Global, Local and Vector-Valued Tb Theorems on Non-Homogeneous Metric Spaces

Various Tb theorems play a key role in the modern harmonic analysis. They provide characterizations for the boundedness of Calderón-Zygmund type singular integral operators. The general philosophy is that to conclude the boundedness of an operator T on some function space, one needs only to test it on some suitable function b. The main object of this dissertation is to prove very general Tb theorems. The dissertation consists of four research articles and an introductory part. The framework is general with respect to the domain (a metric space), the measure (an upper doubling measure) and the range (a UMD Banach space). Moreover, the used testing conditions are weak. In the first article a (global) Tb theorem on non-homogeneous metric spaces is proved. One of the main technical components is the construction of a randomization procedure for the metric dyadic cubes. The difficulty lies in the fact that metric spaces do not, in general, have a translation group. Also, the measures considered are more general than in the existing literature. This generality is genuinely important for some applications, including the result of Volberg and Wick concerning the characterization of measures for which the analytic Besov-Sobolev space embeds continuously into the space of square integrable functions. In the second article a vector-valued extension of the main result of the first article is considered. This theorem is a new contribution to the vector-valued literature, since previously such general domains and measures were not allowed. The third article deals with local Tb theorems both in the homogeneous and non-homogeneous situations. A modified version of the general non-homogeneous proof technique of Nazarov, Treil and Volberg is extended to cover the case of upper doubling measures. This technique is also used in the homogeneous setting to prove local Tb theorems with weak testing conditions introduced by Auscher, Hofmann, Muscalu, Tao and Thiele. This gives a completely new and direct proof of such results utilizing the full force of non-homogeneous analysis. The final article has to do with sharp weighted theory for maximal truncations of Calderón-Zygmund operators. This includes a reduction to certain Sawyer-type testing conditions, which are in the spirit of Tb theorems and thus of the dissertation. The article extends the sharp bounds previously known only for untruncated operators, and also proves sharp weak type results, which are new even for untruncated operators. New techniques are introduced to overcome the difficulties introduced by the non-linearity of maximal truncations.

VEGF-C/VEGFR-3 and PDGF-B/PDGFR-b pathways in embryonic lymphangiogenesis

The circulatory system comprises the blood vascular system and the lymphatic vascular system. These two systems function in parallel. Blood vessels form a closed system that delivers oxygen and nutrients to the tissues and removes waste products from the tissues, while lymphatic vessels are blind-ended tubes that collect extravasated fluid and cells from the tissues and return them back to blood circulation. Development of blood and lymphatic vascular systems occurs in series. Blood vessels are formed via vasculogenesis and angiogenesis whereas lymphatic vessels develop via lymphangiogenesis, after the blood vascular system is already functional. Members of the vascular endothelial growth factor (VEGF) family are regulators of both angiogenesis and lymphangiogenesis, while members of the platelet-derived growth factor (PDGF) family are major mitogens for pericytes and smooth muscle cells and regulate formation of blood vessels. Vascular endothelial growth factor C (VEGF-C) is the major lymphatic growth factor and signaling through its receptor vascular endothelial growth factor receptor 3 (VEGFR-3) is sufficient for lymphangiogenesis in adults. We studied the role of VEGF-C in embryonic lymphangiogenesis and showed that VEGF-C is absolutely required for the formation of lymph sacs from embryonic veins. VEGFR-3 is also required for normal development of the blood vascular system during embryogenesis, as Vegfr3 knockout mice die at mid-gestation due to failure in remodeling of the blood vessels. We showed that sufficient VEGFR-3 signaling in the embryo proper is required for embryonic angiogenesis and in a dosage-sensitive manner for embryonic lymphangiogenesis. Importantly, mice deficient in both VEGFR-3 ligands, Vegfc and Vegfd, developed a normal blood vasculature, suggesting VEGF-C- and VEGF-D- independent functions for VEGFR-3 in the early embryo. Platelet-derived growth factor B (PDGF-B) signals via PDGFR-b and regulates formation of blood vessels by recruiting pericytes and smooth muscle cells around nascent endothelial tubes. We showed that PDGF-B fails to induce lymphangiogenesis when overexpressed in adult mouse skin using adenoviral vectors. However, mouse embryos lacking Pdgfb showed abnormal lymphatic vessels, suggesting that PDGF-B plays a role in lymphatic vessel maturation and separation from blood vessels during embryogenesis. Lymphatic vessels play a key role in immune surveillance, fat absorption and maintenance of fluid homeostasis in the body. However, lymphatic vessels are also involved in various diseases, such as lymphedema and tumor metastasis. These studies elucidate the basic mechanisms of embryonic lymphangiogenesis and add to the knowledge of lymphedema and tumor metastasis treatments by giving novel insights into how lymphatic vessel growth could be induced (in lymphedema) or inhibited (in tumor metastasis).

Cereulide producing B. cereus and amylosin producing B. subtilis and B. mojavensis : characterization of strains and toxigenicities

B. cereus is one of the most frequent occurring bacteria in foods . It produces several heat-labile enterotoxins and one stable non-protein toxin, cereulide (emetic), which may be pre-formed in food. Cereulide is a heat stable peptide whose structure and mechanism of action were in the past decade elucidated. Until this work, the detection of cereulide was done by biological assays. With my mentors, I developed the first quantitative chemical assay for cereulide. The assay is based on liquid chromatography (HPLC) combined with ion trap mass spectrometry and the calibration is done with valinomycin and purified cereulide. To detect and quantitate valinomycin and cereulide, their [NH4+] adducts, m/z 1128.9 and m/z 1171 respectively, were used. This was a breakthrough in the cereulide research and became a very powerful tool of investigation. This tool made it possible to prove for the first time that the toxin produced by B. cereus in heat-treated food caused human illness. Until this thesis work (Paper II), cereulide producing B. cereus strains were believed to represent a homogenous group of clonal strains. The cereulide producing strains investigated in those studies originated mostly from food poisoning incidents. We used strains of many origins and analyzed them using a polyphasic approach. We found that the cereulide producing B. cereus strains are genetically and biologically more diverse than assumed in earlier studies. The strains diverge in the adenylate kinase (adk) gene (two sequence types), in ribopatterns obtained with EcoRI and PvuII (three patterns), tyrosin decomposition, haemolysis and lecithine hydrolysis (two phenotypes). Our study was the first demonstration of diversity within the cereulide producing strains of B. cereus. To manage the risk for cereulide production in food, understanding is needed on factors that may upregulate cereulide production in a given food matrix and the environmental factors affecting it. As a contribution towards this direction, we adjusted the growth environment and measured the cereulide production by strains selected for diversity. The temperature range where cereulide is produced was narrower than that for growth for most of the producer strains. Most cereulide was by most strains produced at room temperature (20 - 23ºC). Exceptions to this were two faecal isolates which produced the same amount of cereulide from 23 ºC up until 39ºC. We also found that at 37º C the choice of growth media for cereulide production differed from that at the room temperature. The food composition and temperature may thus be a key for understanding cereulide production in foods as well as in the gut. We investigated the contents of [K+], [Na+] and amino acids of six growth media. Statistical evaluation indicated a significant positive correlation between the ratio [K+]:[Na+] and the production of cereulide, but only when the concentrations of glycine and [Na+] were constant. Of the amino acids only glycine correlated positively with high cereulide production. Glycine is used worldwide as food additive (E 640), flavor modifier, humectant, acidity regulator, and is permitted in the European Union countries, with no regulatory quantitative limitation, in most types of foods. B. subtilis group members are endospore-forming bacteria ubiquitous in the environment, similar to B. cereus in this respect. Bacillus species other than B. cereus have only sporadically been identified as causative agents of food-borne illnesses. We found (Paper IV) that food-borne isolates of B. subtilis and B. mojavensis produced amylosin. It is possible that amylosin was the agent responsible for the food-borne illness, since no other toxic substance was found in the strains. This is the first report on amylosin production by strains isolated from food. We found that the temperature requirement for amylosin production was higher for the B. subtilis strain F 2564/96, a mesophilic producer, than for B. mojavensis strains eela 2293 and B 31, psychrotolerant producers. We also found that an atmosphere with low oxygen did not prevent the production of amylosin. Ready-to-eat foods packaged in micro-aerophilic atmosphere and/or stored at temperatures above 10 °C, may thus pose a risk when toxigenic strains of B. subtilis or B. mojavensis are present.

Homogeneous model theory of metric structures

This thesis studies homogeneous classes of complete metric spaces. Over the past few decades model theory has been extended to cover a variety of nonelementary frameworks. Shelah introduced the abstact elementary classes (AEC) in the 1980s as a common framework for the study of nonelementary classes. Another direction of extension has been the development of model theory for metric structures. This thesis takes a step in the direction of combining these two by introducing an AEC-like setting for studying metric structures. To find balance between generality and the possibility to develop stability theoretic tools, we work in a homogeneous context, thus extending the usual compact approach. The homogeneous context enables the application of stability theoretic tools developed in discrete homogeneous model theory. Using these we prove categoricity transfer theorems for homogeneous metric structures with respect to isometric isomorphisms. We also show how generalized isomorphisms can be added to the class, giving a model theoretic approach to, e.g., Banach space isomorphisms or operator approximations. The novelty is the built-in treatment of these generalized isomorphisms making, e.g., stability up to perturbation the natural stability notion. With respect to these generalized isomorphisms we develop a notion of independence. It behaves well already for structures which are omega-stable up to perturbation and coincides with the one from classical homogeneous model theory over saturated enough models. We also introduce a notion of isolation and prove dominance for it.

Prognostic molecular factors and algorithms in diffuse large B-cell lymphoma

Diffuse large B-cell lymphoma (DLBCL) is the most common of the non-Hodgkin lymphomas. As DLBCL is characterized by heterogeneous clinical and biological features, its prognosis varies. To date, the International Prognostic Index has been the strongest predictor of outcome for DLBCL patients. However, no biological characters of the disease are taken into account. Gene expression profiling studies have identified two major cell-of-origin phenotypes in DLBCL with different prognoses, the favourable germinal centre B-cell-like (GCB) and the unfavourable activated B-cell-like (ABC) phenotypes. However, results of the prognostic impact of the immunohistochemically defined GCB and non-GCB distinction are controversial. Furthermore, since the addition of the CD20 antibody rituximab to chemotherapy has been established as the standard treatment of DLBCL, all molecular markers need to be evaluated in the post-rituximab era. In this study, we aimed to evaluate the predictive value of immunohistochemically defined cell-of-origin classification in DLBCL patients. The GCB and non-GCB phenotypes were defined according to the Hans algorithm (CD10, BCL6 and MUM1/IRF4) among 90 immunochemotherapy- and 104 chemotherapy-treated DLBCL patients. In the chemotherapy group, we observed a significant difference in survival between GCB and non-GCB patients, with a good and a poor prognosis, respectively. However, in the rituximab group, no prognostic value of the GCB phenotype was observed. Likewise, among 29 high-risk de novo DLBCL patients receiving high-dose chemotherapy and autologous stem cell transplantation, the survival of non-GCB patients was improved, but no difference in outcome was seen between GCB and non-GCB subgroups. Since the results suggested that the Hans algorithm was not applicable in immunochemotherapy-treated DLBCL patients, we aimed to further focus on algorithms based on ABC markers. We examined the modified activated B-cell-like algorithm based (MUM1/IRF4 and FOXP1), as well as a previously reported Muris algorithm (BCL2, CD10 and MUM1/IRF4) among 88 DLBCL patients uniformly treated with immunochemotherapy. Both algorithms distinguished the unfavourable ABC-like subgroup with a significantly inferior failure-free survival relative to the GCB-like DLBCL patients. Similarly, the results of the individual predictive molecular markers transcription factor FOXP1 and anti-apoptotic protein BCL2 have been inconsistent and should be assessed in immunochemotherapy-treated DLBCL patients. The markers were evaluated in a cohort of 117 patients treated with rituximab and chemotherapy. FOXP1 expression could not distinguish between patients, with favourable and those with poor outcomes. In contrast, BCL2-negative DLBCL patients had significantly superior survival relative to BCL2-positive patients. Our results indicate that the immunohistochemically defined cell-of-origin classification in DLBCL has a prognostic impact in the immunochemotherapy era, when the identifying algorithms are based on ABC-associated markers. We also propose that BCL2 negativity is predictive of a favourable outcome. Further investigational efforts are, however, warranted to identify the molecular features of DLBCL that could enable individualized cancer therapy in routine patient care.

First Measurement of the Ratio of Branching Fractions B(Lambda_b to Lambda_c mu nu)/B(Lambda_b to Lambda_c pi)

The analysis uses data from an integrated luminosity of approximately 172 pb-1 of ppbar collisions at sqrt(s)=1.96 TeV, collected with the CDF II detector at the Fermilab Tevatron. The Lambda_b and B0 relative branching fractions are measured to be: B(Lambda_b to Lambda_c+ mu nu)/B(Lambda_b to Lambda_c+ pi) = 16.6 +- 3.0 (stat) +- 1.0 (syst) +2.6 -3.4 (PDG) +- 0.3 (EBR), B(B0 to D+ mu nu)/B(B0 to D+ pi) = 9.9 +- 1.0 (stat) +- 0.6 (syst) +- 0.4 (PDG) +- 0.5 (EBR), B(B0 to D*+ mu nu)/B(B0 to D*+ pi) = 16.5 +- 2.3 (stat) +- 0.6 (syst) +- 0.5 (PDG) +- 0.8 (EBR) This article also presents measurements of the branching fractions of four new Lambda_b semileptonic decays: Lambda_b to Lambda_c(2595)+ mu nu, Lambda_b to Lambda_c(2625)+ mu nu, Lambda_b to Sigma_c(2455)0 pi mu nu, Lambda_b to Sigma_c(2455)++ pi mu nu, relative to the branching fraction of the Lambda_b to Lambda_c mu nu decay. Finally, the transverse-momentum distribution of Lambda_b baryons produced in p-pbar collisions is measured and found to be significantly different from that of B0 mesons.

Search for the rare decays B+→μ+μ-K+, B0→μ+μ-K*(892)0, and Bs0→μ+μ-ϕ at CDF

We search for b to s\mu^+\mu^- transitions in B meson (B^+, B^0, or B^0_s) decays with 924pb^{-1} of p pbar collisions at sqrt(s)=1.96 TeV collected with the CDF II detector at the Fermilab Tevatron. We find excesses with significances of 4.5, 2.9, and 2.4 standard deviations in the B^+ to \mu^+\mu^-K^+, B^0 to \mu^+\mu^-K^*(892)^0, and B_s^0 to \mu^+\mu^-\phi decay modes, respectively. Using B to J/psi h (h = K^+, K^*(892)^0, phi) decays as normalization channels, we report branching fractions for the previously observed B^+ and B^0 decays, BR(B^+ to \mu^+\mu^-K^+)=(0.59\pm0.15\pm0.04) x 10^{-6}, and BR(B^0 to \mu^+\mu^-K^*(892)^0)=(0.81\pm0.30\pm0.10) x 10^{-6}, where the first uncertainty is statistical, and the second is systematic. These measurements are consistent with the world average results, and are competitive with the best available measurements. We set an upper limit on the relative branching fraction BR(B_s^0 to \mu^+\mu^-\phi)/BR(B_s^0 to J/\psi\phi)

First Measurement of the b-Jet Cross Section in Events with a W Boson in pp̅ Collisions at √s=1.96 TeV

The cross section for jets from b quarks produced with a W boson has been measured in ppbar collision data from 1.9/fb of integrated luminosity recorded by the CDF II detector at the Tevatron. The W+b-jets process poses a significant background in measurements of top quark production and prominent searches for the Higgs boson. We measure a b-jet cross section of 2.74 +- 0.27(stat.) +- 0.42(syst.) pb in association with a single flavor of leptonic W boson decay over a limited kinematic phase space. This measured result cannot be accommodated in several available theoretical predictions.

Measurements of branching fraction ratios and CP asymmetries in B±→DCPK± decays in hadron collisions

We reconstruct B+/- -> D K+/- decays in a data sample collected by the CDF II detector at the Tevatron collider corresponding to 1 fb-1 of integrated luminosity. We select decay modes where the D meson decays to either K- pi+ (flavor eigenstate) or K- K+, pi- pi+ (CP-even eigenstates), and measure the direct CP asymmetry A_CP+ = 0.39 +/- 0.17(stat) +/- 0.04(syst), and the double ratio of CP-even to flavor eigenstate branching fractions R_CP+ = 1.30 +/- 0.24(stat) +/- 0.12(syst). These measurements will improve the determination of the CKM angle gamma. They are performed here for the first time using data from hadron collisions.