Composition operators, Aleksandrov measures and value distribution of analytic maps in the unit disc

A composition operator is a linear operator that precomposes any given function with another function, which is held fixed and called the symbol of the composition operator. This dissertation studies such operators and questions related to their theory in the case when the functions to be composed are analytic in the unit disc of the complex plane. Thus the subject of the dissertation lies at the intersection of analytic function theory and operator theory. The work contains three research articles. The first article is concerned with the value distribution of analytic functions. In the literature there are two different conditions which characterize when a composition operator is compact on the Hardy spaces of the unit disc. One condition is in terms of the classical Nevanlinna counting function, defined inside the disc, and the other condition involves a family of certain measures called the Aleksandrov (or Clark) measures and supported on the boundary of the disc. The article explains the connection between these two approaches from a function-theoretic point of view. It is shown that the Aleksandrov measures can be interpreted as kinds of boundary limits of the Nevanlinna counting function as one approaches the boundary from within the disc. The other two articles investigate the compactness properties of the difference of two composition operators, which is beneficial for understanding the structure of the set of all composition operators. The second article considers this question on the Hardy and related spaces of the disc, and employs Aleksandrov measures as its main tool. The results obtained generalize those existing for the case of a single composition operator. However, there are some peculiarities which do not occur in the theory of a single operator. The third article studies the compactness of the difference operator on the Bloch and Lipschitz spaces, improving and extending results given in the previous literature. Moreover, in this connection one obtains a general result which characterizes the compactness and weak compactness of the difference of two weighted composition operators on certain weighted Hardy-type spaces.

New approaches to improve the cord blood unit hematopoietic progenitor cell content

Cord blood is a well-established alternative to bone marrow and peripheral blood stem cell transplantation. To this day, over 400 000 unrelated donor cord blood units have been stored in cord blood banks worldwide. To enable successful cord blood transplantation, recent efforts have been focused on finding ways to increase the hematopoietic progenitor cell content of cord blood units. In this study, factors that may improve the selection and quality of cord blood collections for banking were identified. In 167 consecutive cord blood units collected from healthy full-term neonates and processed at a national cord blood bank, mean platelet volume (MPV) correlated with the numbers of cord blood unit hematopoietic progenitors (CD34+ cells and colony-forming units); this is a novel finding. Mean platelet volume can be thought to represent general hematopoietic activity, as newly formed platelets have been reported to be large. Stress during delivery is hypothesized to lead to the mobilization of hematopoietic progenitor cells through cytokine stimulation. Accordingly, low-normal umbilical arterial pH, thought to be associated with perinatal stress, correlated with high cord blood unit CD34+ cell and colony-forming unit numbers. The associations were closer in vaginal deliveries than in Cesarean sections. Vaginal delivery entails specific physiological changes, which may also affect the hematopoietic system. Thus, different factors may predict cord blood hematopoietic progenitor cell numbers in the two modes of delivery. Theoretical models were created to enable the use of platelet characteristics (mean platelet volume) and perinatal factors (umbilical arterial pH and placental weight) in the selection of cord blood collections with high hematopoietic progenitor cell counts. These observations could thus be implemented as a part of the evaluation of cord blood collections for banking. The quality of cord blood units has been the focus of several recent studies. However, hemostasis activation during cord blood collection is scarcely evaluated in cord blood banks. In this study, hemostasis activation was assessed with prothrombin activation fragment 1+2 (F1+2), a direct indicator of thrombin generation, and platelet factor 4 (PF4), indicating platelet activation. Altogether three sample series were collected during the set-up of the cord blood bank as well as after changes in personnel and collection equipment. The activation decreased from the first to the subsequent series, which were collected with the bank fully in operation and following international standards, and was at a level similar to that previously reported for healthy neonates. As hemostasis activation may have unwanted effects on cord blood cell contents, it should be minimized. The assessment of hemostasis activation could be implemented as a part of process control in cord blood banks. Culture assays provide information about the hematopoietic potential of the cord blood unit. In processed cord blood units prior to freezing, megakaryocytic colony growth was evaluated in semisolid cultures with a novel scoring system. Three investigators analyzed the colony assays, and the scores were highly concordant. With such scoring systems, the growth potential of various cord blood cell lineages can be assessed. In addition, erythroid cells were observed in liquid cultures of cryostored and thawed, unseparated cord blood units without exogenous erythropoietin. This was hypothesized to be due to the erythropoietic effect of thrombopoietin, endogenous erythropoietin production, and diverse cell-cell interactions in the culture. This observation underscores the complex interactions of cytokines and supporting cells in the heterogeneous cell population of the thawed cord blood unit.

A Possible and Necessary Consistency Proof

After Gödel's incompleteness theorems and the collapse of Hilbert's programme Gerhard Gentzen continued the quest for consistency proofs of Peano arithmetic. He considered a finitistic or constructive proof still possible and necessary for the foundations of mathematics. For a proof to be meaningful, the principles relied on should be considered more reliable than the doubtful elements of the theory concerned. He worked out a total of four proofs between 1934 and 1939. This thesis examines the consistency proofs for arithmetic by Gentzen from different angles. The consistency of Heyting arithmetic is shown both in a sequent calculus notation and in natural deduction. The former proof includes a cut elimination theorem for the calculus and a syntactical study of the purely arithmetical part of the system. The latter consistency proof in standard natural deduction has been an open problem since the publication of Gentzen's proofs. The solution to this problem for an intuitionistic calculus is based on a normalization proof by Howard. The proof is performed in the manner of Gentzen, by giving a reduction procedure for derivations of falsity. In contrast to Gentzen's proof, the procedure contains a vector assignment. The reduction reduces the first component of the vector and this component can be interpreted as an ordinal less than epsilon_0, thus ordering the derivations by complexity and proving termination of the process.

United We Stand - Divided We Fall : A Standard Model of Unit Cohesion

Research on unit cohesion has shown positive correlations between cohesion and valued outcomes such as strong performance, reduced stress, less indiscipline, and high re-enlistment intentions. However, the correlations have varied in strength and significance. The purpose of this study is to show that taking into consideration the multi-component nature of cohesion and relating the most applicable components to specific outcomes could resolve much of the inconsistency. Unit cohesion is understood as a process of social integration among members of a primary group with its leaders, and with the larger secondary groups of which they are a part. Correspondingly, included in the framework are four bonding components: horizontal (peer) and vertical (subordinate and leader) and organizational and institutional, respectively. The data were collected as part of a larger research project on cohesion, leadership, and personal adjustment to the military. In all, 1,534 conscripts responded to four questionnaires during their service in 2001-2002. In addition, sociometric questionnaires were given to 537 group members in 47 squads toward the end of their service. The results showed that platoons with strong primary-group cohesion differed from other platoons in terms of performance, training quality, secondary-group experiences, and attitudes toward refresher training. On the sociometric level it was found that soldiers who were chosen as friends by others were more likely to have higher expected performance, better performance ratings, more positive attitudes toward military service, higher levels of well-being during conscript service, and fewer exemptions from duty during it. On the group level, the selection of the respondents own group leader rather than naming a leader from outside (i.e., leader bonding) had a bearing not only on cohesion and performance, but also on the social, attitudinal, and behavioral criteria. Overall, the aim of the study was to contribute to the research on cohesion by introducing a model that takes into account the primary foci of bonding and their impact. The results imply that primary-group and secondary-group bonding processes are equally influential in explaining individual and group performance, whereas the secondary-group bonding components are far superior in explaining career intentions, personal growth, avoidance of duty, and attitudes toward refresher training and national defense. This should be considered in the planning and conducting of training. The main conclusion is that the different types of cohesion components have a unique, positive, significant, but varying impact on a wide range of criteria, confirming the need to match the components with the specific criteria.

Analysing local algorithms in location-aware quasi-unit-disk graphs

A local algorithm with local horizon r is a distributed algorithm that runs in r synchronous communication rounds; here r is a constant that does not depend on the size of the network. As a consequence, the output of a node in a local algorithm only depends on the input within r hops from the node. We give tight bounds on the local horizon for a class of local algorithms for combinatorial problems on unit-disk graphs (UDGs). Most of our bounds are due to a refined analysis of existing approaches, while others are obtained by suggesting new algorithms. The algorithms we consider are based on network decompositions guided by a rectangular tiling of the plane. The algorithms are applied to matching, independent set, graph colouring, vertex cover, and dominating set. We also study local algorithms on quasi-UDGs, which are a popular generalisation of UDGs, aimed at more realistic modelling of communication between the network nodes. Analysing the local algorithms on quasi-UDGs allows one to assume that the nodes know their coordinates only approximately, up to an additive error. Despite the localisation error, the quality of the solution to problems on quasi-UDGs remains the same as for the case of UDGs with perfect location awareness. We analyse the increase in the local horizon that comes along with moving from UDGs to quasi-UDGs.

Interruption and Uncooperativeness in Academic ELF Group Work : An Application of Linear Unit Grammar

This study addresses the challenge of analyzing interruption in spoken interaction. It begins with my observation of eight hours of academic group work among speakers of English as a lingua franca (ELF) in a university course. Unlike the common findings of ELF research which underscore the cooperative orientation of ELF users, this particular group gave strong impressions of interruption and uncooperativeness as they prepared a scientific group presentation. In the effort to investigate these impressions, I found that no satisfactory method exists for systematically identifying and analyzing interruptions. A useful tool was found in Linear Unit Grammar or LUG (Sinclair & Mauranen 2006), which analyzes spoken interaction prospectively as linear text. In the course of transcribing one of the early group work meetings, I developed a model of LUG-based criteria for identifying individual instances of interruption. With this system in place, I was then able to evaluate the aggregate occurrences of interruption in the group work and identify co-occurring interactive features which further influenced the perception of uncooperativeness. Finally, these aggregate statistics directed a return to the data and a contextually sensitive, qualitative analysis. This research cycle illuminates the interactive features which contributed to my own impressions of uncooperativeness, as well as the group members orientations to their own interruptive practice.