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.

Smoking patterns and lung function : A longitudinal twin study

In many countries, the prevalence of smoking and smokers average cigarette consumption have decreased, with occasional smoking and daily light smoking (1-4 cigarettes per day, CPD) becoming more common. Despite these changes in smoking patterns, the prevalence of chronic obstructive pulmonary disease (COPD), a disorder characterized by a progressive decline in lung function, continues to rise globally. Smoking is the most important factor causing COPD, however, not all smokers develop the disease. Genetic factors partly explain the inter-individual differences in lung function and susceptibility of some smokers to COPD. No earlier research on the genetic and environmental determinants of lung function or on the phenomenon of light smoking exists in the Finnish population. Further, the association between low-rate smoking patterns and COPD remains partly unknown. This thesis aimed to study the prevalence and consistency of light smoking longitudinally in the Finnish population, to assess the characteristics of light smokers, and to examine the risks of chronic bronchitis and COPD associated with changing smoking patterns over time. A further aim was to estimate longitudinally the proportions of genetic and environmental factors that explain the inter-individual variances in lung function. Data from the Older Finnish Twin Cohort, including same-sex twin pairs born in Finland before 1958, were used. Smoking patterns and chronic bronchitis symptoms were consistently assessed in surveys conducted in 1975, 1981, and 1990. National registry data on reimbursement eligibilities and medication purchases were used to define COPD. Lung function data were obtained from a subsample of the cohort, 217 female twin pairs, who attended spirometry in 2000 and 2003 as part of the Finnish Twin Study on Ageing. The genetic and environmental influences on lung function were estimated by using genetic modeling. This thesis found that light smokers are more often female, well-educated, and exhibit a healthier lifestyle than heavy smokers. At individual level, light smoking is rarely a constant pattern. Light smoking, reducing from heavier smoking to light smoking, and relapsing to light smoking after quitting, are among patterns associated with an increased risk of chronic bronchitis and COPD. Constant light smoking is associated with an increased use of inhaled anticholinergics, a medication for CODP. In addition to smoking, other environmental factors influence lung function in the older age. During a three-year follow-up, new environmental effects influencing spirometry values were observed, whereas the genes affecting lung function remained mostly the same. In conclusion, no safe level of daily smoking exists with regard to pulmonary diseases. Even daily light smoking in middle-age is associated with increased respiratory morbidity later in life. Smoking reduction does not decrease the risk of COPD, and should not be recommended as an alternative to quitting smoking. In elderly people, attention should also be drawn to other factors that can prevent poor lung function.

Optimum weighting function in bispectral analysis in speckle interferometry - Binary star parity detection

In order to describe the atmospheric turbulence which limits the resolution of long-exposure images obtained using ground-based large telescopes, a simplified model of a speckle pattern, reducing the complexity of calculating field-correlations of very high order, is presented. Focal plane correlations are used instead of correlations in the spatial frequency domain. General tripple correlations for a point source and for a binary are calculated and it is shown that they are not a strong function of the binary separation. For binary separations close to the diffraction limit of the telescope, the genuine triple correlation technique ensures a better SNR than the near-axis Knox-Thompson technique. The simplifications allow a complete analysis of the noise properties at all levels of light.

NK-and T-cell function in chronic myeloid leukemia patients treated with interferon-? monotherapy

Chronic myeloid leukemia (CML) is one of the most studied human malignancies. It is caused by an autonomously active tyrosine kinase BCR-ABL, which is a result from a translocation between chromosomes 9 and 22 in the hematopoietic stem cell. As an outcome, a Philadelphia (Ph) chromosome is formed. BCR-ABL causes disturbed cell proliferation among other things. Although targeted tyrosine kinase inhibitor therapy has been developed in the beginning of the millenium and the survival rate has increased significantly, it is still not known why some patients benefit more from the treatment than others. Furthermore, the therapy is not considered to be curative. Before the era of tyrosine kinase inhibitors, the first-line treatment for CML was interferon-? (IFN-?). However, only a small proportion of patients benefitted from the treatment. Of these patients, a few were able to discontinue the treatment without renewal of the disease. The mechanism of IFN-? is not completely understood, but it is believed that differences in the immune system can be one of the reasons why some patients have better therapy response. Kreutzman, Rohon et al. have recently discovered that patients who have been able to stop IFN-? treatment have an increased number of NK- and T-cells. They also have a unique clonal T-cell population and more cytotoxic CD8+ T-cells and less CD4+ T-cells. The aim of this master’s thesis was to study the function of T- and NK-cells in IFN-? treated patients. Although it was shown earlier that IFN-? treated patients have increased NK-cell count, the function of these cells was unknown. Therefore, we have now investigated the killing potential of patients’ NK-cells, their activation status and cell surface antigen expression. In addition, we have also studied the activation status of patients’ T-cells and their cytotoxic properties. We observed that NK-cells from patients treated with IFN-? are unable to kill leukemic cells (K562) than NK-cells from healthy controls. In addition, patients on IFN-? treatment have more active T-cells and their NK-cells have an undifferentiated immunoregulatory phenotype. Patients that have been able to stop the treatment have anergic T-and NK-cells. As a conclusion our results suggest that IFN-? therapy induces increased NK-cell count, NK-cell immunoregulatory functions and more active T-cells. After stopping IFN-? therapy, NK- and T-cells from CML patients restore anergy typical for CML.

Chronic suppression of testicular function by constant infusion of gonadotropin-releasing hormone agonist and testosterone supplementation in the bonnet monkey (Macaca radiata)

Objective: To study the efficacy of long-term buserelin acetate infusion to desensitize pituitary and block testicular function in adult male monkeys (Macaca radiata). Animals: Proven fertile male monkeys exhibiting normal testicular function. Protocol: Each of the control (n = 5) and experimental monkeys (n = 10) received a fresh miniosmotic pump every 21 days, whereas pumps in controls delivered vehicle of experimentals released 50-mu-g buserelin acetate every 24 hours. On day 170 (renewed every 60 days) a silastic capsule containing crystalline testosterone (T) was implanted in the experimental monkeys. At the end of 3 years, treatment was stopped, and recovery of testicular function and fertility monitored. Results: (1) Treatment resulted in marked reduction of nocturnal but not basal serum T; (2) the pituitary remained desensitized to buserelin acetate throughout the 3-year period; (3) animals were largely azoospermic with occasional oligospermia exhibited by two monkeys; and (4) withdrawal of treatment restored testicular function, with 70% of animals regaining fertility. Conclusion: Long-term infertility (but restorable) can be induced in male monkeys by constant infusion of buserelin acetate and T.

Effect of constant infusion of gonadotropin releasing hormone (GnRH) agonist Buserelin and antagonist CDB 2085 A using osmotic minipumps on testicular function in adult male bonnet monkey (Macaca radiata)

The effect of chronic infusion of gonadotropic hormone agonist Buserelin or antagonist CDB 2085 A for 15 weeks via alzet minipumps in adult male bonnet monkeys was studied. Infusion of Buserelin resulted in a decrease in the difference between serum testosterone values at 22.00 hours and 10.00 hours, decrease in responsiveness to injected Buserelin as judged by change in serum testosterone values from pre-injection values and decrease in sperm counts. Infusion of antagonist resulted in a decrease in the difference between serum testosterone values at 22.00 hours and 10.00 hours.

A structure-preserving energy function for stability analysis of AC/DC systems

Direct stability analysis ofAC/DC power systems using a structure-preserving energy function (SPEF) is proposed in this paper. The system model considered retains the load buses thereby enabling the representation of nonlinear voltage dependent loads. TheHVDC system is represented with the same degree of detail as is normally done in transient stability simulation. The converter controllers can be represented by simplified or detailed models. Two or multi-terminalDC systems can be considered. The stability analysis is illustrated with a 3-machine system example and encouraging results have been obtained.

The function and regulation of the U11-48K protein in U12-dependent splicing

The removal of noncoding sequences, or introns, from the eukaryotic messenger RNA precursors is catalyzed by a ribonucleoprotein complex known as the spliceosome. In most eukaryotes, two distinct classes of introns exist, each removed by a specific type of spliceosome. The major, U2-type introns account for over 99 % of all introns, and are almost ubiquitous. The minor, U12-type introns are found in most but not all eukaryotes, and reside in conserved locations in a specific set of genes. Due to their slow excision rates, the U12-type introns are expected to be involved in the regulation of the genes containing them by inhibiting the maturation of the messenger RNAs. However, little information is currently available on how the activity of the U12-dependent spliceosome itself is regulated. The levels of many known splicing factors are regulated through unproductive alternative splicing events, which lead to inclusion of premature STOP codons, targeting the transcripts for destruction by the nonsense-mediated decay pathway. These alternative splice sites are typically found in highly conserved sequence elements, which also contain binding sites for factors regulating the activation of the splice sites. Often, the activation is achieved by binding of products of the gene in question, resulting in negative feedback loops. In this study, I show that U11-48K, a protein factor specific to the minor spliceosome, specifically recognizes the U12-type 5' splice site sequence, and is essential for proper function of the minor spliceosome. Furthermore, the expression of U11-48K is regulated through a feedback mechanism, which functions through conserved sequence elements that activate alternative splicing and nonsense-mediated decay. This mechanism is conserved from plants to animals, highlighting both the importance and early origin of this mechanism in regulating splicing factors. I also show that the feedback regulation of U11-48K is counteracted by a component of the major spliceosome, the U1 small nuclear ribonucleoprotein particle, as well as members of the hnRNP F/H protein family. These results thus suggest that the feedback mechanism is finely tuned by multiple factors to achieve precise control of the activity of the U12-dependent spliceosome.

Nucleotide sequence of the first cosmid from the Mycobacterium leprae genome project: structure and function of the Rif-Str regions

The nucleotide sequence of cosmid B1790, carrying the Rif-Str regions of the Mycobacterium leprae chromosome, has been determined. Twelve open reading frames were identified in the 36716bp sequence, representing 40% of the coding capacity. Five ribosomal proteins, two elongation factors and the β and β'subunits of RNA polymerase have been characterized and two novel genes were found. One of these encodes a member of the so-called ABC family of ATP-binding proteins while the other appears to encode an enzyme involved in repairing genomic lesions caused by free radicals. This finding may well be significant as M. leprae, an intracellular pathogen, lives within macrophages.

Role of lipid peroxidation in impairment of mitochondrial function at complex I by methyl isocyanate treatment of rats in vivo

The subcutaneous administration of methyl isocyanate (MIC) in 1.0 LD50 dose in rats caused a significant effect on hepatic mitochondrial function only at complex I region of the respiratory chain. MIC administration at 1.0 LD50 dose also resulted in significant increases in malondialdehyde and ferrous ion concentration in liver mitochondria. It is suggested that the augmented lipid peroxidation in hepatic mitochondria, catalyzed by iron, possibly mobilized from intracellular stores leads to the inhibition of enzymes of mitochondrial respiration at complex I region, in vivo, in rats receiving a lethal dose of MIC subcutaneously.

A modified sulphide capacity function

The sulphide capacity as originally defined by Fincham and Richardson is a strong function of composition in pseudobinary oxide melts of interest in extractive metallurgy. From an analysis of data available in the literature, it is shown that sulphide capacity is directly proportional to the activity of the basic oxide in the melt, within the uncertainty of experimental data. A single parameter is sufficient to describe the sulphide capacity of a binary slag system under isothermal and isobaric conditions. The correlation indicates that the activity coefficient of the sulphide ion or the neutral base metal sulphide dissolved in the melt is independent of composition in pseudobinary melts within experimental uncertainty. Structural variations in the melt with composition do not seem to affect the activity coefficient of the sulphide. A modified sulphide capacity function is defined which makes the treatment more elegant and greatly simplifies data storage and retrieval. The modified function is not based on any model for the melt.

An actor-critic algorithm with function approximation for discounted cost constrained Markov decision processes

We develop in this article the first actor-critic reinforcement learning algorithm with function approximation for a problem of control under multiple inequality constraints. We consider the infinite horizon discounted cost framework in which both the objective and the constraint functions are suitable expected policy-dependent discounted sums of certain sample path functions. We apply the Lagrange multiplier method to handle the inequality constraints. Our algorithm makes use of multi-timescale stochastic approximation and incorporates a temporal difference (TD) critic and an actor that makes a gradient search in the space of policy parameters using efficient simultaneous perturbation stochastic approximation (SPSA) gradient estimates. We prove the asymptotic almost sure convergence of our algorithm to a locally optimal policy. (C) 2010 Elsevier B.V. All rights reserved.

Symmetry Properties of the Large-Deviation Function of the Velocity of a Self-Propelled Polar Particle

A geometrically polar granular rod confined in 2D geometry, subjected to a sinusoidal vertical oscillation, undergoes noisy self-propulsion in a direction determined by its polarity. When surrounded by a medium of crystalline spherical beads, it displays substantial negative fluctuations in its velocity. We find that the large-deviation function (LDF) for the normalized velocity is strongly non-Gaussian with a kink at zero velocity, and that the antisymmetric part of the LDF is linear, resembling the fluctuation relation known for entropy production, even when the velocity distribution is clearly non-Gaussian. We extract an analogue of the phase-space contraction rate and find that it compares well with an independent estimate based on the persistence of forward and reverse velocities.