Bayes quadratic unbiased estimator of spatial covariance parameters

This work presents Bayes invariant quadratic unbiased estimator, for short BAIQUE. Bayesian approach is used here to estimate the covariance functions of the regionalized variables which appear in the spatial covariance structure in mixed linear model. Firstly a brief review of spatial process, variance covariance components structure and Bayesian inference is given, since this project deals with these concepts. Then the linear equations model corresponding to BAIQUE in the general case is formulated. That Bayes estimator of variance components with too many unknown parameters is complicated to be solved analytically. Hence, in order to facilitate the handling with this system, BAIQUE of spatial covariance model with two parameters is considered. Bayesian estimation arises as a solution of a linear equations system which requires the linearity of the covariance functions in the parameters. Here the availability of prior information on the parameters is assumed. This information includes apriori distribution functions which enable to find the first and the second moments matrix. The Bayesian estimation suggested here depends only on the second moment of the prior distribution. The estimation appears as a quadratic form y'Ay , where y is the vector of filtered data observations. This quadratic estimator is used to estimate the linear function of unknown variance components. The matrix A of BAIQUE plays an important role. If such a symmetrical matrix exists, then Bayes risk becomes minimal and the unbiasedness conditions are fulfilled. Therefore, the symmetry of this matrix is elaborated in this work. Through dealing with the infinite series of matrices, a representation of the matrix A is obtained which shows the symmetry of A. In this context, the largest singular value of the decomposed matrix of the infinite series is considered to deal with the convergence condition and also it is connected with Gerschgorin Discs and Poincare theorem. Then the BAIQUE model for some experimental designs is computed and compared. The comparison deals with different aspects, such as the influence of the position of the design points in a fixed interval. The designs that are considered are those with their points distributed in the interval [0, 1]. These experimental structures are compared with respect to the Bayes risk and norms of the matrices corresponding to distances, covariance structures and matrices which have to satisfy the convergence condition. Also different types of the regression functions and distance measurements are handled. The influence of scaling on the design points is studied, moreover, the influence of the covariance structure on the best design is investigated and different covariance structures are considered. Finally, BAIQUE is applied for real data. The corresponding outcomes are compared with the results of other methods for the same data. Thereby, the special BAIQUE, which estimates the general variance of the data, achieves a very close result to the classical empirical variance.

Design, implementation and application of a generic framework for integrated regional land-use modeling

Land use is a crucial link between human activities and the natural environment and one of the main driving forces of global environmental change. Large parts of the terrestrial land surface are used for agriculture, forestry, settlements and infrastructure. Given the importance of land use, it is essential to understand the multitude of influential factors and resulting land use patterns. An essential methodology to study and quantify such interactions is provided by the adoption of land-use models. By the application of land-use models, it is possible to analyze the complex structure of linkages and feedbacks and to also determine the relevance of driving forces. Modeling land use and land use changes has a long-term tradition. In particular on the regional scale, a variety of models for different regions and research questions has been created. Modeling capabilities grow with steady advances in computer technology, which on the one hand are driven by increasing computing power on the other hand by new methods in software development, e.g. object- and component-oriented architectures. In this thesis, SITE (Simulation of Terrestrial Environments), a novel framework for integrated regional sland-use modeling, will be introduced and discussed. Particular features of SITE are the notably extended capability to integrate models and the strict separation of application and implementation. These features enable efficient development, test and usage of integrated land-use models. On its system side, SITE provides generic data structures (grid, grid cells, attributes etc.) and takes over the responsibility for their administration. By means of a scripting language (Python) that has been extended by language features specific for land-use modeling, these data structures can be utilized and manipulated by modeling applications. The scripting language interpreter is embedded in SITE. The integration of sub models can be achieved via the scripting language or by usage of a generic interface provided by SITE. Furthermore, functionalities important for land-use modeling like model calibration, model tests and analysis support of simulation results have been integrated into the generic framework. During the implementation of SITE, specific emphasis was laid on expandability, maintainability and usability. Along with the modeling framework a land use model for the analysis of the stability of tropical rainforest margins was developed in the context of the collaborative research project STORMA (SFB 552). In a research area in Central Sulawesi, Indonesia, socio-environmental impacts of land-use changes were examined. SITE was used to simulate land-use dynamics in the historical period of 1981 to 2002. Analogous to that, a scenario that did not consider migration in the population dynamics, was analyzed. For the calculation of crop yields and trace gas emissions, the DAYCENT agro-ecosystem model was integrated. In this case study, it could be shown that land-use changes in the Indonesian research area could mainly be characterized by the expansion of agricultural areas at the expense of natural forest. For this reason, the situation had to be interpreted as unsustainable even though increased agricultural use implied economic improvements and higher farmers' incomes. Due to the importance of model calibration, it was explicitly addressed in the SITE architecture through the introduction of a specific component. The calibration functionality can be used by all SITE applications and enables largely automated model calibration. Calibration in SITE is understood as a process that finds an optimal or at least adequate solution for a set of arbitrarily selectable model parameters with respect to an objective function. In SITE, an objective function typically is a map comparison algorithm capable of comparing a simulation result to a reference map. Several map optimization and map comparison methodologies are available and can be combined. The STORMA land-use model was calibrated using a genetic algorithm for optimization and the figure of merit map comparison measure as objective function. The time period for the calibration ranged from 1981 to 2002. For this period, respective reference land-use maps were compiled. It could be shown, that an efficient automated model calibration with SITE is possible. Nevertheless, the selection of the calibration parameters required detailed knowledge about the underlying land-use model and cannot be automated. In another case study decreases in crop yields and resulting losses in income from coffee cultivation were analyzed and quantified under the assumption of four different deforestation scenarios. For this task, an empirical model, describing the dependence of bee pollination and resulting coffee fruit set from the distance to the closest natural forest, was integrated. Land-use simulations showed, that depending on the magnitude and location of ongoing forest conversion, pollination services are expected to decline continuously. This results in a reduction of coffee yields of up to 18% and a loss of net revenues per hectare of up to 14%. However, the study also showed that ecological and economic values can be preserved if patches of natural vegetation are conservated in the agricultural landscape. -----------------------------------------------------------------------

Acquiring expert knowledge for the design of conceptual information systems

Conceptual Information Systems unfold the conceptual structure of data stored in relational databases. In the design phase of the system, conceptual hierarchies have to be created which describe different aspects of the data. In this paper, we describe two principal ways of designing such conceptual hierarchies, data driven design and theory driven design and discuss advantages and drawbacks. The central part of the paper shows how Attribute Exploration, a knowledge acquisition tool developped by B. Ganter can be applied for narrowing the gap between both approaches.

Protein Folding Simulations: Confinement, External Fields and Sequence Design

The present Thesis looks at the problem of protein folding using Monte Carlo and Langevin simulations, three topics in protein folding have been studied: 1) the effect of confining potential barriers, 2) the effect of a static external field and 3) the design of amino acid sequences which fold in a short time and which have a stable native state (global minimum). Regarding the first topic, we studied the confinement of a small protein of 16 amino acids known as 1NJ0 (PDB code) which has a beta-sheet structure as a native state. The confinement of proteins occurs frequently in the cell environment. Some molecules called Chaperones, present in the cytoplasm, capture the unfolded proteins in their interior and avoid the formation of aggregates and misfolded proteins. This mechanism of confinement mediated by Chaperones is not yet well understood. In the present work we considered two kinds of potential barriers which try to mimic the confinement induced by a Chaperon molecule. The first kind of potential was a purely repulsive barrier whose only effect is to create a cavity where the protein folds up correctly. The second kind of potential was a barrier which includes both attractive and repulsive effects. We performed Wang-Landau simulations to calculate the thermodynamical properties of 1NJ0. From the free energy landscape plot we found that 1NJ0 has two intermediate states in the bulk (without confinement) which are clearly separated from the native and the unfolded states. For the case of the purely repulsive barrier we found that the intermediate states get closer to each other in the free energy landscape plot and eventually they collapse into a single intermediate state. The unfolded state is more compact, compared to that in the bulk, as the size of the barrier decreases. For an attractive barrier modifications of the states (native, unfolded and intermediates) are observed depending on the degree of attraction between the protein and the walls of the barrier. The strength of the attraction is measured by the parameter $\epsilon$. A purely repulsive barrier is obtained for $\epsilon=0$ and a purely attractive barrier for $\epsilon=1$. The states are changed slightly for magnitudes of the attraction up to $\epsilon=0.4$. The disappearance of the intermediate states of 1NJ0 is already observed for $\epsilon =0.6$. A very high attractive barrier ($\epsilon \sim 1.0$) produces a completely denatured state. In the second topic of this Thesis we dealt with the interaction of a protein with an external electric field. We demonstrated by means of computer simulations, specifically by using the Wang-Landau algorithm, that the folded, unfolded, and intermediate states can be modified by means of a field. We have found that an external field can induce several modifications in the thermodynamics of these states: for relatively low magnitudes of the field ($<2.06 \times 10^8$ V/m) no major changes in the states are observed. However, for higher magnitudes than ($6.19 \times 10^8$ V/m) one observes the appearance of a new native state which exhibits a helix-like structure. In contrast, the original native state is a $\beta$-sheet structure. In the new native state all the dipoles in the backbone structure are aligned parallel to the field. The design of amino acid sequences constitutes the third topic of the present work. We have tested the Rate of Convergence criterion proposed by D. Gridnev and M. Garcia ({\it work unpublished}). We applied it to the study of off-lattice models. The Rate of Convergence criterion is used to decide if a certain sequence will fold up correctly within a relatively short time. Before the present work, the common way to decide if a certain sequence was a good/bad folder was by performing the whole dynamics until the sequence got its native state (if it existed), or by studying the curvature of the potential energy surface. There are some difficulties in the last two approaches. In the first approach, performing the complete dynamics for hundreds of sequences is a rather challenging task because of the CPU time needed. In the second approach, calculating the curvature of the potential energy surface is possible only for very smooth surfaces. The Rate of Convergence criterion seems to avoid the previous difficulties. With this criterion one does not need to perform the complete dynamics to find the good and bad sequences. Also, the criterion does not depend on the kind of force field used and therefore it can be used even for very rugged energy surfaces.