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.

Direct and inverse transient eddy current problems

Die vorliegende Arbeit behandelt Vorwärts- sowie Rückwärtstheorie transienter Wirbelstromprobleme. Transiente Anregungsströme induzieren elektromagnetische Felder, welche sogenannte Wirbelströme in leitfähigen Objekten erzeugen. Im Falle von sich langsam ändernden Feldern kann diese Wechselwirkung durch die Wirbelstromgleichung, einer Approximation an die Maxwell-Gleichungen, beschrieben werden. Diese ist eine lineare partielle Differentialgleichung mit nicht-glatten Koeffizientenfunktionen von gemischt parabolisch-elliptischem Typ. Das Vorwärtsproblem besteht darin, zu gegebener Anregung sowie den umgebungsbeschreibenden Koeffizientenfunktionen das elektrische Feld als distributionelle Lösung der Gleichung zu bestimmen. Umgekehrt können die Felder mit Messspulen gemessen werden. Das Ziel des Rückwärtsproblems ist es, aus diesen Messungen Informationen über leitfähige Objekte, also über die Koeffizientenfunktion, die diese beschreibt, zu gewinnen. In dieser Arbeit wird eine variationelle Lösungstheorie vorgestellt und die Wohlgestelltheit der Gleichung diskutiert. Darauf aufbauend wird das Verhalten der Lösung für verschwindende Leitfähigkeit studiert und die Linearisierbarkeit der Gleichung ohne leitfähiges Objekt in Richtung des Auftauchens eines leitfähigen Objektes gezeigt. Zur Regularisierung der Gleichung werden Modifikationen vorgeschlagen, welche ein voll parabolisches bzw. elliptisches Problem liefern. Diese werden verifiziert, indem die Konvergenz der Lösungen gezeigt wird. Zuletzt wird gezeigt, dass unter der Annahme von sonst homogenen Umgebungsparametern leitfähige Objekte eindeutig durch die Messungen lokalisiert werden können. Hierzu werden die Linear Sampling Methode sowie die Faktorisierungsmethode angewendet.

Galactic fountain flows in high-resolution hydrodynamical simulations of galaxy disks

Feedback from the most massive components of a young stellar cluster deeply affects the surrounding ISM driving an expanding over-pressured hot gas cavity in it. In spiral galaxies these structures may have sufficient energy to break the disk and eject large amount of material into the halo. The cycling of this gas, which eventually will fall back onto the disk, is known as galactic fountains. We aim at better understanding the dynamics of such fountain flow in a Galactic context, frame the problem in a more dynamic environment possibly learning about its connection and regulation to the local driving mechanism and understand its role as a metal diffusion channel. The interaction of the fountain with a hot corona is hereby analyzed, trying to understand the properties and evolution of the extraplanar material. We perform high resolution hydrodynamical simulations with the moving-mesh code AREPO to model the multi-phase ISM of a Milky Way type galaxy. A non-equilibrium chemical network is included to self consistently follow the evolution of the main coolants of the ISM. Spiral arm perturbations in the potential are considered so that large molecular gas structures are able to dynamically form here, self shielded from the interstellar radiation field. We model the effect of SN feedback from a new-born stellar cluster inside such a giant molecular cloud, as the driving force of the fountain. Passive Lagrangian tracer particles are used in conjunction to the SN energy deposition to model and study diffusion of freshly synthesized metals. We find that both interactions with hot coronal gas and local ISM properties and motions are equally important in shaping the fountain. We notice a bimodal morphology where most of the ejected gas is in a cold $10^4$ K clumpy state while the majority of the affected volume is occupied by a hot diffuse medium. While only about 20\% of the produced metals stay local, most of them quickly diffuse through this hot regime to great scales.

On a Problem of Burnside

Burnside posed the question as to whether or not there exist groups having an external automorphism that behaves in a certain, specific way like an inner automorphism: we shall define such automorphisms to be nearly-inner. NI-groups are fairly rare. With the aid of the computer algebra system Magma - in particular with the aid of its small group database - we set out to test this hypothesis.

The tolerance of ambiguity in late cochlear-implanted pre-lingually deaf juveniles

OBJECTIVES: To examine the ambiguity tolerance, i.e. the ability to perceive new, contradictory and complex situations as positive challenges, of pre-lingually deafened adolescents who received a cochlear implant after their eighth birthday and to identify those dimensions of ambiguity tolerance which correlate significantly with specific variables of their oral communication. DESIGN AND SETTING: Clinical survey at an academic tertiary referral center. Participants and main outcome measures: A questionnaire concerning communication and subjectively perceived changes compared to the pre-cochlear implant situation was completed by 13 pre-lingually deafened patients aged between 13 and 23 years, who received their cochlear implants between the ages of 8 and 17 years. The results were correlated with the 'Inventory for Measuring Ambiguity Tolerance'. RESULTS: The patients showed a lower ambiguity tolerance with a total score of 134.5 than the normative group with a score of 143.1. There was a positive correlation between the total score for ambiguity tolerance and the frequency of 'use of oral speech', as well as between the subscale 'ambiguity tolerance towards apparently insoluble problems' and all five areas of oral communication that were investigated. Comparison of two variables of oral communication, which shows a significant difference pre- and postoperatively, yields a positive correlation with the subscale 'ambiguity tolerance towards the parental image'. CONCLUSIONS: Pre-lingually deafened juveniles with cochlear implant who increasingly use oral communication seem to regard the limits of a cochlear implant as an interesting challenge rather than an insoluble problem.

Exigencies for engaging undergraduates in rhetorical problem solving : insights from engineering managers and A3 report analyses

Undergraduate education has a historical tradition of preparing students to meet the problem-solving challenges they will encounter in work, civic, and personal contexts. This thesis research was conducted to study the role of rhetoric in engineering problem solving and decision making and to pose pedagogical strategies for preparing undergraduate students for workplace problem solving. Exploratory interviews with engineering managers as well as the heuristic analyses of engineering A3 project planning reports suggest that Aristotelian rhetorical principles are critical to the engineer's success: Engineers must ascertain the rhetorical situation surrounding engineering problems; apply and adapt invention heuristics to conduct inquiry; draw from their investigation to find innovative solutions; and influence decision making by navigating workplace decision-making systems and audiences using rhetorically constructed discourse. To prepare undergraduates for workplace problem solving, university educators are challenged to help undergraduates understand the exigence and realize the kairotic potential inherent in rhetorical problem solving. This thesis offers pedagogical strategies that focus on mentoring learning communities in problem-posing experiences that are situated in many disciplinary, work, and civic contexts. Undergraduates build a flexible rhetorical technê for problem solving as they navigate the nuances of relevant problem-solving systems through the lens of rhetorical practice.

Clinical and esthetic outcomes of implants placed in postextraction sites

PURPOSE: The aim of this review was to evaluate the clinical outcomes for the different time points of implant placement following tooth extraction. MATERIALS AND METHODS: A PubMed search and a hand search of selected journals were performed to identify clinical studies published in English that reported on outcomes of implants in postextraction sites. Only studies that included 10 or more patients were accepted. For implant success/survival outcomes, only studies with a mean follow-up period of at least 12 months from the time of implant placement were included. The following outcomes were identified: (1) change in peri-implant defect dimension, (2) implant survival and success, and (3) esthetic outcomes. RESULTS AND CONCLUSIONS: Of 1,107 abstracts and 170 full-text articles considered, 91 studies met the inclusion criteria for this review. Bone augmentation procedures are effective in promoting bone fill and defect resolution at implants in postextraction sites, and are more successful with immediate (type 1) and early placement (type 2 and type 3) than with late placement (type 4). The majority of studies reported survival rates of over 95%. Similar survival rates were observed for immediate (type 1) and early (type 2) placement. Recession of the facial mucosal margin is common with immediate (type 1) placement. Risk indicators included a thin tissue biotype, a facial malposition of the implant, and a thin or damaged facial bone wall. Early implant placement (type 2 and type 3) is associated with a lower frequency of mucosal recession compared to immediate placement (type 1).

Detection of cryptic pathogenic copy number variations and constitutional loss of heterozygosity using high resolution SNP microarray analysis in 117 patients referred for cytogenetic analysis and impact on clinical practice

BACKGROUND: Microarray genome analysis is realising its promise for improving detection of genetic abnormalities in individuals with mental retardation and congenital abnormality. Copy number variations (CNVs) are now readily detectable using a variety of platforms and a major challenge is the distinction of pathogenic from ubiquitous, benign polymorphic CNVs. The aim of this study was to investigate replacement of time consuming, locus specific testing for specific microdeletion and microduplication syndromes with microarray analysis, which theoretically should detect all known syndromes with CNV aetiologies as well as new ones. METHODS: Genome wide copy number analysis was performed on 117 patients using Affymetrix 250K microarrays. RESULTS: 434 CNVs (195 losses and 239 gains) were found, including 18 pathogenic CNVs and 9 identified as "potentially pathogenic". Almost all pathogenic CNVs were larger than 500 kb, significantly larger than the median size of all CNVs detected. Segmental regions of loss of heterozygosity larger than 5 Mb were found in 5 patients. CONCLUSIONS: Genome microarray analysis has improved diagnostic success in this group of patients. Several examples of recently discovered "new syndromes" were found suggesting they are more common than previously suspected and collectively are likely to be a major cause of mental retardation. The findings have several implications for clinical practice. The study revealed the potential to make genetic diagnoses that were not evident in the clinical presentation, with implications for pretest counselling and the consent process. The importance of contributing novel CNVs to high quality databases for genotype-phenotype analysis and review of guidelines for selection of individuals for microarray analysis is emphasised.

Cell-based therapy facilitates venous thrombus resolution

Endothelial progenitor cells (EPC) are involved in many healing processes in cardiovascular diseases and can be found in spontaneously resolving venous thrombi. The purpose of the present study was to investigate whether the therapeutic administration of EPC might enhance the resolution of venous thrombi. For this purpose, venous thrombosis was induced in the infrarenal inferior vena cava (IVC) in 28 athymic nude rats. Culture expanded EPC derived from human peripheral blood mononuclear cells were injected intravenously two and four days after thrombus induction. Recanalisation of the IVC and thrombus organisation were assessed by laser Doppler measurements of the blood flow and immunohistochemical detection of endothelialised luminal structures in the thrombus. EPC transplantation resulted in significantly enhanced thrombus neovascularisation (capillary density: 186.6 +/- 26.7/HPF vs. 78 +/- 12.3/HPF, p<0.01; area covered by capillaries: 8.9 +/- 1.7 microm(2) vs. 2.5 +/- 1.3 microm(2), p<0.01) and was accompanied by a substantial increase in intra-thrombus blood flow (perfusion ratio: 0.7 +/- 0.07 vs. 0.3 +/- 0.08, p<0.02). These results were paralleled by augmented macrophage recruitment into resolving thrombi in the animals treated with EPC (39.4 +/- 4.7/HPF vs. 11.6 +/- 1.9/HPF, p<0.01). Our data suggest that EPC transplantation might be of clinical value to facilitate venous thrombus resolution in cases where current therapeutic options have limited success.

Genetic diversity and ecological success of Staphylococcus aureus strains colonizing humans

The genetic determinants and phenotypic traits which make a Staphylococcus aureus strain a successful colonizer are largely unknown. The genetic diversity and population structure of 133 S. aureus isolates from healthy, generally risk-free adult carriers were investigated using four different typing methods: multilocus sequence typing (MLST), amplified fragment length polymorphism analysis (AFLP), double-locus sequence typing (DLST), and spa typing were compared. Carriage isolates displayed great genetic diversity which could only be revealed fully by DLST. Results of AFLP and MLST were highly concordant in the delineation of genotypic clusters of closely related isolates, roughly equivalent to clonal complexes. spa typing and DLST provided considerably less phylogenetic information. The resolution of spa typing was similar to that of AFLP and inferior to that of DLST. AFLP proved to be the most universal method, combining a phylogeny-building capacity similar to that of MLST with a much higher resolution. However, it had a lower reproducibility than sequencing-based MLST, DLST, and spa typing. We found two cases of methicillin-resistant S. aureus colonization, both of which were most likely associated with employment at a health service. Of 21 genotypic clusters detected, 2 were most prevalent: cluster 45 and cluster 30 each colonized 24% of the carrier population. The number of bacteria found in nasal samples varied significantly among the clusters, but the most prevalent clusters were not particularly numerous in the nasal samples. We did not find much evidence that genotypic clusters were associated with different carrier characteristics, such as age, sex, medical conditions, or antibiotic use. This may provide empirical support for the idea that genetic clusters in bacteria are maintained in the absence of adaptation to different niches. Alternatively, carrier characteristics other than those evaluated here or factors other than human hosts may exert selective pressure maintaining genotypic clusters.

Gender in Theology and Religion: a Success Story?! Report from a Conference

In January 2011 some fifty scholars from different parts of Europe met in Groningen, the Netherlands for an expert meeting entitled Gender in theology and religion: a success story?! to analyze the factors that contribute to the successful mainstreaming of gender in a theological discipline and to reflect on the future of gender studies in theology and religious studies. Different speakers highlighted the many successes of gender studies in theology and religious studies: its power to 'trouble' the disciplines and their heuristic categories; its contribution to the development of other disciplines such as queer studies and postcolonial studies; the many PhD studies produced; the number of significant publications that had appeared over the last years. All indicate that gender studies in theology and religious studies have matured. But the participants also pointed towards the ambiguity of the success of gender studies in the academy: the indeterminacy of the institutional position and positions of gender studies in the theological disciplines in seminaries, departments faculties and universities; the lack of male scholars’ engagement in gender studies, which is expressed by their absence in these studies and/or the low reception of gender studies publications in their disciplines. Both ambiguities represent a danger for the future of gender studies, according to the participants in the meeting. In order to further the success of gender in theology and religion they formulated the following recommendations: to analyze the position of these studies in their institutions from the perspective of the implied audience (church, academy, ordinary theologians); engage men in gender studies; embrace the cultural turn in religious studies; develop interdisciplinary cooperations with gender studies in the humanities; engage creatively with the changing role of religion in contemporary society; analyze whose perspective one follows and authorizes in the perception of theology, religious studies and gender studies themselves; record the history of women’s and gender studies in theology and religion, and honor and celebrate the successes.

A comment on the article “A collinearity diagnosis of the GNSS geocenter determination” by P. Rebischung, Z. Altamimi, and T. Springer

Meindl et al. (Adv Space Res 51(7):1047–1064, 2013) showed that the geocenter z -component estimated from observations of global navigation satellite systems (GNSS) is strongly correlated to a particular parameter of the solar radiation pressure (SRP) model developed by Beutler et al. (Manuscr Geod 19:367–386, 1994). They analyzed the forces caused by SRP and the impact on the satellites’ orbits. The authors achieved their results using perturbation theory and celestial mechanics. Rebischung et al. (J Geod doi:10.1016/j.asr.2012.10.026, 2013) also deal with the geocenter determination with GNSS. The authors carried out a collinearity diagnosis of the associated parameter estimation problem. They conclude “without much exaggerating that current GNSS are insensitive to any component of geocenter motion”. They explain this inability by the high degree of collinearity of the geocenter coordinates mainly with satellite clock corrections. Based on these results and additional experiments, they state that the conclusions drawn by Meindl et al. (Adv Space Res 51(7):1047–1064, 2013) are questionable. We do not agree with these conclusions and present our arguments in this article. In the first part, we review and highlight the main characteristics of the studies performed by Meindl et al. (Adv Space Res 51(7):1047–1064, 2013) to show that the experiments are quite different from those performed by Rebischung et al. (J Geod doi:10.1016/j.asr.2012.10.026,2013) . In the second part, we show that normal equation (NEQ) systems are regular when estimating geocenter coordinates, implying that the covariance matrices associated with the NEQ systems may be used to assess the sensitivity to geocenter coordinates in a standard way. The sensitivity of GNSS to the components of the geocenter is discussed. Finally, we comment on the arguments raised by Rebischung et al. (J Geod doi:10.1016/j.asr.2012.10.026, 2013) against the results of Meindl et al. (Adv Space Res 51(7):1047–1064, 2013).

Automatic multi-resolution shape modeling of multi-organ structures.

Point Distribution Models (PDM) are among the most popular shape description techniques and their usefulness has been demonstrated in a wide variety of medical imaging applications. However, to adequately characterize the underlying modeled population it is essential to have a representative number of training samples, which is not always possible. This problem is especially relevant as the complexity of the modeled structure increases, being the modeling of ensembles of multiple 3D organs one of the most challenging cases. In this paper, we introduce a new GEneralized Multi-resolution PDM (GEM-PDM) in the context of multi-organ analysis able to efficiently characterize the different inter-object relations, as well as the particular locality of each object separately. Importantly, unlike previous approaches, the configuration of the algorithm is automated thanks to a new agglomerative landmark clustering method proposed here, which equally allows us to identify smaller anatomically significant regions within organs. The significant advantage of the GEM-PDM method over two previous approaches (PDM and hierarchical PDM) in terms of shape modeling accuracy and robustness to noise, has been successfully verified for two different databases of sets of multiple organs: six subcortical brain structures, and seven abdominal organs. Finally, we propose the integration of the new shape modeling framework into an active shape-model-based segmentation algorithm. The resulting algorithm, named GEMA, provides a better overall performance than the two classical approaches tested, ASM, and hierarchical ASM, when applied to the segmentation of 3D brain MRI.

Dus grose success lied "Unser neue Heim" : sung by Joseph Shoengold in Isidore Solotorefsky's "Yesoimem fin der Welt" (Orphan's of the world) ; played at Liberty Theatre East New York

music by Peretz Sandler. Words by Isidor Lilien