Adaptive deterministic dyadic grids on spaces of homogeneous type

In the context of spaces of homogeneous type, we develop a method to deterministically construct dyadic grids, specifically adapted to a given combinatorial situation. This method is used to estimate vector-valued operators rearranging martingale difference sequences such as the Haar system.Comment: 17 pages, 2 figure

A Donsker Theorem for Lévy Measures

Given n equidistant realisations of a Lévy process (Lt; t >= 0), a natural estimator for the distribution function N of the Lévy measure is constructed. Under a polynomial decay restriction on the characteristic function, a Donsker-type theorem is proved, that is, a functional central limit theorem for the process in the space of bounded functions away from zero. The limit distribution is a generalised Brownian bridge process with bounded and continuous sample paths whose covariance structure depends on the Fourier-integral operator. The class of Lévy processes covered includes several relevant examples such as compound Poisson, Gamma and self-decomposable processes. Main ideas in the proof include establishing pseudo-locality of the Fourier-integral operator and recent techniques from smoothed empirical processes.uniform central limit theorem, nonlinear inverse problem, smoothed empirical processes, pseudo-differential operators, jump measure

Phase retrieval for characteristic functions of convex bodies and reconstruction from covariograms

We propose strongly consistent algorithms for reconstructing the characteristic function 1_K of an unknown convex body K in R^n from possibly noisy measurements of the modulus of its Fourier transform \hat{1_K}. This represents a complete theoretical solution to the Phase Retrieval Problem for characteristic functions of convex bodies. The approach is via the closely related problem of reconstructing K from noisy measurements of its covariogram, the function giving the volume of the intersection of K with its translates. In the many known situations in which the covariogram determines a convex body, up to reflection in the origin and when the position of the body is fixed, our algorithms use O(k^n) noisy covariogram measurements to construct a convex polytope P_k that approximates K or its reflection -K in the origin. (By recent uniqueness results, this applies to all planar convex bodies, all three-dimensional convex polytopes, and all symmetric and most (in the sense of Baire category) arbitrary convex bodies in all dimensions.) Two methods are provided, and both are shown to be strongly consistent, in the sense that, almost surely, the minimum of the Hausdorff distance between P_k and K or -K tends to zero as k tends to infinity.Comment: Version accepted on the Journal of the American Mathematical Society. With respect to version 1 the noise model has been greatly extended and an appendix has been added, with a discussion of rates of convergence and implementation issues. 56 pages, 4 figure

Convergence of algorithms for reconstructing convex bodies and directional measures

We investigate algorithms for reconstructing a convex body $K$ in $\mathbb {R}^n$ from noisy measurements of its support function or its brightness function in $k$ directions $u_1,...,u_k$. The key idea of these algorithms is to construct a convex polytope $P_k$ whose support function (or brightness function) best approximates the given measurements in the directions $u_1,...,u_k$ (in the least squares sense). The measurement errors are assumed to be stochastically independent and Gaussian. It is shown that this procedure is (strongly) consistent, meaning that, almost surely, $P_k$ tends to $K$ in the Hausdorff metric as $k\to\infty$. Here some mild assumptions on the sequence $(u_i)$ of directions are needed. Using results from the theory of empirical processes, estimates of rates of convergence are derived, which are first obtained in the $L_2$ metric and then transferred to the Hausdorff metric. Along the way, a new estimate is obtained for the metric entropy of the class of origin-symmetric zonoids contained in the unit ball. Similar results are obtained for the convergence of an algorithm that reconstructs an approximating measure to the directional measure of a stationary fiber process from noisy measurements of its rose of intersections in $k$ directions $u_1,...,u_k$. Here the Dudley and Prohorov metrics are used. The methods are linked to those employed for the support and brightness function algorithms via the fact that the rose of intersections is the support function of a projection body.Comment: Published at http://dx.doi.org/10.1214/009053606000000335 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Renewable energy and its impact on agricultural and rural development: Findings of a comparative study in Central, Eastern and Southern Europe

Rising energy prices for fossil fuels, the unreliable supply of energy imports during the last winters and - concerning the 12 new members states (NMS) - the demand by the European Union (EU) for developing National Renewable Energy Action Plans have stimulated the national discussion and political action on renewable energy (RE) among all European countries. Particularly among the 12 NMS the share of RE has increased during the last years. Among the candidate and potential candidate countries (CC and PCC) the discussion on RE has just started. When looking at the impact of RE on agricultural and rural development the effects are relatively small. An expansion of rape seed cultivation and, to a smaller extent, of the production of wood pellets could be observed. But overall the impact of RE on agricultural and rural income and employment seems to be marginal up to now. Whether it will be so in the future, depends on national policies and support programme as none of the various types of RE is competitive to fossil fuels for the time being. -- Die öffentliche Diskussion sowie die politischen Maßnahmen im Hinblick auf erneuerbare Energien haben im Laufe der vergangenen Jahre bei allen europäischen Staaten erheblich zugenommen. Die Gründe liegen bei den stetig steigenden Preisen für fossile Energieträger, den unzuverlässigen Lieferungen in den vergangenen Wintern sowie - besonders bei den 12 Neuen Mitgliedsstaaten (NMS) der Europäischen Union (EU) - die verbindliche Maßgabe, einen Nationalen Aktionsplan für Erneuerbare Energien zu entwickeln. Besonders innerhalb der 12 NMS hat der Anteil der erneuerbaren Energie am Gesamtenergieverbrauch zugenommen. Allerdings sind die Auswirkungen der erweiterten Nutzung von erneuerbaren Energien auf die landwirtschaftliche und ländliche Entwicklung bis dato relativ gering. Lediglich eine Ausweitung des Rapsanbau sowie in einem geringerem Maße von Holzpellets war zu beobachten. Die Auswirkungen auf Einkommen und Beschäftigung sind jedoch (noch) marginal. Inwieweit sich dies in der Zukunft ändern wird, hängt von den nationalen Politiken und Unterstützungsprogrammen ab, da bis jetzt keine Art der erneuerbaren Energien gegenüber den fossilen Brennstoffen konkurrenzfähig ist.Renewable energy,comparative survey,agricultural and rural development,New members states of the EU,candidate and potential candidate countries,Erneuerbare Energien,vergleichende Analyse,landwirtschaftliche und ländliche Entwicklung,Neue Mitgliedsstaaten sowie (potenzielle) Beitrittsländer der EU.

Lipid-laden alveolar macrophages and pH monitoring in gastroesophageal reflux-related respiratory symptoms

Lipid-laden alveolar macrophages and pH monitoring have been used in the diagnosis of chronic aspiration in children with gastroesophageal reflux (GER). This study was conducted to prove a correlation between the detection of alimentary pulmonary fat phagocytosis and an increasing amount of proximal gastroesophageal reflux. It was assumed that proximal gastroesophageal reflux better correlates with aspiration than distal GER. Patients from 6 months to 16 years with unexplained recurrent wheezy bronchitis and bronchial hyperreactivity, or recurrent pneumonia with chronic cough underwent 24-hour double-channel pH monitoring and bronchoscopy with bronchoalveolar lavage (BAL). Aspiration of gastric content was determined by counting lipid laden alveolar macrophages from BAL specimens. There were no correlations between any pH-monitoring parameters and counts of lipid-laden macrophages in the whole study population, even when restricting analysis to those with abnormal reflux index expressing clinically significant GER. Quantifying lipid-laden alveolar macrophages from BAL in children with gastroesophageal-related respiratory disorders does not have an acceptable specificity to prove chronic aspiration as an underlying etiology. Therefore, research for other markers of pulmonary aspiration is needed