The present thesis is dedicated to two topics in Dynamics of Holomorphic maps. The first topic is dynamics of simple parabolic germs at the origin. The second topic is Polynomial-time Computability of Julia sets.\\ Dynamics of simple parabolic germs. Let $F$ be a germ with a simple parabolic fixed point at the origin: $F(w)=w+w^2+O(w^3).$ It is convenient to apply the change of coordinates $z=-1/w$ and consider the germ at infinity $$f(z)=-1/F(-1/z)=z+1+O(z^{-1}).$$ The dynamics of a germ $f$ can be described using Fatou coordinates. Fatou coordinates are analytic solutions of the equation $\phi(f(z))=\phi(z)+1.$ This equation has a formal solution \[\tilde\phi(z)=\text{const}+z+A\log z+\sum_{j=1}^\infty b_jz^{-j},\] where $\sum b_jz^{-j}$ is a divergent power series. Using \'Ecalle's Resurgence Theory we show that $\tilde$ can be interpreted as the asymptotic expansion of the Fatou coordinates at infinity. Moreover, the Fatou coordinates can be obtained from $\tilde \phi$ using Borel-Laplace summation. J.~\'Ecalle and S.~Voronin independently constructed a complete set of invariants of analytic conjugacy classes of germs with a parabolic fixed point. We give a new proof of validity of \'Ecalle's construction. \\ Computability of Julia sets. Informally, a compact subset of the complex plane is called \emph if it can be visualized on a computer screen with an arbitrarily high precision. One of the natural open questions of computational complexity of Julia sets is how large is the class of rational functions (in a sense of Lebesgue measure on the parameter space) whose Julia set can be computed in a polynomial time. The main result of Chapter II is the following: Theorem. Let $f$ be a rational function of degree $d\ge 2$. Assume that for each critical point $c\in J_f$ the $\omega$-limit set $\omega(c)$ does not contain either a critical point or a parabolic periodic point of $f$. Then the Julia set $J_f$ is computable in a polynomial time.

Measures of data quality are important for the evaluation and improvement of survey design and procedures. A detailed investigation of the sources, magnitude and impact of errors is necessary to identify how survey design and procedures may be improved and how resources allocated more efficiently among various aspects of the survey operation. A major part of this thesis is devoted to the overview of statistical theory and methods for measuring the contribution of response variability to the overall error of a survey. A very common practice in surveys is to select groups (clusters) of elements together instead of independent selection of elements. In practice cluster samples tend to produce higher sampling variance for statistics than element samples of the same size. Their frequent use stems from the desirable cost features that they have. Most data collection and sample designs involve some overlapping between interviewer workload and the sampling units (clusters). For those cases, a proportion of the measurement variance, which is due to interviewers, is reflected to some degree in the sampling variance calculations. The prime purpose in this thesis is to determine a variance formula that decomposes the total variance into sampling and measurement variance components for two commonly used data collection and sample designs. Once such a decomposition is obtained, determining an optimum allocation in existence of measurement errors would be possible.

A group G is called an FC-group if the conjugacy class of every element is finite. G is called a minimal non-FC-group if G is not an FC-group, but every proper subgroup of G is an FC-group. The first part of this thesis is on minimal non-FC-groups and their finitary permutational representations. Belyaev proved in 1998 that, every perfect locally finite minimal non-FC-group has non-trivial finitary permutational representation. In Chapter 3, we write the proof of Belyaev in detail. Recall that a group G is called quasi-simple if G is perfect and G/Z(G) is simple. The second part of this thesis is on finite quasi-simple groups and their coprime automorphisms. In Chapter 4, the result of Parker and Quick is written in detail: Namely / if Q is a quasi-simple group and A is a non-trivial group of coprime automorphisms of Q satisfying |Q: C_{Q}(A)| &lt / n then |Q| &lt / n3, that is |Q| is bounded by a function of n.

In this study, a method is proposed for decision making for multiobjective recreational areas, by using multi attribute decision making rules within GIS. The method provides integration of ecological, sociocultural and economic considerations of an ecologically valuable area in a systematic way. The first stage of the methodology includes determination of suitable areas for three usages of forest area / outdoor recreation, timber production and protection needed areas. The second stage comprises decision making analyses. In this stage, two of multi attribute decision rule methods / simple additive weighting method and ideal point method, are used. As a result of these analyses alternative proposal maps for study area and ideal areas for recreation and timber production are acquired. Finally, in the third stage these alternative proposal maps and ideal area are compared with each other and with defined protection zone in the study area. Ideal areas for recreation and timber production are defined by also considering the protection needed areas. The methodology is applied on Eastern Black Sea Region. As a result of the study, ideal areas both for recreational usage and timber production are defined. According to these ideal areas, best fitting alternative map is selected. Finally recreation and timber production proposals are compared with protection needed areas. Results of this study provide a general decision for multipurposed areas in regional scale. The suggested protection zones and suitable areas for recreation and timber production should provide a primary information for forest management studies which must be done in more detailed scales.

Microsatellites are strings of short DNA motifs (≤6 bp) repeated in tandem across genomes of both prokaryotes and eukaryotes. In 20 years, they became popular genetic markers, successfully employed in the field of genetic mapping and gene hunting, as well as to address various biological questions at the individual, family, population and species level. However, evolutionary and demographic inferences from microsatellite polymorphism are hampered by controversy and ambiguity in the mutational processes of microsatellite sequences. Drawing on new data from genome projects, I review in Chapter 1 the concept of a microsatellite life cycle, which hypothesizes that microsatellites follow a life cycle from birth, through expansion, contraction, death and potentially resurrection. To document and understand this integrative concept of evolution, which could help improve current models of microsatellite evolution, there is an implicit need to study the evolution of microsatellites above the species level. A prerequisite of such comparative studies is therefore to find microsatellite loci that are conserved between different species. The near or full completion of many vertebrate genomes and their alignment against one another offer the ultimate approach to find genomic elements conserved over a large evolutionary scale. In Chapter 2, I present a new comprehensive method to find conserved microsatellites in whole genomes. Using the multiple-alignment of the human genome against those of 11 mammalian and five non-mammalian vertebrates, I examine the genomewide conservation of microsatellites, and challenge the general assumption that microsatellites are too labile to be maintained in distant species. In Chapter 3, I present similar results using the alignment of the newly sequenced platypus genome against those of three mammals, the chicken and the lizard, and incorporate these data into the framework created by the 17-genome analysis. This enlarged dataset was ground for attempting to reconstruct a vertebrate phylogeny from the presence/absence of microsatellites in the different genomes. Maximum parsimony analyses resulted in a tree much similar to that of the current view of the vertebrate phylogeny, while Bayesian analyses showed some discrepancies. This work opens a way for novel theoretical developments regarding the inference of ancestral states of microsatellites. In Chapter 4, I show how knowledge on conserved microsatellite sites can help for the development of a set of comparative primers useful across the Mammalia; implementing a similar protocol, nine conserved dinucleotide repeats were genotyped in 20 unrelated individuals of 18 species (nine sister species) encompassing the mammalian phylogeny, including marsupials and monotremes, and four microsatellites were sequenced in 4 individuals per species. My results emphasize conserved microsatellites as a new resource for genetic mapping and population studies. Finally, in Chapter 5, I recount the unexpected extent of structural change among mammalian orthologous microsatellites, including change of complexity, motif replacement and overall length variability. Altogether, these findings provide a comprehensive framework that may help in many areas of research, including molecular ecology, genome mapping, population genetics, and genome and microsatellite evolution.

Thesis (M. Sc.)--Carleton University, 2002. / Includes bibliographical references (p. 117-122). Also available in electronic format on the Internet.

Thesis (M. Sc.)--Carleton University, 2003. / Includes bibliographical references (p. 115-117). Also available in electronic format on the Internet.

Thesis (M.S. in Electrical Engineering)--Naval Postgraduate School, March 2005. / Thesis Advisor(s): John C. McEachen. Includes bibliographical references (p. 51-53). Also available online.

Riesenhuber \& Poggio recently proposed a model of object recognitionin cortex which, beyond integrating general beliefs about the visualsystem in a quantitative framework, made testable predictions aboutvisual processing. In particular, they showed that invariant objectrepresentation could be obtained with a selective pooling mechanismover properly chosen afferents through a {\sc max} operation: Forinstance, at the complex cells level, pooling over a group of simplecells at the same preferred orientation and position in space but atslightly different spatial frequency would provide scale tolerance,while pooling over a group of simple cells at the same preferredorientation and spatial frequency but at slightly different positionin space would provide position tolerance. Indirect support for suchmechanisms in the visual system come from the ability of thearchitecture at the top level to replicate shape tuning as well asshift and size invariance properties of ``view-tuned cells'' (VTUs)found in inferotemporal cortex (IT), the highest area in the ventralvisual stream, thought to be crucial in mediating object recognitionin cortex. There is also now good physiological evidence that a {\scmax} operation is performed at various levels along the ventralstream. However, in the original paper by Riesenhuber \& Poggio,tuning and pooling parameters of model units in early and intermediateareas were only qualitatively inspired by physiological data. Inparticular, many studies have investigated the tuning properties ofsimple and complex cells in primary visual cortex, V1. We show thatunits in the early levels of HMAX can be tuned to produce realisticsimple and complex cell-like tuning, and that the earlier findings onthe invariance properties of model VTUs still hold in this morerealistic version of the model.

Η θεωρία κβαντικού ελέγχου είναι μια νέα αναπτυσσόμενη μαθηματική θεωρία, η οποία ανζητά μεθόδους για τον καθορισμό της συμπεριφοράς των κβαντικών συστημάτων. Ο πρώτος στόχος της παρούσης εργασίας είναι η επισήμανση και η διευκρίνηση των θεωρητικών ερωτημάτων που προκύπτουν από την παρουσίαση της θεωρίας του κβαντικού ελέγχου ως προέκτασης του κλασικού ελέγχου. Ο δεύτερος στόχος της εργασίας είναι η παρουσίαση ορισμένων απλών παραδειγμάτων και μεθόδων κβαντικού ελέγχου, έτσι ώστε ο αναγνώστης να αποκτήσει μιά πρώτη εικόνα σχετικά με τα προβλήματα που ανακύπτουν στην προσπάθεια των ερευνητών να τιθασεύσουν τον μικρόκοσμο. Καθώς ο κβαντικός έλεγχος είναι κοινό ερευνητικό πεδίο για την επιστήμη των ηλεκτρολόγων μηχανικών και των φυσικών, η εργασία αυτή είναι φτιαγμένη έτσι ώστε να παρέχει σε ένα μηχανικό και ένα φυσικό τις γνώσεις που είναι απαραίτητες για τη μελέτη του κβαντικού ελέγχου. Για το σκοπό αυτό το πρώτο κεφάλαιο απευθύνεται κυρίως σε φυσικούς και αποτελεί μια παρουσίαση των βασικών αρχών της κλασικής θεωρίας ελέγχου. Αντίστοιχα, το δεύτερο κεφάλαιο απευθύνεται σε μηχανικούς και παρέχει τις απαραίτητες γνώσεις κβαντομηχανικής. Τέλος, το τρίτο κεφάλαιο αποτελεί τον κύριο κορμό της εργασίας και απευθύνεται σε αναγνώστες που προέρχονται και από τους δύο επιστημονικούς κλάδους. / The theory of quantum control is a new mathematical theory, which investigates methods for the description of the behaviour of quantum systems. The first target of this work is the identification and discussion of the theoretical questions of the quantum control theory as an extension of the classical control theory. The second target is to present some simple examples and methos of of quantum control in order to give to the reader a first insight to the related problems. The work contains three chapters. The first one gives an overview of the principales of the classic control theory. The second chapter provides the basic principals of quantum mechanics. Finally, the third chapter, which is the main part of the work, contains the examples and their discussion.