Pseudodifferential operators on Hilbert space riggings with associated psi *-algebras and generalized Hörmander classes

The present thesis is concerned with certain aspects of differential and pseudodifferential operators on infinite dimensional spaces. We aim to generalize classical operator theoretical concepts of pseudodifferential operators on finite dimensional spaces to the infinite dimensional case. At first we summarize some facts about the canonical Gaussian measures on infinite dimensional Hilbert space riggings. Considering the naturally unitary group actions in $L^2(H_-,gamma)$ given by weighted shifts and multiplication with $e^{iSkp{t}{cdot}_0}$ we obtain an unitary equivalence $F$ between them. In this sense $F$ can be considered as an abstract Fourier transform. We show that $F$ coincides with the Fourier-Wiener transform. Using the Fourier-Wiener transform we define pseudodifferential operators in Weyl- and Kohn-Nirenberg form on our Hilbert space rigging. In the case of this Gaussian measure $gamma$ we discuss several possible Laplacians, at first the Ornstein-Uhlenbeck operator and then pseudo-differential operators with negative definite symbol. In the second case, these operators are generators of $L^2_gamma$-sub-Markovian semi-groups and $L^2_gamma$-Dirichlet-forms. In 1992 Gramsch, Ueberberg and Wagner described a construction of generalized Hörmander classes by commutator methods. Following this concept and the classical finite dimensional description of $Psi_{ro,delta}^0$ ($0leqdeltaleqroleq 1$, $delta< 1$) in the $C^*$-algebra $L(L^2)$ by Beals and Cordes we construct in both cases generalized Hörmander classes, which are $Psi^*$-algebras. These classes act on a scale of Sobolev spaces, generated by our Laplacian. In the case of the Ornstein-Uhlenbeck operator, we prove that a large class of continuous pseudodifferential operators considered by Albeverio and Dalecky in 1998 is contained in our generalized Hörmander class. Furthermore, in the case of a Laplacian with negative definite symbol, we develop a symbolic calculus for our operators. We show some Fredholm-criteria for them and prove that these Fredholm-operators are hypoelliptic. Moreover, in the finite dimensional case, using the Gaussian-measure instead of the Lebesgue-measure the index of these Fredholm operators is still given by Fedosov's formula. Considering an infinite dimensional Heisenberg group rigging we discuss the connection of some representations of the Heisenberg group to pseudo-differential operators on infinite dimensional spaces. We use this connections to calculate the spectrum of pseudodifferential operators and to construct generalized Hörmander classes given by smooth elements which are spectrally invariant in $L^2(H_-,gamma)$. Finally, given a topological space $X$ with Borel measure $mu$, a locally compact group $G$ and a representation $B$ of $G$ in the group of all homeomorphisms of $X$, we construct a Borel measure $mu_s$ on $X$ which is invariant under $B(G)$.

Topological aspects of the human protein interaction network

It is currently widely accepted that the understanding of complex cell functions depends on an integrated network theoretical approach and not on an isolated view of the different molecular agents. Aim of this thesis was the examination of topological properties that mirror known biological aspects by depicting the human protein network with methods from graph- and network theory. The presented network is a partial human interactome of 9222 proteins and 36324 interactions, consisting of single interactions reliably extracted from peer-reviewed scientific publications. In general, one can focus on intra- or intermodular characteristics, where a functional module is defined as "a discrete entity whose function is separable from those of other modules". It is found that the presented human network is also scale-free and hierarchically organised, as shown for yeast networks before. The interactome also exhibits proteins with high betweenness and low connectivity which are biologically analyzed and interpreted here as shuttling proteins between organelles (e.g. ER to Golgi, internal ER protein translocation, peroxisomal import, nuclear pores import/export) for the first time. As an optimisation for finding proteins that connect modules, a new method is developed here based on proteins located between highly clustered regions, rather than regarding highly connected regions. As a proof of principle, the Mediator complex is found in first place, the prime example for a connector complex. Focusing on intramodular aspects, the measurement of k-clique communities discriminates overlapping modules very well. Twenty of the largest identified modules are analysed in detail and annotated to known biological structures (e.g. proteasome, the NFκB-, TGF-β complex). Additionally, two large and highly interconnected modules for signal transducer and transcription factor proteins are revealed, separated by known shuttling proteins. These proteins yield also the highest number of redundant shortcuts (by calculating the skeleton), exhibit the highest numbers of interactions and might constitute highly interconnected but spatially separated rich-clubs either for signal transduction or for transcription factors. This design principle allows manifold regulatory events for signal transduction and enables a high diversity of transcription events in the nucleus by a limited set of proteins. Altogether, biological aspects are mirrored by pure topological features, leading to a new view and to new methods that assist the annotation of proteins to biological functions, structures and subcellular localisations. As the human protein network is one of the most complex networks at all, these results will be fruitful for other fields of network theory and will help understanding complex network functions in general.

Italian texts as networks: Topological measurements, Zipf and Heaps' laws

In questa tesi si è studiato un corpus di importanti testi della letteratura Italiana utilizzando la teoria dei network. Le misure topologiche tipiche dei network sono state calcolate sui testi letterari, poi sono state studiate le loro distribuzioni e i loro valori medi, per capire quali di esse possono distinguere un testo reale da sue modificazioni. Inoltre si è osservato come tutti i testi presentino due importanti leggi statistiche: la legge di Zipf e quella di Heaps.

Envy: A Psychometric Refinement of the Construct

The noticeable differences in the theoretical and operative definitions of envy across studies and approaches have produced a fragmentary representation and understanding of the envious emotion. The present dissertation aimed to clarify the inherent nature of the construct of envy through the integration of findings from three independent studies. We focused on malicious envy, and investigated it from both a dispositional and an episodic perspective. Studies 1 and 2 investigated the dimensionality of envy as a stable individual characteristic and an episodic emotional state, respectively. In order to elicit episodic envy, a scenario-based experiment was conducted. Results indicated that, in both its dispositional and episodic facets, envy is a bidimensional construct composed by an inner-directed dimension of inferiority and helplessness, and an outer-directed dimension of feelings of anger and ill will. Moreover, findings from Study 1 allowed to establish boundaries between envy and competing constructs that have often been included in conceptualizations of envy. The psychometrically validated definition of envy provided by Studies 1 and 2 represents a valuable contribution to empirical research. Implications for envy research concern the promotion of a shared operationalization of envy in future studies, which will arguably facilitate the comparison of findings between studies and between approaches. Study 3 examined the mechanisms through which dispositional envy affects individuals’ social adjustment and psychological wellbeing. Findings revealed that the detrimental effects of envy on perceived social support and subjective well-being are mostly mediated by other personal characteristics, such as neuroticism and self-esteem. By reducing global self-esteem, the envious disposition may damage supportive social networks via antisocial direct and indirect behaviors that may arise from envy and that are likely to drive others away. On the other hand, by damaging both emotional stability and self-worth, dispositional envy leads to reduced subjective well-being. Implications for clinical practice are discussed.

Quantum Einstein gravity - advancements of heat kernel-based renormalization group studies

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory.rnAs its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained.rnThe constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point.rnFinally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of existing computations, taking the independent running of the Euler topological term into account. Known perturbative results are reproduced in this case from the renormalization group equation, identifying however a unique non-Gaussian fixed point.rn

Topological mass of magnetic Skyrmions probed by ultrafast dynamic imaging

In dieser Arbeit untersuchen wir mittels zeitaufgelöster Abbildungen die Gigahertz-Dynamik von magnetischen Skyrmionen, um die Bewegungsgleichungen für diese Quasiteilchen zu bestimmen. Um dieses Ziel zu erreichen haben wir zunächst ein CoB/Pt Schichtsystem entwickelt, das starke senkrechte magnetische Anisotropie mit einer besonders geringen Rauigkeit der Energielandschaft verbindet. Diese Eigenschaften sind für das repetitive dynamische Abbildungsverfahren unerlässlich. In einem zweiten Schritt haben wir das Probendesign optimiert und so weiterentwickelt, dass eine Beobachtung der Skyrmionenbewegung mit einer Auflösung von besser als 3 nm möglich wurde. Aufgrund dieser Verbesserungen ist es uns gelungen, die Trajektorie eines Skyrmionen aufzuzeichnen. Diese Bewegung ist eine Superposition von zwei Drehbewegungen, einer im Uhrzeigersinn und einer gegen läufigen. Aus der Existenz dieser zwei Moden lässt sich schließen, dass Skyrmionen träge Quasiteilchen sind, und aus den Frequenzen können wir einen Wert für die träge Masse ableiten. Es stellt sich heraus, dass die Masse von Skyrmion fünfmal größer ist als von existierenden Theorien vorhergesagt. Die Masse wird folglich durch einen neuartigen Mechanismus bestimmt, der sich aus der räumlichen Beschränkung der Skyrmionen ergibt, welche sich direkt aus der Topologie bleitenrnlässt.

Reliability, construct and criterion validity of the KIDSCREEN-10 score: a short measure for children and adolescents' well-being and health-related quality of life

Background To assess the criterion and construct validity of the KIDSCREEN-10 well-being and health-related quality of life (HRQoL) score, a short version of the KIDSCREEN-52 and KIDSCREEN-27 instruments. Methods The child self-report and parent report versions of the KIDSCREEN-10 were tested in a sample of 22,830 European children and adolescents aged 8–18 and their parents (n = 16,237). Correlation with the KIDSCREEN-52 and associations with other generic HRQoL measures, physical and mental health, and socioeconomic status were examined. Score differences by age, gender, and country were investigated. Results Correlations between the 10-item KIDSCREEN score and KIDSCREEN-52 scales ranged from r = 0.24 to 0.72 (r = 0.27–0.72) for the self-report version (proxy-report version). Coefficients below r = 0.5 were observed for the KIDSCREEN-52 dimensions Financial Resources and Being Bullied only. Cronbach alpha was 0.82 (0.78), test–retest reliability was ICC = 0.70 (0.67) for the self- (proxy-)report version. Correlations between other children self-completed HRQoL questionnaires and KIDSCREEN-10 ranged from r = 0.43 to r = 0.63 for the KIDSCREEN children self-report and r = 0.22–0.40 for the KIDSCREEN parent proxy report. Known group differences in HRQoL between physically/mentally healthy and ill children were observed in the KIDSCREEN-10 self and proxy scores. Associations with self-reported psychosomatic complaints were r = −0.52 (−0.36) for the KIDSCREEN-10 self-report (proxy-report). Statistically significant differences in KIDSCREEN-10 self and proxy scores were found by socioeconomic status, age, and gender. Conclusions Our results indicate that the KIDSCREEN-10 provides a valid measure of a general HRQoL factor in children and adolescents, but the instrument does not represent well most of the single dimensions of the original KIDSCREEN-52. Test–retest reliability was slightly below a priori defined thresholds.

Sleep quality, the neglected outcome variable in clinical studies focusing on locomotor system; a construct validation study

In addition to general health and pain, sleep is highly relevant to judging the well-being of an individual. Of these three important outcome variables, however, sleep is neglected in most outcome studies.Sleep is a very important resource for recovery from daily stresses and strains, and any alteration of sleep will likely affect mental and physical health, especially during disease. Sleep assessment therefore should be standard in all population-based or clinical studies focusing on the locomotor system. Yet current sleep assessment tools are either too long or too specific for general use.

Face, content and construct validity of a novel robotic surgery simulator

We evaluated the face, content and construct validity of the novel da Vinci® Skills Simulator™ using the da Vinci Si™ Surgeon Console as the surgeon interface.

Psychological Sense of Community: A New Construct for the Field of Management

This article introduces a new construct to the field of management called Psychological Sense of Community (PSOC). This is important because management scholars are calling for the creation of communities in organizations in an environment that lacks appropriate construct development. The aims of this article are threefold: (a) develop a working definition of PSOC via a review of the extant literature on PSOC from other disciplines with the goal of translating it into the domain of management, (b) synthesize findings from parallel literatures on the outcomes of PSOC with an eye toward exploring the relevance of such outcomes in management contexts, and (c) assess the value of PSOC as it relates to its uniqueness in relation to other prominent management constructs and its scope of applicability in a variety of management inquiry areas.