Complex and real Hausdorff operators

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Absolute convergence of Fourier integrals

In this survey, results on the representation of a function as an absolutely convergent Fourier integral are collected, classified and discussed. Certain applications are also given.

Moduli of smoothness and rate of a.e. convergence for some convolution operators

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Quantitative genetic modeling and inference in the presence of nonignorable missing data.

Natural selection is typically exerted at some specific life stages. If natural selection takes place before a trait can be measured, using conventional models can cause wrong inference about population parameters. When the missing data process relates to the trait of interest, a valid inference requires explicit modeling of the missing process. We propose a joint modeling approach, a shared parameter model, to account for nonrandom missing data. It consists of an animal model for the phenotypic data and a logistic model for the missing process, linked by the additive genetic effects. A Bayesian approach is taken and inference is made using integrated nested Laplace approximations. From a simulation study we find that wrongly assuming that missing data are missing at random can result in severely biased estimates of additive genetic variance. Using real data from a wild population of Swiss barn owls Tyto alba, our model indicates that the missing individuals would display large black spots; and we conclude that genes affecting this trait are already under selection before it is expressed. Our model is a tool to correctly estimate the magnitude of both natural selection and additive genetic variance.

Quantitative electroencephalography reveals different physiological profiles between benign and remitting-relapsing multiple sclerosis patients

BACKGROUND A possible method of finding physiological markers of multiple sclerosis (MS) is the application of EEG quantification (QEEG) of brain activity when the subject is stressed by the demands of a cognitive task. In particular, modulations of the spectral content that take place in the EEG of patients with multiple sclerosis remitting-relapsing (RRMS) and benign multiple sclerosis (BMS) during a visuo-spatial task need to be observed. METHODS The sample consisted of 19 patients with RRMS, 10 with BMS, and 21 control subjects. All patients were free of medication and had not relapsed within the last month. The power spectral density (PSD) of different EEG bands was calculated by Fast-Fourier-Transformation (FFT), those analysed being delta, theta, alpha, beta and gamma. Z-transformation was performed to observe individual profiles in each experimental group for spectral modulations. Lastly, correlation analyses was performed between QEEG values and other variables from participants in the study (age, EDSS, years of evolution and cognitive performance). RESULTS Nearly half (42%) the RRMS patients showed a statistically significant increase of two or more standard deviations (SD) compared to the control mean value for the beta-2 and gamma bands (F = 2.074, p = 0.004). These alterations were localized to the anterior regions of the right hemisphere, and bilaterally to the posterior areas of the scalp. None of the BMS patients or control subjects had values outside the range of +/- 2 SD. There were no significant correlations between these values and the other variables analysed (age, EDSS, years of evolution or behavioural performance). CONCLUSION During the attentional processing, changes in the high EEG spectrum (beta-2 and gamma) in MS patients exhibit physiological alterations that are not normally detected by spontaneous EEG analysis. The different spectral pattern between pathological and controls groups could represent specific changes for the RRMS patients, indicative of compensatory mechanisms or cortical excitatory states representative of some phases during the RRMS course that are not present in the BMS group.

Hereditary completeness for systems of exponentials and reproducing kernels

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Sexual dimorphism of the human mandible: demonstration by elliptical Fourier analysis.

A new quantitative approach of the mandibular sexual dimorphism, based on computer-aided image analysis and elliptical Fourier analysis of the mandibular outline in lateral view is presented. This method was applied to a series of 117 dentulous mandibles from 69 male and 48 female individuals native of Rhenish countries. Statistical discriminant analysis of the elliptical Fourier harmonics allowed the demonstration of a significant sexual dimorphism in 97.1% of males and 91.7% of females, i.e. in a higher proportion than in previous studies using classical metrical approaches. This original method opens interesting perspectives for increasing the accuracy of sex identification in current anthropological practice and in forensic procedures.

The mapping of the local contributions of Fermi and Coulomb correlation into intracule and extracule density distributions

The contributions of the correlated and uncorrelated components of the electron-pair density to atomic and molecular intracule I(r) and extracule E(R) densities and its Laplacian functions ∇2I(r) and ∇2E(R) are analyzed at the Hartree-Fock (HF) and configuration interaction (CI) levels of theory. The topologies of the uncorrelated components of these functions can be rationalized in terms of the corresponding one-electron densities. In contrast, by analyzing the correlated components of I(r) and E(R), namely, IC(r) and EC(R), the effect of electron Fermi and Coulomb correlation can be assessed at the HF and CI levels of theory. Moreover, the contribution of Coulomb correlation can be isolated by means of difference maps between IC(r) and EC(R) distributions calculated at the two levels of theory. As application examples, the He, Ne, and Ar atomic series, the C2-2, N2, O2+2 molecular series, and the C2H4 molecule have been investigated. For these atoms and molecules, it is found that Fermi correlation accounts for the main characteristics of IC(r) and EC(R), with Coulomb correlation increasing slightly the locality of these functions at the CI level of theory. Furthermore, IC(r), EC(R), and the associated Laplacian functions, reveal the short-ranged nature and high isotropy of Fermi and Coulomb correlation in atoms and molecules

The relevance of the Laplacian of intracule and extracule density distributions for analyzing electron-electron interactions in molecules

A topological analysis of intracule and extracule densities and their Laplacians computed within the Hartree-Fock approximation is presented. The analysis of the density distributions reveals that among all possible electron-electron interactions in atoms and between atoms in molecules only very few are located rigorously as local maxima. In contrast, they are clearly identified as local minima in the topology of Laplacian maps. The conceptually different interpretation of intracule and extracule maps is also discussed in detail. An application example to the C2H2, C2H4, and C2H6 series of molecules is presented

Hemoglobin enhances the biological activity of synthetic and natural bacterial (endotoxic) virulence factors: a general principle.

Although hemoglobin (Hb) is mainly present in the cytoplasm of erythrocytes (red blood cells), lower concentrations of pure, cell-free Hb are released permanently into the circulation due to an inherent intravascular hemolytic disruption of erythrocytes. Previously it was shown that the interaction of Hb with bacterial endotoxins (lipopolysaccharides, LPS) results in a significant increase of the biological activity of LPS. There is clear evidence that the enhancement of the biological activity of LPS by Hb is connected with a disaggregation of LPS. From these findings one questions whether the property to enhance the biological activity of endotoxin, in most cases proven by the ability to increase the cytokine (tumor-necrosis-factor-alpha, interleukins) production in human mononuclear cells, is restricted to bacterial endotoxin or is a more general principle in nature. To elucidate this question, we investigated the interaction of various synthetic and natural virulence (pathogenicity) factors with hemoglobin of human or sheep origin. In addition to enterobacterial R-type LPS a synthetic bacterial lipopeptide and synthetic phospholipid-like structures mimicking the lipid A portion of LPS were analysed. Furthermore, we also tested endotoxically inactive LPS and lipid A compounds such as those from Chlamydia trachomatis. We found that the observations made for endotoxically active form of LPS can be generalized for the other synthetic and natural virulence factors: In every case, the cytokine-production induced by them is increased by the addition of Hb. This biological property of Hb is connected with its physical property to convert the aggregate structures of the virulence factors into one with cubic symmetry, accompanied with a considerable reduction of the size and number of the original aggregates.

Bubbly collateral and economic activity

This paper develops a model of the bubbly economy and uses it to study the effects of bailoutpolicies. In the bubbly economy, weak enforcement institutions do not allow firms to pledge futurerevenues to their creditors. As a result, "fundamental" collateral is scarce and this impairs the intermediationprocess that transforms savings into capital. To overcome this shortage of "fundamental"collateral, the bubbly economy creates "bubbly" collateral. This additional collateral supports anintricate array of intra- and inter-generational transfers that allow savings to be transformed intocapital and bubbles. Swings in investor sentiment lead to fluctuations in the amount of bubblycollateral, giving rise to bubbly business cycles with very rich and complex dynamics.Bailout policies can affect these dynamics in a variety of ways. Expected bailouts provideadditional collateral and expand investment and the capital stock. Realized bailouts reduce thesupply of funds and contract investment and the capital stock. Thus, bailout policies tend to fosterinvestment and growth in normal times, but to depress investment and growth during crisis periods.We show how to design bailout policies that maximize various policy objectives.

Dispersal probability distributions and the wave-front speed problem

The speed and width of front solutions to reaction-dispersal models are analyzed both analytically and numerically. We perform our analysis for Laplace and Gaussian distribution kernels, both for delayed and nondelayed models. The results are discussed in terms of the characteristic parameters of the models

Policy attitudes, ideological values and social representations

This article reviews research on policy attitudes and ideological values from the perspective of social representations theory. In the first part of the paper, key features of lay political thinking are presented, its pragmatic imperative, its focus on communication and the social functions of shared knowledge. Objectification transforms abstract and group-neutral ideological values into concrete and socially useful knowledge, in particular stereotypes of value-conforming and value-violating groups. Such shared understandings of intergroup relations provide citizens with common reference knowledge which provides the cognitive and cultural basis of policy attitudes. Social representations theory further suggests that lay knowledge reflects the social context in which it has been elaborated (anchoring), an aspect which allows conceptualising aggregate-level differences in policy attitudes. In the second part of the paper, a model of lay conceptions of social order is outlined which organises four shared conceptions of social order, along with the stereotype-based thinking associated with each conception: Moral order, Free Market, Social diversity and Structural inequality. We conclude by arguing that policy attitudes are symbolic devices expressed to justify or to challenge existing social arrangements.

Chemical characterization and infrared spectroscopy of soil organic matter from two southern brazilian soils

Soil organic matter from the surface horizon of two Brazilian soils (a Latosol and a Chernosol), in bulk samples (in situ SOM) and in HF-treated samples (SOM), was characterized by elemental analyses, diffuse reflectance (DRIFT) and transmission Fourier transform infrared spectroscopy (T-FTIR). Humic acids (HA), fulvic acids (FA) and humin (HU) isolated from the SOM were characterized additionally by ultraviolet-visible spectroscopy (UV-VIS). After sample oxidation and alkaline treatment, the DRIFT technique proved to be more informative for the detection of "in situ SOM" and of residual organic matter than T-FTIR. The higher hydrophobicity index (HI) and H/C ratio obtained in the Chernosol samples indicate a stronger aliphatic character of the organic matter in this soil than the Latosol. In the latter, a pronounced HI decrease was observed after the removal of humic substances (HS). The weaker aliphatic character, the higher O/C ratio, and the T-FTIR spectrum obtained for the HU fraction in the Latosol suggest the occurrence of surface coordination of carboxylate ions. The Chernosol HU fraction was also oxygenated to a relatively high extent, but presented a stronger hydrophobic character in comparison with the Latosol HU. These differences in the chemical and functional group composition suggest a higher organic matter protection in the Latosol. After the HF treatment, decreases in the FA proportion and the A350/A550 ratio were observed. A possible loss of FA and condensation of organic molecules due to the highly acid medium should not be neglected.

Direct Fourier Tomographic Reconstruction Image-To-Image Filter

We present an open-source ITK implementation of a directFourier method for tomographic reconstruction, applicableto parallel-beam x-ray images. Direct Fourierreconstruction makes use of the central-slice theorem tobuild a polar 2D Fourier space from the 1D transformedprojections of the scanned object, that is resampled intoa Cartesian grid. Inverse 2D Fourier transform eventuallyyields the reconstructed image. Additionally, we providea complex wrapper to the BSplineInterpolateImageFunctionto overcome ITKâeuro?s current lack for image interpolatorsdealing with complex data types. A sample application ispresented and extensively illustrated on the Shepp-Loganhead phantom. We show that appropriate input zeropaddingand 2D-DFT oversampling rates together with radial cubicb-spline interpolation improve 2D-DFT interpolationquality and are efficient remedies to reducereconstruction artifacts.