the accuracy of the analysis and the eventual interpretation of the data. Researchers in the field contended with such a dilemma for many years, resorting either to hardware approaches that are rather costly with inherent calibration and noise effects; or have developed software techniques based on filtering the binning effect but without successfully preserving the statistical content of the original data. The mathematical approach introduced in this dissertation is so appealing that a patent application has been filed. The contribution of this dissertation is an incremental scientific innovation based on a mathematical framework that will allow researchers in the field of flow cytometry to improve the interpretation of data knowing that its statistical meaning has been faithfully preserved for its optimized analysis. Furthermore, with the same mathematical foundation, proof of the origin of such an inherent artifact is provided. These results are unique in that new mathematical derivations are established to define and solve the critical problem of the binning effect faced at the experimental assessment level, providing a data platform that preserves its statistical content. In addition, a novel method for accumulating the log-transformed data was developed. This new method uses the properties of the transformation of statistical distributions to accumulate the output histogram in a non-integer and multi-channel fashion. Although the mathematics of this new mapping technique seem intricate, the concise nature of the derivations allow for an implementation procedure that lends itself to a real-time implementation using lookup tables, a task that is also introduced in this dissertation.

Mapping tissue inhomogeneity in acute myocarditis: a novel analytical approach to quantitative myocardial edema imaging by T2-mapping

BACKGROUND: The purpose of the present study was to investigate the diagnostic value of T2-mapping in acute myocarditis (ACM) and to define cut-off values for edema detection. METHODS: Cardiovascular magnetic resonance (CMR) data of 31 patients with ACM were retrospectively analyzed. 30 healthy volunteers (HV) served as a control. Additionally to the routine CMR protocol, T2-mapping data were acquired at 1.5 T using a breathhold Gradient-Spin-Echo T2-mapping sequence in six short axis slices. T2-maps were segmented according to the 16-segments AHA-model and segmental T2 values as well as the segmental pixel-standard deviation (SD) were analyzed. RESULTS: Mean differences of global myocardial T2 or pixel-SD between HV and ACM patients were only small, lying in the normal range of HV. In contrast, variation of segmental T2 values and pixel-SD was much larger in ACM patients compared to HV. In random forests and multiple logistic regression analyses, the combination of the highest segmental T2 value within each patient (maxT2) and the mean absolute deviation (MAD) of log-transformed pixel-SD (madSD) over all 16 segments within each patient proved to be the best discriminators between HV and ACM patients with an AUC of 0.85 in ROC-analysis. In classification trees, a combined cut-off of 0.22 for madSD and of 68 ms for maxT2 resulted in 83% specificity and 81% sensitivity for detection of ACM. CONCLUSIONS: The proposed cut-off values for maxT2 and madSD in the setting of ACM allow edema detection with high sensitivity and specificity and therefore have the potential to overcome the hurdles of T2-mapping for its integration into clinical routine.