Differential forms on Carnot groups

The main goal of this thesis is to understand and link together some of the early works by Michel Rumin and Pierre Julg. The work is centered around the so-called Rumin complex, which is a construction in subRiemannian geometry. A Carnot manifold is a manifold endowed with a horizontal distribution. If further a metric is given, one gets a subRiemannian manifold. Such data arise in different contexts, such as: - formulation of the second principle of thermodynamics; - optimal control; - propagation of singularities for sums of squares of vector fields; - real hypersurfaces in complex manifolds; - ideal boundaries of rank one symmetric spaces; - asymptotic geometry of nilpotent groups; - modelization of human vision. Differential forms on a Carnot manifold have weights, which produces a filtered complex. In view of applications to nilpotent groups, Rumin has defined a substitute for the de Rham complex, adapted to this filtration. The presence of a filtered complex also suggests the use of the formal machinery of spectral sequences in the study of cohomology. The goal was indeed to understand the link between Rumin's operator and the differentials which appear in the various spectral sequences we have worked with: - the weight spectral sequence; - a special spectral sequence introduced by Julg and called by him Forman's spectral sequence; - Forman's spectral sequence (which turns out to be unrelated to the previous one). We will see that in general Rumin's operator depends on choices. However, in some special cases, it does not because it has an alternative interpretation as a differential in a natural spectral sequence. After defining Carnot groups and analysing their main properties, we will introduce the concept of weights of forms which will produce a splitting on the exterior differential operator d. We shall see how the Rumin complex arises from this splitting and proceed to carry out the complete computations in some key examples. From the third chapter onwards we will focus on Julg's paper, describing his new filtration and its relationship with the weight spectral sequence. We will study the connection between the spectral sequences and Rumin's complex in the n-dimensional Heisenberg group and the 7-dimensional quaternionic Heisenberg group and then generalize the result to Carnot groups using the weight filtration. Finally, we shall explain why Julg required the independence of choices in some special Rumin operators, introducing the Szego map and describing its main properties.

Compliance lebertransplantierter Patienten mit dem Immunsuppressivum Tacrolimus bei 2x täglicher im Vergleich zu 1x täglicher Einnahme

Compliance lebertransplantierter Patienten mit der immunsuppressiven Therapie ist unerlässlich für den lang-fristigen Erfolg der Lebertransplantation. Aus Non-Compliance mit der immunsuppressiven Therapie können Abstoßungsreaktionen, Organverlust oder sogar Tod resultieren. Hauptziel der vorliegenden Studie war die erstmalige Evaluation der Compliance bei Einnahme von Prograf® (zweimal tägliche Einnahme von Tacrolimus) im Vergleich zur Einnahme von Advagraf® (einmal tägliche Einnahme von Tacrolimus). Von Interesse war außerdem die Fragestellung, ob sich die Compliance bezüglich der immunsuppressiven Therapie mit dem Zeitabstand zur Transplantation verändert. rnDie Compliancemessung wurde offen mittels MEMS® (Aardex Ltd., Schweiz) durchgeführt, der Patient war also über die Compliancekontrolle informiert. Mittels MEMS® konnten Datum und Uhrzeit der Dosisentnahme dokumentiert und damit zuverlässig das gesamte Compliancemuster über im Durchschnitt 176 Tage mit der zweimal täglichen Einnahme und 188 Tage mit der einmal täglichen Einnahme pro Patient erfasst werden. 65 Patienten mit dem Basisimmunsuppressivum Prograf® wurden in die prospektive, nicht-interventionelle Studie eingeschlossen und nach Per Protokoll-Analyse konnten die Daten von 63 in Mainz lebertransplantierten Patienten ausgewertet werden (Prograf®: Gruppe 1: 15 Patienten (Pat.), Gruppe 2: 23 Pat., Gruppe 3: 22 Pat., Drop-outs: 3 Pat.; Advagraf®: Gruppe 1: 16 Pat., Gruppe 2: 23 Pat., Gruppe 3: 23 Pat., Drop-outs: 1 Pat.). Die Dosing Compliance (DC), definiert als Prozent der Tage, an denen der MEMS®-Behälter korrekt geöffnet und die Dosis höchstwahrscheinlich korrekt eingenommen wurde, war der primäre Zielparameter. Weitere Methoden der Compliancemessung, wie der Pill Count, mehrere Fragebögen (Selbsteinschätzung, Patientenwissen-, Morisky-, MESI-, HADS-, SF-36- und Patientenzufriedenheit-Fragebogen) sowie die Blutspiegelmessung wurden eingesetzt, um die Compliance der Patienten umfassend charakterisieren zu können. rnDer Median der DC mit der zweimal täglichen Einnahme betrug 97% bei Pat. > 6 m.p.t. < 2 y.p.t., 97% bei Pat. > 2 y.p.t. < 5 y.p.t. und 98% bei Pat. > 5 y.p.t. (p=0,931; Kruskal-Wallis-Test). Der Median der DC von Tacroli-mus bei einmal täglicher Einnahme (Advagraf®) betrug 99% bei Pat. > 6 m.p.t. < 2 y.p.t., 98% bei Pat. > 2 y.p.t. < 5 y.p.t. und 97% bei Pat. > 5 y.p.t. (p=0,158; Kruskal-Wallis-Test). Insgesamt zeigten die Patienten während des gesamten Beobachtungszeitraums von 12 Monaten eine gute Compliance für die Einnahme ihres Immun-suppressivums. Die Timing Compliance (TiC)-raten lagen auf einem niedrigeren Niveau als die Dosing- und Taking Compliance (TC)-raten. Die Complianceraten der drei Subgruppen unterschieden sich nicht signifikant. Die Patienten mit dem geringsten Abstand zur Transplantation zeigten bei beinahe allen Messmethoden die höchste Compliance im Gegensatz zur etwas geringeren Compliance der Patienten mit größerem Abstand zur Transplantation. Die während der Advagraf®-Phase mittels MEMS® gemessenen DC-, TC- und TiC-raten fielen höher aus als bei Einnahme von Prograf® (p(DC)=0,003; p(TC)=0,077; p(TiC)=0,003; Wilcoxon Vorzeichen-Rang-Test). Dieses Ergebnis untermauert die in anderen Indikationen gefundene Complianceverbesserung durch die einmal tägliche Arzneimittelgabe im Vergleich zur zweimal täglichen Gabe. Die Auswertung der Drug Holidays ergab für die Advagraf®-Phase hingegen niedrigere Complianceraten als für die Prograf®-Phase. Dieses Ergebnis ist auf die Definition des Drug Holidays (keine Arzneimitteleinnahme über 48 h) zurück zu führen. Die Chance Advagraf® einmal pro Tag zu vergessen ist doppelt so hoch, als Prograf® dreimal aufeinander fol-gend zu vergessen. Mit einer verhältnismäßigeren Definition von Drug Holidays (Einnahmepause von 72 Stun-den bei einmal täglicher Einnahme von Advagraf® entsprechend drei ausgelassenen Dosen von Prograf®) ist die Compliancerate 81%. Die Ergebnisse des Pill Counts waren sowohl bei Einnahme von Prograf® als auch von Advagraf® mit der jeweils gemessenen TC vergleichbar, was die Zuverlässigkeit der Messergebnisse bes-tätigt. rnDie zusätzlich eingesetzten Methoden verifizierten das Ergebnis der höheren Compliance mit der einmal tägli-chen Einnahme. Die während der Advagraf®-Phase beantworteten Fragebögen zeigten einen Trend zu besserer Compliance und Lebensqualität. Lediglich die Ergebnisse des MESI-Fragebogens und der Blutspiegelmessungen wichen sowohl während der Prograf®- als auch während der Advagraf®-Phase stark von den Ergebnis-sen der anderen Methoden ab. rnUnter Einbeziehung aller mittels MEMS® und Pill Count objektiv gemessenen Complianceparameter konnten während der Prograf®-Einnahme 54 von 60 Pat. (90%) und während der Advagraf®-Phase 59 von 62 Pat. (95%) als compliant eingestuft werden. Aufgrund subjektiver Compliancemessungen waren 49 von 58 Pat. (84%) während der Prograf®- und 54 von 59 Pat. (92%) während der Advagraf®-Phase als compliant einzustufen. Es wurde beobachtet, dass die zeitlich korrekte Einnahme der Morgendosis einfacher und bei Einmalgabe zu bevorzugen ist. Die wochentagsbezogene Auswertung ergab erwartungsgemäß, dass am Wochenende (Samstag und Sonntag) am häufigsten Dosen ausgelassen wurden. rnDie Umstellung von Prograf® auf Advagraf® stellte kein Problem dar. Beinahe alle Patienten waren dankbar und zufrieden mit der Reduzierung der Dosierungsfrequenz und der größeren Unabhängigkeit durch die entfallene abendliche Einnahme. Der positive Einfluss der geringeren Dosierungshäufigkeit auf die Langzeitcompliance der Patienten, ist ein hinreichender Grund die Entwicklung von Formulierungen zur einmal täglichen Ein-nahme für weitere Immunsuppressiva zu fordern. Insbesondere bei den häufig eingesetzten Kombinationstherapien von Immunsuppressiva würde der Effekt der Complianceverbesserung noch verstärkt werden, wenn alle eingesetzten Immunsuppressiva zur einmal täglichen Gabe geeignet wären.

Social inclusion of vulnerable groups through participatory and emancipatory approaches. Implementing active citizenship and socially innovative actions in the framework of civil & human rights model of disability

The research hypothesis of the thesis is that “an open participation in the co-creation of the services and environments, makes life easier for vulnerable groups”; assuming that the participatory and emancipatory approaches are processes of possible actions and changes aimed at facilitating people’s lives. The adoption of these approaches is put forward as the common denominator of social innovative practices that supporting inclusive processes allow a shift from a medical model to a civil and human rights approach to disability. The theoretical basis of this assumption finds support in many principles of Inclusive Education and the main focus of the hypothesis of research is on participation and emancipation as approaches aimed at facing emerging and existing problems related to inclusion. The framework of reference for the research is represented by the perspectives adopted by several international documents concerning policies and interventions to promote and support the leadership and participation of vulnerable groups. In the first part an in-depth analysis of the main academic publications on the central themes of the thesis has been carried out. After investigating the framework of reference, the analysis focuses on the main tools of participatory and emancipatory approaches, which are able to connect with the concepts of active citizenship and social innovation. In the second part two case studies concerning participatory and emancipatory approaches in the areas of concern are presented and analyzed as example of the improvement of inclusion, through the involvement and participation of persons with disability. The research has been developed using a holistic and interdisciplinary approach, aimed at providing a knowledge-base that fosters a shift from a situation of passivity and care towards a new scenario based on the person’s commitment in the elaboration of his/her own project of life.

Higher order Sobolev Spaces and polyharmonic boundary value problems in Carnot Groups

The main task of this work is to present a concise survey on the theory of certain function spaces in the contexts of Hörmander vector fields and Carnot Groups, and to discuss briefly an application to some polyharmonic boundary value problems on Carnot Groups of step 2.

Context-dependent interpretation of the conjunction 'und' in different age-groups

In contrast to formal semantics, the conjunction and is nonsymmetrical in pragmatics. The events in Marc went to bed and fell asleep seem to have occurred chronologically although no explicit time reference is given. As the temporal interpretation appears to be weaker in Mia ate chocolate and drank milk, it seems that the kind and nature of events presented in a context influences the interpretation of the conjunction. This work focuses on contextual influences on the interpretation of the German conjunction und (‘and’). A variety of theoretic approaches are concerned with whether and contributes to the establishment of discourse coherence via pragmatic processes or whether the conjunction has complex semantic meaning. These approaches are discussed with respect to how they explain the temporal and additive interpretation of the conjunction and the role of context in the interpre-tation process. It turned out that most theoretic approaches do not consider the importance of different kinds of context in the interpretation process.rnIn experimental pragmatics there are currently only very few studies that investigate the inter-pretation of the conjunction. As there are no studies that investigate contextual influences on the interpretation of und systematically or investigate preschoolers interpretation of the con-junction, research questions such as How do (preschool) children interpret ‘und’? and Does the kind of events conjoined influence children’s and adults’ interpretation? are yet to be answered. Therefore, this dissertation systematically investigates how different types of context influence children’s interpretation of und. Three auditory comprehension studies were conducted in German. Of special interest was whether and how the order of events introduced in a context contributes to the temporal read-ing of the conjunction und. Results indicate that the interpretation of und is – at least in Ger-man – context-dependent: The conjunction is interpreted temporally more often when events that typical occur in a certain order are connected (typical contexts) compared to events with-out typical event order (neutral contexts). This suggests that the type of events conjoined in-fluences the interpretation process. Moreover, older children and adults interpret the conjunc-tion temporally more often than the younger cohorts if the conjoined events typically occur in a certain order. In neutral contexts, additive interpretations increase with age. 5-year-olds reject reversed order statements more often in typical contexts compared to neutral contexts. However, they have more difficulties with reversed order statements in typical contexts where they perform at chance level. This suggests that not only the type of event but also other age-dependent factors such as knowledge about scripts influence children’s performance. The type of event conjoined influences children’s and adults’ interpretation of the conjunction. There-fore, the influence of different event types and script knowledge on the interpretation process does not only have to be considered in future experimental studies on language acquisition and pragmatics but also in experimental pragmatics in general. In linguistic theories, context has to be given a central role and a commonly agreed definition of context that considers the consequences arising from different event types has to be agreed upon.

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.

A study of the turbulence of the neutral medium in two nearby spiral galaxies

The width of the 21 cm line (HI) emitted by spiral galaxies depends on the physical processes that release energy in the Interstellar Medium (ISM). This quantity is called velocity dispersion (σ) and it is proportional first of all to the thermal kinetic energy of the gas. The accepted theoretical picture predicts that the neutral hydrogen component (HI) exists in the ISM in two stable phases: a cold one (CNM, with σ~0.8 km/s) and a warm one (WNM, with σ~8 km/s). However, this is called into question by the observation that the HI gas has usually larger velocity dispersions. This suggests the presence of turbulence in the ISM, although the energy sources remain unknown. In this thesis we want to shed new light on this topic. We have studied the HI line emission of two nearby galaxies: NGC6946 and M101. For the latter we used new deep observations obtained with the Westerbork radio interferometer. Through a gaussian fitting procedure, we produced dispersion maps of the two galaxies. For both of them, we compared the σ values measured in the spiral arms with those in the interarms. In NGC6946 we found that, in both arms and interarms, σ grows with the column density, while we obtained the opposite for M 101. Using a statistical analysis we did not find a significant difference between arm and interarm dispersion distributions. Producing star formation rate density maps (SFRD) of the galaxies, we studied their global and local relations with the HI kinetic energy, as inferred from the measured dispersions. For NGC6946 we obtained a good log-log correlation, in agreement with a simple model of supernova feedback driven turbulence. This shows that in this galaxy turbulent motions are mainly induced by the stellar activity. For M 101 we did not find an analogous correlation, since the gas kinetic energy appears constant with the SFRD. We think that this may indicate that in this galaxy turbulence is driven also by accretion of extragalactic material.

Fine particulate matter measurements in Swiss restaurants, cafés and bars: what is the effect of spatial separation between smoking and non-smoking areas?

We performed 124 measurements of particulate matter (PM(2.5)) in 95 hospitality venues such as restaurants, bars, cafés, and a disco, which had differing smoking regulations. We evaluated the impact of spatial separation between smoking and non-smoking areas on mean PM(2.5) concentration, taking relevant characteristics of the venue, such as the type of ventilation or the presence of additional PM(2.5) sources, into account. We differentiated five smoking environments: (i) completely smoke-free location, (ii) non-smoking room spatially separated from a smoking room, (iii) non-smoking area with a smoking area located in the same room, (iv) smoking area with a non-smoking area located in the same room, and (v) smoking location which could be either a room where smoking was allowed that was spatially separated from non-smoking room or a hospitality venue without smoking restriction. In these five groups, the geometric mean PM(2.5) levels were (i) 20.4, (ii) 43.9, (iii) 71.9, (iv) 110.4, and (v) 110.3 microg/m(3), respectively. This study showed that even if non-smoking and smoking areas were spatially separated into two rooms, geometric mean PM(2.5) levels in non-smoking rooms were considerably higher than in completely smoke-free hospitality venues. PRACTICAL IMPLICATIONS: PM(2.5) levels are considerably increased in the non-smoking area if smoking is allowed anywhere in the same location. Even locating the smoking area in another room resulted in a more than doubling of the PM(2.5) levels in the non-smoking room compared with venues where smoking was not allowed at all. In practice, spatial separation of rooms where smoking is allowed does not prevent exposure to environmental tobacco smoke in nearby non-smoking areas.

Numerical model of the human cornea based on stromal microstructure: identification of mechanical properties for two age groups

The optical quality of the human eye mainly depends on the refractive performance of the cornea. The shape of the cornea is a mechanical balance between intraocular pressure and tissue intrinsic stiffness. Several surgical procedures in ophthalmology alter the biomechanics of the cornea to provoke local or global curvature changes for vision correction. Legitimated by the large number of surgical interventions performed every day, the demand for a deeper understanding of corneal biomechanics is rising to improve the safety of procedures and medical devices. The aim of our work is to propose a numerical model of corneal biomechanics, based on the stromal microstructure. Our novel anisotropic constitutive material law features a probabilistic weighting approach to model collagen fiber distribution as observed on human cornea by Xray scattering analysis (Aghamohammadzadeh et. al., Structure, February 2004). Furthermore, collagen cross-linking was explicitly included in the strain energy function. Results showed that the proposed model is able to successfully reproduce both inflation and extensiometry experimental data (Elsheikh et. al., Curr Eye Res, 2007; Elsheikh et. al., Exp Eye Res, May 2008). In addition, the mechanical properties calculated for patients of different age groups (Group A: 65-79 years; Group B: 80-95 years) demonstrate an increased collagen cross-linking, and a decrease in collagen fiber elasticity from younger to older specimen. These findings correspond to what is known about maturing fibrous biological tissue. Since the presented model can handle different loading situations and includes the anisotropic distribution of collagen fibers, it has the potential to simulate clinical procedures involving nonsymmetrical tissue interventions. In the future, such mechanical model can be used to improve surgical planning and the design of next generation ophthalmic devices.

Gender, age and ethnic aspects of analgesia in acute abdominal pain: is analgesia even across the groups?

Numerous studies have shown differences in pain perception between men and women, which may affect pain management strategies.

Risk factors of mortality in different age groups after thoracic endovascular aortic repair

The aim of this study was to determine risk factors for mortality in different age groups after thoracic endovascular aortic repair (TEVAR).