Integral Transformations of Volterra Gaussian Processes

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.

On Games on Non-Wellfounded Sets and Stationary Sets

In this thesis we study a few games related to non-wellfounded and stationary sets. Games have turned out to be an important tool in mathematical logic ranging from semantic games defining the truth of a sentence in a given logic to for example games on real numbers whose determinacies have important effects on the consistency of certain large cardinal assumptions. The equality of non-wellfounded sets can be determined by a so called bisimulation game already used to identify processes in theoretical computer science and possible world models for modal logic. Here we present a game to classify non-wellfounded sets according to their branching structure. We also study games on stationary sets moving back to classical wellfounded set theory. We also describe a way to approximate non-wellfounded sets with hereditarily finite wellfounded sets. The framework used to do this is domain theory. In the Banach-Mazur game, also called the ideal game, the players play a descending sequence of stationary sets and the second player tries to keep their intersection stationary. The game is connected to precipitousness of the corresponding ideal. In the pressing down game first player plays regressive functions defined on stationary sets and the second player responds with a stationary set where the function is constant trying to keep the intersection stationary. This game has applications in model theory to the determinacy of the Ehrenfeucht-Fraisse game. We show that it is consistent that these games are not equivalent.

Bayesian statistical analysis of bacterial diversity

Bacteria play an important role in many ecological systems. The molecular characterization of bacteria using either cultivation-dependent or cultivation-independent methods reveals the large scale of bacterial diversity in natural communities, and the vastness of subpopulations within a species or genus. Understanding how bacterial diversity varies across different environments and also within populations should provide insights into many important questions of bacterial evolution and population dynamics. This thesis presents novel statistical methods for analyzing bacterial diversity using widely employed molecular fingerprinting techniques. The first objective of this thesis was to develop Bayesian clustering models to identify bacterial population structures. Bacterial isolates were identified using multilous sequence typing (MLST), and Bayesian clustering models were used to explore the evolutionary relationships among isolates. Our method involves the inference of genetic population structures via an unsupervised clustering framework where the dependence between loci is represented using graphical models. The population dynamics that generate such a population stratification were investigated using a stochastic model, in which homologous recombination between subpopulations can be quantified within a gene flow network. The second part of the thesis focuses on cluster analysis of community compositional data produced by two different cultivation-independent analyses: terminal restriction fragment length polymorphism (T-RFLP) analysis, and fatty acid methyl ester (FAME) analysis. The cluster analysis aims to group bacterial communities that are similar in composition, which is an important step for understanding the overall influences of environmental and ecological perturbations on bacterial diversity. A common feature of T-RFLP and FAME data is zero-inflation, which indicates that the observation of a zero value is much more frequent than would be expected, for example, from a Poisson distribution in the discrete case, or a Gaussian distribution in the continuous case. We provided two strategies for modeling zero-inflation in the clustering framework, which were validated by both synthetic and empirical complex data sets. We show in the thesis that our model that takes into account dependencies between loci in MLST data can produce better clustering results than those methods which assume independent loci. Furthermore, computer algorithms that are efficient in analyzing large scale data were adopted for meeting the increasing computational need. Our method that detects homologous recombination in subpopulations may provide a theoretical criterion for defining bacterial species. The clustering of bacterial community data include T-RFLP and FAME provides an initial effort for discovering the evolutionary dynamics that structure and maintain bacterial diversity in the natural environment.

Physiological basis of yield variation in response to row spacing and plant density of mungbean grown in subtropical environments

In this study, we investigated the extent and physiological bases of yield variation due to row spacing and plant density configuration in the mungbean Vigna radiata (L.) Wilczek variety “Crystal” grown in different subtropical environments. Field trials were conducted in six production environments; one rain-fed and one irrigated trial each at Biloela and Emerald, and one rain-fed trial each at Hermitage and Kingaroy sites in Queensland, Australia. In each trial, six combinations of spatial arrangement of plants, achieved through two inter-row spacings of 1 m or 0.9 m (wide row), 0.5 m or 0.3 m (narrow row), with three plant densities, 20, 30 and 40 plants/m2, were compared. The narrow row spacing resulted in 22% higher shoot dry matter and 14% more yield compared to the wide rows. The yield advantage of narrow rows ranged from 10% to 36% in the two irrigated and three rain-fed trials. However, yield loss of up to 10% was also recorded from narrow rows at Emerald where the crop suffered severe drought. Neither the effects of plant density, nor the interaction between plant density and row spacing, however, were significant in any trial. The yield advantage of narrow rows was related to 22% more intercepted radiation. In addition, simulations by the Agricultural Production Systems Simulator model, using site-specific agronomy, soil and weather information, suggested that narrow rows had proportionately greater use of soil water through transpiration, compared to evaporation resulting in higher yield per mm of soil water. The long-term simulation of yield probabilities over 123 years for the two row configurations showed that the mungbean crop planted in narrow rows could produce up to 30% higher grain yield compared to wide rows in 95% of the seasons.

Efficient search for statistically significant dependency rules in binary data

Analyzing statistical dependencies is a fundamental problem in all empirical science. Dependencies help us understand causes and effects, create new scientific theories, and invent cures to problems. Nowadays, large amounts of data is available, but efficient computational tools for analyzing the data are missing. In this research, we develop efficient algorithms for a commonly occurring search problem - searching for the statistically most significant dependency rules in binary data. We consider dependency rules of the form X->A or X->not A, where X is a set of positive-valued attributes and A is a single attribute. Such rules describe which factors either increase or decrease the probability of the consequent A. A classical example are genetic and environmental factors, which can either cause or prevent a disease. The emphasis in this research is that the discovered dependencies should be genuine - i.e. they should also hold in future data. This is an important distinction from the traditional association rules, which - in spite of their name and a similar appearance to dependency rules - do not necessarily represent statistical dependencies at all or represent only spurious connections, which occur by chance. Therefore, the principal objective is to search for the rules with statistical significance measures. Another important objective is to search for only non-redundant rules, which express the real causes of dependence, without any occasional extra factors. The extra factors do not add any new information on the dependence, but can only blur it and make it less accurate in future data. The problem is computationally very demanding, because the number of all possible rules increases exponentially with the number of attributes. In addition, neither the statistical dependency nor the statistical significance are monotonic properties, which means that the traditional pruning techniques do not work. As a solution, we first derive the mathematical basis for pruning the search space with any well-behaving statistical significance measures. The mathematical theory is complemented by a new algorithmic invention, which enables an efficient search without any heuristic restrictions. The resulting algorithm can be used to search for both positive and negative dependencies with any commonly used statistical measures, like Fisher's exact test, the chi-squared measure, mutual information, and z scores. According to our experiments, the algorithm is well-scalable, especially with Fisher's exact test. It can easily handle even the densest data sets with 10000-20000 attributes. Still, the results are globally optimal, which is a remarkable improvement over the existing solutions. In practice, this means that the user does not have to worry whether the dependencies hold in future data or if the data still contains better, but undiscovered dependencies.

Salutogenic design: The neurological basis of health-promoting environments

All architecture embodies narratives that may either support or work against a state of good health. Neurological theory can be used to explain why salutogenic environments work, and how they can improve health outcomes.

Molecular basis of nitrate reductase induction in Candida utilis

Temporal separaton of transcription and translation during nitrate reductase induction oin Candida utilis was achieved by the use of actinomycin D and cycloheximide. The yeast failed to synthesize nitrate reductase when nitrate was not provided during transcription. Nitrate thus appeared to induce during transcription the capacity to synthesize nitrate reductase. Presence of nitrate, on the other hand, was not obligatory during translation except for its essential role in maintaining the stability of nitrate reductase after its formation as well as its mRNA.

Matrices of finite Lorentz transformations in a noncompact basis. III. Completeness relation for O(2, 1)

A parametrization of the elements of the three-dimensional Lorentz group O(2, 1), suited to the use of a noncompact O(1, 1) basis in its unitary representations, is derived and used to set up the representation matrices for the entire group. The Plancherel formula for O(2, 1) is then expressed in this basis.

Structural basis of cytoskeletal regulation by twinfilin

The actin cytoskeleton is required, in all eukaryotic organisms, for several key cellular functions such as cell motility, cytokinesis, and endocytosis. In cells, actin exists either in a monomeric state (G-actin) or in a filamentous form (F-actin). F-actin is the functional form, which can assemble into various structures and produce direct pushing forces that are required for different motile processes. The assembly of actin monomers into complicated three-dimensional structures is tightly regulated by a large number of actin regulating proteins. One central actin regulating protein is twinfilin. Twinfilin consists of two actin depolymerizing-factor homology (ADF-H) domains, which are capable of binding actin, and is conserved from yeast to mammals. Previously it has been shown that twinfilin binds to and sequesters G-actin, and interacts with the heterodimeric capping protein. More recently it has been found that twinfilin also binds to the fast growing actin filament ends and prevents their growth. However, the cellular role of twinfilin and the molecular mechanisms of these interactions have remained unclear. In this study we characterized the molecular mechanisms behind the functions of twinfilin. We demonstrated that twinfilin forms a high-affinity complex with ADP-bound actin monomers (ADP-G-actin). Both ADF-H domains are capable of binding G-actin, but the C-terminal domain contains the high-affinity binding site. Our biochemical analyses identified twinfilin s C-terminal tail region as the interaction site for capping protein. Contrary to G-actin binding, both ADF-H domains of twinfilin are required for the actin filament barbed end capping activity. The C-terminal domain is structurally homologous to ADF/cofilin and binds to filament sides in a similar manner, providing the main affinity for F-actin during barbed end capping. The structure of the N-terminal domain is more distant from ADF/cofilin, and thus it can only associate with G-actin or the terminal actin monomer at the filament barbed end, where it regulates twinfilin s affinity for barbed ends. These data suggest that the mechanism of barbed end capping is similar for twinfilin and gelsolin family proteins. Taken together, these studies revealed how twinfilin interacts with G-actin, filament barbed ends, and capping protein, and also provide a model for how these activities evolved through a duplication of an ancient ADF/cofilin-like domain.

GPRA and the asthma locus on chromosome 7p14-p15

The basis of this work was the identification of a genomic region on chromosome 7p14-p15 that strongly associated with asthma and high serum total immunoglobulin E in a Finnish founder population from Kainuu. Using a hierarchical genotyping approach the linkage region was narrowed down until an evolutionary collectively inherited 133-kb haplotype block was discovered. The results were confirmed in two independent data sets: Asthma families from Quebec and allergy families from North-Karelia. In all the three cohorts studied, single nucleotide polymorphisms tagging seven common gene variants (haplotypes) were identified. Over half of the asthma patients carried three evolutionary closely related susceptibility haplotypes as opposed to approximately one third of the healthy controls. The risk effects of the gene variants varied from 1.4 to 2.5. In the disease-associated region, there was one protein-coding gene named GPRA (G Protein-coupled Receptor for Asthma susceptibility also known as NPSR1) which displayed extensive alternative splicing. Only the two isoforms with distinct intracellular tail sequences, GPRA-A and -B, encoded a full-length G protein-coupled receptor with seven transmembrane regions. Using various techniques, we showed that GPRA is expressed in multiple mucosal surfaces including epithelial cells throughout the respiratory tract. GPRA-A has additional expression in respiratory smooth muscle cells. However, in bronchial biopsies with unknown haplotypes, GPRA-B was upregulated in airways of all patient samples in contrast to the lack of expression in controls. Further support for GPRA as a common mediator of inflammation was obtained from a mouse model of ovalbumin-induced inflammation, where metacholine-induced airway hyperresponsiveness correlated with elevated GPRA mRNA levels in the lung and increased GPRA immunostaining in pulmonary macrophages. A novel GPRA agonist, Neuropeptide S (NPS), stimulated phagocytosis of Esterichia coli bacteria in a mouse macrophage cell line indicating a role for GPRA in the removal of inhaled allergens. The suggested GPRA functions prompted us to study, whether GPRA haplotypes associate with respiratory distress syndrome (RDS) and bronchopulmonary dysplasia (BPD) in infants sharing clinical symptoms with asthma. According to the results, near-term RDS and asthma may also share the same susceptibility and protective GPRA haplotypes. As in asthma, GPRA-B isoform expression was induced in bronchial smooth muscle cells in RDS and BPD suggesting a role for GPRA in bronchial hyperresponsiveness. In conclusion, the results of the present study suggest that the dysregulation of the GPRA/NPS pathway may not only be limited to the individuals carrying the risk variants of the gene but is also involved in the regulation of immune functions of asthma.

The Molecular Basis of Hydrolethalus Syndrome

Hydrolethalus syndrome (HLS) is a severe fetal malformation syndrome that is inherited by an autosomal recessive manner. HLS belongs to the Finnish disease heritage, an entity of rare diseases that are more prevalent in Finland than in other parts of the world. The phenotypic spectrum of the syndrome is wide and it is characterized by several developmental abnormalities, including hydrocephalus and absent midline structures in the brain, abnormal lobation of the lungs, polydactyly as well as micrognathia and other craniofacial anomalies. Polyhydramnios are relatively frequent during pregnancy. HLS can nowadays be effectively identified by ultrasound scan already at the end of the first trimester of pregnancy. One of the main goals in this study was to identify and characterize the gene defect underlying HLS. The defect was found from a previously unknown gene that was named HYLS1. Identification of the gene defect made it possible to confirm the HLS diagnosis genetically, an aspect that provides valuable information for the families in which a fetus is suspected to have HLS. Neuropathological findings of mutation confirmed HLS cases were described for the first time in detail in this study. Also, detailed general pathological findings were described. Since HYLS1 was an unknown gene with no relatives in the known gene families, many functional studies were performed in order to unravel the function of the gene and of the protein it codes for. Studies showed, for example, that the subcellular localization of the HYLS1 protein was different when the normal and the defective forms were compared. In addition, HYLS1 was shown to possess transactivation potential which was significantly diminished in the defective form. According to the results of this study it can be stated that HYLS1 most likely participates in transcriptional regulation and also in the regulation of cholesterol metabolism and that the function of HYLS1 is critical for normal fetal development.

On Sharma-Swarup algorithm for time minimising transportation problems

In this note, the fallacy in the method given by Sharma and Swarup, in their paper on time minimising transportation problem, to determine the setS hkof all nonbasic cells which when introduced into the basis, either would eliminate a given basic cell (h, k) from the basis or reduce the amountx hkis pointed out.

A parameter characterizing plowing nature of surfaces close to Gaussian

A non-dimensional parameter descriptive of the plowing nature of surfaces is proposed for the case of sliding between a soft and a relatively hard metallic pair. From a set of potential parameters which can be descriptive of the phenomenon, dimensionless groups are formulated and the influence of each one of them is analyzed. A non-dimensional parameter involving the root-mean square deviation (R-q) and the centroidal frequency (F-mean) deducted from the power-spectrum is found to have a high degree of correlation (as high as 0.93) with the coefficient of friction obtained in sliding experiments under lubricated condition.

Beyond Gauss: Image-set matching on the Riemannian manifold of PDFs

State-of-the-art image-set matching techniques typically implicitly model each image-set with a Gaussian distribution. Here, we propose to go beyond these representations and model image-sets as probability distribution functions (PDFs) using kernel density estimators. To compare and match image-sets, we exploit Csiszar´ f-divergences, which bear strong connections to the geodesic distance defined on the space of PDFs, i.e., the statistical manifold. Furthermore, we introduce valid positive definite kernels on the statistical manifold, which let us make use of more powerful classification schemes to match image-sets. Finally, we introduce a supervised dimensionality reduction technique that learns a latent space where f-divergences reflect the class labels of the data. Our experiments on diverse problems, such as video-based face recognition and dynamic texture classification, evidence the benefits of our approach over the state-of-the-art image-set matching methods.