Efficient parallel proximity queries and an application to highly complex motion planning problems with many narrow passages

In vielen Bereichen der industriellen Fertigung, wie zum Beispiel in der Automobilindustrie, wer- den digitale Versuchsmodelle (sog. digital mock-ups) eingesetzt, um die Entwicklung komplexer Maschinen m ̈oglichst gut durch Computersysteme unterstu ̈tzen zu k ̈onnen. Hierbei spielen Be- wegungsplanungsalgorithmen eine wichtige Rolle, um zu gew ̈ahrleisten, dass diese digitalen Pro- totypen auch kollisionsfrei zusammengesetzt werden k ̈onnen. In den letzten Jahrzehnten haben sich hier sampling-basierte Verfahren besonders bew ̈ahrt. Diese erzeugen eine große Anzahl von zuf ̈alligen Lagen fu ̈r das ein-/auszubauende Objekt und verwenden einen Kollisionserken- nungsmechanismus, um die einzelnen Lagen auf Gu ̈ltigkeit zu u ̈berpru ̈fen. Daher spielt die Kollisionserkennung eine wesentliche Rolle beim Design effizienter Bewegungsplanungsalgorith- men. Eine Schwierigkeit fu ̈r diese Klasse von Planern stellen sogenannte “narrow passages” dar, schmale Passagen also, die immer dort auftreten, wo die Bewegungsfreiheit der zu planenden Objekte stark eingeschr ̈ankt ist. An solchen Stellen kann es schwierig sein, eine ausreichende Anzahl von kollisionsfreien Samples zu finden. Es ist dann m ̈oglicherweise n ̈otig, ausgeklu ̈geltere Techniken einzusetzen, um eine gute Performance der Algorithmen zu erreichen.rnDie vorliegende Arbeit gliedert sich in zwei Teile: Im ersten Teil untersuchen wir parallele Kollisionserkennungsalgorithmen. Da wir auf eine Anwendung bei sampling-basierten Bewe- gungsplanern abzielen, w ̈ahlen wir hier eine Problemstellung, bei der wir stets die selben zwei Objekte, aber in einer großen Anzahl von unterschiedlichen Lagen auf Kollision testen. Wir im- plementieren und vergleichen verschiedene Verfahren, die auf Hu ̈llk ̈operhierarchien (BVHs) und hierarchische Grids als Beschleunigungsstrukturen zuru ̈ckgreifen. Alle beschriebenen Verfahren wurden auf mehreren CPU-Kernen parallelisiert. Daru ̈ber hinaus vergleichen wir verschiedene CUDA Kernels zur Durchfu ̈hrung BVH-basierter Kollisionstests auf der GPU. Neben einer un- terschiedlichen Verteilung der Arbeit auf die parallelen GPU Threads untersuchen wir hier die Auswirkung verschiedener Speicherzugriffsmuster auf die Performance der resultierenden Algo- rithmen. Weiter stellen wir eine Reihe von approximativen Kollisionstests vor, die auf den beschriebenen Verfahren basieren. Wenn eine geringere Genauigkeit der Tests tolerierbar ist, kann so eine weitere Verbesserung der Performance erzielt werden.rnIm zweiten Teil der Arbeit beschreiben wir einen von uns entworfenen parallelen, sampling- basierten Bewegungsplaner zur Behandlung hochkomplexer Probleme mit mehreren “narrow passages”. Das Verfahren arbeitet in zwei Phasen. Die grundlegende Idee ist hierbei, in der er- sten Planungsphase konzeptionell kleinere Fehler zuzulassen, um die Planungseffizienz zu erh ̈ohen und den resultierenden Pfad dann in einer zweiten Phase zu reparieren. Der hierzu in Phase I eingesetzte Planer basiert auf sogenannten Expansive Space Trees. Zus ̈atzlich haben wir den Planer mit einer Freidru ̈ckoperation ausgestattet, die es erlaubt, kleinere Kollisionen aufzul ̈osen und so die Effizienz in Bereichen mit eingeschr ̈ankter Bewegungsfreiheit zu erh ̈ohen. Optional erlaubt unsere Implementierung den Einsatz von approximativen Kollisionstests. Dies setzt die Genauigkeit der ersten Planungsphase weiter herab, fu ̈hrt aber auch zu einer weiteren Perfor- mancesteigerung. Die aus Phase I resultierenden Bewegungspfade sind dann unter Umst ̈anden nicht komplett kollisionsfrei. Um diese Pfade zu reparieren, haben wir einen neuartigen Pla- nungsalgorithmus entworfen, der lokal beschr ̈ankt auf eine kleine Umgebung um den bestehenden Pfad einen neuen, kollisionsfreien Bewegungspfad plant.rnWir haben den beschriebenen Algorithmus mit einer Klasse von neuen, schwierigen Metall- Puzzlen getestet, die zum Teil mehrere “narrow passages” aufweisen. Unseres Wissens nach ist eine Sammlung vergleichbar komplexer Benchmarks nicht ̈offentlich zug ̈anglich und wir fan- den auch keine Beschreibung von vergleichbar komplexen Benchmarks in der Motion-Planning Literatur.

Entanglement entropy in 1-d quantum spin chains

In questa tesi abbiamo studiato il comportamento delle entropie di Entanglement e dello spettro di Entanglement nel modello XYZ attraverso delle simulazioni numeriche. Le formule per le entropie di Von Neumann e di Renyi nel caso di una catena bipartita infinita esistevano già, ma mancavano ancora dei test numerici dettagliati. Inoltre, rispetto alla formula per l'Entropia di Entanglement di J. Cardy e P. Calabrese per sistemi non critici, tali relazioni presentano delle correzioni che non hanno ancora una spiegazione analitica: i risultati delle simulazioni numeriche ne hanno confermato la presenza. Abbiamo inoltre testato l'ipotesi che lo Schmidt Gap sia proporzionale a uno dei parametri d'ordine della teoria, e infine abbiamo simulato numericamente l'andamento delle Entropie e dello spettro di Entanglement in funzione della lunghezza della catena di spin. Ciò è stato possibile solo introducendo dei campi magnetici ''ad hoc'' nella catena, con la proprietà che l'andamento delle suddette quantità varia a seconda di come vengono disposti tali campi. Abbiamo quindi discusso i vari risultati ottenuti.

Spectral theory of differential operators on finite metric graphs and on bounded domains

Die vorliegende Arbeit widmet sich der Spektraltheorie von Differentialoperatoren auf metrischen Graphen und von indefiniten Differentialoperatoren auf beschränkten Gebieten. Sie besteht aus zwei Teilen. Im Ersten werden endliche, nicht notwendigerweise kompakte, metrische Graphen und die Hilberträume von quadratintegrierbaren Funktionen auf diesen betrachtet. Alle quasi-m-akkretiven Laplaceoperatoren auf solchen Graphen werden charakterisiert, und Abschätzungen an die negativen Eigenwerte selbstadjungierter Laplaceoperatoren werden hergeleitet. Weiterhin wird die Wohlgestelltheit eines gemischten Diffusions- und Transportproblems auf kompakten Graphen durch die Anwendung von Halbgruppenmethoden untersucht. Eine Verallgemeinerung des indefiniten Operators $-tfrac{d}{dx}sgn(x)tfrac{d}{dx}$ von Intervallen auf metrische Graphen wird eingeführt. Die Spektral- und Streutheorie der selbstadjungierten Realisierungen wird detailliert besprochen. Im zweiten Teil der Arbeit werden Operatoren untersucht, die mit indefiniten Formen der Art $langlegrad v, A(cdot)grad urangle$ mit $u,vin H_0^1(Omega)subset L^2(Omega)$ und $OmegasubsetR^d$ beschränkt, assoziiert sind. Das Eigenwertverhalten entspricht in Dimension $d=1$ einer verallgemeinerten Weylschen Asymptotik und für $dgeq 2$ werden Abschätzungen an die Eigenwerte bewiesen. Die Frage, wann indefinite Formmethoden für Dimensionen $dgeq 2$ anwendbar sind, bleibt offen und wird diskutiert.

Fontaine modules and F-T-crystals, a dévissage

Das Hauptziel der Arbeit ist es, die Beziehung zwischen Fontaine Modulen und F-T-Kristall zu studieren. Im ersten Kapitel wird die Definition von Fontaine Modulen, die auf die inversen Cartier Transform setzt erinnern wir von Ogus und Vologodsky errichtet. Neben der Erinnerung an die urspruengliche Konstruktion des inversen Cartier Transform, eine direktere Konstruktion, die wir auch vorstellen von G.T. Lan, M. Sheng und K. Zuo. Darueber hinaus beweisen wir diernGleichwertigkeit der beiden Konstruktion.rnrnrnIm zweiten Kapitel werden wir uns daran erinnern, den Konstruktion von inversen Cartier Transform in der Log Einstellung von D. Schepler und verallgemeinern die Lan-Sheng-Zuo Konstruktion an dieser Einstellung. Darueber hinaus geben wir eine Definition von Log FontainernModulen. Im dritten Kapitel werden wir erinnern an die Definition von F-T-Kristall und beweisen das wichtigste Ergebnis dieser Arbeit: Sei $Y$ eine glatte $S_{nu}$-Schema, wobei $S_{nu}$ ist eine flache $W_{nu+1}(k)$-Schema, $nugeq1$, und $X/S_0$ seine Reduction modulo $p$ sein. Bei einem F-T-Kristall $(E,Phi,B)$ auf $Y$ der Breite von weniger als $p$ und let $(E_Y ,B_Y ,nabla_Y)$ die entsprechende gefilterte $O_Y$-modulen mit einer integrierbar Zusammenhang ausgestattet. Anschliesend wird die Reduktion dieses Objekt modulo $p$ definiert eine Fontaine Modulen auf $X/S_0$ im dem Sinnernder Ogus und Vologodsky.

Hunting for warped extra dimensions via loop-induced processes

This thesis is on loop-induced processes in theories with warped extra dimensions where the fermions and gauge bosons are allowed to propagate in the bulk, while the Higgs sector is localized on or near the infra-red brane. These so-called Randall-Sundrum (RS) models have the potential to simultaneously explain the hierarchy problem and address the question of what causes the large hierarchies in the fermion sector of the Standard Model (SM). The Kaluza-Klein (KK) excitations of the bulk fields can significantly affect the loop-level processes considered in this thesis and, hence, could indirectly indicate the existence of warped extra dimensions. The analytical part of this thesis deals with the detailed calculation of three loop-induced processes in the RS models in question: the Higgs production process via gluon fusion, the Higgs decay into two photons, and the flavor-changing neutral current b → sγ. A comprehensive, five-dimensional (5D) analysis will show that the amplitudes of the Higgs processes can be expressed in terms of integrals over 5D propagators with the Higgs-boson profile along the extra dimension, which can be used for arbitrary models with a compact extra dimension. To this end, both the boson and fermion propagators in a warped 5D background are derived. It will be shown that the seemingly contradictory results for the gluon fusion amplitude in the literature can be traced back to two distinguishable, not smoothly-connected incarnations of the RS model. The investigation of the b → sγ transition is performed in the KK decomposed theory. It will be argued that summing up the entire KK tower leads to a finite result, which can be well approximated by a closed, analytical expression.rnIn the phenomenological part of this thesis, the analytic results of all relevant Higgs couplings in the RS models in question are compared with current and in particular future sensitivities of the Large Hadron Collider (LHC) and the planned International Linear Collider. The latest LHC Higgs data is then used to exclude significant portions of the parameter space of each RS scenario. The analysis will demonstrate that especially the loop-induced Higgs couplings are sensitive to KK particles of the custodial RS model with masses in the multi tera-electronvolt range. Finally, the effect of the RS model on three flavor observables associated with the b → sγ transition are examined. In particular, we study the branching ratio of the inclusive decay B → X_s γ

Applications of elliptic functions to solve differential equations

In questa tesi si mostrano alcune applicazioni degli integrali ellittici nella meccanica Hamiltoniana, allo scopo di risolvere i sistemi integrabili. Vengono descritte le funzioni ellittiche, in particolare la funzione ellittica di Weierstrass, ed elenchiamo i tipi di integrali ellittici costruendoli dalle funzioni di Weierstrass. Dopo aver considerato le basi della meccanica Hamiltoniana ed il teorema di Arnold Liouville, studiamo un esempio preso dal libro di Moser-Integrable Hamiltonian Systems and Spectral Theory, dove si prendono in considerazione i sistemi integrabili lungo la geodetica di un'ellissoide, e il sistema di Von Neumann. In particolare vediamo che nel caso n=2 abbiamo un integrale ellittico.

A Divided City in a Common Market: EU Citizenship and Everyday Instrumentalities on the Polish-German Border

Based on an ethnographic case study in the border cities of Frankfurt (Oder), Germany and Słubice, Poland, this article explores the construction and maintenance of ethnic difference within the transnational economic and social spaces created by the European Union's common market. Through an examination of three domains of cross-border citizenship practice - shopping and consumption, housing and work - this article argues that even as the European Union deploys policies aimed at creating de-territorialised and supranational forms of identity and citizenship, economic asymmetries and hierarchies of value embedded within these policies grant rights differentially in ways that continue to be linked to ethnicity and nationality.

Porous silicon technology for integrated microsystems

With the development of micro systems, there is an increasing demand for integrable porous materials. In addition to those conventional applications, such as filtration, wicking, and insulating, many new micro devices, including micro reactors, sensors, actuators, and optical components, can benefit from porous materials. Conventional porous materials, such as ceramics and polymers, however, cannot meet the challenges posed by micro systems, due to their incompatibility with standard micro-fabrication processes. In an effort to produce porous materials that can be used in micro systems, porous silicon (PS) generated by anodization of single crystalline silicon has been investigated. In this work, the PS formation process has been extensively studied and characterized as a function of substrate type, crystal orientation, doping concentration, current density and surfactant concentration and type. Anodization conditions have been optimized for producing very thick porous silicon layers with uniform pore size, and for obtaining ideal pore morphologies. Three different types of porous silicon materials: meso porous silicon, macro porous silicon with straight pores, and macro porous silicon with tortuous pores, have been successfully produced. Regular pore arrays with controllable pore size in the range of 2µm to 6µm have been demonstrated as well. Localized PS formation has been achieved by using oxide/nitride/polysilicon stack as masking materials, which can withstand anodization in hydrofluoric acid up to twenty hours. A special etching cell with electrolytic liquid backside contact along with two process flows has been developed to enable the fabrication of thick macro porous silicon membranes with though wafer pores. For device assembly, Si-Au and In-Au bonding technologies have been developed. Very low bonding temperature (~200 degrees C) and thick/soft bonding layers (~6µm) have been achieved by In-Au bondi ng technology, which is able to compensate the potentially rough surface on the porous silicon sample without introducing significant thermal stress. The application of the porous silicon material in micro systems has been demonstrated in a micro gas chromatograph system by two indispensable components: an integrated vapor source and an inlet filter, wherein porous silicon performs the basic functions of porous media: wicking and filtration. By utilizing a macro porous silicon wick, the calibration vapor source was able to produce a uniform and repeatable vapor generation for n-decane with less than a 0.1% variation in 9 hours, and less than a 0.5% variation in rate over 7 days. With engineered porous silicon membranes the inlet filter was able to show a depth filtration with nearly 100% collection efficiency for particles larger than 0.3µm in diameter, a low pressure-drop of 523Pa at 20sccm flow rate, and a filter capacity of 500µg/cm2.

Large deviations for heavy-tailed random elements in convex cones

We prove large deviation results for sums of heavy-tailed random elements in rather general convex cones being semigroups equipped with a rescaling operation by positive real numbers. In difference to previous results for the cone of convex sets, our technique does not use the embedding of cones in linear spaces. Examples include the cone of convex sets with the Minkowski addition, positive half-line with maximum operation and the family of square integrable functions with arithmetic addition and argument rescaling.

Statusinkonsistenz im Lebensverlauf

Sozialbiographische Überlegungen und die Lebensverlaufsperspektive tragen zu einem Fortschritt in der Inkonsistenzforschung bei. Wichtige theoretische und methodische Voraussetzungen sind dabei die Berücksichtigung der Dynamik von Statusinkonsistenz und die Kontrolle der Zeitabhängigkeit von Statuslagen. Dadurch wird es möglich, Entstehen, Verschwinden, Dauer und Folgen von Statusinkonsistenz detailliert zu untersuchen. Die empirischen Befunde des Artikels zeigen, daß die Verortung von Individuen in einer Statushierarchie im Lebenslauf zunehmend mit vergleichbaren Plazierungen in anderen Statusdimensionen übereinstimmt. Dies verstärkt sich in der Abfolge von Geburtskohorten; ferner finden sich eher Frauen als Männer in ungünstigen statusinkonsistenten Lagen. Schließlich hat Statusinkonsistenz deutliche Auswirkungen auf berufliche Mobilität von Männern. Eine ungünstige Statuslage 'erzwingt' Mobilität, wenn, gemessen an der Bildung, unerwartete Statusverluste ausgeglichen werden sollen. Männer mit unerwarteten Statusgewinnen versuchen dagegen, ihre vorteilhafte Statuslage abzusichern, und sind eher immobil.

Hybrid bodies in cyborg sports? The case of Oscar Pistorius

The capabilities of postmodern biotechnology inevitably lead to questioning if it is morally acceptable to use all possibilities offered by technology. In sport, this very complex issue is dealt with by drawing clear boundaries between naturalness and artificiality. Currently, new biotechnology is constantly being produced and with this, boundaries between naturalness and artificiality, between normal and abnormal, human and hybrid are constantly shifting . “Human enhancement” is a fascinating prism that reflects contemporary questions of participation, justice, equality and the autonomy of the subject in all social fields. The area of elite sports is particularly affected by “human enhancement”, according to the principle of exceeding what has come before, of aiming higher, faster and further. This paper analyses the postulated “naturalness” in the regulative and normalising function in the area of elite sports, in connection with Foucault’s theory of governmentality. The example of the South African sprinter Oscar Pistorius appears to be particularly suited to illustrate current definition difficulties in the area of disabled and non-disabled people in differentiated competitive sports. His is a vivid example of a multifaceted body-sociological analysis of current sport culture and the construction of reality or naturalness in the framework of the discourse of drafting and negotiating the accreditation for sprint competitions of non-disabled athletes, most recently in the London Olympics 2012. Using the case study of Oscar Pistorius, the negotiating processes in relation to the argumentation logic, dynamics and resistance in shifting distinctions are presented in detail using the fundamental documents of the IOC, IPC, CAS and IAAF. Represented through the inclusion and exclusion processes are hierarchies of the body that are (re)consolidated and transformed. The central question emerges as to how the worth of equal opportunity and fairness in regard to “naturalness” can be reconsolidated or transformed.

The diffusion of /l/ -vocalization in Swiss German

Several western Swiss German dialects roughly grouped around the nation's capital Bern show /l/ > [u] vocalization in various contexts. The spatial boundaries of /l/-vocalization in Swiss German are suspected to have been expanding since being described in the Linguistic Atlas of German-Speaking Switzerland in the middle of the 20th century. The present study assesses the overall expansion of /l/-vocalization by means of a rapid anonymous survey in 20 urban regional centers situated just beyond the traditional boundaries of /l/-vocalization highlighted by the Atlas. Results show that the expansion of /l/-vocalization mainly progresses in southeasterly, southerly, and westerly directions, but with much less success to the north and northwest, where the equally influential dialectal areas of Basel and Zürich seem to exert opposing influences. Further analysis of the data indicates that somewhat differing constraint hierarchies are at work in the different places to which vocalization has diffused.

Current State of Reporting Pain Outcomes in Cochrane Reviews of Chronic Musculoskeletal Pain Conditions and Considerations for an OMERACT Research Agenda.

OBJECTIVE To assess the current state of reporting of pain outcomes in Cochrane reviews on chronic musculoskeletal painful conditions and to elicit opinions of patients, healthcare practitioners, and methodologists on presenting pain outcomes to patients, clinicians, and policymakers. METHODS We identified all reviews in the Cochrane Library of chronic musculoskeletal pain conditions from Cochrane review groups (Back, Musculoskeletal, and Pain, Palliative, and Supportive Care) that contained a summary of findings (SoF) table. We extracted data on reported pain domains and instruments and conducted a survey and interviews on considerations for SoF tables (e.g., pain domains, presentation of results). RESULTS Fifty-seven SoF tables in 133 Cochrane reviews were eligible. SoF tables reported pain in 56/57, with all presenting results for pain intensity (20 different outcome instruments), pain interference in 8 SoF tables (5 different outcome instruments), and pain frequency in 1 multiple domain instrument. Other domains like pain quality or pain affect were not reported. From the survey and interviews [response rate 80% (36/45)], we derived 4 themes for a future research agenda: pain domains, considerations for assessing truth, discrimination, and feasibility; clinically important thresholds for responder analyses and presenting results; and establishing hierarchies of outcome instruments. CONCLUSION There is a lack of standardization in the domains of pain selected and the manner that pain outcomes are reported in SoF tables, hampering efforts to synthesize evidence. Future research should focus on the themes identified, building partnerships to achieve consensus and develop guidance on best practices for reporting pain outcomes.

Yang-Baxter deformations of Minkowski spacetime

We study Yang-Baxter deformations of 4D Minkowski spacetime. The Yang-Baxter sigma model description was originally developed for principal chiral models based on a modified classical Yang-Baxter equation. It has been extended to coset curved spaces and models based on the usual classical Yang-Baxter equation. On the other hand, for flat space, there is the obvious problem that the standard bilinear form degenerates if we employ the familiar coset Poincaré group/Lorentz group. Instead we consider a slice of AdS5 by embedding the 4D Poincaré group into the 4D conformal group SO(2, 4) . With this procedure we obtain metrics and B-fields as Yang-Baxter deformations which correspond to well-known configurations such as T-duals of Melvin backgrounds, Hashimoto-Sethi and Spradlin-Takayanagi-Volovich backgrounds, the T-dual of Grant space, pp-waves, and T-duals of dS4 and AdS4. Finally we consider a deformation with a classical r-matrix of Drinfeld-Jimbo type and explicitly derive the associated metric and B-field which we conjecture to correspond to a new integrable system.