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.

Service Composition on a Mobile Phone

With the recent increase in interest in service-oriented architectures (SOA) and Web services, developing applications with the Web services paradigm has become feasible. Web services are self-describing, platform-independent computational elements. New applications can be assembled from a set of previously created Web services, which are composed together to make a service that uses its components to perform a certain task. This is the idea of service composition. To bring service composition to a mobile phone, I have created Interactive Service Composer for mobile phones. With Interactive Service Composer, the user is able to build service compositions on his mobile phone, consisting of Web services or services that are available from the mobile phone itself. The service compositions are reusable and can be saved in the phone's memory. Previously saved compositions can also be used in new compositions. While developing applications for mobile phones has been possible for some time, the usability of the solutions is not the same as when developing for desktop computers. When developing for mobile phones, the developer has to more carefully consider the decisions he is going to make with the program he is developing. With the lack of processing power and memory, the applications cannot function as well as on desktop PCs. On the other hand, this does not remove the appeal of developing applications for mobile devices.

Using Mathematical Morphology for Geometric Music Retrieval

The usual task in music information retrieval (MIR) is to find occurrences of a monophonic query pattern within a music database, which can contain both monophonic and polyphonic content. The so-called query-by-humming systems are a famous instance of content-based MIR. In such a system, the user's hummed query is converted into symbolic form to perform search operations in a similarly encoded database. The symbolic representation (e.g., textual, MIDI or vector data) is typically a quantized and simplified version of the sampled audio data, yielding to faster search algorithms and space requirements that can be met in real-life situations. In this thesis, we investigate geometric approaches to MIR. We first study some musicological properties often needed in MIR algorithms, and then give a literature review on traditional (e.g., string-matching-based) MIR algorithms and novel techniques based on geometry. We also introduce some concepts from digital image processing, namely the mathematical morphology, which we will use to develop and implement four algorithms for geometric music retrieval. The symbolic representation in the case of our algorithms is a binary 2-D image. We use various morphological pre- and post-processing operations on the query and the database images to perform template matching / pattern recognition for the images. The algorithms are basically extensions to classic image correlation and hit-or-miss transformation techniques used widely in template matching applications. They aim to be a future extension to the retrieval engine of C-BRAHMS, which is a research project of the Department of Computer Science at University of Helsinki.

AndroMedia - Towards a Context-aware Mobile Music Recommender

Portable music players have made it possible to listen to a personal collection of music in almost every situation, and they are often used during some activity to provide a stimulating audio environment. Studies have demonstrated the effects of music on the human body and mind, indicating that selecting music according to situation can, besides making the situation more enjoyable, also make humans perform better. For example, music can boost performance during physical exercises, alleviate stress and positively affect learning. We believe that people intuitively select different types of music for different situations. Based on this hypothesis, we propose a portable music player, AndroMedia, designed to provide personalised music recommendations using the user’s current context and listening habits together with other user’s situational listening patterns. We have developed a prototype that consists of a central server and a PDA client. The client uses Bluetooth sensors to acquire context information and logs user interaction to infer implicit user feedback. The user interface also allows the user to give explicit feedback. Large user interface elements facilitate touch-based usage in busy environments. The prototype provides the necessary framework for using the collected information together with other user’s listening history in a context- enhanced collaborative filtering algorithm to generate context-sensitive recommendations. The current implementation is limited to using traditional collaborative filtering algorithms. We outline the techniques required to create context-aware recommendations and present a survey on mobile context-aware music recommenders found in literature. As opposed to the explored systems, AndroMedia utilises other users’ listening habits when suggesting tunes, and does not require any laborious set up processes.

Spectroscopy of tissue triglyceride composition : In vitro and in vivo studies

Lipid analysis is commonly performed by gas chromatography (GC) in laboratory conditions. Spectroscopic techniques, however, are non-destructive and can be implemented noninvasively in vivo. Excess fat (triglycerides) in visceral adipose tissue and liver is known predispose to metabolic abnormalities, collectively known as the metabolic syndrome. Insulin resistance is the likely cause with diets high in saturated fat known to impair insulin sensitivity. Tissue triglyceride composition has been used as marker of dietary intake but it can also be influenced by tissue specific handling of fatty acids. Recent studies have shown that adipocyte insulin sensitivity correlates positively with their saturated fat content, contradicting the common view of dietary effects. A better understanding of factors affecting tissue triglyceride composition is needed to provide further insights into tissue function in lipid metabolism. In this thesis two spectroscopic techniques were developed for in vitro and in vivo analysis of tissue triglyceride composition. In vitro studies (Study I) used infrared spectroscopy (FTIR), a fast and cost effective analytical technique well suited for multivariate analysis. Infrared spectra are characterized by peak overlap leading to poorly resolved absorbances and limited analytical performance. In vivo studies (Studies II, III and IV) used proton magnetic resonance spectroscopy (1H-MRS), an established non-invasive clinical method for measuring metabolites in vivo. 1H-MRS has been limited in its ability to analyze triglyceride composition due to poorly resolved resonances. Using an attenuated total reflection accessory, we were able to obtain pure triglyceride infrared spectra from adipose tissue biopsies. Using multivariate curve resolution (MCR), we were able to resolve the overlapping double bond absorbances of monounsaturated fat and polyunsaturated fat. MCR also resolved the isolated trans double bond and conjugated linoleic acids from an overlapping background absorbance. Using oil phantoms to study the effects of different fatty acid compositions on the echo time behaviour of triglycerides, it was concluded that the use of long echo times improved peak separation with T2 weighting having a negligible impact. It was also discovered that the echo time behaviour of the methyl resonance of omega-3 fats differed from other fats due to characteristic J-coupling. This novel insight could be used to detect omega-3 fats in human adipose tissue in vivo at very long echo times (TE = 470 and 540 ms). A comparison of 1H-MRS of adipose tissue in vivo and GC of adipose tissue biopsies in humans showed that long TE spectra resulted in improved peak fitting and better correlations with GC data. The study also showed that calculation of fatty acid fractions from 1H-MRS data is unreliable and should not be used. Omega-3 fatty acid content derived from long TE in vivo spectra (TE = 540 ms) correlated with total omega-3 fatty acid concentration measured by GC. The long TE protocol used for adipose tissue studies was subsequently extended to the analysis of liver fat composition. Respiratory triggering and long TE resulted in spectra with the olefinic and tissue water resonances resolved. Conversion of the derived unsaturation to double bond content per fatty acid showed that the results were in accordance with previously published gas chromatography data on liver fat composition. In patients with metabolic syndrome, liver fat was found to be more saturated than subcutaneous or visceral adipose tissue. The higher saturation observed in liver fat may be a result of a higher rate of de-novo-lipogenesis in liver than in adipose tissue. This thesis has introduced the first non-invasive method for determining adipose tissue omega-3 fatty acid content in humans in vivo. The methods introduced here have also shown that liver fat is more saturated than adipose tissue fat.

IL-10 in Human Newborns : Ontogeny of IL-10 secretion and relation to the secretion of IFN-g, immunoglobulin M, G, and A, and mononuclear cell composition in newborns

The purpose of this work was to elucidate the ontogeny of interleukin-10 (IL-10) secretion from newborn mononuclear cells (MCs), and to examine its relation to the secretion of interferon-g (IFN-g) and immunoglobulins (Igs). The initial hypothesis was that the decreased immunoglobulin (Ig) synthesis of newborn babies was the result of immature cytokine synthesis regulation, which would lead to excessive IL-10 production, leading in turn to suppressed IFN-g secretion. Altogether 57 full-term newborns and 34 adult volunteers were enrolled. Additionally, surface marker compositions of 29 premature babies were included. Enzyme-linked immunoassays were used to determine the amount of secreted IL-10, IFN-g, and Igs, and the surface marker composition of MC were analyzed with a FACScan flow cytometer. The three most important findings were: 1. Cord blood MC, including CD5+ B cells, are able to secrete IL-10. However, when compared with adults, the secretion of IL-10 was decreased. This indicates that reasons other than excessive IL-10 secretion are responsible of reduced IFN-g secretion in newborns. 2. As illustrated by the IL-10 and IFN-g secretion pattern, newborn cytokine profile was skewed towards the Th2 type. However, approximately 25% of newborns had an adult like cytokine profile with both good IL10 and IFN-g secretion, demonstrating that fullterm newborns are not an immunologically homogenous group at the time of birth. 3. There were significant differences in the surface marker composition of MCs between individual neonates. While gestational age correlated with the proportion of some MC types, it is evident that there are many other maternal and fetal factors that influence the maturity and nature of lymphocyte subpopulations in individual neonates. In conclusion, the reduced ability of neonates to secrete Ig and IFN-g is not a consequence of high IL-10 secretion. However, individual newborns differ significantly in their ability to secrete cytokines as well as Igs.

Spectroscopy of tissue triglyceride composition : In vitro and in vivo studies

Lipid analysis is commonly performed by gas chromatography (GC) in laboratory conditions. Spectroscopic techniques, however, are non-destructive and can be implemented noninvasively in vivo. Excess fat (triglycerides) in visceral adipose tissue and liver is known predispose to metabolic abnormalities, collectively known as the metabolic syndrome. Insulin resistance is the likely cause with diets high in saturated fat known to impair insulin sensitivity. Tissue triglyceride composition has been used as marker of dietary intake but it can also be influenced by tissue specific handling of fatty acids. Recent studies have shown that adipocyte insulin sensitivity correlates positively with their saturated fat content, contradicting the common view of dietary effects. A better understanding of factors affecting tissue triglyceride composition is needed to provide further insights into tissue function in lipid metabolism. In this thesis two spectroscopic techniques were developed for in vitro and in vivo analysis of tissue triglyceride composition. In vitro studies (Study I) used infrared spectroscopy (FTIR), a fast and cost effective analytical technique well suited for multivariate analysis. Infrared spectra are characterized by peak overlap leading to poorly resolved absorbances and limited analytical performance. In vivo studies (Studies II, III and IV) used proton magnetic resonance spectroscopy (1H-MRS), an established non-invasive clinical method for measuring metabolites in vivo. 1H-MRS has been limited in its ability to analyze triglyceride composition due to poorly resolved resonances. Using an attenuated total reflection accessory, we were able to obtain pure triglyceride infrared spectra from adipose tissue biopsies. Using multivariate curve resolution (MCR), we were able to resolve the overlapping double bond absorbances of monounsaturated fat and polyunsaturated fat. MCR also resolved the isolated trans double bond and conjugated linoleic acids from an overlapping background absorbance. Using oil phantoms to study the effects of different fatty acid compositions on the echo time behaviour of triglycerides, it was concluded that the use of long echo times improved peak separation with T2 weighting having a negligible impact. It was also discovered that the echo time behaviour of the methyl resonance of omega-3 fats differed from other fats due to characteristic J-coupling. This novel insight could be used to detect omega-3 fats in human adipose tissue in vivo at very long echo times (TE = 470 and 540 ms). A comparison of 1H-MRS of adipose tissue in vivo and GC of adipose tissue biopsies in humans showed that long TE spectra resulted in improved peak fitting and better correlations with GC data. The study also showed that calculation of fatty acid fractions from 1H-MRS data is unreliable and should not be used. Omega-3 fatty acid content derived from long TE in vivo spectra (TE = 540 ms) correlated with total omega-3 fatty acid concentration measured by GC. The long TE protocol used for adipose tissue studies was subsequently extended to the analysis of liver fat composition. Respiratory triggering and long TE resulted in spectra with the olefinic and tissue water resonances resolved. Conversion of the derived unsaturation to double bond content per fatty acid showed that the results were in accordance with previously published gas chromatography data on liver fat composition. In patients with metabolic syndrome, liver fat was found to be more saturated than subcutaneous or visceral adipose tissue. The higher saturation observed in liver fat may be a result of a higher rate of de-novo-lipogenesis in liver than in adipose tissue. This thesis has introduced the first non-invasive method for determining adipose tissue omega-3 fatty acid content in humans in vivo. The methods introduced here have also shown that liver fat is more saturated than adipose tissue fat.