Browsing by Subject "Topology"
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Item 3D face recognition with wireless transportation(2009-05-15) Zou, LeIn this dissertation, we focus on two related parts of a 3D face recognition system with wireless transportation. In the ?rst part, the core components of the system, namely, the feature extraction and classi?cation component, are introduced. In the feature extraction component, range images are taken as inputs and processed in order to extract features. The classi?cation component uses the extracted features as inputs and makes classi?cation decisions based on trained classi?ers. In the second part, we consider the wireless transportation problem of range images, which are captured by scattered sensor nodes from target objects and are forwarded to the core components (i.e., feature extraction and classi?cation components) of the face recognition system. Contrary to the conventional de?nition of being a transducer, a sensor node can be a person, a vehicle, etc. The wireless transportation component not only brings ?exibility to the system but also makes the ?proactive? face recognition possible. For the feature extraction component, we ?rst introduce the 3D Morphable Model. Then a 3D feature extraction algorithm based on the 3D Morphable Model is presented. The algorithm is insensitive to facial expression. Experimental results show that it can accurately extract features. Following that, we discuss the generic face warping algorithm that can quickly extract features with high accuracy. The proposed algorithm is robust to holes, facial expressions and hair. Furthermore, our experimental results show that the generated features can highly di?erentiate facial images. For the classi?cation component, a classi?er based on Mahalanobis distance is introduced. Based on the classi?er, recognition performances of the extracted features are given. The classi?cation results demonstrate the advantage of the features from the generic face warping algorithm. For the wireless transportation of the captured images, we consider the location-based wireless sensor networks (WSN). In order to achieve e?cient routing perfor?mance, a set of distributed stateless routing protocols (PAGER) are proposed for wireless sensor networks. The loop-free and delivery-guaranty properties of the static version (PAGER-S) are proved. Then the performance of PAGER protocols are compared with other well-known routing schemes using network simulator 2 (NS2). Simulation results demonstrate the advantages of PAGER.Item A topological method of synthesis for a class of biquadratic input impedance functions(Texas Tech University, 1965-08) Beene, Reagan HNot availableItem A Topological Theory of Weaving and Its Applications in Computer Graphics(2013-07-24) Hu, ShiyuRecent advances in the computer graphics of woven images on surfaces in 3-space motivate the development of weavings for arbitrary genus surfaces. We present herein a general framework for weaving structures on general surfaces in 3-space, and through it, we demonstrate how weavings on such surfaces are inducible from connected graph imbeddings on the same surfaces. The necessary and sufficient conditions to identify the inducible weavings in our framework are also given. For low genus surfaces, like plane and torus, we extend our framework to the weavings which are inducible from disconnected imbedded graphs. In particular, we show all weavings on a plane are inducible in our framework, including most Celtic Knots. Moreover, we study different weaving structures on general surfaces in 3-space based on our framework. We show that any weaving inducible in our framework can be converted into an alternating weaving by appropriately changing the strand orders at some crossings. By applying a topological surgery operation, called doubling operation, we can refine a weaving or convert certain non-twillable weavings into twillable weavings on the same surfaces. Interestingly, two important subdivision algorithms on graphs imbeddings, the Catmull-Clark and Doo-Sabin algorithms, correspond nicely to our doubling operation on induced weavings. Another technique we used in studying weaving structures is repetitive patterns. A weaving that can be converted into a twillable weaving by our doubling operation has a highly-symmetric structure, which consists of only two repetitive patterns. An extension of the symmetric structure leads to Quad-Pattern Coverable meshes, which can be seamlessly covered with only one periodic pattern. Both of these two topological structures can be represented with simple Permutation Voltage graphs. A considerable advantage of our model is that it is topological. This permits the graphic designer to superimpose strand colors and geometric attributes ? distances, angles, and curvatures ? that conform to manufacturing or artistic criteria. We also give a software example for plane weaving construction. A benefit of the software is that it supports plane weaving reconstructions from an image of a plane weaving, which could be useful for recording and modifying existing weavings in real life.Item Advanced compulsator topologies and technologies(2002-05) Walls, William Alan; Driga, Mricea D.Increasing the compactness of compensated pulsed alternators (compulsators) has been an ongoing effort at since the mid-1980’s, when the U. S. Army interest in electric armaments began to emerge in a significant way. Much progress has been made from the early proof of concept machine built at UTCEM in the late 1970’s after its invention by Weldon, Driga, and Woodson. Today, the compulsator is the best approach for achieving compact energy storage and pulsed power generation for multi-MJ, multi-GW applications requiring voltages of up to 20 kV and discharge durations between 1 and 10 milliseconds. Electromagnetic railguns, coil launchers, and directed energy systems requiring high-power, high-energy pulsed-power in compact form are ideal candidate loads for compulsators. Since the initial validation of compulsator theory in the late 1970’s, a transition from iron-core to air-core magnetic circuits and the associated incorporation of composite materials for the rotor and self-excitation has provided substantial increases in both stored energy density and power density. While the advancement has been significant, further gains in compactness are possible by exploiting continued innovation in the topology of the machine, the mode in which it operates, and by developing new component technologies specifically for compulsator application. In addition, the use of this type of machine in very high voltage (>50 kV) pulsed power application, a concept not previously explored, is considered through the novel integration of resonant and cascaded transformer arrangements to boost the output voltage. In contributing to the continued compulsator performance improvement, this research effort has performed an in depth study of machine topologies and identified a new topology, the flywheel-compulsator. When combined with improvements in materials and switching technologies, this new machine configuration can improve energy and power density by factors of three and five, respectively, compared to the current state of the art. To allow rapid sizing of compulsator systems, a scaling algorithm was developed, validated against demonstrated machines and advanced designs, and used to design systems for advanced applications. Reduced to a set of linked spreadsheets, the scaling algorithms were also used to identify compulsator component technologies areas where improvements will provide the greatest overall performance impact. Another area of significant contribution to compulsator technology embodied in this research is the application of these machines to very high voltage systems. Two general concepts were conceived and developed. The first combines the energy storage and pulsed power generation of the compulsator with voltage increasing circuits, including both resonant and cascaded transformers. For compact high voltage systems, the concept of generating the high voltage directly within the compulsator was evaluated, and a high voltage compulsator using a helical winding was optimized for a specific set of requirements.Item Comparable topologies and extension topologies(Texas Tech University, 1965-05) Anderson, James AlanNot availableItem Course summary of geometry and topology(2010-08) Craig, Tara Theresa; Armendáriz, Efraim P.; Daniels, Mark L.The foundation of Luecke’s course M: 396 Geometry and Topology is that collaboration amongst mathematicians and biologists caused tremendous gains in DNA research. The field of topology has led to significant strides in understanding of the topological properties of the genetic molecule DNA. Through the integration of biological phenomena and knowledge of topology and Euclidean geometry, biologists can describe and quantize enzyme mechanisms and therefore determine enzyme mechanisms causing the changes. Understanding mathematical applications in contexts outside of mathematics on any level helps to explain why mathematics is a core content area in primary and secondary education. Requiring secondary educators to take such a course could result in mathematics taught with real world application on the secondary level as well as on the graduate level, as shown in Luecke’s course.Item Creating and utilizing symbolic representations of spatial knowledge using mobile robots(2008-08) Beeson, Patrick Foil, 1977-; Kuipers, BenjaminA map is a description of an environment allowing an agent--a human, or in our case a mobile robot--to plan and perform effective actions. From a single location, an agent’s sensors can not observe the whole structure of a complex, large environment. For this reason, the agent must build a map from observations gathered over time and space. We distinguish between large-scale space, with spatial structure larger than the agent’s sensory horizon, and small-scale space, with structure within the sensory horizon. We propose a factored approach to mobile robot map-building that handles qualitatively different types of uncertainty by combining the strengths of topological and metrical approaches. Our framework is based on a computational model of the human cognitive map; thus it allows robust navigation and communication within several different spatial ontologies. Our approach factors the mapping problem into natural sub-goals: building a metrical representation for local small-scale spaces; finding a topological map that represents the qualitative structure of large-scale space; and (when necessary) constructing a metrical representation for large-scale space using the skeleton provided by the topological map. The core contributions of this thesis are a formal description of the Hybrid Spatial Semantic Hierarchy (HSSH), a framework for both small-scale and large-scale representations of space, and an implementation of the HSSH that allows a robot to ground the largescale concepts of place and path in a metrical model of the local surround. Given metrical models of the robot’s local surround, we argue that places at decision points in the world can be grounded by the use of a primitive called a gateway. Gateways separate different regions in space and have a natural description at intersections and in doorways. We provide an algorithmic definition of gateways, a theory of how they contribute to the description of paths and places, and practical uses of gateways in spatial mapping and learning.Item Developing a qualitative geometry from the conceptions of young children(2010-05) Greenstein, Steven Baron; Stroup, Walter M.; Empson, Susan B.; Carmona, Guadalupe; Petrosino, Anthony; Starbird, MichaelMore than half a century ago, Piaget concluded from an investigation of children’s representational thinking about the nature of space that the development of children’s representational thought is topological before it is Euclidean. This conclusion, commonly referred to as the “topological primacy thesis,” has essentially been rejected. By giving emphasis to the ideas that develop rather than the order in which they develop, this work set out to develop a new form of non-metric geometry from young children’s early and intuitive topological, or at least non-metric, ideas. I conducted an eighteen-week teaching experiment with two children, ages six and seven. I developed a new dynamic geometry environment called Configure that I used in tandem with clinical interviews in each of the episodes of the experiment to elicit these children’s non-metric conceptions and subsequently support their development. I found that these children developed significant and authentic forms of geometric reasoning. It is these findings, which I refer to as qualitative geometry, that have implications for the teaching of geometry and for research into students’ mathematical reasoning.Item Exotic smoothings via large R⁴’s in Stein surfaces(2015-12) Bennett, Julia C.; Gompf, Robert E., 1957-; Etnyre, John; Gordon, Cameron; Luecke, John; Reid, AlanWe study the relationship between exotic R⁴'s and Stein surfaces as it applies to smoothing theory on more general open 4–manifolds. In particular, we construct the first known examples of large exotic R⁴'s that embed in Stein surfaces. This relies on an extension of Casson's Embedding Theorem for locating Casson handles in closed 4–manifolds. Under sufficiently nice conditions, we show that using these R⁴'s as end-summands produces uncountably many diffeomorphism types while maintaining independent control over the genus-rank function and the Taylor invariant. Additionally, we prove that a family of knots known to be topologically slice but not smoothly slice is rationally slice, realizing a combination of slice properties that seems to have been previously unknown to exist.Item Explorations in algebra and topology(2016-05) Gal, Itamar; Hadani, Ronny; Allcock, Daniel; Blumberg, Andrew; Vaaler, JeffreyThree independent investigations are expounded, two in the domain of algebra and one in the domain of topology. We first consider algebraic extensions generated by elements of bounded degree and consider the question of whether or not the finite sub-extensions of such fields can be bounded. We give partial results which will hopefully lead to a full classification in the future. These results are fundamentally group theoretic but have applications to number theory. Next we develop the notational system originated by Conway and Sloane for working with quadratic forms over the 2-adic integers and prove its correctness. This provides a proof which was missing from the literature. Finally we study distributions of persistent homology barcodes obtained by sampling finite point sets from metric measure spaces. The main result here is the derivation of robust statistics for topological data analysis.Item Integrating topology into the standard high school geometry curriculum(2012-08) Kiker, William George; Odell, E. (Edward); Daniels, MarkThis report conveys some of the modern investigations surrounding the use of topology in a contextual setting. Topics discussed include applications of topology relating to the modeling of biological structures and common objects like sunshades, elementary knot theory, and the connection between the fields of topology and algebra. A brief overview and discussion of the incorporation of elementary topology into the standard Geometry curriculum of secondary schools is also examined.Item Item Network-on-chip architectures for scalability and service guarantees(2011-08) Grot, Boris; Keckler, Stephen W.; Burger, Douglas C.; Mutlu, Onur; Witchel, Emmett; Zhang, YinRapidly increasing transistor densities have led to the emergence of richly-integrated substrates in the form of chip multiprocessors and systems-on-a-chip. These devices integrate a variety of discrete resources, such as processing cores and cache memories, on a single die with the degree of integration growing in accordance with Moore's law. In this dissertation, we address challenges of scalability and quality-of-service (QOS) in network architectures of highly-integrated chips. The proposed techniques address the principal sources of inefficiency in networks-on-chip (NOCs) in the form of performance, area, and energy overheads. We also present a comprehensive network architecture capable of interconnecting over a thousand discrete resources with high efficiency and strong guarantees. We first show that mesh networks, commonly employed in existing chips, fall significantly short of achieving their performance potential due to transient congestion effects that diminish network performance. Adaptive routing has the potential to improve performance through better load distribution. However, we find that existing approaches are myopic in that they only consider local congestion indicators and fail to take global network state into account. Our approach, called Regional Congestion Awareness (RCA), improves network visibility in adaptive routers via a light-weight mechanism for propagating and integrating congestion information. By leveraging both local and non-local congestion indicators, RCA improves network load balance and boosts throughput. Under a set of parallel workloads running on a 49-node substrate, RCA reduces on-chip network latency by 16%, on average, compared to a locally-adaptive router. Next, we target NOC latency and energy efficiency through a novel point-to-multipoint topology. Ring and mesh networks, favored in existing on-chip interconnects, often require packets to go through a number of intermediate routers between source and destination nodes, resulting in significant latency and energy overheads. Topologies that improve connectivity, such as fat tree and flattened butterfly, eliminate much of the router overhead, but require non-minimal channel lengths or large channel count, reducing energy-efficiency and/or performance as a result. We propose a new topology, called Multidrop Express Channels (MECS), that augments minimally-routed express channels with multi-drop capability. The resulting richly-connected NOC enjoys a low hop count with favorable delay and energy characteristics, while improving wire utilization over prior proposals. Applications such as virtualized servers-on-a-chip and real-time systems require chip-level quality-of-service (QOS) support to provide fairness, service differentiation, and guarantees. Existing network QOS approaches suffer from considerable performance and area overheads that limit their usefulness in a resource-limited on-die network. In this dissertation, we propose a new QOS scheme called Preemptive Virtual Clock (PVC). PVC uses a preemptive approach to provide hard guarantees and strong performance isolation while dramatically reducing queuing requirements that burden prior proposals. Finally, we introduce a comprehensive network architecture that overcomes the bottlenecks of earlier designs with respect to area, energy, and QOS in future highly-integrated chips. The proposed NOC uses a topology-centric QOS approach that restricts the extent of hardware QOS support to a fraction of the network without compromising guarantees. In doing so, network area and energy efficiency are significantly improved. Further improvements are derived through a novel flow-control mechanism, along with switch- and link-level optimizations. In concert, these techniques yield a network capable of interconnecting over a thousand terminals on a die while consuming 47% less area and 26% less power than a state-of-the-art QOS-enabled NOC. The mechanisms proposed in this dissertation are synergistic and enable efficient, high-performance interconnects for future chips integrating hundreds or thousands of on-die resources. They address deficiencies in routing, topologies, and flow control of existing architectures with respect to area, energy, and performance scalability. They also serve as a building block for cost-effective advanced services, such as QOS guarantees at the die level.Item Non-locally convex linear topological spaces(Texas Tech University, 1966-08) Parker, Horace NealNot availableItem On some residual and locally virtual properties of groups(2010-05) Katerman, Eric Michael; Reid, Alan W.; Gordon, Cameron; Luecke, John; Allcock, Daniel; G�l, AnnaWe define a strong form of subgroup separability, which we call RS separability, and we use this to combine LERF and Agol’s RFRS condition on groups into a property called LVRSS. We show that some infinite classes of groups that are known to be both subgroup separable and virtually RFRS are also LVRSS. We also provide evidence for the naturalness of RS separability and LVRSS by showing that they are preserved under various operations on groups.Item PipeSynth : automated topological and parametric design of fluid networks(2010-12) Patterson, William Rey; Campbell, Matthew I.; Seepersad, Carolyn C.PipeSynth is a design automation approach that combines various optimization research and artificial intelligence methods for synthesizing fluid networks. Starting with only the port locations, PipeSynth generates and optimizes the most effective network for a given application. This ideal network is found by not only optimizing the sizes of each pipe and orientation of fittings in the network (parameters), but also optimizing the layouts of how they are all connected (topology). Using Uniform-Cost-Search for topology optimization, and a combination of non-gradient based parametric optimization methods,PipeSynth demonstrates how advances in automated design can enable engineers to manage much more complex fluid network problems. PipeSynth uses a unique representation of fluid networks that synthesizes and optimizes networks one pipe at a time, in three-dimensional space. PipeSynth has successfully solved several problems containing multiple interlaced networks concurrently with multiple inputs and outputs. PipeSynth shows the power of automated design and optimization in producing solutions more effectively and efficiently than traditional design approaches.Item Pretzel knots of length three with unknotting number one(2012-05) Staron, Eric Joseph; Gordon, Cameron, 1945-; Gompf, Robert; Luecke, John; Namazi, Hossein; Ozsvath, Peter; Reid, AlanThis thesis provides a partial classification of all 3-stranded pretzel knots K=P(p,q,r) with unknotting number one. Scharlemann-Thompson, and independently Kobayashi, have completely classified those knots with unknotting number one when p, q, and r are all odd. In the case where p=2m, we use the signature obstruction to greatly limit the number of 3-stranded pretzel knots which may have unknotting number one. In Chapter 3 we use Greene's strengthening of Donaldson's Diagonalization theorem to determine precisely which pretzel knots of the form P(2m,k,-k-2) have unknotting number one, where m is an integer, m>0, and k>0, k odd. In Chapter 4 we use Donaldson's Diagonalization theorem as well as an unknotting obstruction due to Ozsv\'ath and Szab\'o to partially classify which pretzel knots P(2,k,-k) have unknotting number one, where k>0, odd. The Ozsv\'ath-Szab\'o obstruction is a consequence of Heegaard Floer homology. Finally in Chapter 5 we explain why the techniques used in this paper cannot be used on the remaining cases.Item Selected theorems on contraction and retraction mapping(Texas Tech University, 1966-05) Crossley, Sterling GeneNot availableItem Selected theorems on the fixed point property(Texas Tech University, 1966-05) Burton, Jonathan SNot availableItem Semi-topological properties and related topics(Texas Tech University, 1968-05) Crossley, Sterling GeneNot available