Periodic Higgs-de Rham flows and representations of algebraic fundamental groups

Let k := bar{F}_p for p > 2, W_n(k) := W(k)/p^n and X_n be a projective smooth W_n(k)-scheme which is W_{n+1}(k)-liftable. For all n > 1, we construct explicitly a functor, which we call the inverse Cartier functor, from a subcategory of Higgs bundles over X_n to a subcategory of flat Bundles over X_n. Then we introduce the notion of periodic Higgs-de Rham flows and show that a periodic Higgs-de Rham flow is equivalent to a Fontaine-Faltings module. Together with a p-adic analogue of Riemann-Hilbert correspondence established by Faltings, we obtain a coarse p-adic Simpson correspondence.

The integration of curriculum and assessment in interpreter education

In dieser interdisziplinären, translationswissenschaftlichen Studie wird die Integration von Curriculum und Evaluierung in der Dolmetscherausbildung theoretisch fundiert und im Rahmen einer Fallstudie empirisch untersucht. Dolmetschkompetenz wird als ein durch zweckgerechte und messgenaue (valid and reliable) Bewertungsmethoden dokumentiertes Ergebnis der Curriculumanwendung betrachtet. Definitionen, Grundlagen, Ansätze, Ausbildungs- und Lernziele werden anhand der Curriculumtheorie und Dolmetschwissenschaft beschrieben. Traditionelle und alternative Evaluierungsmethoden werden hinsichtlich ihrer Anwendbarkeit in der Dolmetscherausbildung erprobt. In der Fallstudie werden die Prüfungsergebnisse zweier Master-Studiengänge-MA Konferenzdolmetschen und MA Dolmetschen und Übersetzen-quantitativ analysiert. Die zur Dokumentation der Prüfungsergebnisse eingesetzte Bewertungsmethodik wird qualitativ untersucht und zur quantitativen Analyse in Bezug gesetzt. Die Fallstudie besteht aus 1) einer chi-square-Analyse der Abschlussprüfungsnoten getrennt nach Sprachkombination und Prüfungskategorie (n=260), 2) einer Umfrage unter den Jurymitgliedern hinsichtlich der Evaluierungsansätze, -verfahren, und -kriterien (n = 45; 62.22% Rücklaufrate); und 3) einer Analyse des ausgangssprachlichen Prüfungsmaterials ebenfalls nach Sprachkombination und Prüfungskategorie. Es wird nachgewiesen, dass Studierende im MA Dolmetschen und Übersetzen tendenziell schlechtere Prüfungsleistungen erbringen als Studierende im MA Konferenzdolmetschen. Die Analyseergebnisse werden jedoch als aussageschwach betrachtet aufgrund mangelnder Evaluierungsvalidität. Schritte zur Curriculum- und Evaluierungsoptimierung sowie ein effizienteres Curriculummodell werden aus den theoretischen Ansätzen abgeleitet. Auf die Rolle der Ethik in der Evaluierungsmethodik wird hingewiesen.

Simulations of physics and chemistry of polar stratospheric clouds with a general circulation model

A polar stratospheric cloud submodel has been developed and incorporated in a general circulation model including atmospheric chemistry (ECHAM5/MESSy). The formation and sedimentation of polar stratospheric cloud (PSC) particles can thus be simulated as well as heterogeneous chemical reactions that take place on the PSC particles. For solid PSC particle sedimentation, the need for a tailor-made algorithm has been elucidated. A sedimentation scheme based on first order approximations of vertical mixing ratio profiles has been developed. It produces relatively little numerical diffusion and can deal well with divergent or convergent sedimentation velocity fields. For the determination of solid PSC particle sizes, an efficient algorithm has been adapted. It assumes a monodisperse radii distribution and thermodynamic equilibrium between the gas phase and the solid particle phase. This scheme, though relatively simple, is shown to produce particle number densities and radii within the observed range. The combined effects of the representations of sedimentation and solid PSC particles on vertical H2O and HNO3 redistribution are investigated in a series of tests. The formation of solid PSC particles, especially of those consisting of nitric acid trihydrate, has been discussed extensively in recent years. Three particle formation schemes in accordance with the most widely used approaches have been identified and implemented. For the evaluation of PSC occurrence a new data set with unprecedented spatial and temporal coverage was available. A quantitative method for the comparison of simulation results and observations is developed and applied. It reveals that the relative PSC sighting frequency can be reproduced well with the PSC submodel whereas the detailed modelling of PSC events is beyond the scope of coarse global scale models. In addition to the development and evaluation of new PSC submodel components, parts of existing simulation programs have been improved, e.g. a method for the assimilation of meteorological analysis data in the general circulation model, the liquid PSC particle composition scheme, and the calculation of heterogeneous reaction rate coefficients. The interplay of these model components is demonstrated in a simulation of stratospheric chemistry with the coupled general circulation model. Tests against recent satellite data show that the model successfully reproduces the Antarctic ozone hole.

On the geometry of the spin-statistics connection in quantum mechanics

The Spin-Statistics theorem states that the statistics of a system of identical particles is determined by their spin: Particles of integer spin are Bosons (i.e. obey Bose-Einstein statistics), whereas particles of half-integer spin are Fermions (i.e. obey Fermi-Dirac statistics). Since the original proof by Fierz and Pauli, it has been known that the connection between Spin and Statistics follows from the general principles of relativistic Quantum Field Theory. In spite of this, there are different approaches to Spin-Statistics and it is not clear whether the theorem holds under assumptions that are different, and even less restrictive, than the usual ones (e.g. Lorentz-covariance). Additionally, in Quantum Mechanics there is a deep relation between indistinguishabilty and the geometry of the configuration space. This is clearly illustrated by Gibbs' paradox. Therefore, for many years efforts have been made in order to find a geometric proof of the connection between Spin and Statistics. Recently, various proposals have been put forward, in which an attempt is made to derive the Spin-Statistics connection from assumptions different from the ones used in the relativistic, quantum field theoretic proofs. Among these, there is the one due to Berry and Robbins (BR), based on the postulation of a certain single-valuedness condition, that has caused a renewed interest in the problem. In the present thesis, we consider the problem of indistinguishability in Quantum Mechanics from a geometric-algebraic point of view. An approach is developed to study configuration spaces Q having a finite fundamental group, that allows us to describe different geometric structures of Q in terms of spaces of functions on the universal cover of Q. In particular, it is shown that the space of complex continuous functions over the universal cover of Q admits a decomposition into C(Q)-submodules, labelled by the irreducible representations of the fundamental group of Q, that can be interpreted as the spaces of sections of certain flat vector bundles over Q. With this technique, various results pertaining to the problem of quantum indistinguishability are reproduced in a clear and systematic way. Our method is also used in order to give a global formulation of the BR construction. As a result of this analysis, it is found that the single-valuedness condition of BR is inconsistent. Additionally, a proposal aiming at establishing the Fermi-Bose alternative, within our approach, is made.

Mathematical aspects of Feynman integrals

In the present dissertation we consider Feynman integrals in the framework of dimensional regularization. As all such integrals can be expressed in terms of scalar integrals, we focus on this latter kind of integrals in their Feynman parametric representation and study their mathematical properties, partially applying graph theory, algebraic geometry and number theory. The three main topics are the graph theoretic properties of the Symanzik polynomials, the termination of the sector decomposition algorithm of Binoth and Heinrich and the arithmetic nature of the Laurent coefficients of Feynman integrals.rnrnThe integrand of an arbitrary dimensionally regularised, scalar Feynman integral can be expressed in terms of the two well-known Symanzik polynomials. We give a detailed review on the graph theoretic properties of these polynomials. Due to the matrix-tree-theorem the first of these polynomials can be constructed from the determinant of a minor of the generic Laplacian matrix of a graph. By use of a generalization of this theorem, the all-minors-matrix-tree theorem, we derive a new relation which furthermore relates the second Symanzik polynomial to the Laplacian matrix of a graph.rnrnStarting from the Feynman parametric parameterization, the sector decomposition algorithm of Binoth and Heinrich serves for the numerical evaluation of the Laurent coefficients of an arbitrary Feynman integral in the Euclidean momentum region. This widely used algorithm contains an iterated step, consisting of an appropriate decomposition of the domain of integration and the deformation of the resulting pieces. This procedure leads to a disentanglement of the overlapping singularities of the integral. By giving a counter-example we exhibit the problem, that this iterative step of the algorithm does not terminate for every possible case. We solve this problem by presenting an appropriate extension of the algorithm, which is guaranteed to terminate. This is achieved by mapping the iterative step to an abstract combinatorial problem, known as Hironaka's polyhedra game. We present a publicly available implementation of the improved algorithm. Furthermore we explain the relationship of the sector decomposition method with the resolution of singularities of a variety, given by a sequence of blow-ups, in algebraic geometry.rnrnMotivated by the connection between Feynman integrals and topics of algebraic geometry we consider the set of periods as defined by Kontsevich and Zagier. This special set of numbers contains the set of multiple zeta values and certain values of polylogarithms, which in turn are known to be present in results for Laurent coefficients of certain dimensionally regularized Feynman integrals. By use of the extended sector decomposition algorithm we prove a theorem which implies, that the Laurent coefficients of an arbitrary Feynman integral are periods if the masses and kinematical invariants take values in the Euclidean momentum region. The statement is formulated for an even more general class of integrals, allowing for an arbitrary number of polynomials in the integrand.

Feasibility studies of the pp pi 0 e + e - electromagnetic channel at PANDA

Among all possible realizations of quark and antiquark assembly, the nucleon (the proton and the neutron) is the most stable of all hadrons and consequently has been the subject of intensive studies. Mass, shape, radius and more complex representations of its internal structure are measured since several decades using different probes. The proton (spin 1/2) is described by the electric GE and magnetic GM form factors which characterise its internal structure. The simplest way to measure the proton form factors consists in measuring the angular distribution of the electron-proton elastic scattering accessing the so-called Space-Like region where q2 < 0. Using the crossed channel antiproton proton <--> e+e-, one accesses another kinematical region, the so-called Time-Like region where q2 > 0. However, due to the antiproton proton <--> e+e- threshold q2th, only the kinematical domain q2 > q2th > 0 is available. To access the unphysical region, one may use the antiproton proton --> pi0 e+ e- reaction where the pi0 takes away a part of the system energy allowing q2 to be varied between q2th and almost 0. This thesis aims to show the feasibility of such measurements with the PANDA detector which will be installed on the new high intensity antiproton ring at the FAIR facility at Darmstadt. To describe the antiproton proton --> pi0 e+ e- reaction, a Lagrangian based approach is developed. The 5-fold differential cross section is determined and related to linear combinations of hadronic tensors. Under the assumption of one nucleon exchange, the hadronic tensors are expressed in terms of the 2 complex proton electromagnetic form factors. An extraction method which provides an access to the proton electromagnetic form factor ratio R = |GE|/|GM| and for the first time in an unpolarized experiment to the cosine of the phase difference is developed. Such measurements have never been performed in the unphysical region up to now. Extended simulations were performed to show how the ratio R and the cosine can be extracted from the positron angular distribution. Furthermore, a model is developed for the antiproton proton --> pi0 pi+ pi- background reaction considered as the most dangerous one. The background to signal cross section ratio was estimated under different cut combinations of the particle identification information from the different detectors and of the kinematic fits. The background contribution can be reduced to the percent level or even less. The corresponding signal efficiency ranges from a few % to 30%. The precision on the determination of the ratio R and of the cosine is determined using the expected counting rates via Monte Carlo method. A part of this thesis is also dedicated to more technical work with the study of the prototype of the electromagnetic calorimeter and the determination of its resolution.

Global modeling of pollutant transport and deposition from anthropogenic emission hot spots on global scale

Urban centers significantly contribute to anthropogenic air pollution, although they cover only a minor fraction of the Earth's land surface. Since the worldwide degree of urbanization is steadily increasing, the anthropogenic contribution to air pollution from urban centers is expected to become more substantial in future air quality assessments. The main objective of this thesis was to obtain a more profound insight in the dispersion and the deposition of aerosol particles from 46 individual major population centers (MPCs) as well as the regional and global influence on the atmospheric distribution of several aerosol types. For the first time, this was assessed in one model framework, for which the global model EMAC was applied with different representations of aerosol particles. First, in an approach with passive tracers and a setup in which the results depend only on the source location and the size and the solubility of the tracers, several metrics and a regional climate classification were used to quantify the major outflow pathways, both vertically and horizontally, and to compare the balance between pollution export away from and pollution build-up around the source points. Then in a more comprehensive approach, the anthropogenic emissions of key trace species were changed at the MPC locations to determine the cumulative impact of the MPC emissions on the atmospheric aerosol burdens of black carbon, particulate organic matter, sulfate, and nitrate. Ten different mono-modal passive aerosol tracers were continuously released at the same constant rate at each emission point. The results clearly showed that on average about five times more mass is advected quasi-horizontally at low levels than exported into the upper troposphere. The strength of the low-level export is mainly determined by the location of the source, while the vertical transport is mainly governed by the lifting potential and the solubility of the tracers. Similar to insoluble gas phase tracers, the low-level export of aerosol tracers is strongest at middle and high latitudes, while the regions of strongest vertical export differ between aerosol (temperate winter dry) and gas phase (tropics) tracers. The emitted mass fraction that is kept around MPCs is largest in regions where aerosol tracers have short lifetimes; this mass is also critical for assessing the impact on humans. However, the number of people who live in a strongly polluted region around urban centers depends more on the population density than on the size of the area which is affected by strong air pollution. Another major result was that fine aerosol particles (diameters smaller than 2.5 micrometer) from MPCs undergo substantial long-range transport, with about half of the emitted mass being deposited beyond 1000 km away from the source. In contrast to this diluted remote deposition, there are areas around the MPCs which experience high deposition rates, especially in regions which are frequently affected by heavy precipitation or are situated in poorly ventilated locations. Moreover, most MPC aerosol emissions are removed over land surfaces. In particular, forests experience more deposition from MPC pollutants than other land ecosystems. In addition, it was found that the generic treatment of aerosols has no substantial influence on the major conclusions drawn in this thesis. Moreover, in the more comprehensive approach, it was found that emissions of black carbon, particulate organic matter, sulfur dioxide, and nitrogen oxides from MPCs influence the atmospheric burden of various aerosol types very differently, with impacts generally being larger for secondary species, sulfate and nitrate, than for primary species, black carbon and particulate organic matter. While the changes in the burdens of sulfate, black carbon, and particulate organic matter show an almost linear response for changes in the emission strength, the formation of nitrate was found to be contingent upon many more factors, e.g., the abundance of sulfuric acid, than only upon the strength of the nitrogen oxide emissions. The generic tracer experiments were further extended to conduct the first risk assessment to obtain the cumulative risk of contamination from multiple nuclear reactor accidents on the global scale. For this, many factors had to be taken into account: the probability of major accidents, the cumulative deposition field of the radionuclide cesium-137, and a threshold value that defines contamination. By collecting the necessary data and after accounting for uncertainties, it was found that the risk is highest in western Europe, the eastern US, and in Japan, where on average contamination by major accidents is expected about every 50 years.

Picard-Fuchs equations of dimensionally regulated Feynman integrals

Zusammenfassung In der vorliegenden Arbeit besch¨aftige ich mich mit Differentialgleichungen von Feynman– Integralen. Ein Feynman–Integral h¨angt von einem Dimensionsparameter D ab und kann f¨ur ganzzahlige Dimension als projektives Integral dargestellt werden. Dies ist die sogenannte Feynman–Parameter Darstellung. In Abh¨angigkeit der Dimension kann ein solches Integral divergieren. Als Funktion in D erh¨alt man eine meromorphe Funktion auf ganz C. Ein divergentes Integral kann also durch eine Laurent–Reihe ersetzt werden und dessen Koeffizienten r¨ucken in das Zentrum des Interesses. Diese Vorgehensweise wird als dimensionale Regularisierung bezeichnet. Alle Terme einer solchen Laurent–Reihe eines Feynman–Integrals sind Perioden im Sinne von Kontsevich und Zagier. Ich beschreibe eine neue Methode zur Berechnung von Differentialgleichungen von Feynman– Integralen. ¨ Ublicherweise verwendet man hierzu die sogenannten ”integration by parts” (IBP)– Identit¨aten. Die neue Methode verwendet die Theorie der Picard–Fuchs–Differentialgleichungen. Im Falle projektiver oder quasi–projektiver Variet¨aten basiert die Berechnung einer solchen Differentialgleichung auf der sogenannten Griffiths–Dwork–Reduktion. Zun¨achst beschreibe ich die Methode f¨ur feste, ganzzahlige Dimension. Nach geeigneter Verschiebung der Dimension erh¨alt man direkt eine Periode und somit eine Picard–Fuchs–Differentialgleichung. Diese ist inhomogen, da das Integrationsgebiet einen Rand besitzt und daher nur einen relativen Zykel darstellt. Mit Hilfe von dimensionalen Rekurrenzrelationen, die auf Tarasov zur¨uckgehen, kann in einem zweiten Schritt die L¨osung in der urspr¨unglichen Dimension bestimmt werden. Ich beschreibe außerdem eine Methode, die auf der Griffiths–Dwork–Reduktion basiert, um die Differentialgleichung direkt f¨ur beliebige Dimension zu berechnen. Diese Methode ist allgemein g¨ultig und erspart Dimensionswechsel. Ein Erfolg der Methode h¨angt von der M¨oglichkeit ab, große Systeme von linearen Gleichungen zu l¨osen. Ich gebe Beispiele von Integralen von Graphen mit zwei und drei Schleifen. Tarasov gibt eine Basis von Integralen an, die Graphen mit zwei Schleifen und zwei externen Kanten bestimmen. Ich bestimme Differentialgleichungen der Integrale dieser Basis. Als wichtigstes Beispiel berechne ich die Differentialgleichung des sogenannten Sunrise–Graphen mit zwei Schleifen im allgemeinen Fall beliebiger Massen. Diese ist f¨ur spezielle Werte von D eine inhomogene Picard–Fuchs–Gleichung einer Familie elliptischer Kurven. Der Sunrise–Graph ist besonders interessant, weil eine analytische L¨osung erst mit dieser Methode gefunden werden konnte, und weil dies der einfachste Graph ist, dessen Master–Integrale nicht durch Polylogarithmen gegeben sind. Ich gebe außerdem ein Beispiel eines Graphen mit drei Schleifen. Hier taucht die Picard–Fuchs–Gleichung einer Familie von K3–Fl¨achen auf.

Conceptual and normative issues of memory enhancement

Our growing understanding of human mind and cognition and the development of neurotechnology has triggered debate around cognitive enhancement in neuroethics. The dissertation examines the normative issues of memory enhancement, and focuses on two issues: (1) the distinction between memory treatment and enhancement; and (2) how the issue of authenticity concerns memory interventions, including memory treatments and enhancements. rnThe first part consists of a conceptual analysis of the concepts required for normative considerations. First, the representational nature and the function of memory are discussed. Memory is regarded as a special form of self-representation resulting from a constructive processes. Next, the concepts of selfhood, personhood, and identity are examined and a conceptual tool—the autobiographical self-model (ASM)—is introduced. An ASM is a collection of mental representations of the system’s relations with its past and potential future states. Third, the debate between objectivist and constructivist views of health are considered. I argue for a phenomenological account of health, which is based on the primacy of illness and negative utilitarianism.rnThe second part presents a synthesis of the relevant normative issues based on the conceptual tools developed. I argue that memory enhancement can be distinguished from memory treatment using a demarcation regarding the existence of memory-related suffering. That is, memory enhancements are, under standard circumstances and without any unwilling suffering or potential suffering resulting from the alteration of memory functions, interventions that aim to manipulate memory function based on the self-interests of the individual. I then consider the issue of authenticity, namely whether memory intervention or enhancement endangers “one’s true self”. By analyzing two conceptions of authenticity—authenticity as self-discovery and authenticity as self-creation, I propose that authenticity should be understood in terms of the satisfaction of the functional constraints of an ASM—synchronic coherence, diachronic coherence, and global veridicality. This framework provides clearer criteria for considering the relevant concerns and allows us to examine the moral values of authenticity. rn