In this thesis, we study the group of base-point preserving homotopy classes of homotopy self-equivalences of a four-manifold. Based on the approach of Hambleton and Kreck, an explicit description of this group is obtained when the fundamental group of the manifold is either a free group or a two-dimensional Poincare duality group. As a byproduct, a classification of such four-manifolds up to s-cobordism is obtained by using the modified surgery theory of Kreck. / Thesis / Doctor of Philosophy (PhD)

We consider the problem of narrow-band signal detection in a passive sonar environment. The collected signals are passed to a fast Fourier Transform (FFT) delay-sum beamformer. In classical signal detection, the output of the FFT spectrum analyser in each frequency bin is the signal power spectrum which is used as the signal feature for detection. The observed signal power is compared to a locally estimated mean noise power and a log likelihood ratio test (LLRT) can then be established. In this thesis, we propose the use of the power spectral density (PSD) matrix of the spectrum analyser output as the feature for detection due to the additional cross-correlation information contained in such matrices. However, PSD matrices are structurally constrained and therefore form a manifold in the signal space. Thus, to find the distance between two matrices, the measurement must be carried out using Riemannian distance (RD) along the tangent of the manifold, instead of using the common Euclidean distance (ED). In this thesis, we develop methods for measuring the Frechet mean of noise PSD matrices using the RD and weighted RD. Further, we develop an optimum weighting matrix for use in signal detection by RD so as to further enhance the detection performance. These concepts and properties are then used to develop a decision rule for the detection of narrow-band sonar signals using PSD matrices. The results yielded by the new detection method are very encouraging. / Thesis / Master of Applied Science (MASc)

Flow in the Moderator of a CANDU reactor can be very complex due to the interplay of convective and buoyant effects. Experiments have been performed to measure temperature and velocity fields for these kind of flows, although concerns still exist. As a result a Moderator test facility has been built in order to validate CFD models for future predictions and safety analysis. To properly validate this experiment an accurate set of inlet flow conditions must be established in order to ensure a fair comparison. A series of flow conditions indicative of the header assemblies which feed flow into the moderator test facility have been investigated through experimentation, empirical evaluation and numerical simulation. They include flow through curved tubes, turbulent free jets and flow through dividing manifolds. The goal of the present study is to establish the modelling approach to predict the flow distribution inside the manifold and velocity field out of the J-nozzles. A variety of RANS based turbulence models and computational meshes were employed in the numerical study. The turbulence model that was found to perform best was the realizable k- model. It was also found that the velocity field of the J-nozzles is constant between Reynolds numbers of 6800-9300. These Reynolds numbers are indicative of those expected out of the header assemblies. / Thesis / Master of Applied Science (MASc)

This thesis presents an algorithm for producing 4–manifold triangulations with boundary an arbitrary orientable, closed, triangulated 3–manifold. The research is an extension of Costantino and Thurston’s work on determining upper bounds on the number of 4–dimensional simplices necessary to construct such a triangulation. Our first step in this bordism construction is the geometric partitioning of an initial 3–manifold M using smooth singularity theory. This partition provides handle attachment sites on the 4–manifold Mx[0,1] and the ensuing handle attachments eliminate one of the boundary components of Mx[0,1], yielding a 4-manifold with boundary exactly M. We first present the construction in the smooth case before extending the smooth singularity theory to triangulated 3–manifolds. / Graduate

The aim of this diploma thesis is the design and tuning of the exhaust manifold and muffler for the Formula Student car. The single cylinder atmospheric spark ignition engine Husaberg FE 570 is used as a powertrain unit. The exhaust system is designed according to the Formula Student rules. To design the exhaust system has been used as theoretical knowledge as well as software Lotus Engine Simulation.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18048号 / 理博第3926号 / 新制||理||1566(附属図書館) / 30906 / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 森 重文, 教授 玉川 安騎男, 教授 向井 茂 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

The coding and feedback inaccuracies of the channel state information (CSI) in limited feedback multiple-input multiple-output (MIMO) wireless systems can severely impact the achievable data rate and reliability. The CSI is mathematically represented as a Grassmann manifold or manifold of unitary matrices. These are non-Euclidean spaces with special constraints that makes efficient and high fidelity coding especially challenging. In addition, the CSI inaccuracies may occur due to digital representation, time variation, and delayed feedback of the CSI. To overcome these inaccuracies, the manifold structure of the CSI can be exploited. The objective of this dissertation is to develop a new signal processing techniques on the manifolds to harvest the benefits of MIMO wireless systems. First, this dissertation presents the Kerdock codebook design to represent the CSI on the Grassmann manifold. The CSI inaccuracy due to digital representation is addressed by the finite alphabet structure of the Kerdock codebook. In addition, systematic codebook construction is identified which reduces the resource requirement in MIMO wireless systems. Distance properties on the Grassmann manifold are derived showing the applicability of the Kerdock codebook to beam-forming and spatial multiplexing systems. Next, manifold-constrained algorithms to predict and encode the CSI with high fidelity are presented. Two prominent manifolds are considered; the Grassmann manifold and the manifold of unitary matrices. The Grassmann manifold is a class of manifold used to represent the CSI in MIMO wireless systems using specific transmission strategies. The manifold of unitary matrices appears as a collection of all spatial information available in the MIMO wireless systems independent of specific transmission strategies. On these manifolds, signal processing building blocks such as differencing and prediction are derived. Using the proposed signal processing tools on the manifold, this dissertation addresses the CSI coding accuracy, tracking of the CSI under time variation, and compensation techniques for delayed CSI feedback. Applications of the proposed algorithms in single-user and multiuser systems show that most of the spatial benefits of MIMO wireless systems can be harvested. / text

The spectral zeta function, introduced by Minakshisundaram and Pleijel in [36] and denoted by ζg(s), encodes important spectral information for the Laplacian on Riemannian manifolds. For instance, the important notions of the determinant of the Laplacian and Casimir energy are defined via the spectral zeta function. On homogeneous manifolds, it is known that the spectral zeta function is critical with respect to conformal metric perturbations, (see e.g Richardson ([47]) and Okikiolu ([41])). In this thesis, we compute a second variation formula of ζg(s) on closed homogeneous Riemannian manifolds under conformal metric perturbations. It is well known that the quadratic form corresponding to this second variation is given by a certain pseudodifferential operator that depends meromorphically on s. The symbol of this operator was analysed by Okikiolu in ([42]). We analyse it in more detail on homogeneous spaces, in particular on the spheres Sn. The case n = 3 is treated in great detail. In order to describe the second variation we introduce a certain distributional integral kernel, analyse its meromorphic properties and the pole structure. The Casimir energy defined as the finite part of ζg(-½) on the n-sphere and other points of ζg(s) are used to illustrate our results. The techniques employed are heat kernel asymptotics on Riemannian manifolds, the associated meromorphic continuation of the zeta function, harmonic analysis on spheres, and asymptotic analysis.

We propose a novel framework for motion planning and control that is based on a manifold encoding of the desired solution set. We present an alternate, model-free, approach to path planning, replanning and control. Our approach is founded on the idea of encoding the set of possible trajectories as a skill manifold, which can be learnt from data such as from demonstration. We describe the manifold representation of skills, a technique for learning from data and a method for generating trajectories as geodesics on such manifolds. We extend the trajectory generation method to handle dynamic obstacles and constraints. We show how a state metric naturally arises from the manifold encoding and how this can be used for reactive control in an on-line manner. Our framework tightly integrates learning, planning and control in a computationally efficient representation, suitable for realistic humanoid robotic tasks that are defined by skill specifications involving high-dimensional nonlinear dynamics, kinodynamic constraints and non-trivial cost functions, in an optimal control setting. Although, in principle, such problems can be handled by well understood analytical methods, it is often difficult and expensive to formulate models that enable the analytical approach. We test our framework with various types of robotic systems – ranging from a 3-link arm to a small humanoid robot – and show that the manifold encoding gives significant improvements in performance without loss of accuracy. Furthermore, we evaluate the framework against a state-of-the-art imitation learning method. We show that our approach, by learning manifolds of robotic skills, allows for efficient planning and replanning in changing environments, and for robust and online reactive control.

The problem of constructing data-based, predictive, reduced models for the Kuramoto–Sivashinsky equation is considered, under circumstances where one has observation data only for a small subset of the dynamical variables. Accurate prediction is achieved by developing a discrete-time stochastic reduced system, based on a NARMAX (Nonlinear Autoregressive Moving Average with eXogenous input) representation. The practical issue, with the NARMAX representation as with any other, is to identify an efficient structure, i.e., one with a small number of terms and coefficients. This is accomplished here by estimating coefficients for an approximate inertial form. The broader significance of the results is discussed.