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Dissertations / Theses on the topic 'Metric'
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Ribeiro, Tiago CaÃla. "Metric homology." Universidade Federal do CearÃ, 2007. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=604.
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Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico<br>CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior<br>No presente trabalho desenvolvemos e aplicamos a teoria de homologia mÃtrica, criada por Jean Paul Brasselet e Lev Birbrair. A cada conjunto semialgÃbrico X associamos uma coleÃÃo de espaÃos vetoriais reais (ou grupos abelianos) {MH_k^ν(X)} _{k є Z} de forma que se à dado um outro semialgÃbrico X' que à semialgebricamente bi-Lipschitz equivalente a X, entÃo MH_k^ν(X) à isomorfo a MH_k^ν(X') para todo k. Assim, a coleÃÃo {MH_k^ν(X)} carrega alguma informaÃÃo mÃtrica do semialgÃbrico X. Em particular, teremos condiÃÃes necessÃrias para que uma singularidade isolada x_0 pertencente a X seja cÃnica. Mais precisamente, dada uma subvariedade compacta L de uma esfera S_{x_0,r}, calculamos os grupos MH_k^ν(x_0*L) em termos da homologia singular de L, onde x_0*L denota o cone {tx_0+(1-t)x ; x pertencente a L, t pertencente a [0,1]}. Aliado à homologia mÃtrica temos os Ciclos de Chegger, objetos geomÃtricos que obstruem a natureza cÃnica de uma singularidade. Como uma aplicaÃÃo da teoria, apresentamos uma classe de superfÃcies complexas cujas singularidades (isoladas) sÃo nÃo-cÃnicas.
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Sidiropoulos, Anastasios. "Computational metric embeddings." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/44712.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.<br>Includes bibliographical references (p. 141-145).<br>We study the problem of computing a low-distortion embedding between two metric spaces. More precisely given an input metric space M we are interested in computing in polynomial time an embedding into a host space M' with minimum multiplicative distortion. This problem arises naturally in many applications, including geometric optimization, visualization, multi-dimensional scaling, network spanners, and the computation of phylogenetic trees. We focus on the case where the host space is either a euclidean space of constant dimension such as the line and the plane, or a graph metric of simple topological structure such as a tree. For Euclidean spaces, we present the following upper bounds. We give an approximation algorithm that, given a metric space that embeds into R1 with distortion c, computes an embedding with distortion c(1) [delta]3/4 (A denotes the ratio of the maximum over the minimum distance). For higher-dimensional spaces, we obtain an algorithm which, for any fixed d > 2, given an ultrametric that embeds into Rd with distortion c, computes an embedding with distortion co(1). We also present an algorithm achieving distortion c logo(1) [delta] for the same problem. We complement the above upper bounds by proving hardness of computing optimal, or near-optimal embeddings. When the input space is an ultrametric, we show that it is NP-hard to compute an optimal embedding into R2 under the ... norm. Moreover, we prove that for any fixed d > 2, it is NP-hard to approximate the minimum distortion embedding of an n-point metric space into Rd within a factor of Q(n1/(17d)). Finally, we consider the problem of embedding into tree metrics. We give a 0(1)approximation algorithm for the case where the input is the shortest-path metric of an unweighted graph.<br>(cont.) For general metric spaces, we present an algorithm which, given an n-point metric that embeds into a tree with distortion c, computes an embedding with distortion (clog n)o ... . By composing this algorithm with an algorithm for embedding trees into R1, we obtain an improved algorithm for embedding general metric spaces into R1.<br>by Anastasios Sidiropoulos.<br>Ph.D.
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Razafindrakoto, Ando Desire. "Hyperconvex metric spaces." Thesis, Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/4106.
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Thesis (MSc (Mathematics))--University of Stellenbosch, 2010.<br>ENGLISH ABSTRACT: One of the early results that we encounter in Analysis is that every metric space admits
a completion, that is a complete metric space in which it can be densely embedded. We
present in this work a new construction which appears to be more general and yet has
nice properties. These spaces subsequently called hyperconvex spaces allow one to extend
nonexpansive mappings, that is mappings that do not increase distances, disregarding the
properties of the spaces in which they are defined. In particular, theorems of Hahn-Banach
type can be deduced for normed spaces and some subsidiary results such as fixed point
theorems can be observed. Our main purpose is to look at the structures of this new type
of “completion”. We will see in particular that the class of hyperconvex spaces is as large
as that of complete metric spaces.<br>AFRIKAANSE OPSOMMING: Een van die eerste resultate wat in die Analise teegekom word is dat enige metriese ruimte
’n vervollediging het, oftewel dat daar ’n volledige metriese ruimte bestaan waarin die
betrokke metriese ruimte dig bevat word. In hierdie werkstuk beskryf ons sogenaamde
hiperkonvekse ruimtes. Dit gee ’n konstruksie wat blyk om meer algemeen te wees,
maar steeds gunstige eienskappe het. Hiermee kan nie-uitbreidende, oftewel afbeeldings
wat nie afstande rek nie, uitgebrei word sodanig dat die eienskappe van die ruimte
waarop dit gedefinieer is nie ’n rol speel nie. In die besonder kan stellings van die Hahn-
Banach-tipe afgelei word vir genormeerde ruimtes en sekere addisionele ressultate ondere
vastepuntstellings kan bewys word. Ons hoofdoel is om hiperkonvekse ruimtes te ondersoek.
In die besonder toon ons aan dat die klas van alle hiperkonvekse ruimtes net so groot
soos die klas van alle metriese ruimtes is.
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Lazaj, Klotilda. "Metric Preserving Functions." Connect to resource online, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1256915437.
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Hussain, Azham. "Metric based evaluation of mobile devices : mobile goal question metric (mGQM)." Thesis, University of Salford, 2012. http://usir.salford.ac.uk/26720/.
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The constant developments in technology of mobile devices are rapidly increasing the demand for applications on these devices. In October 2010, there were 300,000 applications for iPhone available on iTunes store to be downloaded, and as of January 2011, the application store had over 9.9 billion downloads. Moreover, it is reported that the Blackberry phone has been used by more than 28 million people in 91 countries. Demand for Android phones is also increasing and exceeds analysts' expectations. As a result of the rapid evolution of mobile device development, a new challenge has emerged for application developers; how to improve the usability of mobile applications. This research examines usability issues of mobile devices, and proposes a metric based model which may be used to evaluate applications on mobile devices. A number of evaluation methods and tools are readily available to examine software usability. However usability measures that are specifically intended for mobile devices are very limited indeed. Limitations on current measures to evaluate mobile applications include 1) Their ability to generalize to other domains, 2) The focus on mobile devices instead of the applications and 3) They are not designed to measure applications that use new features on mobile devices. In addition to limited usability measures, evaluation becomes more challenging due to the unique features of mobile devices such as limited bandwidth, unreliability of wireless networks, changing mobile context (e.g., location), small screen size, and limited memory. Hence, this study will propose a conceptual model called mGQM to evaluate mobile applications. The objective of this research is to propose a usability metric that can be used to evaluate mobile applications. The proposed evaluation model is based on a goal-driven method for developing and maintaining a meaningful metrics program, Goal Question Metric (GQM). The proposed metric, mGQM (Mobile Goal Question Metric) consists of usability metrics to assess both quantitative and qualitative measures of mobile phone applications, which other models do not offer. In order to derive a usability metric using the GQM approach, a literature search and review are conducted to obtain usability characteristics, which become the goals to the initial model. The questions are subsequently developed to assess each goal and finally the metrics are derived by refining all the questions into metrics.
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Anfinsen, Jarle. "Making substitution matrices metric." Thesis, Norwegian University of Science and Technology, Department of Computer and Information Science, 2005. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9237.
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<p>With the emergence and growth of large databases of information, efficient methods for storage and processing are becoming increasingly important. The existence of a metric distance measure between data entities enables efficient index structures to be applied when storing the data. Unfortunately, this is often not the case. Amino acid substitution matrices, which are used to estimate similarities between proteins, do not yield metric distance measures. Finding efficient methods for converting a non-metric matrix into a metric one is therefore highly desirable. In this work, the problem of finding such conversions is approached by embedding the data contained in the non-metric matrix into a metric space. The embedding is optimized according to a quality measure which takes the original data into account, and a distance matrix is then derived using the metric distance function of the space. More specifically, an evolutionary scheme is proposed for constructing such an embedding. The work shows how a coevolutionary algorithm can be used to find a spatial embedding and a metric distance function which try to preserve as much of the proximity structure of the non-metrix matrix as possible. The evolutionary scheme is compared to three existing embedding algorithms. Some modifications to the existing algorithms are proposed, with the purpose of handling the data in the non-metric matrix more efficiently. At a higher level, the strategy of deriving a metric distance function from a spatial embedding is compared to an existing algorithm which enforces metricity by manipulating the data in the non-metric matrix directly (the triangle fixing algorithm). The methods presented and compared are general in the sense that they can be applied in any case where a non-metric matrix must be converted into a metric one, regardless of how the data in the non-metric matrix was originally derived. The proposed methods are tested empirically on amino acid substitution matrices, and the derived metric matrices are used to search for similarity in a database of proteins. The results show that the embedding approach outperforms the triangle fixing approach when applied to matrices from the PAM family. Moreover, the evolutionary embedding algorithms perform best among the embedding algorithms. In the case of the PAM250 scoring matrix, a metric distance matrix is found which is more sensitive than the mPAM250 matrix presented in a recent paper. Possible advantages of choosing one method over another are shown to be unclear in the case of matrices from the BLOSUM family.</p>
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Bagge, Joar. "A graphotactic language metric." Thesis, KTH, Matematik (Inst.), 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-128781.
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In this bachelor’s thesis, we try to classify and identify written human languages by studying the ordering of letters in text. Automatic language identification is of interest in areas such as text indexing, machine translation and natural language parsing. Eleven written languages which use the Latin alphabet are considered and modelled with a Markov chain on the letter level. Texts from the New Testament and Wikipedia are used as training data. The distances between the languages are then measured by using a matrix-based metric on the transition matrices, and visualized in a dendrogram. A probability-based distance measure is also used. The matrix-based metric is then applied to language identification by creating a transition matrix for the text whose language is to be identified, and comparing the distances from this matrix to those of the known languages; the shortest distance indicates the language of the text. This is compared with maximum-likelihood classification. We compare metrics based on different matrix norms, and also study how the order of the Markov chains and the size of the training data and sample texts for language identification influence the results. The results indicate that the choice of matrix norm is important and that the Frobenius norm and the 1-norm are the best norms for language classification and language identification. Using these, it is possible to generate satisfactory dendrograms, and accurately identify the language of reasonably large texts. On the other hand, the 1-norm cannot be recommended in this context; an explanation is given for its bad performance. Some languages are easier to classify correctly than others; the Scandinavian languages are easy to group together, as are Spanish, Portuguese and Italian. However, English, French, German and Finnish are harder to classify correctly. Keywords: Written human languages, Language classification, Language identification, Markov chain model, Matrix norms, Statistical analysis of text.
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Matthews, S. G. "Metric domains for completeness." Thesis, University of Warwick, 1985. http://wrap.warwick.ac.uk/60775/.
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Completeness is a semantic non-operational notion of program correctness suggested (but not pursued) by W.W.Wadge. Program verification can be simplified using completeness, firstly by removing the approximation relation from proofs, and secondly by removing partial objects from proofs. The dissertation proves the validity of this approach by demonstrating how it can work in the class of metric domains. We show how the use of Tarski's least fixed point theorem can be replaced by a non-operational unique fixed point theorem for many well behaved Programs. The proof of this theorem is also non-operational. After this we consider the problem of deciding what it means f or a function to be "complete". It is shown that combinators such as function composition are not complete, although they are traditionally assumed to be so. Complete versions for these combinators are given. Absolute functions are proposed as a general model for the notion of a complete function. The theory of mategories is introduced as a vehicle for studying absolute functions.
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Al-Harbi, Sami. "Clustering in metric spaces." Thesis, University of East Anglia, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.396604.
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Jensen, Harold Franklin. "Variable buoyancy system metric." Thesis, Massachusetts Institute of Technology, 2009. http://hdl.handle.net/1721.1/58193.
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Thesis (S.M.)--Joint Program in Applied Ocean Science and Engineering (Massachusetts Institute of Technology, Dept. of Mechanical Engineering; and the Woods Hole Oceanographic Institution), 2009.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 111-112).<br>Over the past 20 years, underwater vehicle technology has undergone drastic improvements, and vehicles are quickly gaining popularity as a tool for numerous oceanographic tasks. Systems used on the vehicle to alter buoyancy, or variable buoyancy (VB) systems, have seen only minor improvements during the same time period. Though current VB systems are extremely robust, their lack of performance has become a hinderance to the advancement of vehicle capabilities. This thesis first explores the current status of VB systems, then creates a model of each system to determine performance. Second, in order to quantitatively compare fundamentally different VB systems, two metrics, [beta]m and [beta]vol, are developed and applied to current systems. By determining the ratio of performance to size, these metrics give engineers a tool to aid VB system development. Finally, the fundamental challenges in developing more advanced VB systems are explored, and a couple of technologies are investigated for their potential use in new systems.<br>by Harold Franklin Jensen III.<br>S.M.
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Nordebo, Jonatan. "The Reissner-Nordström metric." Thesis, Umeå universitet, Institutionen för fysik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-118337.
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A brief review of special and general relativity including some classical electrodynamics is given. We then present a detailed derivation of the Reissner-Nordström metric. The derivation is done by solving the Einstein-Maxwell equations for a spherically symmetric electrically charged body. The physics of this spacetime is then studied. This includes gravitational time dilation and redshift, equations of motion for both massive and massless non-charged particles derived from the geodesic equation and equations of motion for a massive charged particle derived with lagrangian formalism. Finally, a quick discussion of the properties of a Reissner-Nordström black hole is given.
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Choy, Tze Leung. "Sparse distance metric learning." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:a98695a3-0a60-448f-9ec0-63da3c37f7fa.
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A good distance metric can improve the accuracy of a nearest neighbour classifier. Xing et al. (2002) proposed distance metric learning to find a linear transformation of the data so that observations of different classes are better separated. For high-dimensional problems where many un-informative variables are present, it is attractive to select a sparse distance metric, both to increase predictive accuracy but also to aid interpretation of the result. In this thesis, we investigate three different types of sparsity assumption for distance metric learning and show that sparse recovery is possible under each type of sparsity assumption with an appropriate choice of L1-type penalty. We show that a lasso penalty promotes learning a transformation matrix having lots of zero entries, a group lasso penalty recovers a transformation matrix having zero rows/columns and a trace norm penalty allows us to learn a low rank transformation matrix. The regularization allows us to consider a large number of covariates and we apply the technique to an expanded set of basis called rule ensemble to allow for a more flexible fit. Finally, we illustrate an application of the metric learning problem via a document retrieval example and discuss how similarity-based information can be applied to learn a classifier.
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Fuhry, David P. "Skylines in Metric Space." Kent State University / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=kent1208562156.
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Büch, Lutz [Verfasser], and Artur [Akademischer Betreuer] Andrzejak. "Metric Selection and Metric Learning for Matching Tasks / Lutz Büch ; Betreuer: Artur Andrzejak." Heidelberg : Universitätsbibliothek Heidelberg, 2020. http://d-nb.info/1224684524/34.
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Laub, Julian. "Non-metric pairwise proximity data." [S.l.] : [s.n.], 2004. http://edocs.tu-berlin.de/diss/2004/laub_julian.pdf.
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Lee, Seunghwan Han. "Probabilistic reasoning on metric spaces." [Bloomington, Ind.] : Indiana University, 2009. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3380096.
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Thesis (Ph.D.)--Indiana University, Dept. of Mathematics and Cognitive Science, 2009.<br>Title from PDF t.p. (viewed on Jul 19, 2010). Source: Dissertation Abstracts International, Volume: 70-12, Section: B, page: 7604. Adviser: Lawrence S. Moss.
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Chang, Hong. "Semi-supervised distance metric learning /." View abstract or full-text, 2006. http://library.ust.hk/cgi/db/thesis.pl?COMP%202006%20CHANG.
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Rekdal, Espen Ekornes. "Metric Indexing in Time Series." Thesis, Norwegian University of Science and Technology, Department of Computer and Information Science, 2008. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-10487.
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Erlandsen, Stian. "Metric indexing by database techniques." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for datateknikk og informasjonsvitenskap, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-12565.
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Similarity search is very useful in many applications. Because of the complex-ity and expensive nature of such search operations, many existing methods re-quire special access methods and cannot be directly integrated with commercialDBMSs(Database Management Systems). NTNUStore is a framework to aid re-search in this eld and focuses on disk-based metric indexing to keep it compatiblewith commercial DBMSs.This project has implemented and experimented with a version of the LAESA(Linear Approximating and Eliminating Search Algorithm) in NTNUStore. Theresults are close to what was represented in Erik Bagge Ottesen's master thesis. The biggest contribution in this project is that the new algorithm solves KNNsearch without the need of providing a range parameter in the query.
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Lemaire-Beaucage, Jonathan. "Voronoi Diagrams in Metric Spaces." Thesis, Université d'Ottawa / University of Ottawa, 2012. http://hdl.handle.net/10393/20736.
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In this thesis, we will present examples of Voronoi diagrams that are not tessellations. Moreover, we will find sufficient conditions on subspaces of E2, S2 and the Poincaré disk and the sets of sites that guarantee that the Voronoi diagrams are pre-triangulations. We will also study g-spaces, which are metric spaces with ‘extendable’ geodesics joining any 2 points and give properties for a set of sites in a g-space that again guarantees that the Voronoi diagram is a pre-triangulation.
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Li, Rong. "A system-wide anonymity metric." Thesis, Wichita State University, 2011. http://hdl.handle.net/10057/5041.
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In this thesis we present a critical analysis of the system-wide anonymity metric by
Edman et al. [1], which is based on the permanent value of a doubly-stochastic matrix.
From the view of intuitive understanding, we show that a metric that looks no further than
the permanent, a composite value, is at best a rough indicator of anonymity, We find the
range where its inaccuracy is acute, and propose a better anonymity indicator. Also, we
show that this metric fails to possess desirable generalization properties by constructing an
information-preserving embedding of a smaller class of attacks into the wider class for which
this metric was proposed. Finally, we show a new general, accurate anonymity metric that
does not exhibit these shortcomings.<br>Thesis (M.S.)--Wichita State University, College of Engineering, Dept. of Electrical Engineering and Computer Science.
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Chandirasekaran, Devasena. "Optimized AODV with modified metric." Thesis, Wichita State University, 2011. http://hdl.handle.net/10057/5162.
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The growth of wireless technology has developed since the invention of wireless devices. With the recent introduction of smart phones and other latest mobile devices, the growing need for networking is limitless. This calls for a more efficient Adhoc network formed on the go. The goal is to improve the MANET type of Adhoc networks. This infrastructure less network has routing protocols to route the packets to the intended recipient in an organized manner. AODV protocol chooses the best path to the destination based on the hop count as metric it has no power, stability and bandwidth optimization. Considering the current need, the resource needs to be utilized in an efficient manner so that the requests are met in a timely manner. This research proposes a stable, energy aware ,bandwidth, optimized metric to load balance the traffic between available non-overlapping channels in 802.11[1] standards. The proposed protocol has proved to have 50% better performance. It has avoided additional overhead for the control packet and accounted for another important broadcast storm problem by avoiding HELLO (Used as keep alive) packets used to discover neighboring nodes.<br>Thesis (M.S.)--Wichita State University, College of Engineering, Dept. of Electrical Engineering & Computer Science.
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Khan, Moazzam. "Security metric based risk assessment." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/47527.
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Modern day computer networks have become very complex and attackers have benefited due to this complexity and have found vulnerabilities and loopholes in the network architecture. In order to identify the attacks from an attacker all aspects of network architecture needs to be carefully examined such as packet headers, network scans, versions of applications, network scans, network anomalies etc. and after the examination attributes playing a significant impact on the security posture of the organization needs to be highlighted so that resources and efforts are directed towards those attributes. In this work we extensively look at network traffic at dormitory network of a large campus and try to identify the attributes that play a significant role in the infection of a machine. Our scheme is to collect as much attributes from the network traffic applying the heuristic of network infection and then devise a scheme called decision centric rank ordering of security metric that gives the priority to the security metrics so that network administrators can channel their efforts in the right direction. Another aspect of this research is to identify the probability of an attack on a communication infrastructure. A communication infrastructure becomes prone to attack if certain elements exist in it, such as vulnerabilities in the comprising elements of the system, existence of an attacker and motivation for him to attack. Focus of this study is on vulnerability assessment and security metrics such as user behavior, operating systems, user applications, and software updates. To achieve a quantified value of risk, a set of machines is carefully observed for the security metrics. Statistical analysis is applied on the data collected from compromised machines and the quantified value of risk is achieved.
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Yusupova, Tatiana. "Problems in metric diophantine approximations." Thesis, University of York, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.534907.
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Holland, Andrew J. "Metric implementation in U.S. construction." Thesis, Gainesville, Florida : University of Florida, 1997. http://hdl.handle.net/10945/26631.
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Throughout the history of industrialization, people have been trying to develop a single system of measurement with a worldwide acceptance. Since its inception two centuries ago, the metric system has been gaining ground over the traditional "inch pound" system. Today, the United States remains as the sole user of the "inch pound" system of measurements. The pressure for unification into the metric system has been mounting. With the emergence of the "global economy," non metric products are becoming increasingly unacceptable in the world markets. Individual industries, societies and organizations in the United States have, however, been making steps to adopt metric for some time. Congress, understanding the need for adoption of the metric system in trade and commerce, has taken steps to introduce metric system into the commercial market of the United States. Federal agencies are now required to use the metric system in governmental related programs including procurements, grants, and other business related activities. However, no nationwide mandate for metric that includes the private sector has been established. This report contains background information on the development of metric to date, status of metric conversion in the federal government, current metric activities of professional and industry groups, planning for the metric change by the private sector, technical implications in the construction industries, metric building products and services, as well as a general explanation of the key aspects of metrication for the construction industry in the United States
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Rowe, Paul Michael Dominic. "Contributions to metric number theory." Thesis, Royal Holloway, University of London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.408263.
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Coffey, Michael R. "Ricci flow and metric geometry." Thesis, University of Warwick, 2015. http://wrap.warwick.ac.uk/67924/.
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This thesis considers two separate problems in the field of Ricci flow on surfaces. Firstly, we examine the situation of the Ricci flow on Alexandrov surfaces, which are a class of metric spaces equipped with a notion of curvature. We extend the existence and uniqueness results of Thomas Richard in the closed case to the setting of non-compact Alexandrov surfaces that are uniformly non-collapsed. We complement these results with an extensive survey that collects together, for the first time, the essential topics in the metric geometry of Alexandrov spaces due to a variety of authors. Secondly, we consider a problem in the well-posedness theory of the Ricci flow on surfaces. We show that given an appropriate initial Riemannian surface, we may construct a smooth, complete, immortal Ricci flow that takes on the initial surface in a geometric sense, in contrast to the traditional analytic notions of initial condition. In this way, we challenge the contemporary understanding of well-posedness for geometric equations.
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van, Staden Wernd Jakobus. "Metric aspects of noncommutative geometry." Diss., University of Pretoria, 2019. http://hdl.handle.net/2263/77893.
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We study noncommutative geometry from a metric point of view by
constructing examples of spectral triples and explicitly calculating Connes's
spectral distance between certain associated pure states. After considering
instructive nite-dimensional spectral triples, the noncommutative geometry
of the in nite-dimensional Moyal plane is studied. The corresponding
spectral triple is based on the Moyal deformation of the algebra of Schwartz
functions on the Euclidean plane.<br>Dissertation (MSc)--University of Pretoria, 2019.<br>Physics<br>MSc<br>Unrestricted
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Pan, Jiajun. "Metric learning for structured data." Thesis, Nantes, 2019. http://www.theses.fr/2019NANT4076.
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L’apprentissage à distance métrique est une branche de l’apprentissage par re-présentation des algorithmes d’apprentissage automatique. Nous résumons le développement et la situation actuelle de l’algorithme actuel d’apprentissage à distance métrique à partir des aspects de la base de données plate et de la base de données non plate. Pour une série d’algorithmes basés sur la distance de Mahalanobis pour la base de données plate qui ne parvient pas à exploiter l’intersection de trois dimensions ou plus, nous proposons un algorithme d’apprentissage métrique basé sur la fonction sousmodulaire. Pour le manque d’algorithmes d’apprentissage métrique pour les bases de données relationnelles dans des bases de données non plates, nous proposons LSCS (sélection de contraintes relationnelles de force relationnelle) pour la sélection de contraintes pour des algorithmes d’apprentissage métrique avec informations parallèles et MRML (Multi-Relation d’apprentissage métrique) qui somme la perte des contraintes relationnelles et les contraintes d’etiquetage. Grâce aux expériences de conception et à la vérification sur la base de données réelle, les algorithmes proposés sont meilleurs que les algorithmes actuels<br>Metric distance learning is a branch of re-presentation learning in machine learning algorithms. We summarize the development and current situation of the current metric distance learning algorithm from the aspects of the flat database and nonflat database. For a series of algorithms based on Mahalanobis distance for the flat database that fails to make full use of the intersection of three or more dimensions, we propose a metric learning algorithm based on the submodular function. For the lack of metric learning algorithms for relational databases in non-flat databases, we propose LSCS(Relational Link-strength Constraints Selection) for selecting constraints for metric learning algorithms with side information and MRML (Multi-Relation Metric Learning) which sums the loss from relationship constraints and label constraints. Through the design experiments and verification on the real database, the proposed algorithms are better than the current algorithms
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Erninger, Klas. "Algebraic Simplifications of Metric Information." Thesis, KTH, Matematik (Avd.), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-277744.
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This thesis is about how to interpret metric data with topological tools, such as homology. We show how to go from a metric space to a topological space via Vietoris-Rips complexes. We use the usual approach to Topological Data Analysis (TDA), and transform our metric space into tame parametrised vector spaces. It is then shown how to simplify tame parametrised vector spaces. We also present another approach to TDA, where we transform our metric space into a filtrated tame parametrised chain complex. We then show how to simplify chain complexes over fields in order to simplify tame parametrised filtrated chain complexes.<br>Denna uppsats handlar om att tolka metrisk data med hjälp utav topologiska verktyg, som exempelvis homologi. Vi visar hur man går från ett metriskt rum till ett topologiskt rum via Vieteris-Rips komplex. Vi använder den vanliga metoden till Topologisk Data Analys (TDA), och transformerar vårat metriska rum till tama parametriserade vektorrum. Det visas sedan hur vi kan förenkla tama parametriserade vektorrum. Vi presenterar även en annan metod för TDA, där vi går från ett metriskt rum till ett filtrerat tamt parametriserat kedjekomplex. Sedan visar vi hur man förenklar kedjekomplex över kroppar för att kunna förenkla filtrerade tama parametriserade kedjekomplex.
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Otafudu, Olivier Olela. "Convexity in quasi-metric spaces." Doctoral thesis, University of Cape Town, 2012. http://hdl.handle.net/11427/10950.
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Includes abstract.<br>Includes bibliographical references.<br>The principal aim of this thesis is to investigate the existence of an injective hull in the categories of T-quasi-metric spaces and of T-ultra-quasi-metric spaces with nonexpansive maps.
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Okutan, Osman Berat. "Persistence, Metric Invariants, and Simplification." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1559312147225384.
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Reinke, Kristen Nicole. "SAFETY METRIC THE WEITZ COMPANY." Thesis, The University of Arizona, 2009. http://hdl.handle.net/10150/192951.
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Abou-Moustafa, Karim. "Metric learning revisited: new approaches for supervised and unsupervised metric learning with analysis and algorithms." Thesis, McGill University, 2012. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=106370.
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In machine learning one is usually given a data set of real high dimensional vectors X, based on which it is desired to select a hypothesis θ from the space of hypotheses Θ using a learning algorithm. An immediate assumption that is usually imposed on X is that it is a subset from the very general embedding space Rp which makes the Euclidean distance ∥•∥2 to become the default metric for the elements of X. Since various learning algorithms assume that the input space is Rp with its endowed metric ∥•∥2 as a (dis)similarity measure, it follows that selecting hypothesis θ becomes intrinsically tied to the Euclidean distance. Metric learning is the problem of selecting a specific metric dX from a certain family of metrics D based on the properties of the elements in the set X. Under some performance measure, the metric dX is expected to perform better on X than any other metric d 2 D. If the learning algorithm replaces the very general metric ∥•∥2 with the metric dX , then selecting hypothesis θ will be tied to the more specific metric dX which carries all the information on the properties of the elements in X. In this thesis I propose two algorithms for learning the metric dX ; the first for supervised learning settings, and the second for unsupervised, as well as for supervised and semi-supervised settings. In particular, I propose algorithms that take into consideration the structure and geometry of X on one hand, and the characteristics of real world data sets on the other. However, if we are also seeking dimensionality reduction, then under some mild assumptions on the topology of X, and based on the available a priori information, one can learn an embedding for X into a low dimensional Euclidean space Rp0, p0 << p, where the Euclidean distance better reveals the similarities between the elements of X and their groupings (clusters). That is, as a by-product, we obtain dimensionality reduction together with metric learning. In the supervised setting, I propose PARDA, or Pareto discriminant analysis for discriminative linear dimensionality reduction. PARDA is based on the machinery of multi-objective optimization; simultaneously optimizing multiple, possibly conflicting, objective functions. This allows PARDA to adapt to the class topology in the lower dimensional space, and naturally handles the class masking problem that is inherent in Fisher's discriminant analysis framework for multiclass problems. As a result, PARDA yields significantly better classification results when compared with modern techniques for discriminative dimensionality reduction. In the unsupervised setting, I propose an algorithmic framework, denoted by ?? (note the different notation), that encapsulates spectral manifold learning algorithms and gears them for metric learning. The framework ?? captures the local structure and the local density information from each point in a data set, and hence it carries all the information on the varying sample density in the input space. The structure of ?? induces two distance metrics for its elements, the Bhattacharyya-Riemann metric dBR and the Jeffreys-Riemann metric dJR. Both metrics reorganize the proximity between the points in X based on the local structure and density around each point. As a result, when combining the metric space (??, dBR) or (??, dJR) with spectral clustering and Euclidean embedding, they yield significant improvements in clustering accuracies and error rates for a large variety of clustering and classification tasks.<br>Dans cette thèse, je propose deux algorithmes pour l'apprentissage de la métrique dX; le premier pour l'apprentissage supervisé, et le deuxième pour l'apprentissage non-supervisé, ainsi que pour l'apprentissage supervisé et semi-supervisé. En particulier, je propose des algorithmes qui prennent en considération la structure et la géométrie de X d'une part, et les caractéristiques des ensembles de données du monde réel d'autre part. Cependant, si on cherche également la réduction de dimension, donc sous certaines hypothèses légères sur la topologie de X, et en même temps basé sur des informations disponibles a priori, on peut apprendre une intégration de X dans un espace Euclidien de petite dimension Rp0 p0 << p, où la distance Euclidienne révèle mieux les ressemblances entre les éléments de X et leurs groupements (clusters). Alors, comme un sous-produit, on obtient simultanément une réduction de dimension et un apprentissage métrique. Pour l'apprentissage supervisé, je propose PARDA, ou Pareto discriminant analysis, pour la discriminante réduction linéaire de dimension. PARDA est basé sur le mécanisme d'optimisation à multi-objectifs; optimisant simultanément plusieurs fonctions objectives, éventuellement des fonctions contradictoires. Cela permet à PARDA de s'adapter à la topologie de classe dans un espace dimensionnel plus petit, et naturellement gère le problème de masquage de classe associé au discriminant Fisher dans le cadre d'analyse de problèmes à multi-classes. En conséquence, PARDA permet des meilleurs résultats de classification par rapport aux techniques modernes de réduction discriminante de dimension. Pour l'apprentissage non-supervisés, je propose un cadre algorithmique, noté par ??, qui encapsule les algorithmes spectraux d'apprentissage formant an algorithme d'apprentissage de métrique. Le cadre ?? capture la structure locale et la densité locale d'information de chaque point dans un ensemble de données, et donc il porte toutes les informations sur la densité d'échantillon différente dans l'espace d'entrée. La structure de ?? induit deux métriques de distance pour ses éléments: la métrique Bhattacharyya-Riemann dBR et la métrique Jeffreys-Riemann dJR. Les deux mesures réorganisent la proximité entre les points de X basé sur la structure locale et la densité autour de chaque point. En conséquence, lorsqu'on combine l'espace métrique (??, dBR) ou (??, dJR) avec les algorithmes de "spectral clustering" et "Euclidean embedding", ils donnent des améliorations significatives dans les précisions de regroupement et les taux d'erreur pour une grande variété de tâches de clustering et de classification.
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Powell, J. E. "Metric versus non-metric skeletal traits : which is the more reliable indicator of genetic distance?" Thesis, University of Bristol, 1989. http://hdl.handle.net/1983/e44b5162-0f9d-4f0a-afdf-2eac49563e4b.
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Gupta, Kishan. "Metric and non-metric inputs influence spatial and working memory processes of medial entorhinal neurons." Thesis, Boston University, 2013. https://hdl.handle.net/2144/12771.
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Thesis (Ph.D.)--Boston University<br>The medial entorhinal cortex (MEC) contains spatial cell types including grid and head direction (HD) cells. Grid cells fire action potentials when animals pass through environmental locations that form vertices of tessellating triangles. HD cells fire when animals face a preferred direction along their azimuth. These cells have been widely studied for their potential metric role in spatial navigation, but considerably less is known about their non-metric functions. This thesis examines non-metric influences on the MEC during working memory maintenance, 'look-ahead' activity, and 'more familiar' or 'less familiar' environmental rotations.
The first experiment tests the hypothesis that persistent spiking of MEC neurons could represent a sensory cue during a working memory task. Animals ran a T-Maze where an auditory stimulus cued rats to move toward left- or right-reward arms. Instead of the hypothesized increase in spike rate during the delay period between cue and reward, MEC spike rates were suppressed. Additionally, MEC ensemble firing at the choice point suggests that these cells encoded reward locations. This indicates the MEC displays forward activation of possible future locations ('look-ahead' activity).
To model this experiment's look-ahead results, a recent model of goal-directed navigation was adapted to the previous T-Maze task. This adaptation trains a virtual rat to associate cues to reward cells and corresponding place cells, a difference from previous models where goal locations were not cueassociated. The rat reliably learns goal locations, performs look-ahead scans at the choice point, and simulated MEC activity decodes to reward locations, successfully modeling look-ahead behavior.
The final experiment examines effects of environmental recency on spatial tuning of MEC neurons. Rats performed spatial alternation on a T-Maze rotated into 'more familiar' or 'less familiar' configurations as MEC units were recorded. Spatial cells oriented their firing fields in register with the T-Maze more often during less familiar rotations. This implies a shift in animals' reference frame with learned experience suggesting the MEC is comparing contexts in the same environment.
In summary, these results highlight previously uninvestigated, non-metric influences over MEC activity with strong implications for goal-directed behavior and spatial navigation.
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Lease, Loren Rosemond. "Ancestral determination of African American and European American deciduous dentition using metric and non-metric analysis." Columbus, OH : Ohio State University, 2003. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1054742334.
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Thesis (Ph. D.)--Ohio State University, 2003.<br>Title from first page of PDF file. Document formatted into pages; contains xvii, 421 p.: ill. (some col.). Includes abstract and vita. Advisor: Paul W. Sciulli, Dept. of Anthropology. Includes bibliographical references (p. 130-152).
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Calisti, Matteo. "Differential calculus in metric measure spaces." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21781/.
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L'obbiettivo di questa tesi è la definizione del calcolo differenziale e dell'operatore di Laplace in spazi metrici di misura. Nel primo capitolo vengono introdotte le definizioni e proprietà principali degli spazi metrici di misura mentre nel secondo quelle riguardanti le funzioni lipschitziane e la derivata metrica di curve assolutamente continue. Nel terzo capitolo quindi viene definito il concetto di p-supergradiente debole e di conseguenza la classe di Sobolev S^p. Nel quarto capitolo viene poi studiata la generalizzazione del concetto di differenziale di f applicato al gradiente di g che da luogo a due funzioni che in generale risultano diverse, ma se coincidono lo spazio verrà detto q-infinitesimamente strettamente convesso.
Vengono quindi dimostrate alcune regole della catena per per queste due funzioni attraverso la dualità fra lo spazio S^p e un opportuno spazio di misure dette q-piani test. In particolare mediante l'introduzione del funzionale energia di Cheeger e il suo flusso-gradiente sarà possibile associare un piano di trasporto al gradiente di una funzione in S^p. Nel quinto capitolo viene definito il p-laplaciano e le regole di calcolo provate precedentemente saranno usate per provare quelle per il laplaciano. Verranno poi definiti gli spazi infitesimamente di Hilbert: in questo caso il laplaciano assume un solo valore e risulta linearmente dipendente da g e si dimostra un'identificazione tra differenziali e gradienti. Nell'ultima parte del quinto capitolo infine viene mostrata un'applicazione del calcolo differenziale in spazi metrici di misura al gruppo di Heisenberg, considerandolo uno spazio metrico di misura munito della metrica di Korany e la misura di Lebesgue. Nella prima parte si mostra che il laplaciano metrico coincide con quello subriemanniano. Viene poi considerata nella seconda parte la sottovarietà {x=0} e si dimostra come il laplaciano metrico sia diverso da quello differenziale.
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Neri, Giulio. "Effective metric for bootstrapped Newtonian sources." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21717/.
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In this work, we address the problem of constructing an effective space-time picture for the gravitational field in the bootstrapped Newtonian theory (BNT). After a short review of the singularity problem and the corpuscular model of black holes, we present a
detailed introduction to the BNT. This theory provides us with an exact formula for the gravitational potential felt by slowly-moving particles outside a static and spherically symmetric source. Our goal is to determine the most general metric tensor that reproduces this potential in the Newtonian limit and use it in relativistic or strong-gravity scenarios. After we make so that the effective space-time agrees with the experimental constraints and contains a black hole region, we study its properties in two opposite limits: the weak- and the strong-field regime. In the first case, we find departures from the predictions of General Relativity as early as order GNM=R2, where R is the characteristic length scale of a given system. In the second case, we discover that the BN black hole is different from the Schwarzschild one, and it generally violates the first law of black hole mechanics. In the end, we restore time-dependence to study the propagation of gravitational waves in the reconstructed space-time. The upshot is that we cannot exclude the existence of scalar waves.
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Amato, Giuseppe. "Approximate similarity search in metric spaces." [S.l.] : [s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=964997347.
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Grossman, Mary Alice. "Validation of a Quality Management Metric." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2000. http://handle.dtic.mil/100.2/ADA384217.
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Thesis (M.S. in Software Engineering) Naval Postgraduate School, Sept. 2000.<br>"September 2000." Thesis advisor(s): Osmundson, John; Michael, J. Bret. Includes bibliographical references (p. 121). Also available online.
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Fevang, Rune, and Arne Bergene Fossaa. "Empirical evaluation of metric indexing methods." Thesis, Norwegian University of Science and Technology, Department of Computer and Information Science, 2008. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-8902.
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<p>Metric indexing is a branch of search technology that is designed for search non-textual data. Examples of this includes image search (where the search query is an image), document search (finding documents that are roughly equal) to search in high-dimensional Euclidean spaces. Metric indexing is based on the theory of metric spaces, where the only thing known about a set of objects is the distance between them (defined by a metric distance function). A large number of methods have been proposed to solve the metric indexing problem. In this thesis, we have concentrated on new approaches to solving these problems, as well as combining existing methods to create better ones. The methods studied in this thesis include D-Index, GNAT, EMVP-Forest, HC, SA-Tree, SSS-Tree, M-Tree, PM-Tree, M*-Tree and PM*-Tree. These have all been implemented and tested against each other to find strengths and weaknesses. This thesis also studies a group of indexing methods called hybrid methods which combines tree-based methods (like SA-Tree, SSS-tree and M-Tree), with pivoting methods (like AESA and LAESA). The thesis also proposes a method to create hybrid trees from existing trees by using features in the programming language. Hybrid methods have been shown in this thesis to be very promising. While they may have a considerable overhead in construction time,CPU usage and/or memory usage, they show large benefits in reduced number of distance computations. We also propose a new way of calculating the Minimal Spanning Tree of a graph operating on metric objects, and show that it reduces the number of distance computations needed.</p>
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Palmer, Ian Christian. "Riemannian geometry of compact metric spaces." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/34744.
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A construction is given for which the Hausdorff measure and dimension of an arbitrary abstract compact metric space (X, d) can be encoded in a spectral triple. By introducing the concept of resolving sequence of open covers, conditions are given under which the topology, metric, and Hausdorff measure can be recovered from a spectral triple dependent on such a sequence. The construction holds for arbitrary compact metric spaces, generalizing previous results for fractals, as well as the original setting of manifolds, and also holds when Hausdorff and box dimensions differ---in particular, it does not depend on any self-similarity or regularity conditions on the space. The only restriction on the space is that it have positive s₀ dimensional Hausdorff measure, where s₀ is the Hausdorff dimension of the
space, assumed to be finite. Also, X does not need to be embedded in another space, such as Rⁿ.
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Nomura, Kouichi. "A recipe for multi-metric gravity." 京都大学 (Kyoto University), 2015. http://hdl.handle.net/2433/199102.
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Jones, Miranda Rose. "Conformal deformation of a conic metric." Thesis, Wichita State University, 2011. http://hdl.handle.net/10057/3996.
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The problem studied here focuses on a compact manifold M without boundary in which the Riemannian metric g is on Λ = M – {p1, p2,…,pκ}. Near the pi 's, g has a particular type of singularity in which locally M = (0, δ)x × Ywhere Y is a Riemannian manifold with metric h. Calculation techniques involving Christoffel symbols, scalar curvature, and the Lapalacian of the manifold are used to reduce the Yamabe equation to a system of partial differential equations. After assuming that a function u > 0 satisfying the Yamabe equation exists, the most singular partial differential equation is solved using integration techniques to find necessary conditions on Y and h. Also studied in this paper are the conditions on Y and h for which M is already a manifold with constant scalar curvature.<br>Thesis (M.S.)--Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics and Statistics.
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Jägrell, Linus. "Geometry of the Lunin-Maldacena metric." Thesis, KTH, Teoretisk fysik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-153502.
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Witt, Frederik. "Special metric structures and closed forms." Thesis, University of Oxford, 2005. http://ora.ox.ac.uk/objects/uuid:30b7a34b-cc46-4981-aee5-964787c1235e.
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In recent work, N. Hitchin described special geometries in terms of a variational problem for closed generic $p$-forms. In particular, he introduced on 8-manifolds the notion of an integrable $PSU(3)$-structure which is defined by a closed and co-closed 3-form. In this thesis, we first investigate this $PSU(3)$-geometry further. We give necessary conditions for the existence of a topological $PSU(3)$-structure (that is, a reduction of the structure group to $PSU(3)$ acting through its adjoint representation). We derive various obstructions for the existence of a topological reduction to $PSU(3)$. For compact manifolds, we also find sufficient conditions if the $PSU(3)$-structure lifts to an $SU(3)$-structure. We find non-trivial, (compact) examples of integrable $PSU(3)$-structures. Moreover, we give a Riemannian characterisation of topological $PSU(3)$-structures through an invariant spinor valued 1-form and show that the $PSU(3)$-structure is integrable if and only if the spinor valued 1-form is harmonic with respect to the twisted Dirac operator. Secondly, we define new generalisations of integrable $G_2$- and $Spin(7)$-manifolds which can be transformed by the action of both diffeomorphisms and 2-forms. These are defined by special closed even or odd forms. Contraction on the vector bundle $Toplus T^*$ defines an inner product of signature $(n,n)$, and even or odd forms can then be naturally interpreted as spinors for a spin structure on $Toplus T^*$. As such, the special forms we consider induce reductions from $Spin(7,7)$ or $Spin(8,8)$ to a stabiliser subgroup conjugate to $G_2 times G_2$ or $Spin(7) times Spin(7)$. They also induce a natural Riemannian metric for which we can choose a spin structure. Again we state necessary and sufficient conditions for the existence of such a reduction by means of spinors for a spin structure on $T$. We classify topological $G_2 times G_2$-structures up to vertical homotopy. Forms stabilised by $G_2 times G_2$ are generic and an integrable structure arises as the critical point of a generalised variational principle. We prove that the integrability conditions on forms imply the existence of two linear metric connections whose torsion is skew, closed and adds to 0. In particular we show these integrability conditions to be equivalent to the supersymmetry equations on spinors in supergravity theory of type IIA/B with NS-NS background fields. We explicitly determine the Ricci-tensor and show that over compact manifolds, only trivial solutions exist. Using the variational approach we derive weaker integrability conditions analogous to weak holonomy $G_2$. Examples of generalised $G_2$- and $Spin(7)$ structures are constructed by the device of T-duality.
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Velani, Sanju Lalji. "Metric diophantine approximation in hyperbolic space." Thesis, University of York, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.304351.
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Salp, Cem. "Metric diophantine approximation and cantor sets." Thesis, University of York, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.444750.
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Kilbane, James. "Finite metric subsets of Banach spaces." Thesis, University of Cambridge, 2019. https://www.repository.cam.ac.uk/handle/1810/288272.
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The central idea in this thesis is the introduction of a new isometric invariant of a Banach space. This is Property AI-I. A Banach space has Property AI-I if whenever a finite metric space almost-isometrically embeds into the space, it isometrically embeds. To study this property we introduce two further properties that can be thought of as finite metric variants of Dvoretzky's Theorem and Krivine's Theorem. We say that a Banach space satisfies the Finite Isometric Dvoretzky Property (FIDP) if it contains every finite subset of $\ell_2$ isometrically. We say that a Banach space has the Finite Isometric Krivine Property (FIKP) if whenever $\ell_p$ is finitely representable in the space then it contains every subset of $\ell_p$ isometrically. We show that every infinite-dimensional Banach space \emph{nearly} has FIDP and every Banach space nearly has FIKP. We then use convexity arguments to demonstrate that not every Banach space has FIKP, and thus we can exhibit classes of Banach spaces that fail to have Property AI-I. The methods used break down when one attempts to prove that there is a Banach space without FIDP and we conjecture that every infinite-dimensional Banach space has Property FIDP.