This thesis provides a case study on how the wind direction plays an important role in the amount of rainfall, in the village of Somi$acute{o}$. The primary goal is to illustrate how a meta-analysis, together with circular data analytic methods, helps in analyzing certain environmental issues. The existing GLS meta-analysis combines the merits of usual meta-analysis that yields a better precision and also accounts for covariance among coefficients. But, it is quite limited since information about the covariance among coefficients is not utilized. Hence, in my proposed meta-analysis, I take the correlations between adjacent studies into account when employing the GLS meta-analysis. Besides, I also fit a time series linear-circular regression as a comparable model. By comparing the confidence intervals of parameter estimates, covariance matrix, AIC, BIC and p-values, I discuss an improvement on the GLS meta analysis model in its application to forecasting problem in Environmental study.

Regression analysis is one of the most applied statistical techniques. The sta- tistical inference of a linear regression model with a monotone constraint had been discussed in early analysis. A natural question arises when it comes to the difference between the cases of with and without the constraint. Although the comparison be- tween confidence intervals of linear regression models with and without restriction for one predictor variable had been considered, this discussion for multiple regres- sion is required. In this thesis, I discuss the comparison of the confidence intervals between a multiple linear regression model with and without constraints.

Regression analyses constitutes an important part of the statistical inference and has great applications in many areas. In some applications, we strongly believe that the regression function changes monotonically with some or all of the predictor variables in a region of interest. Deriving analyses under such constraints will be an enormous task. In this work, the restricted prediction interval for the mean of the regression function is constructed when two predictors are present. I use a modified likelihood ratio test (LRT) to construct prediction intervals.

This dissertation consists of three chapters on semi-parametric Bayesian Econometric methods. Chapter 1 applies a semi-parametric method to demand systems, and compares the abilities to recover the true elasticities of different approaches to linearly estimating the widely used Almost Ideal demand model, by either iteration or approximation. Chapter 2 co-authored with Dr. Melvyn Weeks introduces a new semi-parametric Bayesian Generalized Least Square estimator, which employs the Dirichlet Process prior to cope with potential heterogeneity in the error distributions. Two methods are discussed as special cases of the GLS estimator, the Seemingly Unrelated Regression for equation systems, and the Random Effects Model for panel data, which can be applied to many fields such as the demand analysis in Chapter 1. Chapter 3 focuses on the subset selection for the efficiencies of firms, which addresses the influence of heterogeneity in the distributions of efficiencies on subset selections by applying the semi-parametric Bayesian Random Effects Model introduced in Chapter 2.

Enligt vår teoretiska referensram samt enligt en undersökning som genomfördes åt Statensoffentliga utredninger, (SOU 1997:188), kan ett samband mellan motionsutövande och hälsapåvisas. Det finns däremot ingen entydig forskning som visar på att motionsutövande leder tillminskad sjukfrånvaro. Vår studie utgår från grundhypotesen att det finns ett positivt sambandmellan företagssubventionerad friskvård och minskad sjukfrånvaro. Genom enenkätundersökning där 48 ICA-butiker medverkade samt där butikernas årsredovisningargranskades, insamlades data relaterad till butikernas friskvårdssubventionering ochsjukfrånvaro. Enligt ett Chi-square test kunde ett svagt samband mellanfriskvårdssubventionering och sjukfrånvaro skönjas, och även beräkningarna för korrelationenmellan de två variablerna för den insamlade datamängden påvisade ett samband.Nyttjandegraden av friskvårdsbidraget visade sig vara högst vid en subventioneringsnivå på3000 kr per år och anställd, och uppgick vid nämnda nivå till i genomsnitt 30 procent. Vid engrov schablonberäkning av kostnadsbesparingarna som den minskade sjukfrånvaron medför,fann vi att en subventioneringsnivå på maximalt 1000 kronor per år och anställd är olönsammedan en motsvarande nivå på 3000 kronor i bidrag per år och anställd gav ett positivtnettoresultat på nära 3000 kronor per anställd. Vi rekommenderar därför ensubventioneringsnivå på 3000 kronor per år och anställd då den nivån visade sig generera bästlönsamhet och även högst nyttjandegrad bland de anställda.

I am exploring the new shapes in garments by using pieces of the quadrate shape, in contrast to the body shape, as a tool. By setting the amount of the pieces for each garment, new shapes occur because particular connecting techniques are used in order to join every piece to make a garment. The garments still look dynamic because of the visible seam allowances which creates lines all over. Moreover, the primary colours are scattered into many tones used in the collection. One tone is for one garment in an outfit. The materials are various. These make the expression energetic although the quadrilateral itself and the strong primary colours look quite static. / Program: Master Programme in Fashion and Textile Design

A adequada quantificação do transporte interfacial de escalares em escoamentos turbulentos é de interesse prático para os processos industriais e para a gestão dos problemas ambientais. O fenômeno é matematicamente complexo devido ao uso de equações governantes estatísticas não lineares e não fechadas. Neste estudo, analisam-se detalhes do método de Ondas Quadradas Aleatórias (OQA), o qual fornece uma quantificação estatística que permite fechar as equações e obter um perfil normalizado da grandeza de interesse para a transferência unidimensional turbulenta de escalares, que, num caso idealizado, depende de apenas dois parâmetros adimensionais, A e k (neste caso, k representa um coeficiente de transferência e A depende da interação entre os fenômenos de transporte molecular e turbulento). Simulações numéricas foram realizadas no intuito de se verificar a influência das derivadas de ordem superior para a função normalizada de concentração. A sensibilidade do modelo e a análise de aspectos intrínsecos ao mesmo foram também realizadas. Importante análise das condições de contorno empregadas foi desenvolvida com a inserção de um contorno adicional, com base física, no seio líquido. Como os estudos iniciais tinham se concentrado em exemplos de transferência de massa, uma extensão para o caso de transporte de calor foi considerada. Os resultados obtidos reproduzem o comportamento dos dados experimentais observados na literatura. / The adequate quantification of interfacial scalar transport in turbulent flows is of practical interest for industrial processes and in environmental problems. The phenomenon is mathematically complex due to the use of unclosed nonlinear statistical equations. In this study, we analyze details of the method of Random Square Waves (RSW), which provides a statistical quantification that allows closing the set of equations and getting the normalized scalar profile of the one-dimensional turbulent scalar variable, which, in an idealized case, depends on only two nondimensional parameters, k and A (in this case, k represents a transfer coefficient and A depends on the interaction between the molecular and turbulent transports). Numerical simulations were performed in order to verify the influence of the higher order of derivatives over the normalized concentration function. The sensitivity of the model to the relevant parameters and the analysis of its intrinsic parameters were also performed. An important aspect is the analysis of the boundary conditions, for which an additional condition was proposed and employed in the bulk liquid (with based on physical grounds). Because the initial studies have focused on examples of mass transfer, an extension to the case of heat transport was here considered. The results reproduce the behavior of experimental data reported in the literature.

The growing interest in computing structured matrix functions stems from the fact that preserving and exploiting the structure of matrices can help us gain physically meaningful solutions with less computational cost and memory requirement. The work presented here is divided into two parts. The first part deals with the computation of functions of structured matrices. The second part is concerned with the structured error analysis in the computation of matrix functions. We present algorithms applying the inverse scaling and squaring method and using the Schur-like form of the symplectic matrices as an alternative to the algorithms using the Schur decomposition to compute the logarithm of symplectic matrices. There are two main calculations in the inverse scaling and squaring method: taking a square root and evaluating the Padé approximants. Numerical experiments suggest that using the Schur-like form with the structure preserving iterations for the square root helps us to exploit the Hamiltonian structure of the logarithm of symplectic matrices. Some type of matrices are nearly structured. We discuss the conditions for using the nearest structured matrix to the nearly structured one by analysing the forward error bounds. Since the structure preserving algorithms for computing the functions of matrices provide advantages in terms of accuracy and data storage we suggest to compute the function of the nearest structured matrix. The analysis is applied to the nearly unitary, nearly Hermitian and nearly positive semi-definite matrices for the matrix logarithm, square root, exponential, cosine and sine functions. It is significant to investigate the effect of the structured perturbations in the sensitivity analysis of matrix functions. We study the structured condition number of matrix functions defined between smooth square matrix manifolds. We develop algorithms computing and estimating the structured condition number. We also present the lower and upper bounds on the structured condition number, which are cheaper to compute than the "exact" structured condition number. We observe that the lower bounds give a good estimation for the structured condition numbers. Comparing the structured and unstructured condition number reveals that they can differ by several orders of magnitude. Having discussed how to compute the structured condition number of matrix functions defined between smooth square matrix manifolds we apply the theory of structured condition numbers to the structured matrix factorizations. We measure the sensitivity of matrix factors to the structured perturbations for the structured polar decomposition, structured sign factorization and the generalized polar decomposition. Finally, we consider the unstructured perturbation analysis for the canonical generalized polar decomposition by using three different methods. Apart from theoretical aspect of the perturbation analysis, perturbation bounds obtained from these methods are compared numerically and our findings show an improvement on the sharpness of the perturbation bounds in the literature.

Protein misfolding and aggregation are the cause of many problems within the biopharmaceutical industry and medical fields. Although many experimental studies have been implemented in vivo in order to understand this process, the mechanism occurs in time and length scales inaccessible to conventional experiments. On the other hand, computational studies have shown significant improvement in elucidating key aspects of the aggregation pathways and gain insights to the folding behavior of the proteins. Consequently, this makes computational modeling an ideal complement to experiment in understanding the generic behavior and mechanisms of aggregation. This study is concerned with DynamO, a coarse-grained, off-lattice, general event-driven discontinuous molecular-dynamics simulation package. This simulator offers a unique opportunity to gain insight into the process of protein aggregation by displaying the optimal O(N) asymptotic scaling of the computational cost with the number of particles N, rather than O(NlogN) scaling found in most standard algorithms. The study was split into two loosely related projects: in the first project, a computer model was developed in which the effect of model parameters on folding behavior and characteristics of isolated peptides is investigated. The model parameters include chain stiffness (an overlap parameter defined as the ratio of the hard-core diameter to bond length 'sigma/l'), range of interaction potential 'Gamma', sequence, and chains length 'N '. Based on the model chosen from systems of isolated chains, aggregation in multichain systems is studied. In another project, we simulate various square-well fluid systems with different ranges of interaction potential in order to understand the phase behavior of proteins due to its relevance to aggregation and many bioprocessing events. Changing the model parameters shows different folding behaviors. The model-chains with 64 residues, Gamma equal to 1.1 and sigma/l equal to 1.9 is the least computationally expensive model displaying all the characteristics found in real proteins. We introduce a new order parameter which divides the conformational space into folded and unfolded ensemble-structures, this order parameter corresponds to a transition in the folding behavior of the chains. We define a native state ensemble as an ensemble of structures with small deviation in contact maps for spheres inaccessible to the solvent defined as the core of the chain. This native ensemble corresponds to the structures exhibiting low-temperature fluctuations simulating the 'breathing motions' of real proteins which is considered responsible for their catalytic activities. On the other hand, the non-native ensemble unfolds at higher temperatures, which increases the propensity for aggregation by forming intermolecular contacts, and therefore reproduce the behavior of proteins under severe solution conditions which occurs in bio- processing (this includes high concentration, temperature, pressure, pH ...). The behavior of multichain systems shows that it is possible to correlate the aggregation propensity of chains at room temperature from the behavior of chains in isolated system at the collapse temperature, which in turn correlate with the stability of the low-T ensemble. In the second project, we developed a more efficient way of calculating the critical temperature in SW fluids even for strongly short-ranged systems which are especially difficult to simulate. In the supercritical region, every isotherm obeys the linear equation for the pressure with a high precision within the bounds of uncertainty. The linear equation pm = p0 + Rm with Rm being the constant isothermal rigidity (dp/d)T . The constant rigidity can be used to estimate directly a critical temperature (Tc) and critical pressure (pc), respectively, and also to obtain the pressures and densities of the percolation loci based on an empirical quadratic nature of change in pressure with densities outside the percolation loci. Identifying the critical temperature and how it depends on the pair potential is very important in formulations with a growing need to predict when the solution will go opalescent.

The main purpose of this thesis is to calculate the integral cohomology ring of the symmetric square of quaternionic projective space, which has been an open problem since computations with symmetric squares were first proposed in the 1930's. The geometry of this particular case forms an essential part of the thesis, and unexpected results concerning two universal Pin(4) bundles are also included. The cohomological computations involve a commutative ladder of long exact sequences, which arise by decomposing the symmetric square and the corresponding Borel space in compatible ways. The geometry and the cohomology of the configuration space of unordered pairs of distinct points in quaternionic projective space, and of the Thom space MPin(4), also feature, and seem to be of independent interest.