Properties of Toeplitz operators on analytic function spaces : from function symbols to distributions

Toeplitz operators are among the most important classes of concrete operators with applications to several branches of pure and applied mathematics. This doctoral thesis deals with Toeplitz operators on analytic Bergman, Bloch and Fock spaces. Usually, a Toeplitz operator is a composition of multiplication by a function and a suitable projection. The present work deals with generalizing the notion to the case where the function is replaced by a distributional symbol. Fredholm theory for Toeplitz operators with matrix-valued symbols is also considered. The subject of this thesis belongs to the areas of complex analysis, functional analysis and operator theory. This work contains five research articles. The articles one, three and four deal with finding suitable distributional classes in Bergman, Fock and Bloch spaces, respectively. In each case the symbol class to be considered turns out to be a certain weighted Sobolev-type space of distributions. The Bergman space setting is the most straightforward. When dealing with Fock spaces, some difficulties arise due to unboundedness of the complex plane and the properties of the Gaussian measure in the definition. In the Bloch-type spaces an additional logarithmic weight must be introduced. Sufficient conditions for boundedness and compactness are derived. The article two contains a portion showing that under additional assumptions, the condition for Bergman spaces is also necessary. The fifth article deals with Fredholm theory for Toeplitz operators having matrix-valued symbols. The essential spectra and index theorems are obtained with the help of Hardy space factorization and the Berezin transform, for instance. The article two also has a part dealing with matrix-valued symbols in a non-reflexive Bergman space, in which case a condition on the oscillation of the symbol (a logarithmic VMO-condition) must be added.

Nonverbal predication in Erzya : Studies on morphosyntactic variation and part of speech distinctions

This dissertation consists of four articles and an introduction. The five parts address the same topic, nonverbal predication in Erzya, from different perspectives. The work is at the same time linguistic typology and Uralic studies. The findings based on a large corpus of empirical Erzya data, which was collected using several different methods and included recordings of the spoken language, made it possible for the present study to apply, then test and finally discuss the previous theories based on cross-linguistic data. Erzya makes use of multiple predication patterns which vary from totally analytic to the morphologically very complex. Nonverbal predicate clause types are classified on the basis of propositional acts in clauses denoting class-membership, identity, property and location. The predicates of these clauses are nouns, adjectives and locational expressions, respectively. The following three predication strategies in Erzya nonverbal predication can be identified: i. the zero-copula construction, ii. the predicative suffix construction and iii. the copula construction. It has been suggested that verbs and nouns cannot be clearly distinguished on morphological grounds when functioning as predicates in Erzya. This study shows that even though predicativity must not be considered a sufficient tool for defining parts of speech in any language, the Erzya lexical classes of adjective, noun and verb can be distinguished from each other also in predicate position. The relative frequency and degree of obligation for using the predicative suffix construction decreases when moving left to right on the scale verb adjective/locative noun ( identificational statement). The predicative suffix is the main pattern in the present tense over the whole domain of nonverbal predication in Standard Erzya, but if it is replaced it is most likely to be with a zero-copula construction in a nominal predication. This study exploits the theory of (a)symmetry for the first time in order to describe verbal vs. nonverbal predication. It is shown that the asymmetry of paradigms and constructions differentiates the lexical classes. Asymmetrical structures are motivated by functional level asymmetry. Variation in predication as such adds to the complexity of the grammar. When symmetric structures are employed, the functional complexity of grammar decreases, even though morphological complexity increases. The genre affects the employment of predication strategies in Erzya. There are differences in the relative frequency of the patterns, and some patterns are totally lacking from some of the data. The clearest difference is that the past tense predicative suffix construction occurs relatively frequently in Standard Erzya, while it occurs infrequently in the other data. Also, the predicative suffixes of the present tense are used more regularly in written Standard Erzya than in any other genre. The genre also affects the incidence of the translative in uľ(ń)ems copula constructions. In translations from Russian to Erzya the translative case is employed relatively frequently in comparison to other data. This study reveals differences between the two Mordvinic languages Erzya and Moksha. The predicative suffixes (bound person markers) of the present tense are used more regularly in Moksha in all kinds of nonverbal predicate clauses compared to Erzya. It should further be observed that identificational statements are encoded with a predicative suffix in Moksha, but seldom in Erzya. Erzya clauses are more frequently encoded using zero-constructions, displaying agreement in number only.

Expression of functional GABAc receptors in the brain

γ-aminobutyric acid (GABA) is the main inhibitory transmitter in the nervous system and acts via three distinct receptor classes: A, B, and C. GABAC receptors are ionotropic receptors comprising ρ subunits. In this work, we aimed to elucidate the expression of ρ subunits in the postnatal brain, the characteristics of ρ2 homo-oligomeric receptors, and the function of GABAC receptors in the hippocampus. In situ hybridization on rat brain slices showed ρ2 mRNA expression from the newborn in the superficial grey layer of the superior colliculus, from the first postnatal week in the hippocampal CA1 region and the pretectal nucleus of the optic tract, and in the adult dorsal lateral geniculate nucleus. Quantitative RT-PCR revealed expression of all three ρ subunits in the hippocampus and superior colliculus from the first postnatal day. In the hippocampus, ρ2 mRNA expression clearly dominated over ρ1 and ρ3. GABAC receptor protein expression was confirmed in the adult hippocampus, superior colliculus, and dorsal lateral geniculate nucleus by immunohistochemistry. From the selective distribution of ρ subunits, GABAC receptors may be hypothesized to be specifically involved in aspects of visual image motion processing in the rat brain. Although previous data had indicated a much higher expression level for ρ2 subunit transcripts than for ρ1 or ρ3 in the brain, previous work done on Xenopus oocytes had suggested that rat ρ2 subunits do not form functional homo-oligomeric GABAC receptors but need ρ1 or ρ3 subunits to form hetero-oligomers. Our results demonstrated, for the first time, that HEK 293 cells transfected with ρ2 cDNA displayed currents in whole-cell patch-clamp recordings. Homomeric rat ρ2 receptors had a decreased sensitivity to, but a high affinity for picrotoxin and a marked sensitivity to the GABAC receptor agonist CACA. Our results suggest that ρ2 subunits may contribute to brain function, also in areas not expressing other ρ subunits. Using extracellular electrophysiological recordings, we aimed to study the effects of the GABAC receptor agonists and antagonists on responses of the hippocampal neurons to electrical stimulation. Activation of GABAC receptors with CACA suppressed postsynaptic excitability and the GABAC receptor antagonist TPMPA inhibited the effects of CACA. Next, we aimed to display the activation of the GABAC receptors by synaptically released GABA using intracellular recordings. GABA-mediated long-lasting depolarizing responses evoked by high-frequency stimulation were prolonged by TPMPA. For weaker stimulation, the effect of TPMPA was enhanced after GABA uptake was inhibited. Our data demonstrate that GABAC receptors can be activated by endogenous synaptic transmitter release following strong stimulation or under conditions of reduced GABA uptake. The lack of GABAC receptor activation by less intensive stimulation under control conditions suggests that these receptors are extrasynaptic and activated via spillover of synaptically released GABA. Taken together with the restricted expression pattern of GABAC receptors in the brain and their distinctive pharmacological and biophysical properties, our findings supporting extrasynaptic localization of these receptors raise interesting possibilities for novel pharmacological therapies in the treatment of, for example, epilepsy and sleep disorders.

Developmental, functional brain imaging and electrophysiological evidence of visual and auditory working memory

Intact function of working memory (WM) is essential for children and adults to cope with every day life. Children with deficits in WM mechanisms have learning difficulties that are often accompanied by behavioral problems. The neural processes subserving WM, and brain structures underlying this system, continue to develop during childhood till adolescence and young adulthood. With functional magnetic resonance imaging (fMRI) it is possible to investigate the organization and development of WM. The present thesis aimed to investigate, using behavioral and neuroimaging methods, whether mnemonic processing of spatial and nonspatial visual information is segregated in the developing and mature human brain. A further aim in this research was to investigate the organization and development of audiospatial and visuospatial information processing in WM. The behavioral results showed that spatial and nonspatial visual WM processing is segregated in the adult brain. The fMRI result in children suggested that memory load related processing of spatial and nonspatial visual information engages common cortical networks, whereas selective attention to either type of stimuli recruits partially segregated areas in the frontal, parietal and occipital cortices. Deactivation mechanisms that are important in the performance of WM tasks in adults are already operational in healthy school-aged children. Electrophysiological evidence suggested segregated mnemonic processing of visual and auditory location information. The results of the development of audiospatial and visuospatial WM demonstrate that WM performance improves with age, suggesting functional maturation of underlying cognitive processes and brain areas. The development of the performance of spatial WM tasks follows a different time course in boys and girls indicating a larger degree of immaturity in the male than female WM systems. Furthermore, the differences in mastering auditory and visual WM tasks may indicate that visual WM reaches functional maturity earlier than the corresponding auditory system. Spatial WM deficits may underlie some learning difficulties and behavioral problems related to impulsivity, difficulties in concentration, and hyperactivity. Alternatively, anxiety or depressive symptoms may affect WM function and the ability to concentrate, being thus the primary cause of poor academic achievement in children.

On the functional ordering of biomembranes : Implications for drug binding

Cells are packed with membrane structures, defining the inside and outside, and the different subcellular compartments. These membranes consisting mainly of phospholipids have a variety of functions in addition to providing a permeability barrier for various compounds. These functions involve cellular signaling, where lipids can act as second messengers, or direct regulation of membrane associating proteins. The first part of this study focuses on relating some of the physicochemical properties of membrane lipids to the association of drug compounds to membranes. A fluorescence based method is described allowing for determination of the membrane association of drugs. This method was subsequently applied to a novel drug, siramesine, previously shown to have anti-cancer activity. Siramesine was found to associate with anionic lipids. Especially interesting is its strong affinity for a second messenger lipid phosphatidic acid. This is the first example of a small molecule drug compound specifically interacting with a cellular lipid. Phosphatidic acid in cells is required for the activation of many signaling pathways mediating growth and proliferation. This provides an intriguing possibility for a simple molecular mechanism of the observed anti-cancer activity of siramesine. In the second part the thermal behavior and self assembly of charged and uncharged membrane assemblies was studied. Strong inter-lamellar co-operativity was observed for multilamellar DPPC vesicles using fluorescence techniques together with calorimetry. The commonly used membrane models, large unilamellar vesicles (LUV) and multilamellar vesicles (MLV) were found to possess different biophysical properties as interlamellar interactions of MLVs drive segregation of a pyrene labeled lipid analogue into clusters. The effect of a counter-ion lattice on the self assembly of a cationic gemini surfactant was studied. The presence of NaCl strongly influenced the thermal phase behavior of M-1 vesicles, causing formation of giant vesicles upon exceeding a phase transition temperature, followed by a subsequent transition into a more homogenous dispersion. Understanding the underlying biophysical aspects of cellular membranes is of fundamental importance as the complex picture of the structure and function of cells is evolving. Many of the cellular reactions take place on membranes and membranes are known to regulate the activity of many peripheral and intergral membrane associating proteins. From the point of view of drug design and gene technology, membranes can provide an interesting target for future development of drugs, but also a vehicle sensitive for environmental changes allowing for encapsulating drugs and targeting them to the desired site of action.

Genomic and functional profiling of gastric cancer

Helicobacter pylori infection is a risk factor for gastric cancer, which is a major health issue worldwide. Gastric cancer has a poor prognosis due to the unnoticeable progression of the disease and surgery is the only available treatment in gastric cancer. Therefore, gastric cancer patients would greatly benefit from identifying biomarker genes that would improve diagnostic and prognostic prediction and provide targets for molecular therapies. DNA copy number amplifications are the hallmarks of cancers in various anatomical locations. Mechanisms of amplification predict that DNA double-strand breaks occur at the margins of the amplified region. The first objective of this thesis was to identify the genes that were differentially expressed in H. pylori infection as well as the transcription factors and signal transduction pathways that were associated with the gene expression changes. The second objective was to identify putative biomarker genes in gastric cancer with correlated expression and copy number, and the last objective was to characterize cancers based on DNA copy number amplifications. DNA microarrays, an in vitro model and real-time polymerase chain reaction were used to measure gene expression changes in H. pylori infected AGS cells. In order to identify the transcription factors and signal transduction pathways that were activated after H. pylori infection, gene expression profiling data from the H. pylori experiments and a bioinformatics approach accompanied by experimental validation were used. Genome-wide expression and copy number microarray analysis of clinical gastric cancer samples and immunohistochemistry on tissue microarray were used to identify putative gastric cancer genes. Data mining and machine learning techniques were applied to study amplifications in a cross-section of cancers. FOS and various stress response genes were regulated by H. pylori infection. H. pylori regulated genes were enriched in the chromosomal regions that are frequently changed in gastric cancer, suggesting that molecular pathways of gastric cancer and premalignant H. pylori infection that induces gastritis are interconnected. 16 transcription factors were identified as being associated with H. pylori infection induced changes in gene expression. NF-κB transcription factor and p50 and p65 subunits were verified using elecrophoretic mobility shift assays. ERBB2 and other genes located in 17q12- q21 were found to be up-regulated in association with copy number amplification in gastric cancer. Cancers with similar cell type and origin clustered together based on the genomic localization of the amplifications. Cancer genes and large genes were co-localized with amplified regions and fragile sites, telomeres, centromeres and light chromosome bands were enriched at the amplification boundaries. H. pylori activated transcription factors and signal transduction pathways function in cellular mechanisms that might be capable of promoting carcinogenesis of the stomach. Intestinal and diffuse type gastric cancers showed distinct molecular genetic profiles. Integration of gene expression and copy number microarray data allowed the identification of genes that might be involved in gastric carcinogenesis and have clinical relevance. Gene amplifications were demonstrated to be non-random genomic instabilities. Cell lineage, properties of precursor stem cells, tissue microenvironment and genomic map localization of specific oncogenes define the site specificity of DNA amplifications, whereas labile genomic features define the structures of amplicons. These conclusions suggest that the definition of genomic changes in cancer is based on the interplay between the cancer cell and the tumor microenvironment.

Consumers and the conceptual and practical appropriation of functional foods

Taking the appropriation of objects as a theoretical starting point, this study makes a distinction between a conceptual and practical level of adopting new objects and products in everyday life. The study applies the concept of appropriation in social food research and examines consumers appropriation of functional foods, i.e., foods developed to improve health and well-being or reduce the risk of disease beyond the usual nutritional effects of foods. The study uses the concept of appropriation to understand the adoption and the process of making functional foods our own . First, the study focuses on the conceptual appropriation by analysing consumers interpretations and opinions on functional foods. Second, it analyses the use of functional foods and examines the role of sociodemographic and food- and health-related background factors in the use of functional foods. Both quantitative and qualitative data were used in the study. Altogether 1210 Finns representative of the population took part in a survey carried out in 2002 as computer-assisted telephone interviews (CATI). The survey examined the acceptability and use of functional foods in Finland. In 2004, eight focus group discussions were organised for 45 users and non-users of cholesterol-lowering spreads. The qualitative study focused on consumers interpretative perspectives on healthy eating and functional foods. The findings are reported in four original articles and a summary article. The results show that the appropriation of functional foods is a multifaceted phenomenon. The conceptual appropriation is related to consumers interpretations of functional foods in the context of healthy foods and healthy eating; their trust in the products, their manufacturers, research and control; and the relationship of functional foods and the ideal of natural foods. The analysis of the practical appropriation of four different types of foods marketed as functional showed that there are sociodemographic differences between users and non-users of the products, but more importantly, the differences are related to consumers food- and health-related views and practices. Consumers ways of appropriating functional foods in the conceptual and practical sense take shape in a complex web of ideas and everyday practices concerning food, health and eating as a whole. The results also indicate that the conceptual and practical appropriation are not necessarily uniform or coherent processes. Consumers interpret healthy eating and functional foods from a variety of perspectives and there is a multiplicity of rationales of using functional foods. Appropriation embraces many opposing dimensions simultaneously: good experiences and doubts, approval and criticism, expectations and things taken for granted.