Diagnostic Tests Based on Quantile Residuals for Nonlinear Time Series Models

This thesis studies quantile residuals and uses different methodologies to develop test statistics that are applicable in evaluating linear and nonlinear time series models based on continuous distributions. Models based on mixtures of distributions are of special interest because it turns out that for those models traditional residuals, often referred to as Pearson's residuals, are not appropriate. As such models have become more and more popular in practice, especially with financial time series data there is a need for reliable diagnostic tools that can be used to evaluate them. The aim of the thesis is to show how such diagnostic tools can be obtained and used in model evaluation. The quantile residuals considered here are defined in such a way that, when the model is correctly specified and its parameters are consistently estimated, they are approximately independent with standard normal distribution. All the tests derived in the thesis are pure significance type tests and are theoretically sound in that they properly take the uncertainty caused by parameter estimation into account. -- In Chapter 2 a general framework based on the likelihood function and smooth functions of univariate quantile residuals is derived that can be used to obtain misspecification tests for various purposes. Three easy-to-use tests aimed at detecting non-normality, autocorrelation, and conditional heteroscedasticity in quantile residuals are formulated. It also turns out that these tests can be interpreted as Lagrange Multiplier or score tests so that they are asymptotically optimal against local alternatives. Chapter 3 extends the concept of quantile residuals to multivariate models. The framework of Chapter 2 is generalized and tests aimed at detecting non-normality, serial correlation, and conditional heteroscedasticity in multivariate quantile residuals are derived based on it. Score test interpretations are obtained for the serial correlation and conditional heteroscedasticity tests and in a rather restricted special case for the normality test. In Chapter 4 the tests are constructed using the empirical distribution function of quantile residuals. So-called Khmaladze s martingale transformation is applied in order to eliminate the uncertainty caused by parameter estimation. Various test statistics are considered so that critical bounds for histogram type plots as well as Quantile-Quantile and Probability-Probability type plots of quantile residuals are obtained. Chapters 2, 3, and 4 contain simulations and empirical examples which illustrate the finite sample size and power properties of the derived tests and also how the tests and related graphical tools based on residuals are applied in practice.

Growing Flowers in the Frost: Civic Activity, Citizenship and Gender in Russia

This study analyzes civic activity, citizenship and their gendered manifestations in contemporary Russia. It is based on a case study conducted in the city of Tver , located in the vicinity of Moscow, during 2001-2005. The data consists of interviews with civic activists and municipal and regional authorities; observations of civic organizations; and a quantitative survey conducted among local civic groups. The theoretical and methodological framework of the study draws upon a micro perspective on organization, discourse analysis, gender and citizenship theories and Pierre Bourdieu s theory of fields and capital. This study develops theoretical understanding of the characteristics and logic of civic organization in Russia. It shows that social class centrally structures the field of civic activity. Organizations can be seen as a vehicle of the educated class to advocate their interests, help themselves and seek both social and individual-level change. The study also argues that civic organizations founded during the post-Soviet era are often an institutionalized form of informal social networks. Networks, which were a central element of everyday interaction in Soviet society, are a resource and often the only resource available that can be made use of in contemporary organizational activities. The study argues that gender operates as a key structuring principle in the Russian socio-political community. Civic activity is often discursively associated with femininity and institutional politics with masculinity. Women tend to participate more than men in civic organizations, while men dominate the formal political domain. The study shows that civic organizations are important loci of communality. This communality, however, differs from the communality envisioned in the communitarian and social capital debates in the West. It is selective communality , as it is restricted to the members of the organizations and does not create generalized reciprocity and trust. Civic organizations tend to build upon and reproduce the traditional Russian organizational form of circles , kruzhki. Along with the analysis of civic activities, the study also examines the redefinition of the role and functions of the state. The authorities interviewed in this study understand civic organizations as serving those goals and interests determined by the authorities, instead of viewing them as sites of citizens self-organization around interests and problems citizens themselves deem important, or as a counterforce to the state. By contrast, civic activists understand the core of organizational activity to be advocacy of their interests and rights, tackling social problems, the pursuit of wider social change and self-help. Co-operation between authorities and organizations tends to be personified and based upon unequal, hierarchical patron-client arrangements, which inhibits the development of democratic governance. The study will be published in Routledge Contemporary Russia and Eastern Europe Series later this year.

Augustine and the functions of concupiscence

This study analyses Augustine s concept of concupiscentia, or evil desire (together with two cognate terms, libido and cupiditas) in the context of his entire oeuvre. By the aid of systematic analysis, the concept and its development is explored in four distinct ways. It is claimed that Augustine used the concept of concupiscentia for several theological purposes, and the task of the study is to represent these distinct functions, and their connections to Augustine s general theological and philosophical convictions. The study opens with a survey on terminology. A general overview of the occurrences of the negatively connoted words for desire in Latin literature precedes a corresponding examination of Augustine s own works. In this introductory chapter it is shown that, despite certain preferences in the uses of the words, a sufficient degree of synonymy reigns so as to allow an analysis of the concept without tightly discriminating between the terms. The theological functions of concupiscentia with its distinct contexts are analysed in separate chapters. The function of concupiscentia as a divine punishment is explored first (Ch 3). It is seen how Augustine links together concupiscentia and ideas about divine justice, and finally suggests that in the inordinate, psychologically experienced sexual desire, the original theological disobedience of Adam and Eve can be perceived. Augustine was criticized for this solution already in his own times, and the analysis of the function of concupiscentia as a divine punishment ends in a discussion on the critical response of punitive concupiscentia by Julian of Aeclanum. Augustine also attached to concupiscentia another central theological function by viewing evil desire as an inward originating cause for all external evil actions. In the study, this function is analysed by surveying two formally distinct images of evil desire, i.e. as the root (radix) of all evil, and as a threefold (triplex) matrix of evil actions (Ch 4). Both of these images were based on a single verse of the Bible (1 Jn 2, 16 and 1 Tim 6, 10). This function of concupiscentia was formed both parallel to, and in answer to, Manichaean insights into concupiscentia. Being familiar with the traditional philosophical discussions on the nature and therapy of emotions, Augustine situated concupiscentia also into this context. It is acknowledged that these philosophical traditions had an obvious impact into his way of explaining psychological processes in connection with concupiscentia. Not only did Augustine implicitly receive and exploit these traditions, but he also explicitly moulded and criticized them in connection with concupiscentia. Eventually, Augustine conceives the philosophical traditions of emotions as partly useful but also partly inadequate to deal with concupiscentia (Ch 5). The role of concupiscentia in connection to divine grace and Christian renewal is analysed in the final chapter of the study. Augustine s gradual development in internalizing the effects of concupiscentia also into the life of a baptized Christian are elucidated, as are the strong limitations and mitigations Augustine makes to the concept when attaching it into the life under grace (sub gratia). A crucial part in the development of this function is played by Augustine s changing interpretation of Rom 7, and the way concupiscentia appears in Augustine s readings of this text is therefore also analysed. As a result of the analysis of these four distinct functions and contexts of concupiscentia, it is concluded that Augustine s concept of concupiscentia is fairly tightly and coherently connected to his views of central theological importance. Especially the functions of concupiscentia as a punishment and the function of concupiscentia in Christian renewal were both tightly interwoven into Augustine s view of God s being and God s grace. The study shows the importance of reading Augustine s discussions on evil desire with a constant awareness of their role in their larger context, that is, of their function in each situation. The study warns against too simplistic and unifying readings of Augustine s concupiscentia, emphasizing the need to acknowledge both the necessitating, sinful aspects of concupiscentia, and the domesticated features of concupiscentia during Christian renewal.

The Structure and Functions of Hantavirus Nucleocapsid Protein

Hantaviruses, members of the genus Hantavirus in the Bunyaviridae family, are enveloped single-stranded RNA viruses with tri-segmented genome of negative polarity. In humans, hantaviruses cause two diseases, hemorrhagic fever with renal syndrome (HFRS) and hantavirus pulmonary syndrome (HPS), which vary in severity depending on the causative agent. Each hantavirus is carried by a specific rodent host and is transmitted to humans through excreta of infected rodents. The genome of hantaviruses encodes four structural proteins: the nucleocapsid protein (N), the glycoproteins (Gn and Gc), and the polymerase (L) and also the nonstructural protein (NSs). This thesis deals with the functional characterization of hantavirus N protein with regard to its structure. Structural studies of the N protein have progressed slowly and the crystal structure of the whole protein is still not available, therefore biochemical assays coupled with bioinformatical modeling proved essential for studying N protein structure and functions. Presumably, during RNA encapsidation, the N protein first forms intermediate trimers and then oligomers. First, we investigated the role of N-terminal domain in the N protein oligomerization. The results suggested that the N-terminal region of the N protein forms a coiled-coil, in which two antiparallel alpha helices interact via their hydrophobic seams. Hydrophobic residues L4, I11, L18, L25 and V32 in the first helix and L44, V51, L58 and L65 in the second helix were crucial for stabilizing the structure. The results were consistent with the head-to-head, tail-to-tail model for hantavirus N protein trimerization. We demonstrated that an intact coiled-coil structure of the N terminus is crucial for the oligomerization capacity of the N protein. We also added new details to the head-to-head, tail-to-tail model of trimerization by suggesting that the initial step is based on interaction(s) between intact intra-molecular coiled-coils of the monomers. We further analyzed the importance of charged aa residues located within the coiled-coil for the N protein oligomerization. To predict the interacting surfaces of the monomers we used an upgraded in silico model of the coiled-coil domain that was docked into a trimer. Next the predicted target residues were mutated. The results obtained using the mammalian two-hybrid assay suggested that conserved charged aa residues within the coiled-coil make a substantial contribution to the N protein oligomerization. This contribution probably involves the formation of interacting surfaces of the N monomers and also stabilization of the coiled-coil via intramolecular ionic bridging. We proposed that the tips of the coiled-coils are the first to come into direct contact and thus initiate tight packing of the three monomers into a compact structure. This was in agreement with the previous results showing that an increase in ionic strength abolished the interaction between N protein molecules. We also showed that residues having the strongest effect on the N protein oligomerization are not scattered randomly throughout the coiled-coil 3D model structure, but form clusters. Next we found evidence for the hantaviral N protein interaction with the cytoplasmic tail of the glycoprotein Gn. In order to study this interaction we used the GST pull-down assay in combination with mutagenesis technique. The results demonstrated that intact, properly folded zinc fingers of the Gn protein cytoplasmic tail as well as the middle domain of the N protein (that includes aa residues 80 248 and supposedly carries the RNA-binding domain) are essential for the interaction. Since hantaviruses do not have a matrix protein that mediates the packaging of the viral RNA in other negatve stranded viruses (NSRV), hantaviral RNPs should be involved in a direct interaction with the intraviral domains of the envelope-embedded glycoproteins. By showing the N-Gn interaction we provided the evidence for one of the crucial steps in the virus replication at which RNPs are directed to the site of the virus assembly. Finally we started analysis of the N protein RNA-binding region, which is supposedly located in the middle domain of the N protein molecule. We developed a model for the initial step of RNA-binding by the hantaviral N protein. We hypothesized that the hantaviral N protein possesses two secondary structure elements that initiate the RNA encapsidation. The results suggest that amino acid residues (172-176) presumably act as a hook to catch vRNA and that the positively charged interaction surface (aa residues 144-160) enhances the initial N-RNA interacation. In conclusion, we elucidated new functions of hantavirus N protein. Using in silico modeling we predicted the domain structure of the protein and using experimental techniques showed that each domain is responsible for executing certain function(s). We showed that intact N terminal coiled-coil domain is crucial for oligomerization and charged residues located on its surface form a interaction surface for the N monomers. The middle domain is essential for interaction with the cytoplasmic tail of the Gn protein and RNA binding.

Functions of Alphavirus Macrodomain-containing protein nsP3

Alphaviruses are positive strand RNA viruses that replicate in association with cellular membranes. The viral RNA replication complex consists of four non-structural proteins nsP1-nsP4 which are essential for viral replication. The functions of nsP1, nsP2 and nsP4 are well established, but the roles of nsP3 are mainly unknown. In this work I have clarified some of the functions of nsP3 in order to better understand the importance of this protein in virus replication. Semliki Forest virus (SFV) has been mostly used as a model alphavirus during this work, but some experiments have also been conducted with Sindbis and Chikungunya viruses. NsP3 is composed of three different protein domains. The N-terminus of nsP3 contains an evolutionarily conserved macrodomain, the central part of nsP3 contains a domain that is only found in alphaviruses, and the C-terminus of the protein is hypervariable and predicted to be unstructured. In this work I have analyzed the functions of nsP3 macrodomain, and shown that viral macrodomains bind poly(ADP-ribose) and that they do not resemble cellular macrodomains in their properties. Furthermore, I have shown that some macrodomains, including viral macrodomains of SFV and hepatitis E virus, also bind poly(A). Mutations in the ligand binding pocket of SFV macrodomain hamper virus replication but do not confer lethality, indicating that macrodomain function is beneficial but not mandatory for virus replication. The hypervariable C-terminus of nsP3 is heavily phosphorylated and is enriched in proline residues. In this work it is shown that this region harbors an SH3 domain binding motif (Sh3BM) PxRxPR through which cellular amphiphysin is recruited to viral replication sites and to nsP3 containing cytoplasmic aggregate structures. The function of Sh3BM was destroyed by a single point mutation, which led to impaired viral RNA replication in HeLa cells, pointing out the functional importance of amphiphysin recruitment by the Sh3BM. In addition, evidence is provided tho show that the endosomal localization of alphavirus replication is mediated by nsP3 and that the phosphorylation of hypervariable region might be important for the endosomal targeting. Together these findings demonstrate that nsP3 contains multiple important host interaction motifs and domains, which facilitate successful viral propagation in host cells.

Cognitive functioning and its heritability in bipolar I disorder

Bipolar I disorder is a severe psychiatric disorder characterized by episodic mood alterations that can be manic, depressive or mixed. Bipolar disorder seems to be highly genetic, but the etiology of this complex disorder has remained elusive. In recent years, studies have found that euthymic patients with bipolar disorder may have impairments particularly in executive functioning, verbal learning and memory. These impairments may be present also among some of the relatives of these patients, who may be vulnerable to the disorder. Using neuropsychological variables as endophenotypes, i.e. intermediate phenotypes between genes and the phenotypes, has been suggested to aid search for the etiological background of the disorder, but evidence is sparse on whether these variables fulfill the criteria for endophenotypes. The present thesis is part of the Genetic Epidemiology and Molecular Genetics of Severe Mental Disorders in Finland project. The specific aim was to investigate whether neuropsychological test variables would indicate genetic liability to the disorder and could therefore be regarded as endophenotypes. Thus, cognitive functions and their heritability were studied in bipolar I disorder patients and in their unaffected first-degree relatives from a population-based sample of families, comparing them to a population-based control group. In order to add homogeneity to the subgroups of bipolar disorder patients and their relatives, cognitive functions and their heritability were further studied in a group of families affected by bipolar I disorder only (bipolar families) and another group of families affected by both bipolar I disorder and schizophrenia or schizoaffective disorders (mixed families). Finally, the effect of processing speed on other cognitive functions was investigated. The study showed that especially executive functioning and processing speed fulfilled the endophenotype criteria. Impairments in these functions were found in bipolar patients and in their relatives irrespective of other severe psychopathology in the family. These functions were highly heritable in these families. Study also showed that generalized impairment in verbal memory may associate more with bipolar disorder than to vulnerability to other psychotic disorders, and be more related to fully developed disease; impairments in verbal learning and memory were found only in patients, and they were not found to be highly heritable. Finally, the most potential endophenotype, i.e. processing speed, seemed to contribute to a range of other cognitive dysfunctions seen in bipolar disorder patients. Processing speed, in particular, has also been shown to be a valid endophenotype in subsequent association analyses in psychiatric genetics in Finland and internationally. Information concerning cognitive impairments and their association with the psychosocial consequences of bipolar disorder is important in planning treatment. It is also important to understand and acknowledge that patients may have cognitive impairments that affect their everyday life. Psychosocial interventions and neuropsychological rehabilitation may supplement other conventional treatments for bipolar patients.

Aspiration-based utility functions in a planning model for timber flow management.

The study presents a theory of utility models based on aspiration levels, as well as the application of this theory to the planning of timber flow economics. The first part of the study comprises a derivation of the utility-theoretic basis for the application of aspiration levels. Two basic models are dealt with: the additive and the multiplicative. Applied here solely for partial utility functions, aspiration and reservation levels are interpreted as defining piecewisely linear functions. The standpoint of the choices of the decision-maker is emphasized by the use of indifference curves. The second part of the study introduces a model for the management of timber flows. The model is based on the assumption that the decision-maker is willing to specify a shape of income flow which is different from that of the capital-theoretic optimum. The utility model comprises four aspiration-based compound utility functions. The theory and the flow model are tested numerically by computations covering three forest holdings. The results show that the additive model is sensitive even to slight changes in relative importances and aspiration levels. This applies particularly to nearly linear production possibility boundaries of monetary variables. The multiplicative model, on the other hand, is stable because it generates strictly convex indifference curves. Due to a higher marginal rate of substitution, the multiplicative model implies a stronger dependence on forest management than the additive function. For income trajectory optimization, a method utilizing an income trajectory index is more efficient than one based on the use of aspiration levels per management period. Smooth trajectories can be attained by squaring the deviations of the feasible trajectories from the desired one.

Koneellisen annosjakelupalvelun aloittaminen - lääkehoidon tarkistus ja sen vaikutus potilaan lääkehoitoon

Farmaseuttisilla palveluilla tarkoitetaan apteekkien palveluita, joissa hyödynnetään apteekin farmaseuttisen henkilökunnan tietoja ja taitoja. Farmaseuttiset palvelut voidaan jakaa farmaseuttisiin perus- ja erityispalveluihin. Farmaseuttiset peruspalvelut kattavat apteekkien lakisääteiset tehtävät, kun taas farmaseuttisilla erityispalveluilla pyritään ottamaan aktiivisempi rooli asiakkaan terveyden edistämisessä. Koneellinen annosjakelupalvelu on farmaseuttinen erityispalvelu. Koneellisessa annosjakelupalvelussa lääkkeet jaetaan kerta-annospusseihin annostusajankohdan mukaan. Kun uusi asiakas aloittaa koneellinen annosjakelupalvelun, tarkistetaan asiakkaan lääkitys yhteensopimattomien ja turhien lääkkeiden osalta. Palvelun aloitushetkellä huomioidaan myös lääkevalmisteiden sopivuus koneelliseen annosjakeluun sekä tarkistetaan valmisteiden annosteluajankohdat. Koneellisessa annosjakelupalvelussa asiakkaan lääkehoidosta muodostetaan lääkityskortti, josta kokonaislääkehoito on helppo tarkistaa. Erikoistyön tavoitteena oli selvittää millainen lääkehoidon arviointi tai tarkistus koneellisen annosjakelupalvelun aloittamisen yhteydessä tehdään ja miten palvelun aloittavien asiakkaiden kokonaislääkehoitotieto saadaan selvitettyä. Lisäksi selvitettiin millaisia muutoksia lääkehoitoihin tehdään palvelun aloittamisen yhteydessä, mitkä ovat muutosten syyt sekä millainen on asiakkaan kokonaislääkehoito. Kyselylomake lähetettiin kaikkiin apteekkeihin, jotka tilasivat koneellista annosjakelua sopimusvalmistuksena Espoonlahden apteekilta syyskuussa 2010. Tutkimus suoritettiin semistrukturoidulla kirjallisella kyselyllä, joka sisälsi sekä avoimia kysymyksiä että monivalintakysymyksiä. Kyselyyn saatiin 147 vastausta ja vastausprosentiksi muodostui 45. Vastauksia kyselyyn saatiin koko Mannersuomen alueelta ja kaikkien kokoluokkien apteekeilta. Koneellisen annosjakelupalvelun aloittavat henkilöt ovat pääasiassa iäkkäitä, jotka ovat kotihoidon piirissä, asuvat hoitokodissa tai palveluasumisen yksikössä. Asiakkaiden lääkitystietojen keräämisessä hyödynnetään lääkityskorttia, mutta lääkityskortin tietoja päivitetään myös muista lähteistä. Asiakkaiden lääkityksille tehdään useimmiten lääkehoidon tarkistus moniammatillisena yhteistyönä. Lääkehoidolle tehdyt muutokset johtuvat pääasiassa lääkevaihdosta, annosjakelukoneen lääkevalikoimasta tai puolittamisen välttämisestä. Lääkehoidoissa on vain vähän yhteisvaikutuksia, jotka johtavat lääkevalmisteen käytön lopettamiseen. Lääkehoidon tarkistuksella ei ollut suurta vaikutusta asiakkaiden käyttämien lääkevalmisteiden määrään. Palvelun aloittamisen jälkeen asiakkaalla on käytössään keskimäärin 11 lääkevalmistetta, joista seitsemää jaellaan koneellisesti. Lääkeaineryhmistä eniten käytettyjä ovat hermostoon vaikuttavat sekä sydän- ja verisuonisairauksien lääkkeet, joita kumpaakin on käytössä keskimäärin kolme jokaisella uudella koneellisen annosjakelupalvelun asiakkaalla sekä palvelun aloittamista ennen että sen jälkeen.

Functions of human papillomavirus E5 oncogene in epithelial cells and in the onset of cervical cancer

Human papillomaviruses (HPVs) are the causal agents of cervical cancer, which is the second most common cancer among women worldwide. Cellular transformation and carcinogenesis depend on the activities of viral E5, E6 and E7 proteins. Alterations in cell-cell contacts and in communication between epithelial cells take place during cervical carcinogenesis, leading to changes in cell morphology, increased cell motility and finally invasion. The aim of this thesis was to study genome-wide effects of the HPV type 16 (HPV-16) E5 protein on the expression of host cell messenger RNAs (mRNAs) and microRNAs by applying microarray technology. The results showed that the HPV-16 E5 protein alters several cellular pathways involved in cellular adhesion, motility and proliferation as well as in the extracellular matrix. The E5 protein was observed to enhance wound healing of epithelial cell monolayers by increasing cell motility in vivo. HPV-16 E5-induced alterations in the expression of cellular microRNAs and their target genes seem to favour increased proliferation and tumorigenesis. E5 was also shown to affect the expression of adherens junction proteins in HaCaT epithelial keratinocytes. In addition, a study of a membrane cytoskeletal cross-linker protein, ezrin, revealed that when activated, it localizes to adherens junctions. The results suggest that ezrin distribution to forming adherens junctions is due to Rac1 activity in epithelial cells. These studies reveal for the first time the holistic effects of HPV-16 E5 protein in promoting precancerous events in epithelial cells. The results contribute to identifyinging novel markers for cervical precancerous stages and to predicting disease behaviour.

Playing Games on Sets and Models

The most prominent objective of the thesis is the development of the generalized descriptive set theory, as we call it. There, we study the space of all functions from a fixed uncountable cardinal to itself, or to a finite set of size two. These correspond to generalized notions of the universal Baire space (functions from natural numbers to themselves with the product topology) and the Cantor space (functions from natural numbers to the {0,1}-set) respectively. We generalize the notion of Borel sets in three different ways and study the corresponding Borel structures with the aims of generalizing classical theorems of descriptive set theory or providing counter examples. In particular we are interested in equivalence relations on these spaces and their Borel reducibility to each other. The last chapter shows, using game-theoretic techniques, that the order of Borel equivalence relations under Borel reduciblity has very high complexity. The techniques in the above described set theoretical side of the thesis include forcing, general topological notions such as meager sets and combinatorial games of infinite length. By coding uncountable models to functions, we are able to apply the understanding of the generalized descriptive set theory to the model theory of uncountable models. The links between the theorems of model theory (including Shelah's classification theory) and the theorems in pure set theory are provided using game theoretic techniques from Ehrenfeucht-Fraïssé games in model theory to cub-games in set theory. The bottom line of the research declairs that the descriptive (set theoretic) complexity of an isomorphism relation of a first-order definable model class goes in synch with the stability theoretical complexity of the corresponding first-order theory. The first chapter of the thesis has slightly different focus and is purely concerned with a certain modification of the well known Ehrenfeucht-Fraïssé games. There we (me and my supervisor Tapani Hyttinen) answer some natural questions about that game mainly concerning determinacy and its relation to the standard EF-game

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.

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.