79 resultados para Gaussian probability function
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Psoriasis is a chronic skin disease characterized by abnormal keratinocyte proliferation and differentiation, neoangiogenesis and inflammation. Its etiology is multifactorial, as both the environmental and genetic factors have an important role in the pathogenesis of psoriasis. The exact disease mechanism behind psoriasis still remains unknown. The most important genetic susceptibility region for psoriasis has been located to PSORS1 locus in chromosome 6. The area includes multiply good candidate genes but the strong linkage disequilibrium between them has made genetic studies difficult. One of the candidate genes in PSORS1 is CCHCR1, which has a psoriasis-associated gene form CCHCR1*WWCC. The aim of the study was to elucidate the function of CCHCR1 and its potential role in the pathogenesis of psoriasis. In this study, transgenic mice expressing either the healthy or psoriasis-associated gene form of CCHCR1 were engineered and characterized. Mice were phenotypically normal but their gene expression profiles revealed many similarities to that observed in human psoriatic skin. In addition, the psoriasis-associated gene form had specific impacts on the expression of many genes relevant to the pathogenesis of psoriasis. We also challenged the skin of CCHCR1 transgenic mice with wounding or 12-O-tetradecanoylphorbol-13-acetate (TPA). The experiments revealed that CCHCR1 impacts on keratinocyte proliferation by limiting it. In addition, we demonstrated that CCHCR1 has a role in steroidogenesis and showed that both CCHCR1 forms promote synthesis of steroids. Also many agents relevant either for steroidogenesis or cell proliferation were shown to regulate the expression level of CCHCR1. The present study showed that CCHCR1 has functional properties relevant in the context of psoriasis. Firstly, CCHCR1 affects proliferation of keratinocytes as it may function as a negative regulator of keratinocyte proliferation. Secondly, CCHCR1 also has a role in steroidogenesis, a function relevant both in the pathogenesis of psoriasis and regulation of cell proliferation. This study suggests that aberrant function of CCHCR1 may lead to abnormal keratinocyte proliferation which is a key feature of psoriatic epidermis.
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Skeletal muscle cells are highly specialised in order to accomplish their function. During development, the fusion of hundreds of immature myoblasts creates large syncytial myofibres with a highly ordered cytoplasm filled with packed myofibrils. The assembly and organisation of contractile myofibrils must be tightly controlled. Indeed, the number of proteins involved in sarcomere building is impressive, and the role of many of them has only recently begun to be elucidated. Myotilin was originally identified as a high affinity a-actinin binding protein in yeast twohybrid screen. It was then found to interact also with filamin C, actin, ZASP and FATZ-1. Human myotilin is mainly expressed in striated muscle and induces efficient actin bundling in vitro and in cells. Moreover, mutations in myotilin cause different forms of muscle disease, now collectively known as myotilinopathies. In this thesis, consisting of three publications, the work on the mouse orthologue is presented. First, the cloning and molecular characterisation of the mouse myotilin gene showed that human and mouse myotilin share high sequence homology and a similar expression pattern and gene regulation. Functional analysis of the mouse promoter revealed the myogenic factor-binding elements that are required for myotilin gene transcription. Secondly, expression of myotilin was studied during mouse embryogenesis. Surprisingly, myotilin was expressed in a wide array of tissues at some stages of development; its expression pattern became more restricted at perinatal stages and in adult life. Immunostaining of human embryos confirmed broader myotilin expression compared to the sarcomeric marker titin. Finally, in the third article, targeted deletion of myotilin gene in mice revealed that it is not essential for muscle development and function. These data altogether indicate that the mouse can be used as a model for human myotilinopathy and that loss of myotilin does not alter significantly muscle structure and function. Therefore, disease-associated mutant myotilin may act as a dominant myopathic factor.
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A composition operator is a linear operator between spaces of analytic or harmonic functions on the unit disk, which precomposes a function with a fixed self-map of the disk. A fundamental problem is to relate properties of a composition operator to the function-theoretic properties of the self-map. During the recent decades these operators have been very actively studied in connection with various function spaces. The study of composition operators lies in the intersection of two central fields of mathematical analysis; function theory and operator theory. This thesis consists of four research articles and an overview. In the first three articles the weak compactness of composition operators is studied on certain vector-valued function spaces. A vector-valued function takes its values in some complex Banach space. In the first and third article sufficient conditions are given for a composition operator to be weakly compact on different versions of vector-valued BMOA spaces. In the second article characterizations are given for the weak compactness of a composition operator on harmonic Hardy spaces and spaces of Cauchy transforms, provided the functions take values in a reflexive Banach space. Composition operators are also considered on certain weak versions of the above function spaces. In addition, the relationship of different vector-valued function spaces is analyzed. In the fourth article weighted composition operators are studied on the scalar-valued BMOA space and its subspace VMOA. A weighted composition operator is obtained by first applying a composition operator and then a pointwise multiplier. A complete characterization is given for the boundedness and compactness of a weighted composition operator on BMOA and VMOA. Moreover, the essential norm of a weighted composition operator on VMOA is estimated. These results generalize many previously known results about composition operators and pointwise multipliers on these spaces.
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Advancements in the analysis techniques have led to a rapid accumulation of biological data in databases. Such data often are in the form of sequences of observations, examples including DNA sequences and amino acid sequences of proteins. The scale and quality of the data give promises of answering various biologically relevant questions in more detail than what has been possible before. For example, one may wish to identify areas in an amino acid sequence, which are important for the function of the corresponding protein, or investigate how characteristics on the level of DNA sequence affect the adaptation of a bacterial species to its environment. Many of the interesting questions are intimately associated with the understanding of the evolutionary relationships among the items under consideration. The aim of this work is to develop novel statistical models and computational techniques to meet with the challenge of deriving meaning from the increasing amounts of data. Our main concern is on modeling the evolutionary relationships based on the observed molecular data. We operate within a Bayesian statistical framework, which allows a probabilistic quantification of the uncertainties related to a particular solution. As the basis of our modeling approach we utilize a partition model, which is used to describe the structure of data by appropriately dividing the data items into clusters of related items. Generalizations and modifications of the partition model are developed and applied to various problems. Large-scale data sets provide also a computational challenge. The models used to describe the data must be realistic enough to capture the essential features of the current modeling task but, at the same time, simple enough to make it possible to carry out the inference in practice. The partition model fulfills these two requirements. The problem-specific features can be taken into account by modifying the prior probability distributions of the model parameters. The computational efficiency stems from the ability to integrate out the parameters of the partition model analytically, which enables the use of efficient stochastic search algorithms.
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We study integral representations of Gaussian processes with a pre-specified law in terms of other Gaussian processes. The dissertation consists of an introduction and of four research articles. In the introduction, we provide an overview about Volterra Gaussian processes in general, and fractional Brownian motion in particular. In the first article, we derive a finite interval integral transformation, which changes fractional Brownian motion with a given Hurst index into fractional Brownian motion with an other Hurst index. Based on this transformation, we construct a prelimit which formally converges to an analogous, infinite interval integral transformation. In the second article, we prove this convergence rigorously and show that the infinite interval transformation is a direct consequence of the finite interval transformation. In the third article, we consider general Volterra Gaussian processes. We derive measure-preserving transformations of these processes and their inherently related bridges. Also, as a related result, we obtain a Fourier-Laguerre series expansion for the first Wiener chaos of a Gaussian martingale. In the fourth article, we derive a class of ergodic transformations of self-similar Volterra Gaussian processes.
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The stochastic filtering has been in general an estimation of indirectly observed states given observed data. This means that one is discussing conditional expected values as being one of the most accurate estimation, given the observations in the context of probability space. In my thesis, I have presented the theory of filtering using two different kind of observation process: the first one is a diffusion process which is discussed in the first chapter, while the third chapter introduces the latter which is a counting process. The majority of the fundamental results of the stochastic filtering is stated in form of interesting equations, such the unnormalized Zakai equation that leads to the Kushner-Stratonovich equation. The latter one which is known also by the normalized Zakai equation or equally by Fujisaki-Kallianpur-Kunita (FKK) equation, shows the divergence between the estimate using a diffusion process and a counting process. I have also introduced an example for the linear gaussian case, which is mainly the concept to build the so-called Kalman-Bucy filter. As the unnormalized and the normalized Zakai equations are in terms of the conditional distribution, a density of these distributions will be developed through these equations and stated by Kushner Theorem. However, Kushner Theorem has a form of a stochastic partial differential equation that needs to be verify in the sense of the existence and uniqueness of its solution, which is covered in the second chapter.
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Tools known as maximal functions are frequently used in harmonic analysis when studying local behaviour of functions. Typically they measure the suprema of local averages of non-negative functions. It is essential that the size (more precisely, the L^p-norm) of the maximal function is comparable to the size of the original function. When dealing with families of operators between Banach spaces we are often forced to replace the uniform bound with the larger R-bound. Hence such a replacement is also needed in the maximal function for functions taking values in spaces of operators. More specifically, the suprema of norms of local averages (i.e. their uniform bound in the operator norm) has to be replaced by their R-bound. This procedure gives us the Rademacher maximal function, which was introduced by Hytönen, McIntosh and Portal in order to prove a certain vector-valued Carleson's embedding theorem. They noticed that the sizes of an operator-valued function and its Rademacher maximal function are comparable for many common range spaces, but not for all. Certain requirements on the type and cotype of the spaces involved are necessary for this comparability, henceforth referred to as the “RMF-property”. It was shown, that other objects and parameters appearing in the definition, such as the domain of functions and the exponent p of the norm, make no difference to this. After a short introduction to randomized norms and geometry in Banach spaces we study the Rademacher maximal function on Euclidean spaces. The requirements on the type and cotype are considered, providing examples of spaces without RMF. L^p-spaces are shown to have RMF not only for p greater or equal to 2 (when it is trivial) but also for 1 < p < 2. A dyadic version of Carleson's embedding theorem is proven for scalar- and operator-valued functions. As the analysis with dyadic cubes can be generalized to filtrations on sigma-finite measure spaces, we consider the Rademacher maximal function in this case as well. It turns out that the RMF-property is independent of the filtration and the underlying measure space and that it is enough to consider very simple ones known as Haar filtrations. Scalar- and operator-valued analogues of Carleson's embedding theorem are also provided. With the RMF-property proven independent of the underlying measure space, we can use probabilistic notions and formulate it for martingales. Following a similar result for UMD-spaces, a weak type inequality is shown to be (necessary and) sufficient for the RMF-property. The RMF-property is also studied using concave functions giving yet another proof of its independence from various parameters.
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Optimal Punishment of Economic Crime: A Study on Bankruptcy Crime This thesis researches whether the punishment practise of bankruptcy crimes is optimal in light of Gary S. Becker’s theory of optimal punishment. According to Becker, a punishment is optimal if it eliminates the expected utility of the crime for the offender and - on the other hand - minimizes the cost of the crime to society. The decision process of the offender is observed through their expected utility of the crime. The expected utility is calculated based on the offender's probability of getting caught, the cost of getting caught and the profit from the crime. All objects including the punishment are measured in cash. The cost of crimes to the society is observed defining the disutility caused by the crime to the society. The disutility is calculated based on the cost of crime prevention, crime damages, punishment execution and the probability of getting caught. If the goal is to minimize the crime profits, the punishments of bankruptcy crimes are not optimal. If the debtors would decide whether or not to commit the crime solely based on economical consideration, the crime rate would be multiple times higher than the current rate is. The prospective offender relies heavily on non-economic aspects in their decision. Most probably social pressure and personal commitment to oblige the laws are major factors in the prospective criminal’s decision-making. The function developed by Becker measuring the cost to society was not useful in the measurement of the optimality of a punishment. The premise of the function that the costs of the society correlate to the costs for the offender from the punishment proves to be unrealistic in observation of the bankruptcy crimes. However, it was observed that majority of the cost of crime for the society are caused by the crime damages. This finding supports the preventive criminal politics.
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Transposable elements, transposons, are discrete DNA segments that are able to move or copy themselves from one locus to another within or between their host genome(s) without a requirement for DNA homology. They are abundant residents in virtually all the genomes studied, for instance, the genomic portion of TEs is approximately 3% in Saccharomyces cerevisiae, 45% in humans, and apparently more than 70% in some plant genomes such as maize and barley. Transposons plays essential role in genome evolution, in lateral transfer of antibiotic resistance genes among bacteria and in life cycle of certain viruses such as HIV-1 and bacteriophage Mu. Despite the diversity of transposable elements they all use a fundamentally similar mechanism called transpositional DNA recombination (transposition) for the movement within and between the genomes of their host organisms. The DNA breakage and joining reactions that underlie their transposition are chemically similar in virtually all known transposition systems. The similarity of the reactions is also reflected in the structure and function of the catalyzing enzymes, transposases and integrases. The transposition reactions take place within the context of a transposition machinery, which can be particularly complex, as in the case of the VLP (virus like particle) machinery of retroelements, which in vivo contains RNA or cDNA and a number of element encoded structural and catalytic proteins. Yet, the minimal core machinery required for transposition comprises a multimer of transposase or integrase proteins and their binding sites at the element DNA ends only. Although the chemistry of DNA transposition is fairly well characterized, the components and function of the transposition machinery have been investigated in detail for only a small group of elements. This work focuses on the identification, characterization, and functional studies of the molecular components of the transposition machineries of BARE-1, Hin-Mu and Mu. For BARE-1 and Hin-Mu transpositional activity has not been shown previously, whereas bacteriophage Mu is a general model of transposition. For BARE-1, which is a retroelement of barley (Hordeum vulgare), the protein and DNA components of the functional VLP machinery were identified from cell extracts. In the case of Hin-Mu, which is a Mu-like prophage in Haemophilus influenzae Rd genome, the components of the core machinery (transposase and its binding sites) were characterized and their functionality was studied by using an in vitro methodology developed for Mu. The function of Mu core machinery was studied for its ability to use various DNA substrates: Hin-Mu end specific DNA substrates and Mu end specific hairpin substrates. The hairpin processing reaction by MuA was characterized in detail. New information was gained of all three machineries. The components or their activity required for functional BARE-1 VLP machinery and retrotransposon life cycle were present in vivo and VLP-like structures could be detected. The Hin-Mu core machinery components were identified and shown to be functional. The components of the Mu and Hin-Mu core machineries were partially interchangeable, reflecting both evolutionary conservation and flexibility within the core machineries. The Mu core machinery displayed surprising flexibility in substrate usage, as it was able to utilize Hin-Mu end specific DNA substrates and to process Mu end DNA hairpin substrates. This flexibility may be evolutionarily and mechanistically important.
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Glial cell line-derived neurotrophic factor (GDNF) and its family members neurturin (NRTN), artemin (ARTN) and persephin (PSPN) are growth factors, which are involved in the development, differentiation and maintenance of many neuron types. In addition, they function outside of the nervous system, e.g. in the development of kidney, testis and liver. GDNF family ligand (GFL) signalling happens through a tetrameric receptor complex, which includes two glycosylphosphatidylinositol (GPI)-anchored GDNF family receptor (GFRα) molecules and two RET (rearranged during transfection) receptor tyrosine kinases. Each of the ligands binds preferentially one of the four GFRα receptors: GDNF binds to GFRα1, NRTN to GFRα2, ARTN to GFRα3 and PSPN to GFRα4. The signal is then delivered by RET, which cannot bind the GFLs on its own, but can bind the GFL-GFRα complex. Under normal cellular conditions, RET is only phosphorylated on the cell surface after ligand binding. At least the GDNF-GFRα1 complex is believed to recruit RET to lipid rafts, where downstream signalling occurs. In general, GFRαs consist of three cysteine-rich domains, but all GFRα4s except for chicken GFRα4 lack domain 1 (D1). We characterised the biochemical and cell biological properties of mouse PSPN receptor GFRα4 and showed that it has a significantly weaker capacity than GFRα1 to recruit RET to the lipid rafts. In spite of that, it can phosphorylate RET in the presence of PSPN and contribute to neuronal differentiation and survival. Therefore, the recruitment of RET to the lipid rafts does not seem to be crucial for the biological activity of all GFRα receptors. Secondly, we demonstrated that GFRα1 D1 stabilises the GDNF-GFRα1 complex and thus affects the phosphorylation of RET and contributes to the biological activity. This may be important in physiological conditions, where the concentration of the ligand or the soluble GFRα1 receptor is low. Our results also suggest a role for D1 in heparin binding and, consequently, in the biodistribution of released GFRα1 or in the formation of the GFL-GFRα-RET complex. We also presented the crystallographic structure of GDNF in the complex with GFRα1 domains 2 and 3. The structure differs from the previously published ARTN-GFRα3 structure in three significant ways. The biochemical data verify the structure and reveal residues participating in the interactions between GFRα1 and GDNF, and preliminarily also between GFRα1 and RET and heparin. Finally, we showed that, the precursor of the oncogenic MEN 2B (multiple endocrine neoplasia type 2) form of RET gets phosphorylated already during its synthesis in the endoplasmic reticulum (ER). We also demonstrated that it associates with Src homology 2 domain-containing protein (SHC) and growth factor receptor-bound protein (GRB2) in the ER, and has the capacity to activate several downstream signalling molecules.
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The type III secretion system (T3SS) is an essential requirement for the virulence of many Gram-negative bacteria which infect plants, animals and men. Pathogens use the T3SS to deliver effector proteins from the bacterial cytoplasm to the eukaryotic host cells, where the effectors subvert host defenses. The best candidates for directing effector protein traffic are the bacterial type III-associated appendages, called needles or pili. In plant pathogenic bacteria, the best characterized example of a T3SS-associated appendage is the HrpA pilus of the plant pathogen Pseudomonas syringae pv. tomato DC3000. The components of the T3SS in plant pathogens are encoded by a cluster of hrp (hypersensitive reaction and pathogenicity) genes. Two major classes of T3SS-secreted proteins are: harpin proteins such as HrpZ which are exported into extracellular space, and avirulence (Avr) proteins such as AvrPto which are translocated directly to the plant cytoplasm. This study deals with the structural and functional characterization of the T3SS-associated HrpA pilus and the T3SS-secreted harpins. By insertional mutagenesis analysis of HrpA, we located the optimal epitope insertion site in the amino-terminus of HrpA, and revealed the potential application of the HrpA pilus as a carrier of antigenic determinants for vaccination. By pulse-expression of proteins combined with immuno-electron microscopy, we discovered the Hrp pilus assembly strategy as addition of HrpA subunits to the distal end of the growing pilus, and we showed for the first time that secretion of HrpZ occurs at the tip of the pilus. The pilus thus functions as a conduit delivering proteins to the extracellular milieu. By using phage-display and scanning-insertion mutagenesis methods we identified a conserved HrpZ-binding peptide and localized the peptide-binding site to the central domain of HrpZ. We also found that the HrpZ specifically interacts with a host bean protein. Taken together, the current results provide deeper insight into the molecular mechanism of T3SS-associated pilus assembly and effector protein translocation, which will be helpful for further studies on the pathogenic mechanisms of Gram-negative bacteria and for developing new strategies to prevent bacterial infection.