A maximal operator, Carleson's embedding, and tent spaces for vector-valued functions

This thesis is concerned with the area of vector-valued Harmonic Analysis, where the central theme is to determine how results from classical Harmonic Analysis generalize to functions with values in an infinite dimensional Banach space. The work consists of three articles and an introduction. The first article studies the Rademacher maximal function that was originally defined by T. Hytönen, A. McIntosh and P. Portal in 2008 in order to prove a vector-valued version of Carleson's embedding theorem. The boundedness of the corresponding maximal operator on Lebesgue-(Bochner) -spaces defines the RMF-property of the range space. It is shown that the RMF-property is equivalent to a weak type inequality, which does not depend for instance on the integrability exponent, hence providing more flexibility for the RMF-property. The second article, which is written in collaboration with T. Hytönen, studies a vector-valued Carleson's embedding theorem with respect to filtrations. An earlier proof of the dyadic version assumed that the range space satisfies a certain geometric type condition, which this article shows to be also necessary. The third article deals with a vector-valued generalizations of tent spaces, originally defined by R. R. Coifman, Y. Meyer and E. M. Stein in the 80's, and concerns especially the ones related to square functions. A natural assumption on the range space is then the UMD-property. The main result is an atomic decomposition for tent spaces with integrability exponent one. In order to suit the stochastic integrals appearing in the vector-valued formulation, the proof is based on a geometric lemma for cones and differs essentially from the classical proof. Vector-valued tent spaces have also found applications in functional calculi for bisectorial operators. In the introduction these three themes come together when studying paraproduct operators for vector-valued functions. The Rademacher maximal function and Carleson's embedding theorem were applied already by Hytönen, McIntosh and Portal in order to prove boundedness for the dyadic paraproduct operator on Lebesgue-Bochner -spaces assuming that the range space satisfies both UMD- and RMF-properties. Whether UMD implies RMF is thus an interesting question. Tent spaces, on the other hand, provide a method to study continuous time paraproduct operators, although the RMF-property is not yet understood in the framework of tent spaces.

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.

A proteomic view of probiotic Lactobacillus rhamnosus GG

Lactobacillus rhamnosus GG is a probiotic bacterium that is known worldwide. Since its discovery in 1985, the health effects and biology of this health-promoting strain have been researched at an increasing rate. However, knowledge of the molecular biology responsible for these health effects is limited, even though research in this area has continued to grow since the publication of the whole genome sequence of L. rhamnosus GG in 2009. In this thesis, the molecular biology of L. rhamnosus GG was explored by mapping the changes in protein levels in response to diverse stress factors and environmental conditions. The proteomics data were supplemented with transcriptome level mapping of gene expression. The harsh conditions of the gastro-intestinal tract, which involve acidic conditions and detergent-like bile acids, are a notable challenge to the survival of probiotic bacteria. To simulate these conditions, L. rhamnosus GG was exposed to a sudden bile stress, and several stress response mechanisms were revealed, among others various changes in the cell envelope properties. L. rhamnosus GG also responded in various ways to mild acid stress, which probiotic bacteria may face in dairy fermentations and product formulations. The acid stress response of L. rhamnosus GG included changes in central metabolism and specific responses related to the control of intracellular pH. Altogether, L. rhamnosus GG was shown to possess a large repertoire of mechanisms for responding to stress conditions, which is a beneficial character of a probiotic organism. Adaptation to different growth conditions was studied by comparing the proteome level responses of L. rhamnosus GG to divergent growth media and to different phases of growth. Comparing different growth phases revealed that the metabolism of L. rhamnosus GG is modified markedly during shift from the exponential to the stationary phase of growth. These changes were seen both at proteome and transcriptome levels and in various different cellular functions. When the growth of L. rhamnosus GG in a rich laboratory medium and in an industrial whey-based medium was compared, various differences in metabolism and in factors affecting the cell surface properties could be seen. These results led us to recommend that the industrial-type media should be used in laboratory studies of L. rhamnosus GG and other probiotic bacteria to achieve a similar physiological state for the bacteria as that found in industrial products, which would thus yield more relevant information about the bacteria. In addition, an interesting phenomenon of protein phosphorylation was observed in L. rhamnosus GG. Phosphorylation of several proteins of L. rhamnosus GG was detected, and there were hints that the degree of phosphorylation may be dependent on the growth pH.

Reynolds stress and heat flux in spherical shell convection

Context. Turbulent fluxes of angular momentum and heat due to rotationally affected convection play a key role in determining differential rotation of stars. Aims. We compute turbulent angular momentum and heat transport as functions of the rotation rate from stratified convection. We compare results from spherical and Cartesian models in the same parameter regime in order to study whether restricted geometry introduces artefacts into the results. Methods. We employ direct numerical simulations of turbulent convection in spherical and Cartesian geometries. In order to alleviate the computational cost in the spherical runs and to reach as high spatial resolution as possible, we model only parts of the latitude and longitude. The rotational influence, measured by the Coriolis number or inverse Rossby number, is varied from zero to roughly seven, which is the regime that is likely to be realised in the solar convection zone. Cartesian simulations are performed in overlapping parameter regimes. Results. For slow rotation we find that the radial and latitudinal turbulent angular momentum fluxes are directed inward and equatorward, respectively. In the rapid rotation regime the radial flux changes sign in accordance with earlier numerical results, but in contradiction with theory. The latitudinal flux remains mostly equatorward and develops a maximum close to the equator. In Cartesian simulations this peak can be explained by the strong 'banana cells'. Their effect in the spherical case does not appear to be as large. The latitudinal heat flux is mostly equatorward for slow rotation but changes sign for rapid rotation. Longitudinal heat flux is always in the retrograde direction. The rotation profiles vary from anti-solar (slow equator) for slow and intermediate rotation to solar-like (fast equator) for rapid rotation. The solar-like profiles are dominated by the Taylor-Proudman balance.

The Reception of the Maccabean Martyrs : Their Historiographical and Paradigmatic Functions in Antique and Late-antique Jewish and Christian Sources

The study attempts a reception-historical analysis of the Maccabean martyrs. The concept of reception has fundamentally to do with the re-use and interpretation of a text within new texts. In a religious tradition, certain elements become re-circulated and thus their reception may reflect the development of that particular tradition. The Maccabean martyrs first appear in 2 Maccabees. In my study, it is the Maccabean martyr figures who count as the received text; the focus is shifted from the interrelations between texts onto how the figures have been exploited in early Christian and Rabbinic sources. I have divided my sources into two categories and my analysis is in two parts. First, I analyze the reception of the Maccabean martyrs within Jewish and Christian historiographical sources, focusing on the role given to them in the depictions of the Maccabean Revolt (Chapter 3). I conclude that, within Jewish historiography, the martyrs are given roles, which vary between ultimate efficacy and marginal position with regard to making a historical difference. In Christian historiographical sources, the martyrs role grows in importance by time: however, it is not before a Christian cult of the Maccabean martyrs has been established, that the Christian historiographies consider them historically effective. After the first part, I move on to analyze the reception in sources, which make use of the Maccabean martyrs as paradigmatic figures (Chapter 4). I have suggested that the martyrs are paradigmatic in the context of martyrdom, persecution and destruction, on one hand, and in a homiletic context, inspiring religious celebration, on the other. I conclude that, as the figures are considered pre-Christian and biblical martyrs, they function well in terms of Christian martyrdom and have contributed to the development of its ideals. Furthermore, the presentation of the martyr figures in Rabbinic sources demonstrates how the notion of Jewish martyrdom arises from experiences of destruction and despair, not so much from heroic confession of faith in the face of persecution. Before the emergence of a Christian cult of the Maccabean martyrs, their identity is derived namely from their biblical position. Later on, in the homiletic context, their Jewish identity is debated and sometimes reconstructed as fundamentally Christian , despite of their Jewish origins. Similar debate about their identity is not found in the Rabbinic versions of their martyrdom and nothing there indicates a mutual debate between early Christians and Jews. A thematic comparison shows that the Rabbinic and Christian cases of reception are non-reliant on each other but also that they link to one another. Especially the scriptural connections, often made to the Maccabean mother, reveal the similarities. The results of the analyses confirm that the early history of Christianity and Rabbinic Judaism share, at least partly, the same religious environment and intertwining traditions, not only during the first century or two but until Late Antiquity and beyond. More likely, the reception of the Maccabean martyrs demonstrates that these religious traditions never ceased to influence one another.