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Replikationsdaten für: Excess Mortality in Austria during the COVID-19 Pandemic
No full textThis dataset is provided to replicate the correlation results from
M. Reitzner: Excess Mortality in Austria during the COVID-19 Pandemic
The impact of the COVID-19 pandemic on the mortality in Austria is investigated. Excess mortality for Austria and all Austrian federal states in the years 2020 to 2023 is computed. The results are discussed against some COVID-19 specific quantities, yielding correlations of excess mortality with COVID-19 infections, COVID-19 deaths and vaccination rates
Variational Analysis of Poisson Processes
No full text© 2016 Springer International Publishing Switzerland.The expected value of a functional F(η) of a Poisson process η can be considered as a function of its intensity measure μ. The paper surveys several results concerning differentiability properties of this functional on the space of signed measures with finite total variation. Then, necessary conditions for μ being a local minima of the considered functional are elaborated taking into account possible constraints on μ, most importantly the case of μ with given total mass a. These necessary conditions can be phrased by requiring that the gradient of the functional (being the expected first difference) is constant on the support of μ. In many important cases, the gradient depends only on the local structure of μ in a neighbourhood of x and so it is possible to work out the asymptotics of the minimising measure with the total mass a growing to infinity. Examples include the optimal approximation of convex functions, clustering problem and optimal search. In non-asymptotic cases, it is in general possible to find the optimal measure using steepest descent algorithms which are based on the obtained explicit form of the gradient
Poisson point process convergence and extreme values in stochastic geometry
No full textLet η t be a Poisson point process with intensity measure tμ , t>0 , over a Borel space X , where μ is a fixed measure. Another point process ξ t on the real line is constructed by applying a symmetric function f to every k -tuple of distinct points of η t . It is shown that ξ t behaves after appropriate rescaling like a Poisson point process, as t→∞ , under suitable conditions on η t and f . This also implies Weibull limit theorems for related extreme values. The result is then applied to investigate problems arising in stochastic geometry, including small cells in Voronoi tessellations, random simplices generated by non-stationary hyperplane processes, triangular counts with angular constraints and non-intersecting k -flats. Similar results are derived if the underlying Poisson point process is replaced by a binomial point process
Projection bodies
No full textZiel dieser Diplomarbeit ist es in möglichst geschlossener Darstellung die grundlegenden Eigenschaften von Projektionkörpern zu präsentieren und einige erstaunliche Beispiele ihrer Verwendung in der konvexen und stochastischen Geometrie zu geben.Ein Projektionenkörper ist ein konvexer Körper dessen Stützfunktion durch das Volumen von Projektionen eines anderen Körpers auf Hyperebenen gegeben ist. Ausgehend von dieser anscheinend harmlosen geometrischen Definition stellt sich heraus, dass Projektionenkörper in ganz unerwarteten Situation auftreten. Zum Beispiel erhalten wir folgende Charkterisierung: Ein symmetrischer, -dimensionaler konvexer Körper ist genau dann ein Projektionenkörper, wenn sein Polarenkörper ein endlich-dimensionaler Zentralschnitt durch die Einheitskugel von ist.In Kapitel 3 präsentieren wir die Arbeit von Monika Ludwig über -kontravariante Minkowski-Bewertungen: Jede -kontravariante Minkowski-Bewertung ist im Wesentlichen die Minkowski-Abbildung, d.h. jene Bewertung, die jedem konvexen Körper seinen Projektionenkörper zuweist. Am Ende dieses Kapitel beweisen wir eine Verfeinerung dieses Resultats.Als nächstes betrachten wir affin-isoperimetrische Ungleichungen für Projektionenkörper und geben Beweise der Petty- und der Zhang-Projektionenungleichung.Schließlich, in Kapitel 5, sehen wir wie Projektionenkörper als Hilfskörper in der stochastischen Geometrie auftreten. Wir berechnen die erwartete Anzahl der Ecken eines zufälligen Polytops in Termen des Volumens des mit der Verteilung der Polytope assoziierten Projektionenkörpers und polaren Projektionenkörpers. Eine untere Schranke für die erwartete Anzahl der Ecken eines zufälligen symmetrischen Polytops liefert dann die Reiser-Ungleichung. Reisners Ungleichung löst die Mahler-Vermutung für Zonoide. Im Allgemeinen ist die Mahler-Vermutung noch immer eines der größten ungelösten Probleme der konvexen Geometrie.The aim of this diploma thesis is to present as self-contained as possible the basic properties of projection bodies and to give several astounding examples of their application in convex and stochastic geometry.A projection body is a convex body whose support function gives the volume of projections on hyperplanes of another convex body. Starting from this seemingly innocent geometric definition, it turns out that projection bodies appear quite unexpected in many different guises. For example, we arrive at the following characterization: A centered, -dimensional convex body is a projection body if and only if its polar body is a finite dimensional central section of the unit ball of . In Chapter 3 we present the work of Monika Ludwig on contravariant Minkowski valuations: Every contravariant Minkowski valuation is more or less the Minkowski map, i.e.\ the valuation which assigns each convex body its projection body. At the end of this chapter we prove a refinement of this result. Next we show that projection bodies have applications to affine isoperimetric inequalities and we give proofs of the Petty projection inequality and Zhang projection inequality. Finally, in Chapter 5, we see how projection bodies appear as auxiliary bodies in stochastic geometry. We compute the expected number of vertices of random polytopes in terms of the volume of the projection body and polar projection body associated with the distribution of the random polytopes. Using a lower bound for the expected number of vertices of centered random polytopes, we obtain Reisner's inequality.Reisner's inequality gives a positive solution of Mahler's conjecture for zonoids, but in general Mahler's conjecture is still one of the major open problems in convex geometry
Limit theory for the Gilbert graph
Full text linkFor a given homogeneous Poisson point process in Rd two points are connected by an edge if their distance is bounded by a prescribed distance parameter. The behaviour of the resulting random graph, the Gilbert graph or random geometric graph, is investigated as the intensity of the Poisson point process is increased and the distance parameter goes to zero. The asymptotic expectation and covariance structure of a class of length-power functionals are computed. Distributional limit theorems are derived that have a Gaussian, a stable or a compound Poisson limiting distribution. Finally, concentration inequalities are provided using a concentration inequality for the convex distance
Minkowski valuations and the special linear group
No full textEine Bewertung ist ein Funktional, das auf der Menge aller konvexen Körper definiert ist und die gleiche Additivätseigenschaft bezüglich Vereinigung und Schnitt erfüllt wie das Volumen und die Oberfläche. Das Studium von Bewertungen geht zurück auf Dehn, der mit ihrer Hilfe Hilberts drittes Problem löste. Spätestens seit Hadwigers berühmter Klassifizierung aller stetigen bewegungsinvarianten Bewertungen in den 50er Jahren ist das Studium von Bewertungen ein zentraler Bestandteil der Konvexgeometrie.In den letzten Jahren haben sich sogenannte Minkowski Bewertungen als interessantes und lohnenswertes Studienobjekt erwiesen. Hier werden Bewertungen betrachtet, deren Werte wiederum konvexe Körper sind. Von besonderem geometrischen Interesse sind Minkowski Bewertungen, die verträglich mit volumserhaltenden linearen Transformationen sind, wie etwa der auf Minkowski zurückgehende Projektionenkörperoperator. Nach dem Vorbild des Charakterisierungssatzes von Hadwiger wurden solche Minkowski Bewertungen sowohl im kovarianten als auch im kontravarianten Fall erstmals von Ludwig klassifiziert. Später wurden diese Sätze von Haberl durch Verzicht auf Homogenitätsanforderungen verallgemeinert.Minkowski Bewertungen wiederum treten als Spezialfall p=1 von L_p-Minkowski Bewertungen auf. In dieser Dissertation werden eben solche L_p-Minkowski Bewertungen untersucht. Ludwigs Klassifizierungssätze für L_p-Minkowski Bewertungen werden, ähnlich wie im p=1 Fall von Haberl, durch Verzicht auf Homogenitätsanforderungen verallgemeinert.Alle diese Sätze behandeln Bewertungen, die auf konvexen Polytopen, die den Ursprung enthalten, definiert sind. Im letzten Teil der Dissertation wird eine Klassifizierung aller reellwertigen oberhalbstetigen Bewertungen auf konvexen Polytopen, die den Ursprung im Inneren enthalten, und invariant unter volumserhaltenden linearen Transformationen sind, bewiesen. Dies beantwortet die lange offene Frage nach einer zentroaffinen Version des Satzes von Hadwiger.A valuation is a functional which is defined on the set of all convex bodies and has the same additivity property with respect to union and intersection as the volume and the surface area. The study of valuations goes back to Dehn, who used them to solve Hilberts third Problem. Since Hadwiger's famous classification of all continuous rigid motion invariant valuations in the 50s, the study of valuations has become a central part of convex geometry.In the last few years so called Minkowski valuations became the focus of an interesting and rewarding investigation. Here, valuations with convex bodies as values are being considered. Of particular geometric interest are Minkowski valuations which are compatible with volume preserving linear transformations, such as the projection body operator, which goes back to Minkowski. In the spirit of Hadwiger's characterization theorem such Minkowski valuations have been characterized in the covariant and contravariant case for the first time by Ludwig. Later, these theorems were generalized by Haberl by omitting homogeneity assumptions.Minkowski valuations appear as the special case p=1 of L_p-Minkowski valuations. In this thesis such L_p-Minkowski valuations are investigated. Ludwig's classification theorems for L_p-Minkowski valuations are generalized, similar to the p=1 case by Haberl, by omitting homogeneity assumptions.All these theorems deal with valuations that are defined on convex polytopes containing the origin. In the last part of the thesis, a classification of all real valued upper semicontinuous valuations on convex polytopes containing the origin in their interiors that are invariant under volume preserving linear transformations is proved. This solves the long-standing open problem of finding a centro-affine version of Hadwiger's theorem.<br /
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Stochastic analysis for Poisson point processes: Malliavin calculus, Wiener-Itô chaos expansions and stochastic geometry
No full textVariations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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