The qualitative case study on which this thesis is based was designed to investigate the relationship between migration and identity construction of three young people who immigrated as children and adolescents, two of them as refugees, from the former Yugoslavia to Germany and finally to Canada. The autobiographical narrative interviews of the manifold migration stories were mainly analyzed from the point of view of Vygotsky’s Sociocultural Theory, which considers speech and thought in a close relation, to illustrate how identity must be understood as both individual and social in nature, and as a complex narrative action. The socialization processes in all countries of migration were viewed in order to investigate how the previous acculturation affects the cultural identity of the young people today and how it is unfolded in the story. The study reveals that these subjects with threefold migration position themselves between their lifeworlds which enable them not only to say where they belong to or which is their homeland but to answer the simple question “Who am I?” This is revealed by the way of their narration which contains a lot of contradictions. The individuals deal differently with their dynamic identity construction, while one of them seems to suffer under the instability of his identity, and of being different in all his lifeworlds, other subjects however can see advantages related to it. The way how they deal with this dynamics has a crucial influence on their view of their migrations today and consequently on their identity construction as a narrative action.

In the first part of this thesis, we will explore an iterative procedure to determine the detailed asymptotic behaviour of solutions of a certain class of nonlinear vector differential equations which approach a nonlinear sink as time tends to infinity. This procedure is indifferent to resonance in the eigenvalues. Some attention will be given to finding approximations to solutions which are themselves flows. Moreover, we will address the writing of one component in terms of another in the case of a planar system. In the second part of this thesis, we will explore the Michaelis-Menten mechanism of a single enzyme-substrate reaction. The focus is an analysis of the planar reduction in phase space or, equivalently, solutions of the scalar reduction. In particular, we will prove the existence and uniqueness of a slow manifold between the horizontal and vertical isoclines. Also, we will determine the concavity of all solutions in the first quadrant. Moreover, we will establish the asymptotic behaviour of all solutions near the origin, which generally is not given by a Taylor series. Finally, we will determine the asymptotic behaviour of the slow manifold at infinity. Additionally, we will study the planar reduction. In particular, we will find non-trivial bounds on the length of the pre-steady-state period, determine the asymptotic behaviour of solutions as time tends to infinity, and determine bounds on the solutions valid for all time. In the third part of this thesis, we explore the (nonlinear) Lindemann mechanism of unimolecular decay. The analysis will be similar to that for the Michaelis-Menten mechanism with an emphasis on the differences. In the fourth and final part of this thesis, we will present some open problems.

Let (Mn, g) be a Riemannian manifold. Say K ! E ! M is a principal K-bundle with connection A. We define a natural evolution equation for the pair (g,A) combining the Ricci flow for g and the Yang-Mills flow for A which we dub Ricci Yang-Mills flow. We show that these equations are, up to di eomorphism equivalence, the gradient flow equations for a Riemannian functional on M. Associated to this energy functional is an entropy functional which is monotonically increasing in areas close to a developing singularity. This entropy functional is used to prove a non-collapsing theorem for certain solutions to Ricci Yang-Mills flow. We show that these equations, after an appropriate change of gauge, are equivalent to a strictly parabolic system, and hence prove general unique short-time existence of solutions. Furthermore we prove derivative estimates of Bernstein-Shi type. These can be used to find a complete obstruction to long-time existence, as well as to prove a compactness theorem for Ricci Yang Mills flow solutions. Our main result is a fairly general long-time existence and convergence theorem for volume-normalized solutions to Ricci Yang-Mills flow. The limiting pair (g,A) satisfies equations coupling the Einstein and Yang-Mills conditions on g and A respectively. Roughly these conditions are that the associated curvature FA must be large, and satisfy a certain “stability” condition determined by a quadratic action of FA on symmetric two-tensors.

Lienard Equations serve as the elegant models for oscillating circuits. Motivated by this fact, this thesis addresses the stability property of a class of delayed Lienard equations. It shows the existence of the Hopf bifurcation around the steady state. It has both practical and theoretical importance in determining the criticality of the Hopf bifurcation. For such purpose, center manifold analysis on the bifurcation line is required. This thesis uses operator differential equation formulation to reduce the infinite dimensional delayed Lienard equation onto a two-dimensional manifold on the critical bifurcation line. Based on the reduced two-dimensional system, the so called Poincare-Lyapunov constant is analytically determined, which determines the criticality of the Hopf bifurcation. Numerics based on a Matlab bifurcation toolbox (DDE-Biftool) and Matlab solver (DDE-23) are given to compare with the theoretical calculation. Two examples are given to illustrate the method.

The explosive growth of digital data collection and processing demands a new approach to the historical engineering methods of data correlation and model creation. A new prediction methodology based on high dimensional data has been developed. Since most high dimensional data resides on a low dimensional manifold, the new prediction methodology is one of dimensional reduction with embedding into a diffusion space that allows optimal distribution along the manifold. The resulting data manifold space is then used to produce a probability density function which uses spatial weighting to influence predictions i.e. data nearer the query have greater importance than data further away. The methodology also allows data of differing phenomenology e.g. color, shape, temperature, etc to be handled by regression or clustering classification. The new methodology is first developed, validated, then applied to common engineering situations, such as critical heat flux prediction and shuttle pitch angle determination. A number of illustrative examples are given with a significant focus placed on the objective identification of two-phase flow regimes. It is shown that the new methodology is robust through accurate predictions with even a small number of data points in the diffusion space as well as flexible in the ability to handle a wide range of engineering problems.

To handle broken 3D models can be a very time consuming problem. Several methods aiming for automatic mesh repair have been presented in the recent years. This thesis gives an extensive evaluation of automatic mesh repair algorithms, presents a mesh repair pipeline and describes an implemented automatic mesh repair algorithm. The presented pipeline for automatic mesh repair includes three main steps: octree generation, surface reconstruction and ray casting. Ray casting is for removal of hidden objects. The pipeline also includes a pre processing step for removal of intersecting triangles and a post processing step for error detection. The implemented algorithm presented in this thesis is a volumetric method for mesh repair. It generates an octree in which data from the input model is saved. Before creation of the output, the octree data will be patched to remove inconsistencies. The surface reconstruction is done with a method called Manifold Dual Contouring. First new vertices are created from the information saved in the octree. Then there is a possibility to cluster vertices together for decimation of the output. Thanks to a special Manifold criterion, the output is guaranteedto be manifold. Furthermore the output will have sharp and clear edges and corners thanks to the use of Singular Value Decomposition during determination of the positions of the new vertices.

Šio magistro darbo tikslas yra ištirti daugdarų dimensijos atpažinimo daugiamačiuose duomenyse metodus. Darbe buvo išnagrinėti 3 lokalūs dimensijos vertinimo metodai, koreliacinis, artimiausių kaimynų ir didžiausio tikėtinumo, ir su įvairių matmenų duomenimis atlikti tyrimai. Atstumai tarp kaimyninių taškų buvo skaičiuojami dviem būdais: Euklido ir geodeziniu. Atlikus tyrimus buvo padarytos tokios išvados: • Maksimalaus tikėtinumo vertinimo metodas tiksliausiai vertina vidinį matmenų skaičių dirbtiniams duomenims, taip pat realiems duomenims, kai tarp kaimynų skaičiuojami geodeziniai atstumai. • Koreliacinis vertinimo metodas dirbtiniams duomenims, ir realiems duomenims, kai tarp kaimynų skaičiuojami geodeziniai atstumai, vidinį matmenų skaičių nustato gerai, kai tarp kaimynų skaičiuojami Euklido atstumai, vidinį matmenų skaičių nustato labai blogai. • Koreliacinis metodas nėra geras, nes yra sunku parinkti tinkamus parametrus – spindulius. • Artimiausių kaimynų vertinimo metodas vidinį matmenų skaičių nustato gerai tik realiems duomenims, kai tarp kaimynų skaičiuojami geodeziniai atstumai, visais kitais nagrinėjamais atvejais – blogai. • Artimiausių kaimynų metodas vidinį matmenų skaičių nustato blogiausiai iš visų trijų nagrinėjamų metodų. / The objective of this master thesis is to explore different techniques of dataset intrinsic dimensionality estimation. The purpose was to examine three local estimators for intrinsic dimensionality: the correlation dimension estimator, the nearest neighbor dimension estimator, and the maximum likelihood estimator. Data with various intrinsic dimensionalities were examined. The distances between neighboring points were calculated using two metrics: Euclidean and Geodesic. The investigation revealed the following conclusions: • The results by maximum likelihood estimation method were closest to the real intrinsic dimensionality of an artificial data, as well as real data, in cases when distances between neighbors were calculated using Geodesic metrics. • The correlation dimension estimator showed good results for artificial and real data when distances between neighbors were estimated using Geodesic metrics. When distances between neighbors were calculated by Euclidean metrics, the intrinsic dimension estimation results were very bad. • Correlation dimension estimator is not a good method because it is difficult to select proper settings – radiuses. • The nearest neighbor estimation method works well only when determining intrinsic dimension of real data when distances between neighbors are estimated using Geodesic metrics. In all other cases it is almost useless. • The nearest neighbor method is the worst method amongst all.

Palaeoecological and sedimentological analysis has been applied in the study of Lower Carboniferous Waulsortian 'reefs' exposed in the Manifold Valley, North Staffordshire and in the Meuse Vallley in southern Belgium. Because Waulsortian 'reefs' have similar faunal, lithological and palaeogeographical characteristics in all of their occurrences it is argued that conclusions drawn from the Manifold and Meuse Valleys are applicable to the facies as a whole. Evidence is presented to show that lithological facies previously recognised within the Belgian Waulsortian can also be recognised elsewhere, and that changing sedimentation rates can explain many of their characteristic differences. Faunal and seimentological evidence indicates that the rate of sedimentation increased as the mounds developed. It is argued that the mound sediment was produced in situ and faunal data suggests that the surface of the mounds was firm. Early submarine lithification is thought to have been an important process in producing firm substrates and in maintaining steep depositional slopes. Fabrics and lithological components suggestive of early lithification have been recognised. A general model for Waulsortian development, based on conclusions drawn in this thesis, is presented.

Thesis (M.S.)--Rochester Institute of Technology, 1993. / Typescript. Includes bibliographical references (leaves 93-96).

Many high-dimensional time-varying signals can be modeled as a sequence of noisy nonlinear observations of a low-dimensional dynamical process. Given high-dimensional observations and a distribution describing the dynamical process, we present a computationally inexpensive approximate algorithm for estimating the inverse of this mapping. Once this mapping is learned, we can invert it to construct a generative model for the signals. Our algorithm can be thought of as learning a manifold of images by taking into account the dynamics underlying the low-dimensional representation of these images. It also serves as a nonlinear system identification procedure that estimates the inverse of the observation function in nonlinear dynamic system. Our algorithm reduces to a generalized eigenvalue problem, so it does not suffer from the computational or local minimum issues traditionally associated with nonlinear system identification, allowing us to apply it to the problem of learning generative models for video sequences.