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Troia, Emily M. "Mental Coordinates." Cleveland State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=csu1494167936224508.
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Lidberg, Petter. "Barycentric and harmonic coordinates." Thesis, Uppsala universitet, Algebra och geometri, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-179487.
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Kaafar, Mohamed Ali. "Securiting Internet coordinates systems." Nice, 2007. http://www.theses.fr/2007NICE4023.
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Dans ce type de systèmes, l’idée principale est que si les distances réseau entre différents nœuds Internet peuvent être plongées dans un espace approprié, alors les distances non mesurées peuvent être estimées en utilisant une simple opération de calcul de distance géométrique dans cet espace. Récemment, on a pu prouver que ces systèmes `a base de coordonnées étaient précis, avec une faible erreur de prédiction. Cependant, ces systèmes se basent souvent sur une coordination entre les nœuds, et font l’ hypothèse que les informations reportées par les nœuds sont correctes. Dans cette thèse, nous avons identifie plusieurs attaques, exploitant cette hypothèse d’honnêteté des nœuds, et pouvant être lancées contre des systèmes de positionnement Internet `a base de coordonnées. Nous avons en l’occurrence étudié l’impact qu’ avaient de telles attaques sur deux systèmes représentatifs des systèmes de positionnement actuels : NPS et Vivaldi. Nous avons entre autres montre que ces attaques, pouvaient dangereusement mettre en péril le bon fonctionnement de ces systèmes de coordonnées, et par la même les applications se basant sur ce système pour les estimations de distances. `A travers les simulations de plusieurs attaques, menées par des nœuds malhonnêtes, fournissant des coordonnées biaisées ou retardant les mesures, nous avons expérimenté plusieurs stratégies d’attaques qui ont pour objectifs: (i) d’introduire du désordre dans le système, (ii) de tromper les nœuds honnêtes afin qu’ils se positionnent loin de leurs coordonnées correctes et (iii) d’isoler certains nœuds cibles `a travers des collusions. Nos résultats confirment la vulnérabilité de tels systèmes à ces attaques. Notre contribution majeure a été par la suite de proposer un modèle de détection des comportements malicieux au sein de ces systèmes de positionnement durant le calcul des cordonnées. Nous avons montré en premier lieu que la dynamique d’un nœud, dans un système de coordonnées, exempt de comportements anormaux ou malhonnêtes, peut être modélisée par un modèle d’états linéaire, et traqué par un filtre de Kalman. De plus, les paramètres d’un filtre calibre au niveau d’un nœud donne, peuvent être utilises pour modéliser et prédire le comportement dynamique d’un autre nœud, tant que ces deux nœuds sont proches l’un de l’autre dans le réseau. Nous avons d`es lors propose une infrastructure de nœuds experts : des nœuds de confiance, se positionnant dans l’espace des coordonnées, en utilisant exclusivement d’autres nœuds experts. Ils sont alors immunisés contre n’importe quel comportement malicieux dans le système. Pendant le calcul de leurs propres coordonnées, les autres nœuds utilisent les paramètres du filtre d’un nœud expert proche, comme étant une représentation d’un comportement normal, pour détecter et filtrer toute activité malicieuse ou anormale. Une combinaison de simulations et d’expérimentations PlanetLab a été utilisée pour démontrer la validité, la généralité et l’efficacité de l’approche proposée pour chacun des deux systèmes Vivaldi et NPS. Enfin, nous nous sommes penchés sur le problème de la validité des coordonnées Internet telles qu’ annoncées par les nœuds d’un système de coordonnées durant la phase d’estimation des distances. En effet, certains nœuds peuvent délibérément mentir quant `a la valeur exacte de leurs coordonnées afin de lancer diverses attaques contre les applications et les réseaux de couverture. La méthode proposée se divise en deux étapes : 1)établir l’exactitude des coordonnées annoncées en utilisant l’infrastructure des nœuds experts et la méthode de détection des nœuds malicieux, et 2) délivrer un certificat `a validité limitée pour chaque coordonnée vérifiée. Les périodes de validité sont calculées `a partir d’une analyse des temps d’inter changement observés par les nœuds experts. En faisant cela, chaque nœud expert, peut estimer le temps jusqu’au prochain changement de coordonnées, et ainsi, peut limiter le temps de validité du certificat qu’il délivrerait aux nœuds normaux. Notre méthode est illustrée en utilisant une trace recueillie a partir d’un système Vivaldi déployé sur PlanetLab, ou les distributions de temps d’inter changements suivent des distributions longue traîne (distribution log-normale dans la plupart des cas, et distribution Weilbull sinon). Nous montrons l’efficacité de notre méthode en mesurant l’impact de plusieurs attaques sur les estimations de distance, expérimentées sur PlanetLab<br>Idea is that if network distances between Internet nodes can be embedded in an appropriate space, unmeasured distances can be estimated using a simple distance computation in that space. Recently, these coordinates-based systems have been shown to be accurate, with very low distance prediction error. However, most, if not all, of current proposals for coordinate systems assume that the nodes partaking in the system cooperate fully and honestly with each other – that is that the information reported by probed nodes is correct – this could also make them quite vulnerable to malicious attacks. In particular, insider attacks executed by potentially colluding) legitimate users or nodes infiltrating the system could prove very effective. As the use of overlays and applications relying on coordinates increases, one could imagine the release of worms and other malware, exploiting such cooperation, which could seriously disrupt the operations of these systems and therefore the virtual networks and applications relying on them for distance measurements. In this thesis, we first identify such attacks, and through a simulation study, we observed their impact on two recently proposed positioning systems, namely Vivaldi and NPS. We experimented with attack strategies, carried out by malicious nodes that provide biased coordinates information and delay measurement probes, and that aim to (i) introduce disorder in the system, (ii) fool honest nodes to move far away from their correct positions and (iii) isolate particular target nodes in the system through collusion. Our findings confirm the susceptibility of the coordinate systems to such attacks. Our major contribution is therefore a model for malicious behavior detection during coordinates embedding. We first show that the dynamics of a node, in a coordinate system without abnormal or malicious behavior, can be modeled by a Linear State Space model and tracked by a Kalman filter. Then we show, that the obtained model can be generalized in the sense that the parameters of a filter calibrated at a node can be used effectively to model and predict the dynamic behavior at another node, as long as the two nodes are not too far apart in the network. This leads to the proposal of a Surveyor infrastructure: Surveyor nodes are trusted, honest nodes that use each other exclusively to position themselves in the coordinate space, and are therefore immune to malicious behavior in the system. During their own coordinate embedding, other nodes can then use the filter parameters of a nearby Surveyor as a representation of normal, clean system behavior to detect and filter out abnormal or malicious activity. A combination of simulations and PlanetLab experiments are used to demonstrate the validity, generality, and effectiveness of the proposed approach for both Vivaldi and NPS. Finally, we address the issue of asserting the accuracy of Internet coordinates advertised by nodes of Internet coordinate systems during distance estimations. Indeed, some nodes may even lie deliberately about their coordinates to mount various attacks against applications and overlays. Our proposed method consists in two steps: 1) establish the correctness of a node’s claimed coordinate by using the Surveyor infrastructure and malicious embedding neighbor detection; and 2) issue a time limited validity certificate for each verified coordinate. Validity periods are computed based on an analysis of coordinate inter-shift times observed by Surveyors. By doing this, each surveyor can estimate the time until the next shift and thus, can limit the validity of the certificate it issues to regular nodes for their calculated coordinates. Our method is illustrated using a trace collected from a Vivaldi system deployed on PlanetLab, where intershift times are shown to follow long-tail distribution (log-normal distribution in most cases, or Weibull distribution otherwise). We show the effectiveness of our method by measuring the impact of a variety of attacks, experimented on PlanetLab, on distance estimates
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Myers, Colin. "Reducing clutter in parallel coordinates /." Leeds : University of Leeds, School of Computer Studies, 2008. http://www.comp.leeds.ac.uk/fyproj/reports/0708/Myers.pdf.
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Skelton, George. "Variation of Fenchel Nielsen coordinates." Thesis, University of Warwick, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.247640.
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Mohan, Srividya. "Reaction coordinates for RNA conformational changes." Diss., Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/33815.
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This work investigates pathways of conformational transitions in ubiquitous RNA structural motifs. In our lab, we have developed multi-scale structural datamining techniques for identification of three-dimensional structural patterns in high-resolution crystal structures of globular RNA. I have applied these techniques to identify variations in the conformations of RNA double-helices and tetraloops. The datamined structural information is used to propose reaction coordinates for conformational transitions involved in double-strand helix propagation and tetraloop folding in RNA. I have also presented an algorithm to identify stacked RNA bases. In this work, experimentally derived thermodynamic evaluation of the conformations has been used to as an additional parameter to add detail to RNA structural transitions.
RNA conformational transitions help control processes in small systems such as riboswitches and in large systems such as ribosomes. Adopting functional conformations by globular RNA during a folding process also involves structural transitions. RNA double-helices and tetraloops are common, ubiquitous structural motifs in globular RNA that independently fold in to a thermodynamically stable conformation. Folding models for these motifs are proposed in this work with probable intermediates ordered along the reaction coordinates.
We hypothesize that frequently observed structural states in crystals structures are analogous in conformation to stable thermodynamic â on-pathwayâ folded states. Conversely, we hypothesize that conformations that are rarely observed are improbable folding intermediates, i.e., these conformational states are â off-pathwayâ states. In general on-pathway states are assumed to be thermodynamically more stable than off-pathway states, with the exception of kinetic traps.
Structural datamining shows that double helices in RNA may propagate by the â stack-ratchetâ mechanism proposed here instead of the commonly accepted zipper mechanism. Mechanistic models for RNA tetraloop folding have been proposed and validated with experimentally derived thermodynamic data. The extent of stacking between bases in RNA is variable, indicating that stacking may not be a two-state phenomenon. A novel algorithm to define and identify stacked bases at atomic resolution has also been presented in this work.
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Sharples, Jason, and n/a. "Spacetime initial data and quasispherical coordinates." University of Canberra. Mathematics &Statistics, 2001. http://erl.canberra.edu.au./public/adt-AUC20061108.151839.
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In General Relativity, the Einstein field equations allow us to study the evolution of a
spacelike 3-manifold, provided that its metric and extrinsic curvature satisfy a system of
geometric constraint equations. The so-called Einstein constraint equations, arise as a
consequence of the fact that the 3-manifold in question is necessarily a submanifold of
the spacetime its evolution defines.
This thesis is devoted to a study of the structure of the Einstein constraint system in
the special case when the spacelike 3-manifold also satisfies the quasispherical ansatz of
Bartnik [B93]. We make no mention of the generality of this gauge; the extent to which
the quasispherical ansatz applies remains an open problem.
After imposing the quasispherical gauge, we give an argument to show that the resulting
Einstein constraint system may be viewed as a coupled system of partial differential
equations for the parameters describing the metric and second fundamental form. The
hencenamed quasisperical Einstein constraint system, consists of a parabolic equation, a
first order elliptic system and (essentially) a system of ordinary differential equations.
The question of existence of solutions to this system naturally arises and we provide a
partial answer to this question. We give conditions on the initial data and prescribable
fields under which we may conclude that the quasispherical Einstein constraint system is
uniquley solvable, at least in a region surrounding the unit sphere.
The proof of this fact is centred on a linear iterative system of partial differential equations,
which also consist of a parabolic equation, a first order elliptic system and a system of
ordinary differential equations. We prove that this linear system consistently defines a
sequence, and show via a contraction mapping argument, that this sequence must converge
to a fixed point of the iteration. The iteration, however, has been specifically designed
so that any fixed point of the iteration coincides with a solution of the quasispherical
Einstein constraints.
The contraction mapping argument mentioned above, relies heavily on a priori estimates
for the solutions of linear parabolic equations. We generalise and extend known results
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concerning parabolic equations to establish special a priori estimates which relate a useful
property: the L2-Sobolev regularity of the solution of a parabolic equation is greater
than that of the coefficients of the elliptic operator, provided that the initial data is
sufficiently regular. This 'smoothing' property of linear parabolic equations along with
several estimates from elliptic and ordinary differential equation theory form the crucial
ingredients needed in the proof of the existence of a fixed point of the iteration.
We begin in chapter one by giving a brief review of the extensive literature concerning
the initial value problem in General Relativity. We go on, after mentioning two of the
traditional methods for constructing spacetime initial data, to introduce the notion of a
quasispherical foliation of a 3-manifold and present the Einstein constraint system written
in terms of this gauge.
In chapter two we introduce the various inequalities and tracts of analysis we will make use
of in subsequent chapters. In particular we define the, perhaps not so familiar, complex
differential operator 9 (edth) of Newman and Penrose.
In chapter three we develop the appropriate Sobolev-regularity theory for linear parabolic
equations required to deal with the quasispherical initial data constraint equations. We
include a result due to Polden [P] here, with a corrected proof. This result was essential
for deriving the results contained in the later chapters of [P], and it is for this reason we
include the result. We don't make use of it explicitly when considering the quasispherical
Einstein constraints, but the ideas employed are similar to those we use to tackle the
problem of existence for the quasispherical constraints.
Chapter four is concerned with the local existence of quasispherical initial data. We
firstly consider the question of existence and uniqueness when the mean curvature of
the 3-manifold is prescribed, then after introducing the notion of polar curvature, we also
present another quasispherical constraint system in which we consider the polar curvature
as prescribed. We prove local existence and uniqueness results for both of these alternate
formulations of the quasispherical constraints.
This thesis was typeset using LATEXwith the package amssymb.
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Sharp, J. R. "Reactive scattering calculations in hyperspherical coordinates." Thesis, University of Manchester, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.234214.
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Yurttas, Saadet Öykü. "Dynnikov coordinates and pseudo-Anosov braids." Thesis, University of Liverpool, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.569517.
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The aim of this thesis is to study dynamical properties of pseudo -Anosov braids on the n-times punctured disk Dn making use of a particular coordinate system called the Dynnikov coordinate system. The Dynnikov coordinate system gives a homeomorphism from the space of measured foliations MFn on Dn (up to a certain equivalence relation) to Sn = R2n-4\ {O}, and restricts to a bijection from the set of integral laminations (disjoint unions of finitely many essential simple closed curves) on Dn to Cn = Z2n-4 \ {O}. In the first part of the thesis, we introduce a new method for computing the topological entropy of each member of an infinite family of pseudo -Anosov braids making use of Dynnikov's coordinates. The method is developed using the results in Thurston's seminal paper on the geometry and dynamics of surface automorphisms and builds on, more recent work of Moussafir. To be more spe- cific, the method gives a so-called Dynnikov matrix which describes the action of a given pseudo-Anosov braid B near its invariant unstable measured foliation [F, u] on the projective space PSn, and the eigenvalue \ > 1 of this matrix gives the topological entropy of B. In the second part of the thesis, we compare the spectra of Dynnikov matrices with the spectra of the train track transition matrices of a given pseudo-Anosov braid, and show that these matrices are isospectral up to roots of unity and zeros under some particular conditions.
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Silva, Francisco Allan Quintela. "Geometric coordinates parametric functions in winplot." Universidade Federal do CearÃ, 2014. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=12408.
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nÃo hÃ<br>Desde o princÃpio, as sequÃncias e sÃries numÃricas geraram interesse entre os matemÃticos. Sua aplicabilidade atual à extensa e inclui o cÃlculo refinado da Ãrea da superfÃcie e do volume de uma variedade de sÃlidos. Neste trabalho usaremos as diferenÃas entre os elementos de uma sequÃncia finita a fim de encontrar leis que expressem as tendÃncias nela contidas. Veremos tambÃm como um estudo simples sobre progressÃes aritmÃticas de ordens diversas à capaz de fornecer funÃÃes paramÃtricas de curvas passando por pontos prÃ-definidos, de superfÃcies contendo curvas prÃ-definidas ou, atà mesmo, de regiÃes do R situadas entre duas superfÃcies dadas. AlÃm disso, poderemos, com o auxÃlio do programa computacional Winplot, visualizar as curvas, superfÃcies ou regiÃes obtidas em cada exemplo de nosso estudo, alÃm de, eventualmente, verificar pontos de mÃximo e mÃnimo relativos de uma curva ou calcular a Ãrea de uma superfÃcie e o volume de uma regiÃo limitada do RÂ, tudo isto com um devido e prÃvio embasamento teÃrico.<br>From the beginning, the numeric sequences and series generated interest among mathematicians. Your present applicability is extensive and includes the refined calculation of the surface area and volume of a variety of solids. In this work we will use the differences between the elements of a finite sequence in order to find laws that express the trends contained therein. We will also see how a simple study about arithmetic progressions of various orders is able to provide curves's parametric functions through predefined points, of surfaces containing predefined curves or even regions of the R localized between two given surfaces. Moreover, we will can, with the aid of the computational program Winplot, visualize the curves, surfaces, or regions obtained in each example of our study, in addition to eventually check points of relative maximum and minimum of a curve or calculate the area of a surface and the volume of a limited region of RÂ, all of this with a necessary and previous theoretical background.
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van, Wagtendonk Martijn. "A striving flirtation in spliced coordinates." The Ohio State University, 1998. http://rave.ohiolink.edu/etdc/view?acc_num=osu1102448295.
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Van, Wagtendonk Martijn. "A striving flirtation in spliced coordinates /." Connect to this title online, 1998. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1102448295.
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Voll, Robert W. "Comparing the accuracy and efficiency of algorithms for converting cartesian to geodetic coordinates." Master's thesis, This resource online, 1990. http://scholar.lib.vt.edu/theses/available/etd-02162010-020028/.
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Francis, Gerald. "An Algorithm and System for Measuring Impedance in D-Q Coordinates." Diss., Virginia Tech, 2010. http://hdl.handle.net/10919/26462.
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This dissertation presents work conducted at the Center for Power Electronics Systems (CPES) at Virginia Polytechnic Institute and State University.
Chapter 1 introduces the concept of impedance measurement, and discusses previous work on this topic. This chapter also addresses issues associated with impedance measurement.
Chapter 2 introduces the analyzer architecture and the proposed algorithm. The algorithm involves locking on to the voltage vector at the point of common coupling between the analyzer and the system via a PLL to establish a D-Q frame. A series of sweeps are performed, injecting at least two independent angles in the D-Q plane, acquiring D- and Q-axis voltages and currents for each axis of injection at the point of interest.
Chapter 3 discusses the analyzer hardware and the criteria for selection. The hardware built ranges from large-scale power level hardware to communication hardware implementing a universal serial bus. An eight-layer PCB was constructed implementing analog signal conditioning and conversion to and from digital signals with high resolution. The PCB interfaces with the existing Universal Controller hardware.
Chapter 4 discusses the analyzer software. Software was written in C++, VHDL, and Matlab to implement the measurement process. This chapter also provides a description of the software architecture and individual components.
Chapter 5 discusses the application of the analyzer to various examples. A dynamic model of the analyzer is constructed, considering all components of the measurement system. Congruence with predicted results is demonstrated for three-phase balanced linear impedance networks, which can be directly derived based on stationary impedance measurements. Other impedances measured include a voltage source inverter, Vienna rectifier, six-pulse rectifier and an autotransformer-rectifier unit.<br>Ph. D.
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Heide, Bernd Michael. "Measuring Absolute Space Coordinates in Two Dimensions." Universitätsbibliothek Chemnitz, 2000. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200000758.
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The paper describes how a two-dimensional absolute measuring system can
explicitly be realized. The theoretical background, the experimental setup,
the evaluation algorithm, and the results of measurement are discussed in
detail.
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Chen, Guodong. "Solution of diffusion equation in axisymmetrical coordinates." Ohio : Ohio University, 1994. http://www.ohiolink.edu/etd/view.cgi?ohiou1176840295.
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Oshima, Satoshi, Rika Mochizuki, Reiner Lenz, and Jinhui Chao. "Color-Weakness Compensation using Riemann Normal Coordinates." Linköpings universitet, Medie- och Informationsteknik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-86669.
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We introduce normal coordinates in Riemannspaces as a tool to construct color-weak compensation methods.We use them to compute color stimuli for a color weakobservers that result in the same color perception as theoriginal image presented to a color normal observer in the sensethat perceived color-differences are identical for both. Thecompensation is obtained through a color-difference-preservingmap, i.e. an isometry between the 3D color spaces of a colornormaland any given color-weak observer. This approach usesdiscrimination threshold data and is free from approximationerrors due to local linearization. The performance is evaluatedwith the help of semantic differential (SD) tests.<br>Swedish Foundation for Strategic Research through grant IIS11-0081.<br>European Community’s Seventh Framework Programme FP7/2007-2013 - Challenge 2 Cognitive Systems, Interaction, Robotics - under grant agreement No 247947 - GARNICS.
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Murphy, Ailbhe. "Tower songs : Critical coordinates for collaborative practice." Thesis, Ulster University, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.537601.
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This thesis has explored the possibilities within collaborative arts practice for creating an interdisciplinary form of evaluation to address the centrality and complexity of negotiation in collaborative practice. The navigational challenges for artists negotiating this field were considered in light of the critical debates within socially engaged arts practice (Kester, 2004 and 2005; Kwon 2002: Bishop, 2009, Lind 2004 and Doherty 2008) which tend to organise the field along a series of binary oppositions such as: process v product; aesthetics v ethics; participative v collaborative practice and intersubjectivity v autonomy. The cross-city collaborative project I initiated in Dublin called Tower Songs served as the vehicle for a practice-based investigation of my research questions. Tower Songs was concerned with the dynamics of a changing city amplified in the demise of public housing (flat complex) estates across Dublin. The thesis introduced a theoretical frame drawn from feminist and post colonial theory (Rodríguez 2006) in order to examine a series of reflective processes which sought to make sense of the first two years work of Tower Songs. From there an interdisciplinary turn in practice was described where questions of epistemology and knowledge production from within the social sciences encounter those negotiated practices and critical references from socially engaged arts practice. The question of evaluation of collaborative projects was tested from the point of view of this expanding theoretical register by Vagabond Reviews through the review of a large scale community-based street spectacle called the Night of the Dark Angel. That interdisciplinary practice was examined in relation to a post structuralist critique which drew on arguments for the destabilising of voice in qualitative inquiry (Lather, 2009 and 2004; Mazzei, 2009; Mazzei and Jackson, 2009 and Jackson, 2009) The post structuralist critique of voice was explored as a move away from the binary oppositions of art critical debates and the pre-determined linguistic arenas of formal evaluation frameworks in favour of a transversal reading of the collaborative experience.
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CUSTODIO, LIS INGRID ROQUE LOPES. "EXTENSIONS OF BARYCENTRIC COORDINATES FOR MESH DEFORMATION." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2010. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=16491@1.
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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO<br>Dentro dos métodos deformação de objetos tridimensionais, os que usam poliedros de controle permitem interações rápidas e intuitivas, e assim ganharam bastante interesse nos últimos anos. Essas técnicas expressam os pontos do objeto a partir dos vértices do poliedro de controle, por exemplo usando coordenadas baricêntricas e suas extensões.Assim, ao deformar o poliedro de controle, obtém-se deformações correspondentes sobre o modelo recalculando cada ponto do objeto a partir das novas posições dos vértices de controle. Devido ao grau de flexibilidade em sua construção, diferentes generalizações de coordenadas baricêntricas vem sendo propostas nos últimos anos para modelos 3D. Nesse trabalho apresentamos um estudo das recentes generalizações de coordenadas baricêntricas e as principais características das deformações em modelos em três dimensões obtidas com o uso de cada uma delas. Deduzimos desse estudo uma nova extensão de coordenadas baricêntricas que mantém a simplicidade do método original e corrige alguns dos seus defeitos.<br>Within the thee-dimensional objects deformation techniques, the ones using control polyhedrons allow fast and intuitive interaction, and therefore gained considerable interest in recent years. Those techiques write the model points as function of the vertices of the control polyhedron, for exemple using barycentric coordinates or its extensions. This way, deforming the control polyhedron induces a corresponding strain on the model, recomputing each point of the object from the new positions of control vertices. To do so, due to the flexibility in its construction, different generalizations of barycentric coordinates has been proposed in recent years for 3D models. In this work, we present a study of recent generalizations of barycentric coordinates and the main characteristics of the resulting deformations of three-dimensional model. We deduce from this study a new extension of barycentric coordinates that retains the simplicity of the original method and fixes some of the its defects.
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Ba, Demba Elimane. "Nonlinear transform coding with lossless polar coordinates." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/37937.
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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.<br>Includes bibliographical references (p. 51-52).<br>In conventional transform coding, the importance of preserving desirable quantization partition cell shapes prevents one from considering the use of a nonlinear change of variables. If no linear transformation of a given source would yield independent components, this means having to encode it at a rate higher than its entropy, i.e. suboptimally. This thesis proposes a new transform coding technique where the source samples are first uniformly scalar quantized and then transformed with an integer-to-integer approximation to a nonlinear transformation that would give independent components. In particular, we design a family of integer-to-integer approximations to the Cartesian-to-polar transformation and analyze its behavior for high rate transform coding. Among the benefits of such an approach is the ability to achieve redundancy reduction beyond decorrelation without limitation to orthogonal linear transformations of the original variables. A high resolution analysis is given, and for source models inspired by a sensor network application and by image compression, simulations show improvements over conventional transform coding. A comparison to state-of-the-art entropy-coded polar quantization techniques is also provided.<br>by Demba Elimane Ba.<br>S.M.
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Hernández, Moreno Ricardo Alfonso. "Anti-de Sitter holography in different coordinates /". São Paulo, 2013. http://hdl.handle.net/11449/108898.
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Orientador: Horatiu Stefan Nastase<br>Banca: Ion Vasile Vancea<br>Banca: Andrey Yuryevich Mikhaylov<br>Resumo: O objetivo deste trabalho é mostrar a importância da escolha do sistema de coordenadas e assinatura para descrever o espaço Anti-de Sitter na Correspondência AdS/CFT. Para fazer isto, mostraremos como calcular correlatores em diferentes coordenadas no lado gravitacional da correspondência. Em particular, apresentamos o procedimiento geral para encontrar o propagador bulk-fronteira para um campo escalar, de gauge e espinorial usando o método de Witten em coordenadas de Poincaré com assinatura euclideana. Também mostramos os cálculos das funções de n pontos para um campo escalar interagente em AdS a nível de árvore e comparamos os resultados com os vínculos da teoria de campos conformes. Para comparar as implicações de trabalhar em outro sistema coordenado refazemos os cálculos dos propagadores para o campo escalar em coordenadas globais. Finalmente mostramos como calcular o propagador bulk-fronteira para um campo 3-forma que vive em 'AdS IND. 7' em coordenadas globais e de Poincaré<br>Abstract: The goal of this work is to show the significance of the choice of coordinates system and signature to describe the Anti-de Sitter space within AdS/CFT Correspondence. In order to do so, we will show how to calculate AdS/CFT correlators in different coordinates from the gravity side of the correspondence. In particular, we present the general procedure to find the bulk-to-boundary propagators for scalar, gauge and spinor fields using Witten's method in Poincaré coordinates with Euclidean signature. We also show the calculations ofn-point functions for a classical interacting scalar field in AdS at tree level and compare the results with the CFT constraints. To compare the implications of working in different coordinates, we recalculate the propagators for the scalar field in Global coordinates. Finally, we show the calculations of bulk-to-boundary propagator for a 3-form field living in 'AdS IND. 7' in both Poincaré and Global coordinates<br>Mestre
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Chen, Goudong. "Solution of diffusion equation in axisymmetrical coordinates." Ohio University / OhioLINK, 1994. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1176840295.
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Suma, Christopher G. "Parallel Coordinates Diagram Implementation in 3D Geometry." University of Akron / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=akron1542590859588961.
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Trigui, Aymen. "Natural neighbour coordinates on irregular staggered grids." [S.l. : s.n.], 2005. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB11730079.
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Cai, Liang Bear James E. "Coronin 1B coordinates actin dynamics in lamellipodia." Chapel Hill, N.C. : University of North Carolina at Chapel Hill, 2007. http://dc.lib.unc.edu/u?/etd,2163.
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Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 2007.<br>Title from electronic title page (viewed Feb. 26, 2009). "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Cell and Developmental Biology." Discipline: Cell and Developmental Biology; Department/School: Medicine.
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Zhou, Hong. "Visual clustering in parallel coordinates and graphs /." View abstract or full-text, 2009. http://library.ust.hk/cgi/db/thesis.pl?CSED%202009%20ZHOU.
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Yao, Xueyang. "The Discrete 2D Fourier Transform In Polar Coordinates." Thesis, Université d'Ottawa / University of Ottawa, 2018. http://hdl.handle.net/10393/37656.
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The discrete Fourier transform in Cartesian coordinates has proved to be invaluable in many disciplines. However, less theory has been developed for functions that are best described in polar coordinates. In this thesis, a new discrete 2D-Fourier transform in polar coordinates is proposed and tested by numerical simulations. Guidelines for choosing sample size are developed. Furthermore, to be as useful as its Cartesian counterpart, improvements are made to reduce the computing time.
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Hernández, Moreno Ricardo Alfonso [UNESP]. "Anti-de Sitter holography in di?erent coordinates." Universidade Estadual Paulista (UNESP), 2013. http://hdl.handle.net/11449/108898.
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Made available in DSpace on 2014-08-27T14:36:44Z (GMT). No. of bitstreams: 0
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000778154.pdf: 709298 bytes, checksum: 4e299e7ae9870aa72c05e3f3f6af3c66 (MD5)<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)<br>O objetivo deste trabalho é mostrar a importância da escolha do sistema de coordenadas e assinatura para descrever o espaço Anti-de Sitter na Correspondência AdS/CFT. Para fazer isto, mostraremos como calcular correlatores em diferentes coordenadas no lado gravitacional da correspondência. Em particular, apresentamos o procedimiento geral para encontrar o propagador bulk-fronteira para um campo escalar, de gauge e espinorial usando o método de Witten em coordenadas de Poincaré com assinatura euclideana. Também mostramos os cálculos das funções de n pontos para um campo escalar interagente em AdS a nível de árvore e comparamos os resultados com os vínculos da teoria de campos conformes. Para comparar as implicações de trabalhar em outro sistema coordenado refazemos os cálculos dos propagadores para o campo escalar em coordenadas globais. Finalmente mostramos como calcular o propagador bulk-fronteira para um campo 3-forma que vive em 'AdS IND. 7' em coordenadas globais e de Poincaré<br>The goal of this work is to show the signi?cance of the choice of coordinates system and signature to describe the Anti-de Sitter space within AdS/CFT Correspondence. In order to do so, we will show how to calculate AdS/CFT correlators in di?erent coordinates from the gravity side of the correspondence. In particular, we present the general procedure to ?nd the bulk-to-boundary propagators for scalar, gauge and spinor ?elds using Witten’s method in Poincaré coordinates with Euclidean signature. We also show the calculations ofn-point functions for a classical interacting scalar ?eld in AdS at tree level and compare the results with the CFT constraints. To compare the implications of working in di?erent coordinates, we recalculate the propagators for the scalar ?eld in Global coordinates. Finally, we show the calculations of bulk-to-boundary propagator for a 3-form ?eld living in 'AdS IND. 7' in both Poincaré and Global coordinates
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Gong, Shengjun, and 龔勝軍. "Linear coordinates, test elements, retracts and automorphic orbits." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B40988065.
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Gillette, Andrew, and Alexander Rand. "INTERPOLATION ERROR ESTIMATES FOR HARMONIC COORDINATES ON POLYTOPES." EDP SCIENCES S A, 2016. http://hdl.handle.net/10150/621355.
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Interpolation error estimates in terms of geometric quality measures are established for harmonic coordinates on polytopes in two and three dimensions. First we derive interpolation error estimates over convex polygons that depend on the geometric quality of the triangles in the constrained Delaunay triangulation of the polygon. This characterization is sharp in the sense that families of polygons with poor quality triangles in their constrained Delaunay triangulations are shown to produce large error when interpolating a basic quadratic function. Non-convex polygons exhibit a similar limitation: large constrained Delaunay triangles caused by vertices approaching a non-adjacent edge also lead to large interpolation error. While this relationship is generalized to convex polyhedra in three dimensions, the possibility of sliver tetrahedra in the constrained Delaunay triangulation prevent the analogous estimate from sharply reflecting the actual interpolation error. Non-convex polyhedra are shown to be fundamentally different through an example of a family of polyhedra containing vertices which are arbitrarily close to non-adjacent faces yet the interpolation error remains bounded.
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Gong, Shengjun. "Linear coordinates, test elements, retracts and automorphic orbits." Click to view the E-thesis via HKUTO, 2008. http://sunzi.lib.hku.hk/hkuto/record/B40988065.
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Habermas, Derek. "Compact Symmetric Spaces, Triangular Factorization, and Cayley Coordinates." Diss., The University of Arizona, 2006. http://hdl.handle.net/10150/195953.
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Let X be a simply connected, compact Riemannian symmetric space. We can represent X as the homogeneous space U/K, where U is a simply connected compact Lie group, and K is the fixed point set of an involution θ of U. Let G be the complexification of U. We consider the intersections of the image of the Cartan embedding Φ : U/K → U ⊂ G : uK → uu⁻ᶿ with the strata of the Birkhoff (or triangular, or LDU) decomposition G = ⫫(w∈W) ∑(G/w), ∑(G/w) = N⁻wHN⁺ relative to a θ-stable decomposition of the Lie algebra, g = n⁻ ⊕h ⊕ n⁺. For a generic element g in this intersection, g ∈ Φ(U/K) ∩ ∑(G/1), this yields a unique triangular factorization g = ldu. Our main contribution is to produce explicit formulas for the diagonal term d in classical cases, using Cayley coordinates (this choice of coordinate is motivated by considerations beyond sheer convenience). These formulas have several applications: 1) we can compute π₀(Φ(U/K) \ ∩ ∑(G/1) ) explicitly; 2) we can compute ʃ(Φ(U/K))ᵃΦ^-iλ (where ᵃΦ is the positive part of d) using elementary techniques in rank 1 cases; 3) they are useful in explicitly calculating Evens-Lu Poisson structures on U=K (see [Caine(2006)]). Our set-up involves choosing specific representations of the various u in su(n;C) that are compatible with θ; that is, θ fixes each of the subspaces n⁻; h; and n⁺ which, in our setup, always consist of strictly lower triangular, diagonal, and strictly upper triangular matrices, respectively. The formulas contain determinants such as det(1 + X), where X is in ip, the -1-eigenspace of θ acting on the Lie algebra u. Due to the relatively sparse nature of these matrices, these determinants are often easily calculable, and we illustrate this with many examples.
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Lam, Chi-ming, and 藍志明. "Algorithms to determine tame and wild coordinates of Z[x,y]." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2003. http://hub.hku.hk/bib/B29470560.
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Börjesson, Nils. "Transformations between Camera Images and Map Coordinates with Applications." Thesis, Linköping University, Department of Electrical Engineering, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-3673.
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<p>The quality of cameras is currently increasing very fast meanwhile the price of them is decreasing. The possibilities of using a camera as a measurement and navigation instrument are thus getting bigger all the time. This thesis studies the transformation relations between a camera image and the scene in space that is projected to it. A theoretical derivation of the transform will be presented, and methods and algorithms for applications based on the transform will be developed.</p><p>The above mentioned transform is called the camera matrix, which contains information about the camera attitude, the camera position, and the internal structure of the camera. Useful information for several different applications can be extracted from the camera image with the help of the camera matrix.</p><p>In one of the applications, treated in this Master´s thesis, the camera attitude is estimated when the camera is calibrated and its position is known. Another application is that of absolute target positioning, where a point in a digital map is searched from its position in a camera image. Better accuracy in the measurements can though be obtained with relative target positioning i.e., estimation of distance and angle between two points in the digital map by picking them out in the image. This is because that the errors of the</p><p>absolute target positioning for each of the two points are dependent and thus partly will cancel each other out when their relative position and angle is measured.</p>
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Ljungberg, Malin. "Handling of curvilinear coordinates in a PDE solver framework." Licentiate thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-86138.
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By the use of object-oriented analysis and design combined with variability modeling a highly flexible software model for the metrics handling functionality of a PDE solver framework was obtained. This new model was evaluated in terms of usability, particularly with respect to efficiency and flexibility. The efficiency of a pilot implementation is similar to, or even higher than that of a pre-existing application-specific reference code. With regards to flexibility it is shown that the new software model performs well for a set of four change scenarios selected by an expert user group.
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區榮海 and Wing-hoi Au. "Numerical generation of body-fitted coordinates by multigrid method." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1990. http://hub.hku.hk/bib/B31209555.
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Zhou, You M. Eng Massachusetts Institute of Technology. "Computing network coordinates in the presence of Byzantine faults." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/46365.
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Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>Includes bibliographical references (p. 57-60).<br>Network coordinate systems allow for efficient construction of large-scale distributed systems on the Internet. Coordinates provide locality information in a compact way, without requiring each node to contact every potential neighbor; distances between two nodes' coordinates represent estimates of the network latency between them. Past work on network coordinates has assumed that all nodes in the system behave correctly. The techniques in these systems do not behave well when nodes are Byzantine. These Byzantine failures, wherein a faulty node can behave arbitrarily, can make the coordinate-based distance estimates meaningless. For example, a Byzantine node can delay responding to some other node, thus distorting that node's computation of its own location. We present a network coordinate system based on landmarks, reference nodes that are used for measurements, some of which may be Byzantine faulty. It scales linearly in the number of clients computing their coordinates and does not require excessive network traffic to allow clients to do so. Our results show that our system is able to compute accurate coordinates even when some landmarks are exhibiting Byzantine faults.<br>by You Zhou.<br>M.Eng.
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Chen, Justin Ph D. Massachusetts Institute of Technology. "The extreme anterior domain coordinates brain and craniofacial development." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/117870.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Biology, 2018.<br>Cataloged from PDF version of thesis. Vita.<br>Includes bibliographical references.<br>The head is one of the most complex and important parts of the body. The shape of the head is largely determined by the size of the brain and morphology of the facial skeleton. These tissues consist of different cell types and undergo distinct developmental programs. However, development of the brain and various parts of the face may be coordinated so that tissues form in the correct order and scale to each other appropriately. Work presented here demonstrates that the Xenopus Extreme Anterior Domain (EAD), a group of 500 cells located at the anterior tip of the frog embryo, coordinates brain and craniofacial development through two distinct mechanisms. First, the EAD acts as a long range organizer for head development by regulating the size of both the brain and surrounding facial cartilage. Perturbing expression of frzb and crescent, genes encoding Wnt antagonists, in the EAD is sufficient to decrease cell proliferation in the brain and neural crest. Analysis of transgenic reporter embryos suggests that the EAD affects beta-catenin Wnt signaling over a range of 800 microns. By affecting the growth of both the brain and neural crest-derived cartilage, the EAD determines the overall size of the head. Second, the EAD synchronizes neural crest migration and the formation of two columns of cells, termed the pre-mouth array, that precede mouth opening. During this process, Kinin-Kallikrein signaling from the EAD is required to guide neural crest cells into the face. After their migration, neural crest cells signal back to the EAD to regulate pre-mouth array morphogenesis via Wnt/PCP signaling. Formation of the pre-mouth array involves convergent extension-like behavior where the EAD, originally a wide and short mass of cells, narrows and lengthens to form two columns of cells which later split down the middle during mouth opening. Reciprocal signaling between the EAD and neural crest ensures that mouth opening begins after the neural crest have completed migration. The organizing function of the EAD is likely conserved in vertebrates including humans. Understanding global coordination of brain and craniofacial development provides insight into the causes of facial abnormalities and microcephaly.<br>by Justin Chen.<br>Ph. D.
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Motoike, Toshiyuki, Jeffrey M. Long, Hirokazu Tanaka, Christopher M. Sinton, Amber Skach, S. Clay Williams, Robert E. Hammer, Takeshi Sakurai, and Masashi Yanagisawa. "Mesolimbic neuropeptide W coordinates stress responses under novel environments." NATL ACAD SCIENCES, 2016. http://hdl.handle.net/10150/616999.
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Neuropeptide B (NPB) and neuropeptide W(NPW) are endogenous neuropeptide ligands for the G protein-coupled receptors NPBWR1 and NPBWR2. Here we report that the majority of NPW neurons in the mesolimbic region possess tyrosine hydroxylase immunoreactivity, indicating that a small subset of dopaminergic neurons coexpress NPW. These NPW-containing neurons densely and exclusively innervate two limbic system nuclei in adult mouse brain: the lateral bed nucleus of the stria terminalis and the lateral part of the central amygdala nucleus (CeAL). In the CeAL of wild-type mice, restraint stress resulted in an inhibition of cellular activity, but this stress-induced inhibition was attenuated in the CeAL neurons of NPW-/- mice. Moreover, the response of NPW-/- mice to either formalin-induced pain stimuli or a live rat (i. e., a potential predator) was abnormal only when they were placed in a novel environment: The mice failed to show the normal species-specific self-protective and aversive reactions. In contrast, the behavior of NPW-/- mice in a habituated environment was indistinguishable from that of wildtype mice. These results indicate that the NPW/NPBWR1 system could play a critical role in the gating of stressful stimuli during exposure to novel environments.
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Sanghvi, Saagar K. "Effect of Rat Strain Stereotactic Coordinates on Infarct Volume." Wright State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=wright1364484571.
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Maire, Steven M. "Inverted Edwards Coordinates (Maire Model of an Elliptic Curve)." Case Western Reserve University School of Graduate Studies / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=case1396888557.
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Chung, Peter Kai-Lun. "A comprehensive parallel coordinates system for air pollution analysis /." View abstract or full-text, 2008. http://library.ust.hk/cgi/db/thesis.pl?CSED%202008%20CHUNG.
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Au, Wing-hoi. "Numerical generation of body-fitted coordinates by multigrid method /." [Hong Kong] : University of Hong Kong, 1990. http://sunzi.lib.hku.hk/hkuto/record.jsp?B1296637X.
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Ernst, Matthias [Verfasser], and Gerhard [Akademischer Betreuer] Stock. "Finding reaction coordinates for protein folding and functional motion." Freiburg : Universität, 2018. http://d-nb.info/1224416481/34.
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Duan, Jingxian. "Cell-wide web of cytoplasmic nanocourses coordinates calcium signalling." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/31133.
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Ca2+ signals determine smooth muscle contraction and the switch from a contractile to a migratory-proliferative phenotype(s), which requires changes in gene expression. However, the mechanism by which different Ca2+ signals are selective for these processes is enigmatic. In the thesis, I built on the “panjunctional sarcoplasmic reticulum” hypothesis, and described the evidence in support of the view that a variety of Ca2+ pumps and release channels, with different kinetics and affinities for Ca2+, are strategically positioned within the cytoplasmic nanocourses of pulmonary arterial smooth muscle cells (PASMCs), and they serve to demarcate different Ca2+ signalling. Nanocourses of the SR are formed in the perinuclear, extraperinuclear, subplasmalemmal regions and the nucleus. Different subtypes of ryanodine receptors (RyRs) are targeted to those nanocourses. Immunocytochemistry results suggest that RyR1s was preferentially targeted to the subplasmalemmal and nuclear nanocourses of PASMCs, they gave rise to a spatially restricted Ca2+ signal within the nanocourses upon stimulation, without affecting global Ca2+ concentration. The Ca2+ signals in the subplasmalemmal nanocourses were shown to induce arterial smooth muscle cell relaxation. On the other hand, the RyR2 and 3 were shown to target to the perinuclear and extraperinuclear nanocourses. Upon stimulation, they generate propagating Ca2+ waves in the cytoplasmic nanocourses, which trigger arterial smooth muscle cell contraction. However, during this process, no Ca2+ transient was observed within the subplasmalemmal nanocourses, suggesting that the regulation of both contraction and relaxation of smooth muscle cells are achieved by spatially restricted Ca2+ signals within different nanocourses. Invaginations of the nucleoplasmic reticulum in arterial myocytes form trans-nuclear networks of cytoplasmic nanospaces, generate Ca2+ signals by strategically positioned Ca2+ pumps (SERCA1) and release channels (RyR1). Within a subpopulation of nuclear invaginations, evoked Ca2+ signals via ryanodine receptors exhibited spatial and temporal separation from adjacent Ca2+ signals within a single “activated” nuclear invagination, and also from those Ca2+ signals arising within different nuclear invaginations. Moreover, nuclear invaginations provide sites for transcriptional suppression, because lamin A and/or emerin line the entire surface of their inner nuclear membranes and co-localise with nesprin-1 positive puncta. More intriguing still, a subpopulation of these nuclear invaginations harboured punctate regions of colocalisation between lamin A and the suppressive heterochromatin mark H3K9me2, while emerin-positive invaginations harboured puncta of BAF (Barrior to autointegration factor) co-localisation and thus an alternative pathway to the regulation of gene expression. I propose that nuclear invaginations form cytoplasmic nanotubes within which nano-patterning of Ca2+ signals may support stochastic modulation of transcriptional suppressors. Together, the cytoplasmic nanocourses form a cell-wide web for Ca2+ signalling and the regulation of various arterial smooth muscle functions, ranging from the regulation of blood pressure by vasodilation and vasoconstriction to gene expression.
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Widman, Brooke Ashley. "Comparing feature type and coordinates in aphasia naming therapy." Thesis, Boston University, 2013. https://hdl.handle.net/2144/12889.
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Thesis (M.S.)--Boston University
PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you.<br>Although Semantic Feature Analysis has long been utilized as an effective treatment for aphasic patients suffering anomia, little research has evaluated what types of features are best equipped for improving patients' naming abilities during treatment. The present study evaluated feature type and coordinates to represent two theories oflexical access: spreading activation and feature based semantic activation. Four patients received two rounds of treatment: One that utilizes coordinates in a modified Semantic Feature Analysis and the other that utilizes semantic features in the same treatment. The results indicated that training coordinates leads to a greater level of naming accuracy in patients with less severe (Anomie) aphasia and that based on these findings, a lexical access theory of spreading activation among coordinates may be a more accurate theory than feature based semantic activation.
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Maspero, A. "BIRKHOFF COORDINATES OF INTEGRABLE HAMILTONIAN SYSTEMS IN ASYMPTOTIC REGIMES." Doctoral thesis, Università degli Studi di Milano, 2014. http://hdl.handle.net/2434/246796.
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In this thesis we investigate two examples of infinite dimensional integrable Hamiltonian systems in $1$-space dimension: the Toda chain with periodic boundary conditions and large number of particles, and the Korteweg-de Vries (KdV) equation on $\R$.
In the first part of the thesis we study the Birkhoff coordinates (Cartesian action angle coordinates) of the Toda lattice with periodic boundary condition in the limit where the number $N$ of the particles tends to infinity. We prove that the transformation introducing such coordinates maps analytically a complex ball of radius $R/N^\alpha$
(in discrete Sobolev-analytic norms) into a ball of radius $R'/N^\alpha$ (with $R,R'>0$ independent of $N$) if and only if
$\alpha\geq2$. Then we consider the problem of equipartition of energy in the spirit of Fermi-Pasta-Ulam. We deduce that corresponding to initial data of size $R/N^2$, $0<R\ll 1$, and with only the first Fourier mode excited, the energy remains forever in a packet of Fourier modes exponentially decreasing with the wave number. Finally we consider the original FPU model and prove that energy remains localized in a similar packet of Fourier modes for times one order of magnitude longer than those covered by previous results which is the time of formation of the packet. The proof of the theorem on Birkhoff coordinates is based on a new quantitative version of a Vey type theorem by Kuksin and Perelman which could be interesting in itself.
In the second part of the thesis we study the scattering map of the KdV on $\R$. We prove that in appropriate weighted Sobolev spaces of the form $H^{N} \cap L^2_M$, with integers $N \geq 2M \geq 8$ and in the case of no bound states, the scattering map is a perturbation of the Fourier transform by a regularizing operator. As an application of this result, we show that the difference of the KdV flow and the corresponding Airy flow is 1-smoothing.
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Jedrecy, Alexandre. "Study of phase transformation of matter through topological coordinates." Electronic Thesis or Diss., Sorbonne université, 2020. http://www.theses.fr/2020SORUS386.
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Au cours de cette thèse deux problèmes majeurs pour l’eau ont été étudiés : la transition liquide-liquide et la nucléation homogène de la glace. Pour cela nous avons utilisé l'état de l'art des méthodes d’échantillonnage amélioré, couplé avec une nouvelle variable qui contient les informations topologiques pertinentes des systèmes étudiés, le PIV. En calculant des profils d'énergie libre pour différentes conditions de pression et de température, nous avons pu montrer rigoureusement l’absence de barrière d’énergie libre et de second point critique pour la transition liquide-liquide avec le modèle TIP4P/2005. En échantillonnant l'ensemble des chemins de transition grâce à un nouvel algorithme TPS, nous avons aussi pu étudier précisément le mécanisme de nucléation homogène de l’eau avec le modèle TIP4P/Ice, montrant que la structure optimale des noyaux critiques est un empilement désordonné, les noyaux critiques purement cubique ou hexagonaux évoluant spontanément vers cette structure. De plus, nous avons pu montrer que la glace hexagonale s’agrégeait majoritairement en deux étapes, là où la glace cubique s’agrégeait en une étape. Finalement nous avons quantifié rigoureusement la qualité de notre métrique topologique PIV comme coordonnée de réaction pour étudier la nucléation : une analyse réalisée avec la méthode d'optimisation de la vraisemblance maximale basée sur la fonction de réalisation, indique que cette coordonnée surpasse un large éventail de coordonnées utilisées précédemment pour étudier ce problème<br>During this thesis two major problems were studied : the liquid-liquid transition and the homogeneous nucleation of ice in water. To achieve this, we used state-of-the-art enhanced sampling methods, coupled with a new collective variable which store the relevant topological information of a system, the PIV. By rigorous calculation of free energy profile for various conditions of pressure and temperature, we have been able to show the lack of free energy barrier and thereof a second critical point for the liquid-liquid transition, with the TIP4P/2005 model of water. By sampling the transition path ensemble with a new TPS algorithm, we have been able to precisely study the homogeneous nucleation of ice in water with the TIP4P/Ice model, showing that critical nuclei arrange themselves optimaly in stacking disorder ice, with purely hexagonal or cubic nuclei spontaneously evolving toward this structure. The insight we obtained includes a two-step mechanism for the aggregation of new hexagonal ice molecules to the critical nucleus, compared to a one-step process for the addition of cubic ice molecules. Finally we performed a quantitative assessment of the quality of the PIV topological metric as reaction coordinate for nucleation : analysis by means of a rigorous likelihood optimization technique based on committor information, indicates that this coordinate outperforms a large set of previously considered coordinates
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Boonserm, Petarpa. "Some exact solutions in general relativity : a thesis submitted to the Victoria University of Wellington in fulfilment of the requirements for the degree of Master of Science in Mathematics /." ResearchArchive@Victoria e-Thesis, 2005. http://hdl.handle.net/10063/16.
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Voss, Henry Herbert. "Model reference adaptive control of a manipulator in Cartesian coordinates." Thesis, University of British Columbia, 1986. http://hdl.handle.net/2429/26340.
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Robot performance is limited due to the form of the joint controllers. A model reference adaptive control scheme is proposed in which the reference model is in Cartesian coordinates. The form of the conventional joint controller is retained but the gains are adjusted to make the response similar to the reference model. By use of computer simulation the response of a manipulator to setpoint changes is examined for both the conventional and proposed control schemes. Improvements in path error for a straight line trajectory between starting and ending positions in world coordinates is observed with the new scheme compared with conventional control. The benefit is that fewer setpoints must be specified along a desired path to attain the desired path accuracy and, because of the form of the controller, servo errors will be higher leading to faster performance. Stability of the new scheme is examined by state space Floquet methods and a logical proof based on the adaption method used is given.<br>Applied Science, Faculty of<br>Mechanical Engineering, Department of<br>Graduate