Dissertations / Theses on the topic 'Computational geometry'
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1
Baer, Lawrence H. "Numerical aspects of computational geometry." Thesis, McGill University, 1992. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=22507.
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This thesis is concerned with the numerical issues resulting from the implementation of geometric algorithms on finite precision digital computers. From an examination of the general problem and a survey of previous research, it appears that the central problem of numerical computational geometry is how to deal with degenerate and nearly degenerate input. For some applications, such as solid modeling, degeneracy is often intended but we cannot always ascertain its existence using finite precision. For other applications, degenerate input is unwanted but nearly degenerate input is unavoidable. Near degeneracy is associated with ill-conditioning of the input and can lead to a serious loss of accuracy and program failure. These observations lead us to a discussion of problem condition in the context of computational geometry. We use the Voronoi diagram construction problem as a case study and show that problem condition can also play a role in algorithm design.
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Hussain, R. "Computational geometry using fourier analysis." Thesis, De Montfort University, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.391483.
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Eades, Patrick Fintan. "Uncertainty Models in Computational Geometry." Thesis, University of Sydney, 2020. https://hdl.handle.net/2123/23909.
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In recent years easily and cheaply available internet-connected devices have enabled the collection of vast amounts of data, which has driven a continued interest in efficient, elegant combinatorial algorithms with mathematical guarantees. Much of this data contains an inherent element of uncertainty; whether because of imperfect measurements, because the data contains predictions about the future, or because the data is derived from machine learning algorithms which are inherently probabilistic. There is therefore a need for algorithms which include uncertainty in their definition and give answers in terms of that uncertainty. Questions about the most likely solution, the solution with lowest expected cost or a solution which is correct with high probability are natural here. Computational geometry is the sub-field of theoretical computer science concerned with developing algorithms and data structures for geometric problems, that is problems involving points, distances, angles and shapes. In computational geometry uncertainty is included in the location of the input points, or in which potential points are included in the input. The study of uncertainty in computational geometry is relatively recent; earlier research concerned imprecise points, which are known to appear somewhere in a geometric region. More recently the focus has been on points whose location, or presence, is given by a probability distribution. In this thesis we describe the most commonly used uncertainty models which are the subject of ongoing research in computational geometry. We present specific problems in those models and present new results, both positive and negative. In Chapter 3 we consider universal solutions, and show a new lower bound on the competitive ratio of the Universal Traveling Salesman Problem. In Chapter 4 we describe how to determine if two moving entities are ever mutually visible, and how data structures can be repeatedly queried to simulate uncertainty. In Chapter 5 we describe how to construct a graph on uncertain points with high probability of being a geometric spanner, an example of redundancy protecting against uncertainty. In Chapter 6 we introduce the online ply maintenance problem, an online problem where uncertainty can be reduced at a cost, and give an optimal algorithm.
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Pirzadeh, Hormoz. "Computational Geometry with the Rotating Calipers." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape7/PQDD_0027/MQ50856.pdf.
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Doskas, Michael. "Various stabbing problems in computational geometry." Thesis, McGill University, 1987. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66153.
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Pătrașcu, Mihai. "Computational geometry through the information lens." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/40526.
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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 111-117).
This thesis revisits classic problems in computational geometry from the modern algorithmic perspective of exploiting the bounded precision of the input. In one dimension, this viewpoint has taken over as the standard model of computation, and has led to a powerful suite of techniques that constitute a mature field of research. In two or more dimensions, we have seen great success in understanding orthogonal problems, which decompose naturally into one dimensional problems. However, problems of a nonorthogonal nature, the core of computational geometry, have remained uncracked for many years despite extensive effort. For example, Willard asked in SODA'92 for a o(nlg n) algorithm for Voronoi diagrams. Despite growing interest in the problem, it was not successfully solved until this thesis. Formally, let w be the number of bits in a computer word, and consider n points with O(w)-bit rational coordinates. This thesis describes: * a data structure for 2-d point location with O(n) space, and 0( ... )query time. * randomized algorithms with running time 9 ... ) for 3-d convex hull, 2-d Voronoi diagram, 2-d line segment intersection, and a variety of related problems. * a data structure for 2-d dynamic convex hull, with O ( ... )query time, and O ( ... ) update time. More generally, this thesis develops a suite of techniques for exploiting bounded precision in geometric problems, hopefully laying the foundations for a rejuvenated research direction.
by Mihai Pǎtraşcu.
S.M.
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Scibilia, Francesco. "Explicit Model Predictive Control:Solutions Via Computational Geometry." Doctoral thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for teknisk kybernetikk, 2010. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-11627.
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The thesis is mainly focused on issues involved with explicit model predictive control approaches. Conventional model predictive control (MPC) implementation requires at each sampling time the solution of an open-loop optimal control problem with the current state as the initial condition of the optimization. Formulating the MPC problem as a multi-parametric programming problem, the online optimization effort can be moved offline and the optimal control law given as an explicitly defined piecewise affine (PWA) function with dependence on the current state. The domain where the PWA function is defined corresponds to the feasible set which is partitioned into convex regions. This makes explicit MPC solutions into promising approaches to extend the scope of applicability of MPC schemes. The online computation reduces to simple evaluations of a PWA function, allowing implementations on simple hardware and with fast sampling rates. Furthermore, the closed form of the MPC solutions allows offline analysis of the performance, providing additional insight of the controller behavior. However, explicit MPC implementations may still be prohibitively costly for large optimization problems. The offline computational effort needed to solve the multiparametric optimization problem may be discouraging, and even the online computation needed to evaluate a complex PWA controller may cause difficulties if low-cost hardware is used. The first contribution of this thesis is to propose a technique for computing approximate explicit MPC solutions for the cases where optimal explicit MPC solutions are impractical due to the offline computational effort needed and their complexity for online evaluations. This technique is based on computational geometry, a branch of computer science which focuses heavily on computational complexity since the algorithms are intended to be used on large data-sets. The approximate solution is suboptimal only over the subregion of the feasible set where constraints are active. In this subregion, the ineffective optimal explicit MPC solution is replaced by an approximation based on Delaunay tessellations and is computed from a finite number of samples of the exact solution. Finer tessellations can be obtained in order to achieve a desired level of accuracy Successively, the thesis presents a twofold contribution concerned with the computation of feasible sets for MPC and their suitable approximations. First, an alternative approach is suggested for computing the feasible set which uses set relations instead of the conventional orthogonal projection. The approach can be implemented incrementally on the length of the MPC prediction horizon, and proves to be computationally less demanding than the standard approach. Thereafter, an algorithm for computing suitable inner approximations of the feasible set is proposed, which constitutes the main contribution. Such approximations are characterized by simpler representations and preserve the essential properties of the feasible set as convexity, positive invariance, inclusion of the set of expected initial states. This contribution is particularly important in the context of finding less complex suboptimal explicit MPC solutions, where the complexity of the feasible set plays a decisive role. The last part of the thesis is concerned with robustness of nominal explicit MPC solutions to model uncertainty. In the presence of model mismatch, when the controller designed using the nominal model is applied to the real plant, the feasible set may lose its invariance property, and this means violation of constraints. Also, since the PWA control law is designed only over the feasible set, there is the technical problem that the control action is undefined if the state moves outside of this set. To deal with this issue, a tool is proposed to analyze how uncertainty on the model affects the PWA control law computed using the nominal model. Given the linear system describing the plant and the PWA control law, the algorithm presented considers the polytopic model uncertainty and constructs the maximal robust feasible set, i.e. the largest subset of the feasible set which is guaranteed to be feasible for any model in the family of models described by the polytopic uncertainty. The appendix of the thesis contains two additional contributions which are only marginally related to the main theme of the thesis. MPC approaches are often implemented as state feedback controllers. The state variables are not always measured, and in these cases a state estimation approach has to be adopted to obtain the state from the measurements. The two contributions deal with state estimation in two different applications, but not with the explicit goal of being used in MPC approaches.
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Colley, Paul. "Visibility problems and optimization in computational geometry." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ27818.pdf.
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Teillaud, Monique. "Towards dynamic randomized algorithms in computational geometry /." Berlin [u.a.] : Springer, 1993. http://www.loc.gov/catdir/enhancements/fy0815/93023628-d.html.
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Petrauskas, Karolis. "Computational Modelling of Biosensors of Complex Geometry." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2011. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2011~D_20110701_105911-89480.
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Biosensors are analytical devices mainly used to detect analytes and measure their concentrations. Mathematical modeling is widely used for optimizing and analyzing an operation of biosensors for reducing price of development of new biosensors. The object of this research is mathematical and computer models, describing an operation of biosensors, made of several parts with different properties. The dissertation covers models, formulated in one and two-dimensional spaces by partial differential equations with non-linear members, and solved numerically, using the method of finite differences. The numerical models are implemented by a computer program. An original mathematical model for a biosensor with a carbon nanotube electrode is presented in the dissertation. The conditions at which the one-dimensional mathematical model can be used instead of two-dimensional one for accurate prediction of the biosensor response are investigated. Elements, used to build models of biosensors with a complex structure, were systemized. The biosensor description language is proposed and the computer software, simulating an operation of biosensors in the one-dimensional space and a rectangular domain of the two-dimensional space, is developed. An adequateness of the model for the biosensor with the carbon nanotube electrode and the impact of structural and geometrical properties on a response of the biosensor were investigated, performing computer experiments using the developed software.Biojutikliai yra įrenginiai, skirti medžiagoms aptikti bei jų koncentracijoms matuoti. Siekiant sumažinti biojutiklių gamybos kaštus yra pasitelkiamas matematinis biojutikliuose vykstančių procesų modeliavimas. Disertacijoje nagrinėjami matematiniai ir kompiuteriniai biojutiklių modeliai, aprašantys biojutiklių, sudarytų iš kelių, skirtingas savybes turinčių dalių, veikimą. Nagrinėjami modeliai yra formuluojami vienmatėje bei dvimatėje erdvėse, aprašomi diferencialinėmis lygtimis dalinėmis išvestinėmis su netiesiniais nariais ir yra sprendžiami skaitiškai, naudojant baigtinių skirtumų metodą. Skaitiniai modeliai yra įgyvendinami kompiuterine programa. Disertacijoje pateikiamas originalus matematinis modelis biojutikliui su anglies nanovamzdelių elektrodu, nustatyti kriterijai, apibrėžiantys, kada biojutiklį su perforuota membrana galima modeliuoti vienmačiu modeliu. Darbe susisteminti elementai, naudojami biojutiklių modelių formulavimui, pagrindinį dėmesį skiriant biojutiklio struktūrinėms savybėms modeliuoti. Apibrėžta biojutiklių modelių aprašo kalba ir sukurta programinė įranga, leidžianti modeliuoti biojutiklių veikimą vienmačiais modeliais arba modeliais, formuluojamais stačiakampėje dvimatės erdvės srityje. Taikant sukurtą biojutiklių modeliavimo programinę įrangą, ištirtas biojutiklio su anglies nanovamzdelių elektrodu modelio adekvatumas ir struktūrinių bei geometrinių savybių įtaka biojutiklio elgsenai.
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Shifler, Ryan M. "Computational Algebraic Geometry Applied to Invariant Theory." Thesis, Virginia Tech, 2013. http://hdl.handle.net/10919/23154.
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Commutative algebra finds its roots in invariant theory and the connection is drawn from a modern standpoint. The Hilbert Basis Theorem and the Nullstellenstatz were considered lemmas for classical invariant theory. The Groebner basis is a modern tool used and is implemented with the computer algebra system Mathematica. Number 14 of Hilbert\'s 23 problems is discussed along with the notion of invariance under a group action of GLn(C). Computational difficulties are also discussed in reference to Groebner bases and Invariant theory.The straitening law is presented from a Groebner basis point of view and is motivated as being a key piece of machinery in proving First Fundamental Theorem of Invariant Theory.Master of Science
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Valiveti, Natana Carleton University Dissertation Computer Science. "Parallel computational geometry on Analog Hopfield Networks." Ottawa, 1992.
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Wildman, Raymond A. "Geometry optimization and computational electromagnetics methods and applications /." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 191 p, 2008. http://proquest.umi.com/pqdweb?did=1481670101&sid=23&Fmt=2&clientId=8331&RQT=309&VName=PQD.
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Jost, Christine. "Topics in Computational Algebraic Geometry and Deformation Quantization." Doctoral thesis, Stockholms universitet, Matematiska institutionen, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-87399.
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This thesis consists of two parts, a first part on computations in algebraic geometry, and a second part on deformation quantization. More specifically, it is a collection of four papers. In the papers I, II and III, we present algorithms and an implementation for the computation of degrees of characteristic classes in algebraic geometry. Paper IV is a contribution to the field of deformation quantization and actions of the Grothendieck-Teichmüller group. In Paper I, we present an algorithm for the computation of degrees of Segre classes of closed subschemes of complex projective space. The algorithm is based on the residual intersection theorem and can be implemented both symbolically and numerically. In Paper II, we describe an algorithm for the computation of the degrees of Chern-Schwartz-MacPherson classes and the topological Euler characteristic of closed subschemes of complex projective space, provided an algorithm for the computation of degrees of Segre classes. We also explain in detail how the algorithm in Paper I can be implemented numerically. Together this yields a symbolical and a numerical version of the algorithm. Paper III describes the Macaulay2 package CharacteristicClasses. It implements the algorithms from papers I and II, as well as an algorithm for the computation of degrees of Chern classes. In Paper IV, we show that L-infinity-automorphisms of the Schouten algebra T_poly(R^d) of polyvector fields on affine space R^d which satisfy certain conditions can be globalized. This means that from a given L-infinity-automorphism of T_poly(R^d) an L-infinity-automorphism of T_poly(M) can be constructed, for a general smooth manifold M. It follows that Willwacher's action of the Grothendieck-Teichmüller group on T_poly(R^d) can be globalized, i.e., the Grothendieck-Teichmüller group acts on the Schouten algebra T_poly(M) of polyvector fields on a general manifold M.At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: Manuscript. Paper 3: Manuscript. Paper 4: Accepted.
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Zhu, Binhai. "Computational geometry in two and a half dimensions." Thesis, McGill University, 1994. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=28561.
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In this thesis, we study computational geometry in two and a half dimensions. These so-called polyhedral terrains have many applications in practice: computer graphics, navigation and motion planning, CAD/CAM, military surveillance, forest fire monitoring, etc.We investigate a series of fundamental problems regarding polyhedral terrains and present efficient algorithms to solve them. We propose an O(n) time algorithm to decide whether or not a geometric object is a terrain and an O(n log n) time algorithm to compute the shortest watchtower of a polyhedral terrain. We study the terrain guarding problem, obtain tight bounds for vertex and edge guards and O(n) algorithms to place these guards. We study the tetrahedralization of certain simple and non-simple polyhedra (which include some special classes of solid terrains) and present efficient algorithms to tetrahedralize them. We also investigate the problem of computing the $ alpha$-hull of a terrain. Finally, we present efficient algorithms for the intersection detection and computation of Manhattan terrains.
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Khanban, Ali Asghar. "Basic algorithms in computational geometry with imprecise input." Thesis, Imperial College London, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.423319.
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Smith, Justin W. "Problems and Results in Discrete and Computational Geometry." University of Cincinnati / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1352402504.
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Knight, Alan (Alan Evan) Carleton University Dissertation Computer Science. "Implementation of algorithms in a computational geometry workbench." Ottawa, 1990.
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Machat, Mohamed. "Computational geometry for the determination of biomolecular structures." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066359/document.
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En bioinformatique structurale, une partie des méthodes computationnelles qui calculent les structures de protéines à l'aide de données expérimentales, effectuent une optimisation de la position des atomes sous les contraintes expérimentales mesurées sur le système étudié, ainsi que sous des contraintes provenant de la connaissance générique de la stéréochimie organique. Ces méthodes d'optimisation présentent l'inconvénient de ne pas garantir la détermination de la meilleure solution. De plus, la validation de l'optimisation se fait en comparant les résultats obtenus pour des calculs répétés, et le résultat d'un calcul est accepté dans la mesure où le même résultat est obtenu plusieurs fois. Par cette approche, on rend plus difficile la détection de conformations alternatives de protéines, qui sont pourtant le sujet d'un vif intérêt dans la littérature. En effet, le développement de la sensibilité des techniques de résonance magnétique nucléaire (RMN) a permis de mettre en évidence plusieurs cas d'échange conformationnel reliés à la fonction des protéines. Dans ce projet de thèse, nous avons étudié une nouvelle approche pour le calcul de structures des protéines et l'exploration de leurs espaces conformationnels, basée sur la résolution du problème de Géométrie de Distance associé aux contraintes de distances dans une protéine par l'algorithme "interval Branch and Prune". Le logiciel implémentant cette méthode est appelée iBPprot, il incarne l'une des premières tentatives d'échantillonnage exhaustive des espaces conformationnels des protéines. Dans un premier temps, on s'est intéressé à l'application de la méthode en utilisant exclusivement des constraintes de distances exactes. Les résultats ont démontré que iBPprot était capable de reconstruire des structures références en s'appuyant seulement sur quelques contraintes à courte portée. De plus, la reconstruction a été d'une précision telle que la conformation générée présentait un RMSD de 1 Angstrom maximum avec la structure référence. L'exploration exhaustive de l'espace conformationnel a été possible pour une bonne partie des protéines cibles. Les temps de calcul pour l'exploration des espaces conformationnels ont été très variables allant de quelques secondes pour quelques protéines jusqu'à des semaines pour d'autres. L'évaluation de la qualité des structures obtenues a démontré qu'au moins 68% des valeurs de phi et psi sont localisées dans la zone 'core' du diagramme de Ramachandran. Cependant, des clash stériques ont été détectées dans plusieurs conformations mettant en jeu jusqu'à 7% d'atomes dans quelques unes de ces conformations. Dans un deuxième temps, on s'est intéressé à l'application de la méthode en incluant des intervalles de distances comme contraintes dans les calculs. Dans ce cas de figure, la méthode a réussi a reconstruire des structures références avec un RMSD inférieur à 5 Angstrom pour plus de la moitié des protéines cibles. En contre partie, le parcours complet de l'espace conformationnel n'a été possible que pour la plus petite protéine de l'ensemble des protéines étudiées. Pour la moitié des autres protéines, plus de 70% des atomes ont vu leurs positions échantillonnées. La qualité des structures obtenues a regressé en comparaison avec les simulations faites avec des distances exactes. En effet, seulement 53% des valeurs de phi et psi étaient localisées dans la zone 'core' du diagramme de Ramachandran, et le pourcentage d'atomes impliqués dans un clash stérique s'élevait jusqu'à 22% pour quelques protéines. Concernant le temps de calcul, le taux de génération de conformations a été déterminé pour chaque protéine cible, et il s'est avéré que globalement sa valeur etait compétitive par rapport aux valeurs des taux observables dans la littératureStructural biology has allowed us expand our knowledge of living organisms. It is defined as the investigation of the structure and function of biological systems at the molecular level. Studying a biomolecule's structure offers insight into its geometry, as angles and distances between the biomolecule's atoms are measured in order to determine the biomolecular structure. The values of these geometrical parameters may be obtained from biophysical techniques, such as X-ray crystallography or nuclear magnetic resonance (NMR) spectroscopy. One of the most used methods to calculate protein structures from geometric restraints is simulated annealing. This method does not guarantee an exhaustive sampling of protein conformational space, which is a shortcoming as one protein may adopt multiple functional conformations, and it is important to determine them exhaustively. In this PhD project, the efficiency of a new method - derived from operations research and computational geometry - is studied in order to answer this question: How does this method explore the conformational spaces of small proteins? This method - implemented within the iBPprot software framework - treats protein structure determination as a distance geometry problem, which the interval branch-and-prune algorithm tries to solve by the full exploration of its solutions space. The results obtained by iBPprot on a set of test proteins, with sizes ranging from 24 to 120 residues and with known structures, are analyzed here. Using short-range exact distance restraints, it was possible to rebuild the structure of all protein targets, and for many of them it was possible to exhaustively explore their conformational spaces. In practice, it is not always possible to obtain exact distance restraints from experiments. Therefore, this method was then tested with interval data restraints. In these cases, iBPprot permitted the sampling of the positions of more than 70% of the atoms constituting the protein backbone for most of the targets. Furthermore, conformations whose r.m.s. deviations closer than 6 Angstrom to the target ones were obtained during the conformational space exploration. The quality of the generated structures was satisfactory with respect to Ramachandran plots, but needs improvement because of the presence of steric clashes in some conformers. The runtime for most performed calculations was competitive with existing structure determination method
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Machat, Mohamed. "Computational geometry for the determination of biomolecular structures." Electronic Thesis or Diss., Paris 6, 2017. http://www.theses.fr/2017PA066359.
Full textAbstract:
En bioinformatique structurale, une partie des méthodes computationnelles qui calculent les structures de protéines à l'aide de données expérimentales, effectuent une optimisation de la position des atomes sous les contraintes expérimentales mesurées sur le système étudié, ainsi que sous des contraintes provenant de la connaissance générique de la stéréochimie organique. Ces méthodes d'optimisation présentent l'inconvénient de ne pas garantir la détermination de la meilleure solution. De plus, la validation de l'optimisation se fait en comparant les résultats obtenus pour des calculs répétés, et le résultat d'un calcul est accepté dans la mesure où le même résultat est obtenu plusieurs fois. Par cette approche, on rend plus difficile la détection de conformations alternatives de protéines, qui sont pourtant le sujet d'un vif intérêt dans la littérature. En effet, le développement de la sensibilité des techniques de résonance magnétique nucléaire (RMN) a permis de mettre en évidence plusieurs cas d'échange conformationnel reliés à la fonction des protéines. Dans ce projet de thèse, nous avons étudié une nouvelle approche pour le calcul de structures des protéines et l'exploration de leurs espaces conformationnels, basée sur la résolution du problème de Géométrie de Distance associé aux contraintes de distances dans une protéine par l'algorithme "interval Branch and Prune". Le logiciel implémentant cette méthode est appelée iBPprot, il incarne l'une des premières tentatives d'échantillonnage exhaustive des espaces conformationnels des protéines. Dans un premier temps, on s'est intéressé à l'application de la méthode en utilisant exclusivement des constraintes de distances exactes. Les résultats ont démontré que iBPprot était capable de reconstruire des structures références en s'appuyant seulement sur quelques contraintes à courte portée. De plus, la reconstruction a été d'une précision telle que la conformation générée présentait un RMSD de 1 Angstrom maximum avec la structure référence. L'exploration exhaustive de l'espace conformationnel a été possible pour une bonne partie des protéines cibles. Les temps de calcul pour l'exploration des espaces conformationnels ont été très variables allant de quelques secondes pour quelques protéines jusqu'à des semaines pour d'autres. L'évaluation de la qualité des structures obtenues a démontré qu'au moins 68% des valeurs de phi et psi sont localisées dans la zone 'core' du diagramme de Ramachandran. Cependant, des clash stériques ont été détectées dans plusieurs conformations mettant en jeu jusqu'à 7% d'atomes dans quelques unes de ces conformations. Dans un deuxième temps, on s'est intéressé à l'application de la méthode en incluant des intervalles de distances comme contraintes dans les calculs. Dans ce cas de figure, la méthode a réussi a reconstruire des structures références avec un RMSD inférieur à 5 Angstrom pour plus de la moitié des protéines cibles. En contre partie, le parcours complet de l'espace conformationnel n'a été possible que pour la plus petite protéine de l'ensemble des protéines étudiées. Pour la moitié des autres protéines, plus de 70% des atomes ont vu leurs positions échantillonnées. La qualité des structures obtenues a regressé en comparaison avec les simulations faites avec des distances exactes. En effet, seulement 53% des valeurs de phi et psi étaient localisées dans la zone 'core' du diagramme de Ramachandran, et le pourcentage d'atomes impliqués dans un clash stérique s'élevait jusqu'à 22% pour quelques protéines. Concernant le temps de calcul, le taux de génération de conformations a été déterminé pour chaque protéine cible, et il s'est avéré que globalement sa valeur etait compétitive par rapport aux valeurs des taux observables dans la littératureStructural biology has allowed us expand our knowledge of living organisms. It is defined as the investigation of the structure and function of biological systems at the molecular level. Studying a biomolecule's structure offers insight into its geometry, as angles and distances between the biomolecule's atoms are measured in order to determine the biomolecular structure. The values of these geometrical parameters may be obtained from biophysical techniques, such as X-ray crystallography or nuclear magnetic resonance (NMR) spectroscopy. One of the most used methods to calculate protein structures from geometric restraints is simulated annealing. This method does not guarantee an exhaustive sampling of protein conformational space, which is a shortcoming as one protein may adopt multiple functional conformations, and it is important to determine them exhaustively. In this PhD project, the efficiency of a new method - derived from operations research and computational geometry - is studied in order to answer this question: How does this method explore the conformational spaces of small proteins? This method - implemented within the iBPprot software framework - treats protein structure determination as a distance geometry problem, which the interval branch-and-prune algorithm tries to solve by the full exploration of its solutions space. The results obtained by iBPprot on a set of test proteins, with sizes ranging from 24 to 120 residues and with known structures, are analyzed here. Using short-range exact distance restraints, it was possible to rebuild the structure of all protein targets, and for many of them it was possible to exhaustively explore their conformational spaces. In practice, it is not always possible to obtain exact distance restraints from experiments. Therefore, this method was then tested with interval data restraints. In these cases, iBPprot permitted the sampling of the positions of more than 70% of the atoms constituting the protein backbone for most of the targets. Furthermore, conformations whose r.m.s. deviations closer than 6 Angstrom to the target ones were obtained during the conformational space exploration. The quality of the generated structures was satisfactory with respect to Ramachandran plots, but needs improvement because of the presence of steric clashes in some conformers. The runtime for most performed calculations was competitive with existing structure determination method
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Kellar, William Patrick. "Geometry modeling in computational fluid dynamics and design optimisation." Thesis, University of Cambridge, 2003. https://www.repository.cam.ac.uk/handle/1810/251878.
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Strandell, Ebbe. "Computational Geometry and Surface Reconstruction from Unorganized Point Clouds." Thesis, Linköpings universitet, Institutionen för teknik och naturvetenskap, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-96279.
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This thesis addresses the problem of constructing virtual representations of surfaces only known as clouds of unstructured points in space. This problem is related to many areas including computer graphics, image processing, computer vision, reverse engineering and geometry studies. Data sets can be acquired from a wide range of sources including Computer Tomography (CT), Magnetic Resonance Imaging (MRI), medical cryosections, laser range scanners, seismic surveys or mathematical models. This thesis will furthermost focus on medical samples acquired through cryosections of bodies. In this thesis report various computational geometry approaches of surface reconstruction are evaluated in terms of adequateness for scientific uses. Two methods called “γ-regular shapes” and “the Power Crust” are implemented and evaluated. The contribution of this work is the proposal of a new hybrid method of surface reconstruction in three dimensions. The underlying thought of the hybrid solution is to utilize the inverse medial axis transformation, defined by the Power Crust, to recover holes that may appear in the three dimensional γ-regular shapes.
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TIAN, BINYU. "COMPUTATIONAL AEROELASTIC ANALYSIS OF AIRCRAFT WINGS INCLUDING GEOMETRY NONLINEARITY." University of Cincinnati / OhioLINK, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1070398084.
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Tejada, Pedro J. "A Computational Geometry Approach to Digital Image Contour Extraction." DigitalCommons@USU, 2009. https://digitalcommons.usu.edu/etd/422.
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We present a method for extracting contours from digital images, using techniques from computational geometry. Our approach is different from traditional pixel-based methods in image processing. Instead of working directly with pixels, we extract a set of oriented feature points from the input digital images, then apply classical geometric techniques, such as clustering, linking, and simplification, to find contours among these points. Experiments on synthetic and natural images show that our method can effectively extract contours, even from images with considerable noise; moreover, the extracted contours have a very compact representation.
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Pennec, Xavier. "Statistical Computing on Manifolds for Computational Anatomy." Habilitation à diriger des recherches, Université de Nice Sophia-Antipolis, 2006. http://tel.archives-ouvertes.fr/tel-00633163.
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During the last decade, my main research topic was on medical image analysis, and more particularly on image registration. However, I was also following in background a more theoretical research track on statistical computing on manifolds. With the recent emergence of computational anatomy, this topic gained a lot of importance in the medical image analysis community. During the writing of this habilitation manuscript, I felt that it was time to present a more simple and uni ed view of how it works and why it can be important. This is why the usual short synthesis of the habilitation became a hundred pages long text where I tried to synthesizes the main notions of statistical computing on manifolds with application in registration and computational anatomy. Of course, this synthesis is centered on and illustrated by my personal research work.
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Lundqvist, Samuel. "Computational algorithms for algebras." Doctoral thesis, Stockholm : Department of Mathematics, Stockholm University, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-31552.
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Diss. (sammanfattning) Stockholm : Stockholms universitet, 2009.At the time of doctoral defence, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 4: Manuscript. Paper 5: Manuscript. Paper 6: Manuscript. Härtill 6 uppsatser.
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Botnan, Magnus Bakke. "Three Approaches in Computational Geometry and Topology : Persistent Homology, Discrete Differential Geometry and Discrete Morse Theory." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-14201.
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We study persistent homology, methods in discrete differential geometry and discrete Morse theory. Persistent homology is applied to computational biology and range image analysis. Theory from differential geometry is used to define curvature estimates of triangulated hypersurfaces. In particular, a well-known method for triangulated surfacesis generalised to hypersurfaces of any dimension. The thesis concludesby discussing a discrete analogue of Morse theory.
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Neyer, Gabriele. "Algorithms, complexity, and software engineering in computational geometry : case studies /." [S.l.] : [s.n.], 2000. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=13586.
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McAllister, Michael Joseph. "The computational geometry of hydrology data in geographic information systems." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0016/NQ48670.pdf.
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Voruganti, Ravinder Srinivas. "Symbolic and computational conjugate geometry for design and manufacturing applications." Thesis, This resource online, 1990. http://scholar.lib.vt.edu/theses/available/etd-03032009-041021/.
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Lui, Lok Ming. "Computational conformal geometry and its applications to human brain mapping." Diss., Restricted to subscribing institutions, 2008. http://proquest.umi.com/pqdweb?did=1680018831&sid=1&Fmt=2&clientId=1564&RQT=309&VName=PQD.
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Garcia-Puente, Luis David. "Algebraic Geometry of Bayesian Networks." Diss., Virginia Tech, 2004. http://hdl.handle.net/10919/11133.
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We develop the necessary theory in algebraic geometry to place Bayesian networks into the realm of algebraic statistics. This allows us to create an algebraic geometry--statistics dictionary. In particular, we study the algebraic varieties defined by the conditional independence statements of Bayesian networks. A complete algebraic classification, in terms of primary decomposition of polynomial ideals, is given for Bayesian networks on at most five random variables. Hidden variables are related to the geometry of higher secant varieties. Moreover, a complete algebraic classification, in terms of generating sets of polynomial ideals, is given for Bayesian networks on at most three random variables and one hidden variable. The relevance of these results for model selection is discussed.Ph. D.
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Day, Andrew. "The serial and parallel implementation of geometric algorithms." Thesis, University of East Anglia, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.280057.
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Sharrock, T. J. "Surface design with cyclide patches." Thesis, University of Cambridge, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.383950.
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Murri, Riccardo. "Computational techniques in graph homology of the moduli space of curves." Doctoral thesis, Scuola Normale Superiore, 2013. http://hdl.handle.net/11384/85723.
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The object of this thesis is the automated computation of the rational (co)homology
of the moduli spaces of smooth marked Riemann surfaces Mg;n. This is achieved by
using a computer to generate a chain complex, known in advance to have the same
homology as Mg;n, and explicitly spell out the boundary operators in matrix form.
As an application, we compute the Betti numbers of some moduli spaces Mg;n.
Our original contribution is twofold. In Chapter 3, we develop algorithms for the
enumeration of fatgraphs and their automorphisms, and the computation of the
homology of the chain complex formed by fatgraphs of a given genus g and number
of boundary components n.
In Chapter 4, we describe a new practical parallel algorithm for performing Gaussian
elimination on arbitrary matrices with exact computations: projections indicate
that the size of the matrices involved in the Betti number computation can easily
exceed the computational power of a single computer, so it is necessary to distribute
the work over several processing units. Experimental results prove that our
algorithm is in practice faster than freely available exact linear algebra codes.
An effective implementation of the fatgraph algorithms presented here is available
at http://code.google.com/p/fatghol. It has so far been used to compute the Betti
numbers of Mg;n for (2g + n) 6 6.
The Gaussian elimination code is likewise publicly available as open-source software
from http://code.google.com/p/rheinfall.
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Kettner, Lutz. "Software design in computational geometry and contour-edge based polyhedron visualization /." [S.l.] : [s.n.], 1999. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=13325.
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Côté, Brendan. "Applicability of advanced computational networks to the modelling of complex geometry." Thesis, McGill University, 2000. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=33387.
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This thesis describes a research effort directed at producing a computational model based on artificially intelligent cellular automata. This model was developed for the purpose of learning a mapping from an input space to an output space. A specific problem that occurs in the mining industry was used to develop and test the model's ability to learn the mapping between a three-dimensional input volume and a three-dimensional output volume. In this case, the mapping was a consequence of the industrial processes used in mining as well as the properties of the material being mined.Three main computational tools were combined in this work to form the complete mine stope prediction model. The three modules are a learning module, an optimisation module, and an overall network architecture. The overall network architecture is a 3-D lattice of cellular automata (CA) and has the capability to implicitly capture the complexities in shape that render other types of models arduous or inapplicable. The learning module uses a Discrete Time Cellular Neural Network (DTCNN) to store and recall information about a given mapping. The optimisation module uses the Simulated Annealing (SA) algorithm to perform a non-linear optimisation on the set of weights used by the DTCNN.
Variations of the model, and different experiments, were performed to test and explore the model in depth. Concepts such as "Small-Worlds" and "Forgetting Factor" were investigated. The applicability of a Partial Least Squares (PLS) model as an alternative to the DTCNN transition rule was also explored.
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wang, zhiqiang. "STUDYING COMPUTATIONAL METHODS FOR BIOMEDICAL GEOMETRY EXTRACTION AND PATIENT SPECIFIC HEMODYNAMICS." Kent State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=kent1493042299659479.
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Schkolnik, Müller Demian Aley. "A robust void-finding algorithm using computational geometry and parallelization techniques." Tesis, Universidad de Chile, 2018. http://repositorio.uchile.cl/handle/2250/168498.
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Tesis para optar al grado de Magíster en Ciencias, Mención ComputaciónEl modelo cosmológico actual y más aceptado del universo se llama Lambda Cold Dark Matter. Este modelo nos presenta el modelo más simple que proporciona una explicación razonablemente buena de la evidencia observada hasta ahora. El modelo sugiere la existencia de estructuras a gran escala presentes en nuestro universo: Nodos, filamentos, paredes y vacíos. Los vacíos son de gran interés para los astrofísicos ya que su observación sirve como validación para el modelo. Los vacíos son usualmente definidos como regiones de baja densidad en el espacio, con sólo unas pocas galaxias dentro de ellas. En esta tesis, presentamos un estudio del estado actual de los algoritmos de búsqueda de vacíos. Mostramos las diferentes técnicas y enfoques, e intentamos deducir la complejidad algorítmica y el uso de memoria de cada void-finder presentado. Luego mostramos nuestro nuevo algoritmo de búsqueda de vacíos, llamado ORCA. Fue construido usando triangulaciones de Delaunay para encontrar a los vecinos más cercanos de cada punto. Utilizando esto, clasificamos los puntos en tres categorías: Centro, borde y outliers. Los outliers se eliminan como ruido. Clasificamos los triángulos de la triangulación en triángulos de vacíos y centrales. Esto se hace verificando un criterio de distancia, y si los triángulos contienen outliers. Este método nos permite crear un algoritmo de búsqueda de vacíos rápido y robusto. Adicionalmente, se presenta una versión paralela del algoritmo.
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Selmi-Dei, Fabio Pakk. "Um visualizador para uma extensão de CGAL ao plano projetivo orientado." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/276388.
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Orientadores: Pedro Jussieu de RezendeDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação
Made available in DSpace on 2018-08-04T08:54:01Z (GMT). No. of bitstreams: 1 Selmi-Dei_FabioPakk_M.pdf: 2287860 bytes, checksum: 97e2fc68f82f1ee33b0e737ed3b9f831 (MD5) Previous issue date: 2005
Resumo: Visualizadores são softwares capazes de gerar, através de recursos gráficos computacionais, figuras geométricas a partir de estruturas de dados e seus estados. Suas imagens facilitam a compreensão e depuração de algoritmos, bem como aumentam a intuição do usuário sobre os objetos geométricos e o espaço que os abriga. O presente trabalho descreve o projeto e a criação de um visualizador geométrico para uma extensão de CGAL ao plano projetivo orientado ('T POT 2'). CGAL é uma biblioteca de algoritmos geométricos e estruturas de dados desenvolvida por um consórcio de universidades com o objetivo de ser uma ferramenta de fácil acesso usada no desenvolvimento de aplicações que necessitem resolver problemas geométricos em 'R POT 2'. Através do trabalho [dO04], esta biblioteca foi estendida para incorporar 'T POT 2', preservando sua robustez, corretude e confiabilidade. O plano projetivo orientado é um espaço geométrico estritamente maior que o plano cartesiano 'R POT 2', porém com geometria semelhante. Uma das principais características de 'T POT 2' é o uso de coordenadas homogêneas sinaladas, o que permite lidar com o conceito de pontos no infinito de maneira homogênea ao tratamento dos pontos do plano, possibilitando o projeto de algoritmos geométricos que não mais precisam tratar separadamente muitos casos particulares, tornando-os mais simples e sucintos. Neste contexto, o visualizador aqui descrito tem por finalidade a criação de um ambiente de visualização que permite a observação das características intrínsecas à geometria projetiva orientada, o que é de grande benefício para o usuário-programador da extensão de CGAL para 'T POT 2'
Abstract: A graphical viewer is a software that enables the display of geometric figures from data structures and their varying states. The images it provides improve comprehension, make debugging easier and raise the users' intuition regarding geometric objects and their embedding space. The present work describes the design and creation of a geometrical viewer for an oriented projective plane ('T POT 2') extension of CGAL. CGAL is a library of geometric algorithms and data structures developed by a consortium of universities with the goal of producing an easy-to-use tool for building applications that require problem solving in 'R POT 2'. In [dO04], Oliveira describes an extension of this library that incorporates 'T POT 2' into CGAL, while adhering to its robustness, correctness and reliability. The oriented projective plane is a geometric space strictly larger than the Cartesian plane R2, though with similar geometry. One of the main features of 'T POT 2' is the use of signed homogeneous coordinates, which enables one to work with points at infinity in a way similar to working with proper points on the plane, allowing for the design of algorithms that no longer need to handle many particular cases, making them simpler and shorter. In this context, the viewer described here has the purpose of providing a visualization system that allows for the perception of the intrinsic characteristics of the oriented projective geometry, which is of great benefit to programmers of the extension of CGAL to 'T POT 2'
Mestrado
Geometria Computacional
Mestre em Ciência da Computação
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Rockwood, A. P. "Blending surfaces in solid geometric modelling." Thesis, University of Cambridge, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.234923.
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Mechanical CAD/CAM (computer aided design/manufacturing) as a field research concerns itself with the algorithms and the mathematics necessary to simulate mechanical parts of the computer, that is to produce a computer model. Solid modelling is a subdiscipline in which the computer model accurately simulates volumetric, i.e. 'solid', properties of mechanical parts. This dissertation deals with a particular type of free-form surface, the blending surface, which is particularly well-suited for solid modelling. A blending surface is one which replaces creases and kinks in the original model with smooth surfaces. A fillet surface is a simple example. We introduce an intuitive paradigm for devising different types of blending forms. Using the paradigm, three forms are derived: the circular, the rolling-ball, and the super-elliptic forms. Important mathematical properties are investigated for the blending surfaces, e.g. continuity, smoothness, containment etc. Blending on blends is introduced as a notion which both extends the flexibility of blending surfaces and allows the blending of multiple surfaces. Blending on blends requires one to think about the way in which the defining functions act as a distance measure from a point in space to a surface. The function defining the super-elliptic blend is offered as an example or a poor distance measure. The zero surface of this function is then embedded within a function which provides an improved distance measure. Mathematical properties are derived for the new function. A weakness in the continuity properties of above blending form is rectified by defining another method to embed the super elliptic blend into a function with better distance properties. This is the displacement form. The concern with this form is its computational reliability which is, therefore, considered in more depth. In the process of integrating the blending surface geometry into a solid modelling environment so it was usable, it was discovered that three other formidable problems needed some type of resolution. These were the topological, the intersection and the display problems. We report on the problems, and solutions which we developed.
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Nussbaum, Doron Carleton University Dissertation Computer Science. "Directional separability in two and three dimensional space." Ottawa, 1988.
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Dandekar, Pranav. "Algebraic-geometric methods for complexity lower bounds." [Gainesville, Fla.] : University of Florida, 2004. http://purl.fcla.edu/fcla/etd/UFE0008843.
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Carrigan, Braxton Bezdek András. "Evading triangles without a map." Auburn, Ala., 2010. http://hdl.handle.net/10415/2032.
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Gomes, de Oliveira Rodrigo. "Geographic referring expressions : doing geometry with words." Thesis, University of Aberdeen, 2017. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=232615.
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Jartoux, Bruno. "On combinatorial approximation algorithms in geometry." Thesis, Paris Est, 2018. http://www.theses.fr/2018PESC1078/document.
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L'analyse des techniques d'approximation est centrale en géométrie algorithmique, pour des raisons pratiques comme théoriques. Dans cette thèse nous traitons de l'échantillonnage des structures géométriques et des algorithmes d'approximation géométriques en optimisation combinatoire. La première partie est consacrée à la combinatoire des hypergraphes. Nous débutons par les problèmes de packing, dont des extensions d'un lemme de Haussler, particulièrement le lemme dit de Shallow packing, pour lequel nous donnons aussi un minorant optimal, conjecturé mais pas établi dans les travaux antérieurs. Puis nous appliquons ledit lemme, avec la méthode de partition polynomiale récemment introduite, à l'étude d'un analogue combinatoire des régions de Macbeath de la géométrie convexe : les M-réseaux, pour lesquels nous unifions les résultats d'existence et majorations existants, et donnons aussi quelques minorants. Nous illustrons leur relation aux epsilon-réseaux, structures incontournables en géométrie combinatoire et algorithmique, notamment en observant que les majorants de Chan et al. (SODA 2012) ou Varadarajan (STOC 2010) pour les epsilon-réseaux (uniformes) découlent directement de nos résultats sur les M-réseaux. La deuxième partie traite des techniques de recherche locale appliquées aux restrictions géométriques de problèmes classiques d'optimisation combinatoire. En dix ans, ces techniques ont produit les premiers schémas d'approximation en temps polynomial pour divers problèmes tels que celui de calculer un plus petit ensemble intersectant pour un ensemble de disques donnés en entrée parmi un ensemble de points donnés en entrée. En fait, il a été montré que pour de nombreux tels problèmes, la recherche locale de rayon Θ (1/epsilon²) donne une (1 + epsilon)-approximation en temps n^{O(1/epsilon²)}. Savoir si l'exposant de n pouvait être ramené à o (1/epsilon²) demeurait une question ouverte. Nous répondons par la négative : la garantie d'approximation de la recherche locale n'est améliorable pour aucun desdits problèmesThe analysis of approximation techniques is a key topic in computational geometry, both for practical and theoretical reasons. In this thesis we discuss sampling tools for geometric structures and geometric approximation algorithms in combinatorial optimization. Part I focuses on the combinatorics of geometric set systems. We start by discussing packing problems in set systems, including extensions of a lemma of Haussler, mainly the so-called shallow packing lemma. For said lemma we also give an optimal lower bound that had been conjectured but not established in previous work on the topic. Then we use this lemma, together with the recently introduced polynomial partitioning technique, to study a combinatorial analogue of the Macbeath regions from convex geometry: Mnets, for which we unify previous existence results and upper bounds, and also give some lower bounds. We highlight their connection with epsilon-nets, staples of computational and combinatorial geometry, for example by observing that the unweighted epsilon-net bound of Chan et al. (SODA 2012) or Varadarajan (STOC 2010) follows directly from our results on Mnets. Part II deals with local-search techniques applied to geometric restrictions of classical combinatorial optimization problems. Over the last ten years such techniques have produced the first polynomial-time approximation schemes for various problems, such as that of computing a minimum-sized hitting set for a collection of input disks from a set of input points. In fact, it was shown that for many of these problems, local search with radius Θ(1/epsilon²) gives a (1 + epsilon)-approximation with running time n^{O(1/epsilon²)}. However the question of whether the exponent of n could be decreased to o(1/epsilon²) was left open. We answer it in the negative: the approximation guarantee of local search cannot be improved for any of these problems. The key ingredient is a new lower bound on locally expanding planar graphs, which is then used to show the impossibility results
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Smith, Simeon L. "Influence of Subglottic Geometry on Computational and Synthetic Vocal Fold Model Vibration." BYU ScholarsArchive, 2011. https://scholarsarchive.byu.edu/etd/2836.
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The voice plays a vital role in human communication. The purpose of voice research is to advance the understanding of voice production physics, with the ultimate goal of leading to improved voice care. In this research computational and synthetic vocal fold models were used to explore the role of subglottal geometry in vocal fold vibration. Three specific studies were performed. First, the effect of the inferior vocal fold surface angle on voice production was investigated using a two-dimensional self-oscillating finite element vocal fold model. Varying the inferior angle resulted in significant changes to model vibratory motion, glottal width, flow rate, and energy transfer. The changes were attributed primarily to changes in structural, rather than aerodynamic, factors. Second, subglottic stenosis (SGS) was introduced and parametrically varied in a similar computational model to determine the influence of SGS on vocal fold vibration. High severities of SGS influenced several factors related to vibration, including glottal width, flow rate, flow resistance, and vibration frequency. Subglottal pressure distributions and flow patterns were also affected. Third, the response of a self-oscillating silicone vocal fold model to varying degrees of SGS in an experimental setup was studied. Consistent with the computational SGS study, SGS had an effect on the synthetic model response at high severities. Changes were seen particularly in subglottal pressure and radiated acoustic sound, and consequently glottal efficiency, which may have important implications regarding the effect of SGS on the human voice.
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Bodily, Garrett Clark. "A Computational Hybrid Method for Self-Intersection Free Offsetting of CAD Geometry." BYU ScholarsArchive, 2014. https://scholarsarchive.byu.edu/etd/5293.
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Surface offsetting is a valuable tool used in Computer Aided Design (CAD). An offset surface is a collection of points that are at a constant distance from another surface. An offset surface is created in CAD by selecting a surface and then specifying the distance that the surface is to be offset. If a surface is selected and a distance of D is specified, then the resulting offset surface should always be distance D from the original surface. The surface offset tool can be used for many applications. Modeling of composites or other layered manufacturing processes rely heavily on offset surfaces. Thin walled parts such as injection molded components are often modeled using the offset tool. Coating processes can also be modeled using the offset tool. Modern CAD systems have surface offsetting tools and are widely used throughout industry. However, CAD systems often fail to produce valid results. The process of surface offsetting can often result in surface self-intersections as well as surface degeneracies. Self-intersections and degeneracies make the surfaces invalid because they are physically impossible to create and CAD systems cannot use these invalid surfaces to represent solid bodies. The surface offset tool is therefore, one of the most challenging CAD tools to implement. The process of avoiding, detecting and removing surface self-intersections is extremely challenging. Much research in the field of CAD is dedicated to the detection and removal of surface self-intersections. However, the methods proposed in the literature all suffer from robustness problems. The purpose of this research is to introduce a method that creates valid offset surfaces and does not suffer from the problem of creating surface self-intersections. This method uses a numerical approach that approximates the offset surface and avoids all self-intersections. Because no self-intersections are created, the method does not require intersection tests of any kind. The value of this method is demonstrated by comparing its results with results from leading CAD systems.
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Pearl, Jason M. "Two-Dimensional Numerical Study of Micronozzle Geometry." ScholarWorks @ UVM, 2016. http://scholarworks.uvm.edu/graddis/579.
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Supersonic micronozzles operate in the unique viscosupersonic flow regime, characterized by large Mach numbers (M>1) and low Reynolds numbers (Re<1000). Past research has primarily focused on the design and analysis of converging-diverging de Laval nozzles; however, plug (i.e. centerbody) designs also have some promising characteristics that might make them amenable to microscale operation. In this study, the effects of plug geometry on plug micronozzle performance are examined for the Reynolds number range Re = 80-640 using 2D Navier-Stokes-based simulations. Nozzle plugs are shortened to reduce viscous losses via three techniques: one - truncation, two - the use of parabolic contours, and three - a geometric process involving scaling. Shortened nozzle are derived from a full length geometry designed for optimal isentropic performance. Expansion ratio (ε = 3.19 and 6.22) and shortened plug length (%L = 10-100%) are varied for the full Reynolds number range. The performance of plug nozzles is then compared to that of linear-walled nozzles for equal pressure ratios, Reynolds numbers, and expansion ratios. Linear-walled nozzle half-angle is optimized to to ensure plug nozzles are compared against the best-case linear-walled design.
Results indicate that the full length plug nozzle delivers poor performance on the microscale, incurring excessive viscous losses. Plug performance is increased by shortening the nozzle plug, with the scaling technique providing the best performance. The benefit derived from reducing plug length depends upon the Reynolds number, with a 1-2% increase for high Reynolds numbers an up to 14% increase at the lowest Reynolds number examined. In comparison to Linear-walled nozzle, plug nozzles deliver superior performance when under-expanded, however, this trend reverses at low pressure ratios when the nozzles become over-expanded.
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Demaine, Erik. "Folding and Unfolding." Thesis, University of Waterloo, 2001. http://hdl.handle.net/10012/1068.
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The results of this thesis concern folding of one-dimensional objects in two dimensions: planar linkages. More precisely, a planar linkage consists of a collection of rigid bars (line segments) connected at their endpoints. Foldings of such a linkage must preserve the connections at endpoints, preserve the bar lengths, and (in our context) prevent bars from crossing. The main result of this thesis is that a planar linkage forming a collection of polygonal arcs and cycles can be folded so that all outermost arcs (not enclosed by other cycles) become straight and all outermost cycles become convex. A complementary result of this thesis is that once a cycle becomes convex, it can be folded into any other convex cycle with the same counterclockwise sequence of bar lengths. Together, these results show that the configuration space of all possible foldings of a planar arc or cycle linkage is connected. These results fall into the broader context of folding and unfolding k-dimensional objects in n-dimensional space, k less than or equal to n. Another contribution of this thesis is a survey of research in this field. The survey revolves around three principal aspects that have received extensive study: linkages in arbitrary dimensions (folding one-dimensional objects in two or more dimensions, including protein folding), paper folding (normally, folding two-dimensional objects in three dimensions), and folding and unfolding polyhedra (two-dimensional objects embedded in three-dimensional space).