Progression of diffuse gliomas - from the first diagnosis to recurrence

Gliomas are the most frequent primary brain tumours. The cardinal features of gliomas are infiltrative growth pattern and progression from low-grade tumours to a more malignant phenotype. These features of gliomas generally prevent their complete surgical excision and cause their inherent tendency to recur after initial treatment and lead to poor long-term prognosis. Increasing knowledge about the molecular biology of gliomas has produced new markers that supplement histopathological diagnostics. Molecular markers are also used to evaluate the prognosis and predict therapeutic response. The purpose of this thesis is to study molecular events involved in the malignant progression of gliomas. Gliomas are highly vascularised tumours. Contrast enhancement in magnetic resonance imaging (MRI) reflects a disrupted blood-brain barrier and is often seen in malignant gliomas. In this thesis, 62 astrocytomas, oligodendrogliomas and oligoastrocytomas were studied by MRI and immunohistochemistry. Contrast enhancement in preoperative MRI was associated with angiogenesis, tumour cell proliferation and histological grade of gliomas. Activation of oncogenes by gene amplification is a common genetic aberration in gliomas. EGFR amplification on chromosome 7p12 occurs in 30-40% of glioblastomas. PDGFRA, KIT and VEGFR2 are receptor tyrosine kinase genes located on chromosome 4q12. Amplification of these genes was studied using in situ hybridisation in the primary and recurrent astrocytomas, oligodendrogliomas and oligoastrocytomas of 87 patients. PDGFRA, KIT or VEGFR2 amplification was found in 22% of primary tumours and 36% of recurrent tumours including low-grade and malignant gliomas. The most frequent aberration was KIT amplification, which occurred in 10% of primary tumours and in 27% of recurrent tumours. The expression of ezrin, cyclooxygenase 2 (COX-2) and HuR was studied immunohistochemically in a series of primary and recurrent gliomas of 113 patients. Ezrin is a cell membrane-cytoskeleton linking-protein involved in the migration of glioma cells. The COX-2 enzyme is implicated in the carcinogenesis of epithelial neoplasms and is overexpressed in gliomas. HuR is an RNA-stabilising protein, which regulates the expression of several proteins including COX-2. Ezrin, COX-2 and HuR were associated with histological grade and the overall survival of glioma patients. However, in multivariate analysis they were not independent prognostic factors. In conclusion, these results suggest that contrast enhancement in MRI can be used as a surrogate marker for the proliferative and angiogenic potential of gliomas. Aberrations of PDGFRA, KIT and VEGFR2 genes, as well as the dysregulated expression of ezrin, COX-2 and HuR proteins, are linked to the progression of gliomas.

Poststroke survival and ischemic stroke recurrence : the cerebral small-vessel disease perspective

The aim of the present study was to investigate the influence of different manifestations of cerebral SVD on poststroke survival and ischemic stroke recurrence in long-term follow-up. The core imaging features of small-vessel disease (SVD) are confluent and extensive white matter changes (WMC) and lacunar infarcts. These are associated with minor motor deficits but a major negative influence on cognition, mood, and functioning in daily life, resulting from small-vessel lesions in the fronto-subcortical brain network. These sub-studies were conducted as part of the Helsinki Stroke Aging Memory (SAM) study. The SAM cohort consisted of 486 consecutive patients aged 55 to 85 years who were admitted to Helsinki University Central Hospital with acute ischemic stroke. The study included comprehensive clinical, neuropsychological, psychiatric and radiological assessment three months poststroke. The patients were followed up up for 12 years using extensive national registers. The effect of different manifestations of cerebral SVD on poststroke survival and stroke recurrence was analyzed controlling for factors such as age, education, and cardiovascular risk factors. Poststroke dementia and cognitive impairment relate to poor long-term survival. In particular, deficits in executive functions as well as visuospatial and constructional abilities predict poor outcome. The predictive value of cognitive deficits is further underlined by the finding that depression-executive dysfunction syndrome (DES), but not depression in itself, is associated with poor poststroke survival. Delirium is not independently associated with increased risk for long-term poststroke mortality, although it is associated with poststroke dementia. Furthermore, acute index stroke attributable to SVD is associated with poorer long-term survival and a higher risk for cardiac death than other stroke subtypes. Severe WMC, a surrogate of SVD, is independently related to an increased risk of stroke recurrence at five years. In summary, cognitive poststroke outcomes reflecting changes in the executive network brain, and the presence of cerebral SVD are important determinants of poststroke mortality and ischemic stroke recurrence, regardless of whether SVD is the cause of the index stroke or a condition concurrent to some other etiology.

Truth, Proof and Gödelian Arguments : A Defence of Tarskian Truth in Mathematics

One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established to be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of Jaakko Hintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion.

Inarinsaamen käsitemetaforat

This study discusses the conceptual metaphors of Inari Saami, an endangered, indigenous, Finno-Ugrian language spoken in northern Finland. The research focuses on systematical mappings between source and target domains in conventional Inari Saami metaphors and metonymies. The research material consists of the Inarinsaamen idiomisanakirja [Inari Saami idiom dictionary] which has been compiled by the author in collaboration with an Inari Saami co-author; the Inarilappisches Wörterbuch; Inarinsaamelaista kansantietoutta [Inari Saami folk knowledge]; and Aanaarkiela čájttuzeh [Inari Saami sample texts]. The metaphors and metonymies found in these literary sources are divided into categories on the basis of the target domains and according to the classic model of Lakoff ja Johnson (1980). This method reveals the systematical recurrence of source domains inside each category and thus discovers the systematical patterns of metaphoric mapping, the conceptual metaphors . As a result 44 conceptual metaphors and 16 conceptual metonymies are presented through approximately 500 glossed examples. These findings are discussed against the background of what is known about the cognitive and neural processing of metaphors on the one hand, and what is known about Inari Saami culture on the other. This theoretical framework highlights culture as the underlying force behind conceptual metaphors. The recurring metonymies seem to follow a culturally salient indexicality. For example, the Inari Saami conceptual metonymy TIME IS NATURE reflects the seasonal changes in the year s cycle, which was the salient index of time in traditional Inari Saami culture. The recurring metaphors, for their part, follow a culturally salient iconicity. The conceptual metaphor PRIDE IS ANTLERS is based on an iconicity which is experienced and interpreted by the Inari Saami. A proud person is associated with a reindeer who shows off his impressive antlers. The conceptual metaphor/metonymy seems to be a reflection of culture rather than a cognitive means of understanding an abstract domain in terms of a concrete domain, as hypothesized by certain theoreticians. Repeating this study with other languages may lead to the possibility of typologizing the metaphorical systems of the world s languages and understanding the diversity of metaphor systems in the endangered languages of the world.

Epithelial-mesenchymal transition in oral squamous carcinoma cells

In epithelial-mesenchymal transition (EMT), epithelial cells acquire traits typical for mesenchymal cells, dissociate their cell-cell junctions and gain the ability to migrate. EMT is essential during embryogenesis, but may also mediate cancer progression. Basement membranes are sheets of extracellular matrix that support epithelial cells. They have a major role in maintaining the epithelial phenotype and, in cancer, preventing cell migration, invasion and metastasis. Laminins are the main components of basement membranes and may actively contribute to malignancy. We first evaluated the differences between cell lines obtained from oral squamous cell carcinoma and its recurrence. As the results indicated a change from epithelial to fibroblastoid morphology, E-cadherin to N-cadherin switch, and change in expression of cytokeratins to vimentin intermediate filaments, we concluded that these cells had undergone EMT. We further induced EMT in primary tumour cells to gain knowledge of the effects of transcription factor Snail in this cell model. The E-cadherin repressors responsible for the EMT in these cells were ZEB-1, ZEB-2 and Snail, and ectopic expression of Snail was able to augment the levels of ZEB-1 and ZEB-2. We produced and characterized two monoclonal antibodies that specifically recognized Snail in cell lines and patient samples. By immunohistochemistry, Snail protein was found in mesenchymal tissues during mouse embryonal development, in fibroblastoid cells of healing skin wounds and in fibromatosis and sarcoma specimens. Furthermore, Snail localized to the stroma and borders of tumour cell islands in colon adenocarcinoma, and in laryngeal and cervical squamous cell carcinomas. Immunofluorescence labellings, immunoprecipitations and Northern and Western blots showed that EMT induced a progressive downregulation of laminin-332 and laminin-511 and, on the other hand, an induction of mesenchymal laminin-411. Chromatin immunoprecipitation revealed that Snail could directly bind upstream to the transcription start sites of both laminin α5 and α4 chain genes, thus regulating their expression. The levels of integrin α6β4, a receptor for laminin-332, as well as the hemidesmosomal complex proteins HD1/plectin and BP180 were downregulated in EMT-experienced cells. The expression of Lutheran glycoprotein, a specific receptor for laminin-511, was diminished, whereas the levels of integrins α6β1 and α1β1 and integrin-linked kinase were increased. In quantitative cell adhesion assays, the cells adhered potently to laminin-511 and fibronectin, but only marginally to laminin-411. Western blots and immunoprecipitations indicated that laminin-411 bound to fibronectin and could compromise cell adhesion to fibronectin in a dose-dependent manner. EMT induced a highly migratory and invasive tendency in oral squamous carcinoma cells. Actin-based adhesion and invasion structures, podosomes and invadopodia, were detected in the basal cell membranes of primary tumour and spontaneously transformed cancer cells, respectively. Immunofluorescence labellings showed marked differences in their morphology, as podosomes organized a ring structure with HD1/plectin, αII-spectrin, talin, focal adhesion kinase and pacsin 2 around the core filled with actin, cortactin, vinculin and filamin A. Invadopodia had no division between ring and core and failed to organize the ring proteins, but instead assembled tail-like, narrow actin cables that showed a talin-tensin switch. Time-lapse live-cell imaging indicated that both podosomes and invadopodia were long-lived entities, but the tails of invadopodia vigorously propelled in the cytoplasm and were occasionally released from the cell membrane. Invadopodia could also be externalized outside the cytoplasm, where they still retained the ability to degrade matrix. In 3D confocal imaging combined with in situ gelatin zymography, the podosomes of primary tumour cells were large, cylindrical structures that increased in time, whereas the invadopodia in EMT-driven cells were smaller, but more numerous and degraded the underlying matrix in significantly larger amounts. Fluorescence recovery after photobleaching revealed that the substructures of podosomes were replenished more rapidly with new molecules than those of invadopodia. Overall, our results indicate that EMT has a major effect on the transcription and synthesis of both intra- and extracellular proteins, including laminins and their receptors, and on the structure and dynamics of oral squamous carcinoma cells.

Stem Cell Markers in Cancer: Do They Have Clinical Significance?

In cancer, a subpopulation of malignant cells expresses markers of normal stem cells. These cells have the potential of initiating tumor growth and therefore also tumor recurrence. Thus, these cells are called cancer stem cells. A myriad of markers have been applied to identify these cells, but no single marker can be found exclusively in cancer stem cells. In many types of cancer, clinical recurrence and tumor progression are the main causes of mortality, despite intense oncological treatment. It has been proposed that the presence of cancer stem cells causes this resistance to therapy. The scope of this thesis is to investigate the role of stem cell markers and genes in the clinical setting. Especially, the aim was to elucidate the clinical significance of stem cell markers as novel prognostic and diagnostic tools in cancer. Tumor biopsy material from central nervous system tumors (oligodendroglioma, astrocytoma and glioblatoma), neural crest derived tumors (pheochromocytomas) and oral carcinoma was screened for stem cell markers. Initially, 15 stem cell markers were screened in a test series of gliomas. The markers applied for expanded tumor analyses (in 305 cases of glioma, 42 cases of pheochromocytoma, and 73 cases of oral carcinoma) were BMI-1, Snail, p16, mdm2, and c-Myc. Data on marker expression was compared with clinical and pathological parameters. In gliomas, BMI-1 expression was found in nearly all tumors analyzed, but the frequency of BMI-1 expressing cells was highly variable, ranging from 1 to 100%. In oligodendroglioma, BMI-1 expression was identified as a prognostic marker independent of tumor grade and clinical parameters. In pheochromocytoma, Snail expression was shown to distinguish between the metastatic and non-metastatic forms of the tumor. Snail expression was seen only in metastatic tumors, whereas non-metastatic tumors did not commonly express Snail. Finally, in oral carcinoma, BMI-1 expression was seen in roughly 80% of tumors, and Snail expression was high or very high in all cases. The lack of BMI-1 expression was associated with early relapse in oral carcinoma.

Familial aggregation of type 1 diabetes and diabetic nephropathy in Finland

Type 1 diabetes (T1D) is a common, multifactorial disease with strong familial clustering. In Finland, the incidence of T1D among children aged 14 years or under is the highest in the world. The increase in incidence has been approximately 2.4% per year. Although most new T1D cases are sporadic the first-degree relatives are at an increased risk of developing the same disease. This study was designed to examine the familial aggregation of T1D and one of its serious complications, diabetic nephropathy (DN). More specifically the study aimed (1) to determine the concordance rates of T1D in monozygotic (MZ) and dizygotic (DZ) twins and to estimate the relative contributions of genetic and environmental factors to the variability in liability to T1D as well as to study the age at onset of diabetes in twins; (2) to obtain long-term empirical estimates of the risk of T1D among siblings of T1D patients and the factors related to this risk, especially the effect of age at onset of diabetes in the proband and the birth cohort effect; (3) to establish if DN is aggregating in a Finnish population-based cohort of families with multiple cases of T1D, and to assess its magnitude and particularly to find out whether the risk of DN in siblings is varying according to the severity of DN in the proband and/or the age at onset of T1D: (4) to assess the recurrence risk of T1D in the offspring of a Finnish population-based cohort of patients with childhood onset T1D, and to investigate potential sex-related effects in the transmission of T1D from the diabetic parents to their offspring as well as to study whether there is a temporal trend in the incidence. The study population comprised of the Finnish Young Twin Cohort (22,650 twin pairs), a population-based cohort of patients with T1D diagnosed at the age of 17 years or earlier between 1965 and 1979 (n=5,144) and all their siblings (n=10,168) and offspring (n=5,291). A polygenic, multifactorial liability model was fitted to the twin data. Kaplan-Meier analyses were used to provide the cumulative incidence for the development of T1D and DN. Cox s proportional hazards models were fitted to the data. Poisson regression analysis was used to evaluate temporal trends in incidence. Standardized incidence ratios (SIRs) between the first-degree relatives of T1D patients and background population were determined. The twin study showed that the vast majority of affected MZ twin pairs remained discordant. Pairwise concordance for T1D was 27.3% in MZ and 3.8% in DZ twins. The probandwise concordance estimates were 42.9% and 7.4%, respectively. The model with additive genetic and individual environmental effects was the best-fitting liability model to T1D, with 88% of the phenotypic variance due to genetic factors. The second paper showed that the 50-year cumulative incidence of T1D in the siblings of diabetic probands was 6.9%. A young age at diagnosis in the probands considerably increased the risk. If the proband was diagnosed at the age of 0-4, 5-9, 10-14, 15 or more, the corresponding 40-year cumulative risks were 13.2%, 7.8%, 4.7% and 3.4%. The cumulative incidence increased with increasing birth year. However, SIR among children aged 14 years or under was approximately 12 throughout the follow-up. The third paper showed that diabetic siblings of the probands with nephropathy had a 2.3 times higher risk of DN compared with siblings of probands free of nephropathy. The presence of end stage renal disease (ESRD) in the proband increases the risk three-fold for diabetic siblings. Being diagnosed with diabetes during puberty (10-14) or a few years before (5-9) increased the susceptibility for DN in the siblings. The fourth paper revealed that of the offspring of male probands, 7.8% were affected by the age of 20 compared with 5.3% of the offspring of female probands. Offspring of fathers with T1D have 1.7 times greater risk to be affected with T1D than the offspring of mothers with T1D. The excess risk in the offspring of male fathers manifested itself through the higher risk the younger the father was when diagnosed with T1D. Young age at onset of diabetes in fathers increased the risk of T1D greatly in the offspring, but no such pattern was seen in the offspring of diabetic mothers. The SIR among offspring aged 14 years or under remained fairly constant throughout the follow-up, approximately 10. The present study has provided new knowledge on T1D recurrence risk in the first-degree relatives and the risk factors modifying the risk. Twin data demonstrated high genetic liability for T1D and increased heritability. The vast majority of affected MZ twin pairs, however, remain discordant for T1D. This study confirmed the drastic impact of the young age at onset of diabetes in the probands on the increased risk of T1D in the first-degree relatives. The only exception was the absence of this pattern in the offspring of T1D mothers. Both the sibling and the offspring recurrence risk studies revealed dynamic changes in the cumulative incidence of T1D in the first-degree relatives. SIRs among the first-degree relatives of T1D patients seems to remain fairly constant. The study demonstrates that the penetrance of the susceptibility genes for T1D may be low, although strongly influenced by the environmental factors. Presence of familial aggregation of DN was confirmed for the first time in a population-based study. Although the majority of the sibling pairs with T1D were discordant for DN, its presence in one sibling doubles and presence of ESRD triples the risk of DN in the other diabetic sibling. An encouraging observation was that although the proportion of children to be diagnosed with T1D at the age of 4 or under is increasing, they seem to have a decreased risk of DN or at least delayed onset.

Molecular and clinical characteristics of tricarboxylic acid cycle-associated tumors

Hereditary leiomyomatosis and renal cell cancer (HLRCC) is a rare, dominantly inherited tumor predisposition syndrome characterized by benign cutaneous and uterine (ULM) leiomyomas, and sometimes renal cell cancer (RCC). A few cases of uterine leiomyosarcoma (ULMS) have also been reported. Mutations in a nuclear gene encoding fumarate hydratase (FH), an enzyme of the mitochondrial tricarboxylic acid cycle (TCA cycle), underlie HLRCC. As a recessive condition, germline mutations in FH predispose to a neurological defect, FH deficiency (FHD). Hereditary paragangliomatosis (HPGL) is a dominant disorder associated with paragangliomas and pheochromocytomas. Inherited mutations in three genes encoding subunits of succinate dehydrogenase (SDH), also a TCA cycle enzyme, predispose to HPGL. Both FH and SDH seem to act as tumor suppressors. One of the consequences of the TCA cycle defect is abnormal activation of HIF1 pathway ( pseudohypoxia ) in the HLRCC and HPGL tumors. HIF1 drives transcription of genes encoding e.g. angiogenetic factors which can facilitate tumor growth. Recently hypoxia/HIF1 has been suggested to be one of the causes of genetic instability as well. One of the aims of this study was to broaden the clinical definers of HLRCC. To determine the cancer risk and to identify possible novel tumor types associated with FH mutations eight Finnish HLRCC/FHD families were extensively evaluated. The extension of the pedigrees and the Finnish Cancer Registry based tumor search yielded genealogical and cancer data of altogether 868 individuals. The standardized incidence ratio-based comparison of HLRCC/FHD family members with general Finnish population revealed 6.5-fold risk for RCC. Moreover, risk for ULMS was highly increased. However, according to the recent and more stringent diagnosis criteria of ULMS many of the HLRCC uterine tumors previously considered malignant are at present diagnosed as atypical or proliferative ULMs (with a low risk of recurrence). Thus, the formation of ULMS (as presently defined) in HLRCC appears to be uncommon. Though increased incidence was not observed, interestingly the genetic analyses suggested possible association of breast and bladder cancer with loss of FH. Moreover, cancer cases were exceptionally detected in an FHD family. Another clinical finding was the conventional (clear cell) type RCC of a young Spanish HLRCC patient. Conventional RCC is distinct from the types previously observed in this syndrome but according to these results, FH mutation may underlie some of young conventional cancer cases. Secondly, the molecular pathway from defective TCA cycle to tumor formation was intended to clarify. Since HLRCC and HPGL tumors display abnormally activated HIF1, the hypothesis on the link between HIF1/hypoxia and genetic instability was of interest to study in HLRCC and HPGL tumor material. HIF1α (a subunit of HIF1) stabilization was confirmed in the majority of the specimens. However, no repression of MSH2, a protein of DNA mismatch repair system, or microsatellite instability (MSI), an indicator of genetic instability, was observed. Accordingly, increased instability seems not to play a role in the tumorigenesis of pseudohypoxic TCA cycle-deficient tumors. Additionally, to study the putative alternative functions of FH, a recently identified alternative FH transcript (FHv) was characterized. FHv was found to contain instead of exon 1, an alternative exon 1b. Differential subcellular distribution, lack of FH enzyme activity, low mRNA expression compared to FH, and induction by cellular stress suggest FHv to have a role distinct from FH, for example in apoptosis or survival. However, the physiological significance of FHv requires further elucidation.

The Spin-Statistics Relation and Noncommutative Quantum Field Theory

The efforts of combining quantum theory with general relativity have been great and marked by several successes. One field where progress has lately been made is the study of noncommutative quantum field theories that arise as a low energy limit in certain string theories. The idea of noncommutativity comes naturally when combining these two extremes and has profound implications on results widely accepted in traditional, commutative, theories. In this work I review the status of one of the most important connections in physics, the spin-statistics relation. The relation is deeply ingrained in our reality in that it gives us the structure for the periodic table and is of crucial importance for the stability of all matter. The dramatic effects of noncommutativity of space-time coordinates, mainly the loss of Lorentz invariance, call the spin-statistics relation into question. The spin-statistics theorem is first presented in its traditional setting, giving a clarifying proof starting from minimal requirements. Next the notion of noncommutativity is introduced and its implications studied. The discussion is essentially based on twisted Poincaré symmetry, the space-time symmetry of noncommutative quantum field theory. The controversial issue of microcausality in noncommutative quantum field theory is settled by showing for the first time that the light wedge microcausality condition is compatible with the twisted Poincaré symmetry. The spin-statistics relation is considered both from the point of view of braided statistics, and in the traditional Lagrangian formulation of Pauli, with the conclusion that Pauli's age-old theorem stands even this test so dramatic for the whole structure of space-time.

On probability-based inference under data missing by design

Whether a statistician wants to complement a probability model for observed data with a prior distribution and carry out fully probabilistic inference, or base the inference only on the likelihood function, may be a fundamental question in theory, but in practice it may well be of less importance if the likelihood contains much more information than the prior. Maximum likelihood inference can be justified as a Gaussian approximation at the posterior mode, using flat priors. However, in situations where parametric assumptions in standard statistical models would be too rigid, more flexible model formulation, combined with fully probabilistic inference, can be achieved using hierarchical Bayesian parametrization. This work includes five articles, all of which apply probability modeling under various problems involving incomplete observation. Three of the papers apply maximum likelihood estimation and two of them hierarchical Bayesian modeling. Because maximum likelihood may be presented as a special case of Bayesian inference, but not the other way round, in the introductory part of this work we present a framework for probability-based inference using only Bayesian concepts. We also re-derive some results presented in the original articles using the toolbox equipped herein, to show that they are also justifiable under this more general framework. Here the assumption of exchangeability and de Finetti's representation theorem are applied repeatedly for justifying the use of standard parametric probability models with conditionally independent likelihood contributions. It is argued that this same reasoning can be applied also under sampling from a finite population. The main emphasis here is in probability-based inference under incomplete observation due to study design. This is illustrated using a generic two-phase cohort sampling design as an example. The alternative approaches presented for analysis of such a design are full likelihood, which utilizes all observed information, and conditional likelihood, which is restricted to a completely observed set, conditioning on the rule that generated that set. Conditional likelihood inference is also applied for a joint analysis of prevalence and incidence data, a situation subject to both left censoring and left truncation. Other topics covered are model uncertainty and causal inference using posterior predictive distributions. We formulate a non-parametric monotonic regression model for one or more covariates and a Bayesian estimation procedure, and apply the model in the context of optimal sequential treatment regimes, demonstrating that inference based on posterior predictive distributions is feasible also in this case.

Renormalization methods in KAM theory

It is well known that an integrable (in the sense of Arnold-Jost) Hamiltonian system gives rise to quasi-periodic motion with trajectories running on invariant tori. These tori foliate the whole phase space. If we perturb an integrable system, the Kolmogorow-Arnold-Moser (KAM) theorem states that, provided some non-degeneracy condition and that the perturbation is sufficiently small, most of the invariant tori carrying quasi-periodic motion persist, getting only slightly deformed. The measure of the persisting invariant tori is large together with the inverse of the size of the perturbation. In the first part of the thesis we shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non analytic perturbation (the latter will only be assumed to have continuous derivatives up to a sufficiently large order). We shall proceed by solving a sequence of problems in which theperturbations are analytic approximations of the original one. We will finally show that the approximate solutions will converge to a differentiable solution of our original problem. In the second part we will use an RG scheme using continuous scales, so that instead of solving an iterative equation as in the classical RG KAM, we will end up solving a partial differential equation. This will allow us to reduce the complications of treating a sequence of iterative equations to the use of the Banach fixed point theorem in a suitable Banach space.

Boundedness of weakly singular integral operators on domains

The monograph dissertation deals with kernel integral operators and their mapping properties on Euclidean domains. The associated kernels are weakly singular and examples of such are given by Green functions of certain elliptic partial differential equations. It is well known that mapping properties of the corresponding Green operators can be used to deduce a priori estimates for the solutions of these equations. In the dissertation, natural size- and cancellation conditions are quantified for kernels defined in domains. These kernels induce integral operators which are then composed with any partial differential operator of prescribed order, depending on the size of the kernel. The main object of study in this dissertation being the boundedness properties of such compositions, the main result is the characterization of their Lp-boundedness on suitably regular domains. In case the aforementioned kernels are defined in the whole Euclidean space, their partial derivatives of prescribed order turn out to be so called standard kernels that arise in connection with singular integral operators. The Lp-boundedness of singular integrals is characterized by the T1 theorem, which is originally due to David and Journé and was published in 1984 (Ann. of Math. 120). The main result in the dissertation can be interpreted as a T1 theorem for weakly singular integral operators. The dissertation deals also with special convolution type weakly singular integral operators that are defined on Euclidean spaces.