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.

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.

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.

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.

In vivo and in vitro studies on the differential role of luteinizing hormone and follicle-stimulating hormone in regulating follicular function in the bonnet monkey (Macaca radiata) using specific gonadotropin antibodies

Although a distinct need for FSH in the regulation of follicular maturation in the primate is well recognized, it is not clear how FSH controls the functionality of different cellular compartments of the follicle. It is also not evident whether there is a requirement for LH in follicular maturation in the primate. In the first part of the present study, female bonnet monkeys were administered a well-characterized ovine (o) LH antiserum to neutralize endogenous monkey LH for different periods during the follicular phase, and the effect on the overall follicular maturation process was assessed by analyzing serum estrogen (E) and progesterone (P) profiles. Neither continuous LH deprivation from Day 8 of the cycle nor deprivation of LH on any one day between Days 6 and 10 had a significant effect on serum E and P profiles and the follicular maturation process. The period for which the antiserum was effective was dependent upon the dose injected; 1 ml of the antiserum given on Day 8 blocked ovulation but not follicular maturation. To assess the effect of deprivation of LH/FSH at the cellular level, animals were deprived in vivo of LH (on Days 8 and 9 of the cycle) or of FSH (on Day 6 of the cycle) by injection of highly characterized hCG and ovine (o) FSH antisera, respectively; the in vitro responsiveness of granulosa and thecal cells isolated on Day 10 from these animals was then determined.(ABSTRACT TRUNCATED AT 250 WORDS)

Evidence for follicle-stimulating hormone mediation in the hemiorchidectomy-induced compensatory increase in the function of the remaining testis of the adult male bonnet monkey (Macaca radiata)

Hemiorchidectomy (HO) in the adult male bonnet monkey results in a selective increase in circulating concentrations of FSH and testosterone, and this is accompanied by compensatory increase in sperm production by the remaining testis. We investigated the possible role of increased FSH concentration that occurs after HO in the compensatory increase in the activity of the remaining testis. Of eight adult male bonnet monkeys that underwent HO, four received i.v. injections every other day for 30 days of a well-characterized ovine FSH antiserum (a/s) that cross-reacts with monkey FSH. The remaining four males received normal monkey serum (NMS) as control treatment in a protocol similar to that employed for ais-treated males. Blood samples were collected between 2100 and 2200 h before and 1/2, 1, 3, 5, 7, 14, 22, and 29 days after HO. Testicular weight, number of 3 beta-hydroxy steroid dehydrogenase-positive (3 beta-HSD+) cells, and DNA flow cytometric analysis of germ cell populations were obtained for testes collected before and at the termination of NMS or ais treatment. In NMS-treated males, circulating serum FSH concentrations progressively increased to reach a maximal level by Day 7 after HO (1.95 +/- 0.3 vs. 5.6 +/- 0.7 ng/ml on Days -1 and 7, respectively). Within 30 min of ais injection, FSH antibodies were detected in circulation, and the antibody level was maintained at a constant level between Day 7 and end of treatment (exhibiting 50-60% binding to I-125-hFSH). Although circulating mean nocturnal serum testosterone concentration showed an initial decrease, it rose gradually to pre-HO concentrations by Day 7 in NMS-treated males. In contrast, nocturnal mat serum testosterone concentrations in a/s-treated males remained lower than in NMS-treated controls (p < 0.05) up to Day 22 and thereafter only marginally increased. Testicular weights increased (p < 0.05) over the pre-HO weight in NMS- but not in ais-treated males. After HO, the number of 3 beta-HSD+ cells (Leydig cells) was markedly increased but was significantly (p < 0.05) higher in NMS-treated males compared to a/s-treated males. A significant (p < 0.05) reduction in the primary spermatocyte population of germ cells was observed in ais-treated compared to NMS-treated males. These results suggest that the increased FSH occurring after HO could be intimately involved in increasing the compensatory functional activity of the remaining testis in the male bonnet monkey.

Reinforcement Learning With Function Approximation for Traffic Signal Control

We propose, for the first time, a reinforcement learning (RL) algorithm with function approximation for traffic signal control. Our algorithm incorporates state-action features and is easily implementable in high-dimensional settings. Prior work, e. g., the work of Abdulhai et al., on the application of RL to traffic signal control requires full-state representations and cannot be implemented, even in moderate-sized road networks, because the computational complexity exponentially grows in the numbers of lanes and junctions. We tackle this problem of the curse of dimensionality by effectively using feature-based state representations that use a broad characterization of the level of congestion as low, medium, or high. One advantage of our algorithm is that, unlike prior work based on RL, it does not require precise information on queue lengths and elapsed times at each lane but instead works with the aforementioned described features. The number of features that our algorithm requires is linear to the number of signaled lanes, thereby leading to several orders of magnitude reduction in the computational complexity. We perform implementations of our algorithm on various settings and show performance comparisons with other algorithms in the literature, including the works of Abdulhai et al. and Cools et al., as well as the fixed-timing and the longest queue algorithms. For comparison, we also develop an RL algorithm that uses full-state representation and incorporates prioritization of traffic, unlike the work of Abdulhai et al. We observe that our algorithm outperforms all the other algorithms on all the road network settings that we consider.

Velocity distribution function for a dilute granular material in shear flow

The velocity distribution function for the steady shear flow of disks (in two dimensions) and spheres (in three dimensions) in a channel is determined in the limit where the frequency of particle-wall collisions is large compared to particle-particle collisions. An asymptotic analysis is used in the small parameter epsilon, which is naL in two dimensions and na(2)L in three dimensions, where; n is the number density of particles (per unit area in two dimensions and per unit volume in three dimensions), L is the separation of the walls of the channel and a is the particle diameter. The particle-wall collisions are inelastic, and are described by simple relations which involve coefficients of restitution e(t) and e(n) in the tangential and normal directions, and both elastic and inelastic binary collisions between particles are considered. In the absence of binary collisions between particles, it is found that the particle velocities converge to two constant values (u(x), u(y)) = (+/-V, O) after repeated collisions with the wall, where u(x) and u(y) are the velocities tangential and normal to the wall, V = (1 - e(t))V-w/(1 + e(t)), and V-w and -V-w, are the tangential velocities of the walls of the channel. The effect of binary collisions is included using a self-consistent calculation, and the distribution function is determined using the condition that the net collisional flux of particles at any point in velocity space is zero at steady state. Certain approximations are made regarding the velocities of particles undergoing binary collisions :in order to obtain analytical results for the distribution function, and these approximations are justified analytically by showing that the error incurred decreases proportional to epsilon(1/2) in the limit epsilon --> 0. A numerical calculation of the mean square of the difference between the exact flux and the approximate flux confirms that the error decreases proportional to epsilon(1/2) in the limit epsilon --> 0. The moments of the velocity distribution function are evaluated, and it is found that [u(x)(2)] --> V-2, [u(y)(2)] similar to V-2 epsilon and -[u(x)u(y)] similar to V-2 epsilon log(epsilon(-1)) in the limit epsilon --> 0. It is found that the distribution function and the scaling laws for the velocity moments are similar for both two- and three-dimensional systems.

Physics based basis function for vibration analysis of high speed rotating beams

The natural frequencies of continuous systems depend on the governing partial differential equation and can be numerically estimated using the finite element method. The accuracy and convergence of the finite element method depends on the choice of basis functions. A basis function will generally perform better if it is closely linked to the problem physics. The stiffness matrix is the same for either static or dynamic loading, hence the basis function can be chosen such that it satisfies the static part of the governing differential equation. However, in the case of a rotating beam, an exact closed form solution for the static part of the governing differential equation is not known. In this paper, we try to find an approximate solution for the static part of the governing differential equation for an uniform rotating beam. The error resulting from the approximation is minimized to generate relations between the constants assumed in the solution. This new function is used as a basis function which gives rise to shape functions which depend on position of the element in the beam, material, geometric properties and rotational speed of the beam. The results of finite element analysis with the new basis functions are verified with published literature for uniform and tapered rotating beams under different boundary conditions. Numerical results clearly show the advantage of the current approach at high rotation speeds with a reduction of 10 to 33% in the degrees of freedom required for convergence of the first five modes to four decimal places for an uniform rotating cantilever beam.

Vesicle formation from dimeric ion-paired amphiphiles. Control over vesicular thermotropic and ion-transport properties as a function of intra-amphiphilic headgroup separation

A novel series of vesicle-forming ion-paired amphiphiles, bis(hexadecyldimethylammonium)alkane dipalmitate (1a-1h), containing four chains were synthesized with two isolated headgroups. In each of these amphiphiles, the two headgroup charges are separated by a flexible polymethylene spacer chain -[(CH2)(m)]- of varying lengths (m) such that the length and the conformation of the spacer chain determine the intra-"monomer" headgroup separation. Transmission electron microscopy indicated that each of these forms bilayer membranes upon dispersion in aqueous media. The vesicular properties of these aggregates have been examined by differential scanning calorimetry and temperature-dependent fluorescence anisotropy measurements. Interestingly, their T-m values decreased with the increase in the m value. Thus while the apparent T-m of the lipid with m = 2 (1a) is 74.1 degrees C, the corresponding value observed for the lipid with m = 12 (1h) is 38.9 degrees C. The fluorescence anisotropy values (r) for 1b-1g were quite high (r similar to 0.3) compared to that of 1h (r similar to 0.23) at 20-30 degrees C in their gel states. On the other hand, the r value for vesicular 1b beyond melting was higher (0.1) compared to any of those for 1c-1h (similar to 0.04-0.06). X-ray diffraction of the cast films was performed to understand the nature and the thickness of these membrane organizations. The membrane widths ranged from 30 to 51 A as the m values varied. The entrapment of a small water-soluble solute, riboflavin, by the individual vesicular aggregates, and their sustenance: under an imposed transmembrane pH gradient have also been examined. These results show that all lipid vesicles entrap riboflavin and that generally the resistance to OH- permeation decreases with the increase in m value. Finally,all the above observations were comparatively analyzed, and on the basis of the calculated structures of these lipids, it was possible to conclude that membrane propel-ties can be modulated by spacer chain length variation of the ion-paired amphiphiles.

Localisation of discrete change in a transformer winding: a network-function-loci approach

An entirely different approach for localisation of winding deformation based on terminal measurements is presented. Within the context of this study, winding deformation means, a discrete and specific change externally imposed at a particular position on the winding. The proposed method is based on pre-computing and plotting the complex network-function loci e.g. driving-point impedance (DPI)] at a selected frequency, for a meaningful range of values for each element (increasing and decreasing) of the ladder network which represents the winding. This loci diagram is called the nomogram. After introducing a discrete change, amplitude and phase of DPI are measured. By plotting this single measurement on the nomogram, it is possible to estimate the location and identify the extent of change. In contrast to the existing approach, the proposed method is fast, non-iterative and yields reasonably good localisation. Experimental results for actual transformer windings (interleaved and continuous disc) are presented.