Thesis (M.S.)--Brigham Young University. Dept. of Mathematics, 2005. / Includes bibliographical references (p. 39-40).

Thesis (M.S.)--Duquesne University, 2005. / Title from document title page. Abstract included in electronic submission form. Includes bibliographical references (p. 21) and index.

Thesis (MA)--University of Stellenbosch, 2005. / Bibliography. Also available via the Internet.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Washington, 2000. / Vita. Includes bibliographical references (p. 142-150).

Στην παρούσα Διπλωματική Εργασία θα ασχοληθούμε με το πασίγνωστο πρόβλημα της Παραγοντοποίησης Ακεραίων. Η προσέγγιση μας είναι από τη μεριά της Επιστήμης των Υπολογιστών και της Υπολογιστικής Πολυπλοκότητας. Προσπαθούμε να κατανοήσουμε γιατί η Παραγοντοποίηση Ακεραίων θεωρείται ένα υπολογιστικά δύσκολο πρόβλημα και να δούμε τις πρακτικές εφαρμογές και συνέπειες αυτής της θεώρησης. / In the present Diploma Thesis we are going to deal with the very well known problem of Integer-Factoring. Our approach is from the side of Computer Science and Computational Complexity. We are trying to understand why Integer-Factoring is widely considered as a hard problem to solve and see the practical applications of this consideration.

Various ecological parameters, including soil pH, calcium, and habitat complexity have been suggested in the literature as having influence on land snail abundance and diversity. I compared relationships between 15 ecological parameters and snail abundance and diversity. 5,393 snails of 72 species were collected from 60 sites in 2007. Habitat observations were recorded in the field and soil core samples taken at each site and later analyzed for soil moisture, organic matter, cation exchange capacity, pH, calcium, magnesium, zinc, potassium, phosphorus, sulfur, boron, manganese, iron and copper. Statistical analyses were run using these soil factors plus a habitat complexity index (from combined values assigned to different levels of vegetation, topography and exposed rock), for a total of 15 parameters. To reduce the number of parameters and arrive at a more biologically meaningful model, Bayesian Information Criteria analysis (BIC) was run for abundance and diversity. The resulting best-fitted BIC model for abundance contained 3 parameters (pH, S, and habitat complexity) (R2 = 0.47), all of which were positively associated with abundance in a multiple regression analysis. For diversity, the best-fitted BIC model also contained 3 parameters (Ca, Fe, and habitat complexity) (R2 = 0.54). Ca and habitat complexity showed a positive association in the multiple regression analysis, but Fe was inversely associated with diversity, suggesting Fe could potentially act as an ecological limiting factor to it. These results suggest that land snail abundance and diversity are best treated separately in analyses, as they are influenced by different variables, with the exception of habitat complexity, which is suggested to have a positive association with both abundance and diversity. The regression model equations have potential value in that they can be used to predict snail abundance and diversity in areas that have not been assessed.

Complex System Sciences, as a field of research, has emerged in the past decade. It studies how parts of a system give rise to the collective behaviours of the system and how the system interacts with its environment. It approaches the question of how life on earth could have appeared by searching for inherent structures in living systems and trying to define common patterns within these structures. Complex Systems are also often described as systems where the whole is more complex than the mere sum of its parts, and these systems are also considered to be at the point of maximum computational ability, maximum fitness and maximum evolvability. Several scientific models have simulated Complex Adaptive Systems. These try to model the emergence of complexity within computer-simulated environments inhabited by artificially evolving organisms. My objective in this thesis is to study the application of Complex Systems and Complex Adaptive Systems to Interactive Art and to test how one could construct interactive systems that can create dynamic and open-ended image structures that increase in complexity as users interact with them. Ideally, these interactive artworks should become comparable to Complex Adaptive Systems or even become Complex Systems themselves by satisfying some of the key properties of such systems.

In "decomposition/reconstruction" strategy, we can solve a complex problem by 1) decomposing the problem into simpler sub-problems, 2) solving sub-problems with simpler systems (sub-systems) and 3) combining the results of sub-systems to solve the original problem. In a classification task we may have "label complexity" which is due to high number of possible classes, "function complexity" which means the existence of complex input-output relationship, and "input complexity" which is due to requirement of a huge feature set to represent patterns. Error Correcting Output Code (ECOC) is a technique to reduce the label complexity in which a multi-class problem will be decomposed into a set of binary sub-problems, based oil the sequence of "0"s and "1"s of the columns of a decomposition (code) matrix. Then a given pattern can be assigned to the class having minimum distance to the results of sub-problems. The lack of knowledge about the relationship between distance measurement and class score (like posterior probabilities) has caused some essential shortcomings to answering questions about "source of effectiveness", "error analysis", " code selecting ", and " alternative reconstruction methods" in previous works. Proposing a theoretical framework in this thesis to specify this relationship, our main contributions in this subject are to: 1) explain the theoretical reasons for code selection conditions 2) suggest new conditions for code generation (equidistance code)which minimise reconstruction error and address a search technique for code selection 3) provide an analysis to show the effect of different kinds of error on final performance 4) suggest a novel combining method to reduce the effect of code word selection in non-optimum codes 5) suggest novel reconstruction frameworks to combine the component outputs. Some experiments on artificial and real benchmarks demonstrate significant improvement achieved in multi-class problems when simple feed forward neural networks are arranged based on suggested framework To solve the problem of function complexity we considered AdaBoost, as a technique which can be fused with ECOC to overcome its shortcoming for binary problems. And to handle the problems of huge feature sets, we have suggested a multi-net structure with local back propagation. To demonstrate these improvements on realistic problems a face recognition application is considered. Key words: decomposition/ reconstruction, reconstruction error, error correcting output codes, bias-variance decomposition.

Comparison of Top trees implementations - Abstract Jiří Setnička Definition and description of Top trees and introduction of problems solvable by them including problem of edge 2-connectivity. Definition and description of Topology trees used as one of the drivers for Top trees. After the initial descriptions the two top trees implementations are introduced: one based on self adjusting trees, second based on topology trees. Comparison of these implementations is done by two experiments. Measurements are discussed in conclusion - results corresponds with initial estimates but with different multiplicative constant than expected. 1