Relevant bibliographies by topics / Metric

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Metric'

Author: Grafiati
Published: 4 June 2021
Last updated: 6 September 2023

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Journal articles on the topic "Metric"

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Ab. Rahim, Rosminazuin, Abdallah Awad, Aisha Hassan Abdalla Hashim, and ALIZA AINI MD RALIB. "EVALUATION OF THE ROUTING METIRC W-METRIC USED WITH RPL PRTOCOL IN LLNS." IIUM Engineering Journal 19, no. 2 (December 1, 2018): 80–89. http://dx.doi.org/10.31436/iiumej.v19i2.840.

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ABSTRACT: The current de-facto routing protocol over Low Power and Lossy Networks (LLN) developed by the IETF Working Group (6LOWPAN), is named as Routing Protocol for Low Power and Lossy networks (RPL). RPL in the network layer faces throughput challenges due to the potential large networks, number of nodes, and that multiple coexisting applications will be running in the same physical layer. In this study, a node metric for RPL protocol based on the node’s Queue Backlogs is introduced, which leads to a better throughput performance while maintaining the delay and the ability to use with different network applications. This metric depends on the length of Packet Queue of the nodes with the consideration of other link and node metrics, like ETX or energy usage, leading to better load balancing in the network. To implement and evaluate the proposed metric compared to other RPL metrics, ContikiOS and COOJA simulator are used. Extensive simulations have been carried out in a systematic way resulting in a detailed analysis of the introduced metric namely W-metric, expected transmission count (ETX) and objective function zero (OF0) that uses hop-count as a routing metric. The analysis and comparison are based on five performance parameters, which are throughput, packet delivery ratio (PDR), latency, average queue length, and power consumption. Simulation results show that the introduced W-metric has a good performance compared to other RPL metrics with regards to performance parameters mentioned above. At the same time, the results show that its latency performance is comparable with other RPL routing metrics. In a sample simulation of 500 seconds with 25 nodes and with nodes sending packets periodically to the network root at a rate of 1 packet per 4 seconds, W-metric showed a very efficient throughput of 5.16 kbps, an increase of 8.2% compared to ETX. Results showed that it has a packet delivery ratio of 93.3%, which is higher compared to 83.3% for ETX and 74.2% for OF0. Average queue length of 0.48 packet shows improvement of 15.8% better than ETX. In addition, it exhibits an energy consumption of 5.16 mW which is 2.1% less than ETX. Overall, W-metric appears to be a promising alternative to ETX and OF0 as it selects routes that are more efficient by working on load balancing of the network and by considering the link characteristics. ABSTRAK: Protokol penghalaan de-facto semasa ke atas Rangkaian Kekuatan Rendah dan Lossy yang dibangunkan oleh Kumpulan Kerja IETF (6LOWPAN), dinamakan Protokol Penghalaan untuk Kekuatan Rendah dan Rugi (RPL). RPL dalam lapisan rangkaian menghadapi cabaran throughput berikutan jangkaan rangkaian besar, bilangan nod dan aplikasi berganda bersama akan diproses dalam lapisan fizikal yang sama. Dalam kajian ini, satu metrik nod untuk protokol RPL berdasarkan pada Backend Queue node diperkenalkan, yang membawa kepada prestasi yang lebih baik sambil mengekalkan kelewatan dan keupayaan untuk digunakan dengan aplikasi rangkaian yang berbeza. Metrik ini bergantung pada panjang Packet Queue dari node dengan pertimbangan metrik lain dan nodus lain, seperti ETX atau penggunaan tenaga, yang mengarah kepada keseimbangan beban yang lebih baik dalam rangkaian. Untuk melaksanakan dan menilai metrik yang dicadangkan berbanding metrik RPL lain, ContikiOS dan COOJA simulator telah digunakan. Simulasi meluas telah dijalankan dengan cara yang sistematik yang menghasilkan analisis terperinci mengenai metrik yang diperkenalkan iaitu W-metrik, kiraan penghantaran dijangkakan (ETX) dan fungsi objektif sifar (OF0) yang menggunakan kiraan hop sebagai metrik penghalaan. Analisis dan perbandingan adalah berdasarkan lima parameter prestasi, iaitu throughput, nisbah penghantaran paket (PDR), latency, panjang panjang antrian, dan penggunaan kuasa. Hasil simulasi menunjukkan bahawa W-metrik yang diperkenalkan mempunyai prestasi yang lebih baik berbanding dengan metrik RPL lain berkaitan dengan parameter prestasi yang dinyatakan di atas. Pada masa yang sama, hasil menunjukkan bahawa prestasi latency W-metrik adalah setanding dengan metrik penghalaan RPL yang lain. Dalam simulasi sampel 500 saat dengan 25 nod dan dengan nod yang menghantar paket secara berkala ke akar rangkaian pada kadar 1 paket setiap 4 saat, W-metrik menunjukkan keluaran yang sangat efisien iaitu 5.16 kbps, peningkatan sebanyak 8.2% berbanding ETX. Keputusan menunjukkan bahawa ia mempunyai nisbah penghantaran paket 93.3%, yang lebih tinggi berbanding 83.3% untuk ETX dan 74.2% untuk OF0. Purata panjang giliran 0.48 packet menunjukkan peningkatan 15.8% lebih baik daripada ETX. Di samping itu, ia mempamerkan penggunaan tenaga sebanyak 5.16 mW iaitu 2.1% kurang daripada ETX. Secara keseluruhan, W-metrik nampaknya menjadi alternatif yang berpotensi menggantikan ETX dan OF0 kerana ia memilih laluan yang lebih cekap dengan bekerja pada keseimbangan beban rangkaian dan dengan mempertimbangkan ciri-ciri pautan.
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Öner, Tarkan, and Alexander Šostak. "Some Remarks on Fuzzy sb-Metric Spaces." Mathematics 8, no. 12 (November 27, 2020): 2123. http://dx.doi.org/10.3390/math8122123.

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Fuzzy strong b-metrics called here by fuzzy sb-metrics, were introduced recently as a fuzzy version of strong b-metrics. It was shown that open balls in fuzzy sb-metric spaces are open in the induced topology (as different from the case of fuzzy b-metric spaces) and thanks to this fact fuzzy sb-metrics have many useful properties common with fuzzy metric spaces which generally may fail to be in the case of fuzzy b-metric spaces. In the present paper, we go further in the research of fuzzy sb-metric spaces. It is shown that the class of fuzzy sb-metric spaces lies strictly between the classes of fuzzy metric and fuzzy b-metric spaces. We prove that the topology induced by a fuzzy sb-metric is metrizable. A characterization of completeness in terms of diameter zero sets in these structures is given. We investigate products and coproducts in the naturally defined category of fuzzy sb-metric spaces.
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SABAU, SORIN V., KAZUHIRO SHIBUYA, and HIDEO SHIMADA. "Metric structures associated to Finsler metrics." Publicationes Mathematicae Debrecen 84, no. 1-2 (January 1, 2014): 89–103. http://dx.doi.org/10.5486/pmd.2014.5886.

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Jakfar, Muhammad, Manuharawati, Dwi Nur Yunianti, and Mey Dita Kumala. "Metrics on a G-metric Space." Journal of Physics: Conference Series 1417 (December 2019): 012023. http://dx.doi.org/10.1088/1742-6596/1417/1/012023.

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Zhao, Wen Jing, Yan Yan, Li Nan Shi, and Bo Chao Qu. "The Projectively Flat Conditions of One Special Class (α, β)-Metrics." Advanced Materials Research 756-759 (September 2013): 2528–32. http://dx.doi.org/10.4028/www.scientific.net/amr.756-759.2528.

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The-metric is an important class of Finsler metrics including Randers metric as the simplest class, and many people research the Randers metrics. In this paper, we study a new class of Finsler metrics in the form ,Whereis a Riemannian metric, is a 1-form. Bengling Li had introduced the projective flat of the-Metric F. We find another method which is about flag curvature to prove the projective flat conditions of this kind of-metric.
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Lin, Shuang, Mingxue Guo, and Yu Zhong. "A Representation Theorem for L-fuzzy Pseudo-metrics." Journal of Physics: Conference Series 2449, no. 1 (March 1, 2023): 012010. http://dx.doi.org/10.1088/1742-6596/2449/1/012010.

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Abstract Through this article, the definitions of an L -fuzzy pseudo-metric and a family of pseudo-metric that satisfies the property of lower-semicontinuity (or named nests of pseudo-metrics) are introduced. After that, we indicated that an L -fuzzy pseudo-metric can be constructed from nests of pseudo-metrics and nests of pseudo-metrics can be constructed from an L -fuzzy pseudo-metric. Therefore, we establish a each to each association between L - fuzzy pseudo-metrics and nests of pseudo-metrics.
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Saraswathula, Anirudh, Samantha J. Merck, Ge Bai, Christine M. Weston, Elizabeth Ann Skinner, April Taylor, Allen Kachalia, Renee Demski, Albert W. Wu, and Stephen A. Berry. "The Volume and Cost of Quality Metric Reporting." JAMA 329, no. 21 (June 6, 2023): 1840. http://dx.doi.org/10.1001/jama.2023.7271.

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ImportanceUS hospitals report data on many health care quality metrics to government and independent health care rating organizations, but the annual cost to acute care hospitals of measuring and reporting quality metric data, independent of resources spent on quality interventions, is not well known.ObjectiveTo evaluate externally reported inpatient quality metrics for adult patients and estimate the cost of data collection and reporting, independent of quality-improvement efforts.Design, Setting, and ParticipantsRetrospective time-driven activity-based costing study at the Johns Hopkins Hospital (Baltimore, Maryland) with hospital personnel involved in quality metric reporting processes interviewed between January 1, 2019, and June 30, 2019, about quality reporting activities in the 2018 calendar year.Main Outcomes and MeasuresOutcomes included the number of metrics, annual person-hours per metric type, and annual personnel cost per metric type.ResultsA total of 162 unique metrics were identified, of which 96 (59.3%) were claims-based, 107 (66.0%) were outcome metrics, and 101 (62.3%) were related to patient safety. Preparing and reporting data for these metrics required an estimated 108 478 person-hours, with an estimated personnel cost of $5 038 218.28 (2022 USD) plus an additional $602 730.66 in vendor fees. Claims-based (96 metrics; $37 553.58 per metric per year) and chart-abstracted (26 metrics; $33 871.30 per metric per year) metrics used the most resources per metric, while electronic metrics consumed far less (4 metrics; $1901.58 per metric per year).Conclusions and RelevanceSignificant resources are expended exclusively for quality reporting, and some methods of quality assessment are far more expensive than others. Claims-based metrics were unexpectedly found to be the most resource intensive of all metric types. Policy makers should consider reducing the number of metrics and shifting to electronic metrics, when possible, to optimize resources spent in the overall pursuit of higher quality.
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Houghton, Conor, and Kamal Sen. "A New Multineuron Spike Train Metric." Neural Computation 20, no. 6 (June 2008): 1495–511. http://dx.doi.org/10.1162/neco.2007.10-06-350.

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The Victor-Purpura spike train metric has recently been extended to a family of multineuron metrics and used to analyze spike trains recorded simultaneously from pairs of proximate neurons. The metric is one of the two metrics commonly used for quantifying the distance between two spike trains; the other is the van Rossum metric. Here, we suggest an extension of the van Rossum metric to a multineuron metric. We believe this gives a metric that is both natural and easy to calculate. Both types of multineuron metric are applied to simulated data and are compared.
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Khemaratchatakumthorn, Tammatada, and Prapanpong Pongsriiam. "Remarks on b-Metric and metric-preserving functions." Mathematica Slovaca 68, no. 5 (October 25, 2018): 1009–16. http://dx.doi.org/10.1515/ms-2017-0163.

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Aygün, Halis, Elif Güner, Juan-José Miñana, and Oscar Valero. "Fuzzy Partial Metric Spaces and Fixed Point Theorems." Mathematics 10, no. 17 (August 28, 2022): 3092. http://dx.doi.org/10.3390/math10173092.

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Partial metrics constitute a generalization of classical metrics for which self-distance may not be zero. They were introduced by S.G. Matthews in 1994 in order to provide an adequate mathematical framework for the denotational semantics of programming languages. Since then, different works were devoted to obtaining counterparts of metric fixed-point results in the more general context of partial metrics. Nevertheless, in the literature was shown that many of these generalizations are actually obtained as a corollary of their aforementioned classical counterparts. Recently, two fuzzy versions of partial metrics have been introduced in the literature. Such notions may constitute a future framework to extend already established fuzzy metric fixed point results to the partial metric context. The goal of this paper is to retrieve the conclusion drawn in the aforementioned paper by Haghia et al. to the fuzzy partial metric context. To achieve this goal, we construct a fuzzy metric from a fuzzy partial metric. The topology, Cauchy sequences, and completeness associated with this fuzzy metric are studied, and their relationships with the same notions associated to the fuzzy partial metric are provided. Moreover, this fuzzy metric helps us to show that many fixed point results stated in fuzzy metric spaces can be extended directly to the fuzzy partial metric framework. An outstanding difference between our approach and the classical technique introduced by Haghia et al. is shown.
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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
CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior
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.
Includes bibliographical references (p. 141-145).
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.
(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.
by Anastasios Sidiropoulos.
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.
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.
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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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.

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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.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 111-112).
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.
by Harold Franklin Jensen III.
S.M.
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Books on the topic "Metric"

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K, Jain P. Metric spaces. New Delhi: Narosa Publishing House, 1993.

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Buxton, Pamela, ed. Metric Handbook. Sixth edition. | New York: Routledge, 2018.: Routledge, 2018. http://dx.doi.org/10.4324/9781315230726.

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Buxton, Pamela. Metric Handbook. 7th ed. London: Routledge, 2021. http://dx.doi.org/10.4324/9781003052586.

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Magnus, Robert. Metric Spaces. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-94946-4.

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Beer, David. Metric Power. London: Palgrave Macmillan UK, 2016. http://dx.doi.org/10.1057/978-1-137-55649-3.

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Weller, Susan, and A. Romney. Metric Scaling. 2455 Teller Road, Newbury Park California 91320 United States of America: SAGE Publications, Inc., 1990. http://dx.doi.org/10.4135/9781412985048.

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United States. Congress. House. Committee on Science, Space, and Technology. Subcommittee on Science, Research, and Technology. Metric conversion. Washington, DC: U.S. G.P.O, 1990.

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Metric handbook. 4th ed. New York: Routledge, 2011.

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Montana. Department of Transportation. Metric fundamentals. Helena, Mont: The Department, 1992.

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McKeown, Sally. Metric measures. Coventry: Ben Books, 1989.

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Book chapters on the topic "Metric"

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Weik, Martin H. "metric." In Computer Science and Communications Dictionary, 1010. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_11459.

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Planas, Adrián, Andrés Pascal, and Norma Herrera. "MeTree: A Metric Spatial Index." In Computer Science – CACIC 2019, 250–61. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48325-8_17.

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"Metric." In Encyclopedia of the UN Sustainable Development Goals, 396. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-319-95717-3_300094.

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Fefferman, Charles, and C. Robin Graham. "Poincaré Metrics." In The Ambient Metric (AM-178). Princeton University Press, 2011. http://dx.doi.org/10.23943/princeton/9780691153131.003.0004.

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This chapter considers the formal theory for Poincaré metrics associated to a conformal manifold (M, [g]). It shows that even Poincaré metrics are in one-to-one correspondence with straight ambient metrics, if both are in normal form. Thus, the formal theory for Poincaré metrics is a consequence of the results of Chapter 3. The derivation of a Poincaré metric from an ambient metric was described in [FG], and the inverse construction of an ambient metric as the cone metric over a Poincaré metric was given in § 5 of [GrL].
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"Metric Units and the Preferred Dosing of Orally Administered Liquid Medications." In Pediatric Clinical Practice Guidelines & Policies, 891–96. 16th ed. American Academy of Pediatrics, 2016. http://dx.doi.org/10.1542/9781610020190-part04-metric.

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"Metric Units and the Preferred Dosing of Orally Administered Liquid Medications." In Pediatric Clinical Practice Guidelines & Policies, 1315. 16th ed. American Academy of Pediatrics, 2016. http://dx.doi.org/10.1542/9781610020190-part05-metric.

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"Metric spaces." In Metric Spaces, 12–28. Cambridge University Press, 1985. http://dx.doi.org/10.1017/9781139171854.003.

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"Aids to pedestrian movement." In Metric Handbook, 97–108. Routledge, 2007. http://dx.doi.org/10.4324/9780080523163-10.

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"Landscape design." In Metric Handbook, 109–24. Routledge, 2007. http://dx.doi.org/10.4324/9780080523163-11.

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"Terminals and transport interchanges." In Metric Handbook, 125–43. Routledge, 2007. http://dx.doi.org/10.4324/9780080523163-12.

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Conference papers on the topic "Metric"

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Srivastav, V. S. P., and Piyush Prakash. "Green metrics for OO codes: CAAEC metric." In 2013 International Conference on Green Computing, Communication and Conservation of Energy (ICGCE). IEEE, 2013. http://dx.doi.org/10.1109/icgce.2013.6823448.

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Saurez, Enrique, Bharath Balasubramanian, Richard Schlichting, Brendan Tschaen, Zhe Huang, Shankaranarayanan Puzhavakath Narayanan, and Umakishore Ramachandran. "METRIC." In the 3rd Workshop. New York, New York, USA: ACM Press, 2018. http://dx.doi.org/10.1145/3286685.3286686.

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Mao, Jun-Xiang, Wei Wang, and Min-Ling Zhang. "Label Specific Multi-Semantics Metric Learning for Multi-Label Classification: Global Consideration Helps." In Thirty-Second International Joint Conference on Artificial Intelligence {IJCAI-23}. California: International Joint Conferences on Artificial Intelligence Organization, 2023. http://dx.doi.org/10.24963/ijcai.2023/451.

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In multi-label classification, it is critical to capitalize on complicated data structures and semantic relationships. Metric learning serves as an effective strategy to provide a better measurement of distances between examples. Existing works on metric learning for multi-label classification mainly learn one single global metric that characterizes latent semantic similarity between multi-label instances. However, such single-semantics metric exploitation approaches can not capture the intrinsic properties of multi-label data possessed of rich semantics. In this paper, the first attempt towards multi-semantics metric learning for multi-label classification is investigated. Specifically, the proposed LIMIC approach simultaneously learns one global and multiple label-specific local metrics by exploiting label-specific side information. The global metric is learned to capture the commonality across all the labels and label-specific local metrics characterize the individuality of each semantic space. The combination of global metric and label-specific local metrics is utilized to construct latent semantic space for each label, in which similar intra-class instances are pushed closer and inter-class instances are pulled apart. Furthermore, metric-based label correlation regularization is constructed to maintain similarity between correlated label spaces. Extensive experiments on benchmark multi-label data sets validate the superiority of our proposed approach in learning effective distance metrics for multi-label classification.
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Yanhong Bi, Bin Fan, and Fuchao Wu. "Beyond Mahalanobis metric: Cayley-Klein metric learning." In 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2015. http://dx.doi.org/10.1109/cvpr.2015.7298847.

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Johnson, Tyler A., Avery Cheeley, Benjamin W. Caldwell, and Matthew G. Green. "Comparison and Extension of Novelty Metrics for Problem-Solving Tasks." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-60319.

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Shah’s metrics for measuring ideation effectiveness have been used extensively by the engineering design community to quantify the value of designed concepts. Shah measures novelty as the infrequency of an idea relative to a set of ideas. Vargas-Hernandez extended this novelty metric using partial genealogy trees to consider the frequency of ideas that share the same working principle. These genealogy trees capture differences between individual ideas organized by the following levels of abstraction: physical principle, working principle, and embodiment. Shah’s and Vargas-Hernandez’s metrics both require that all ideas be described at the lowest level (embodiment). This approach excludes ideas that are described at higher levels of abstraction. This paper proposes a new novelty metric that extends Vargas Hernandez’s metrics by including the higher levels of the genealogy trees, allowing abstract ideas to be properly evaluated. This paper compares the newly proposed novelty metric to Shah’s and Vargas Hernandez’s metrics using data from a previous study. The study required participants to perform problem-solving tasks in which they submitted a textual list of ideas for how to solve general day-to-day problems. The proposed novelty metric addresses limitations of the previous metrics when applied to the abstract ideas in the data set and meets established metric requirements. The proposed metric also broadens Shah’s metric in a similar manner as Vargas Hernandez but extends it to capture the entire genealogy tree rather than a subset of the tree.
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Mendel, Manor, and Assaf Naor. "Metric cotype." In the seventeenth annual ACM-SIAM symposium. New York, New York, USA: ACM Press, 2006. http://dx.doi.org/10.1145/1109557.1109567.

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Risi, M., G. Scanniello, and G. Tortora. "Metric Attitude." In 2013 17th European Conference on Software Maintenance and Reengineering (CSMR 2013). IEEE, 2013. http://dx.doi.org/10.1109/csmr.2013.59.

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Henderson, Keith, Tina Eliassi-Rad, Christos Faloutsos, Leman Akoglu, Lei Li, Koji Maruhashi, B. Aditya Prakash, and Hanghang Tong. "Metric forensics." In the 16th ACM SIGKDD international conference. New York, New York, USA: ACM Press, 2010. http://dx.doi.org/10.1145/1835804.1835828.

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Sullivan, Dean, Jeff Biggers, Guidong Zhu, Shaojie Zhang, and Yier Jin. "FIGHT-Metric." In the The 51st Annual Design Automation Conference. New York, New York, USA: ACM Press, 2014. http://dx.doi.org/10.1145/2593069.2596681.

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Lizarraga-Lizarraga, Giovanni, Arturo Hernandez-Aguirre, and Salvador Botello-Rionda. "G-Metric." In the 10th annual conference. New York, New York, USA: ACM Press, 2008. http://dx.doi.org/10.1145/1389095.1389227.

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Reports on the topic "Metric"

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Demichelis, C., and P. Chimento. IP Packet Delay Variation Metric for IP Performance Metrics (IPPM). RFC Editor, November 2002. http://dx.doi.org/10.17487/rfc3393.

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Almes, G., S. Kalidindi, and M. Zekauskas. A One-Way Delay Metric for IP Performance Metrics (IPPM). Edited by A. Morton. RFC Editor, January 2016. http://dx.doi.org/10.17487/rfc7679.

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Almes, G., S. Kalidindi, and M. Zekauskas. A One-Way Loss Metric for IP Performance Metrics (IPPM). Edited by A. Morton. RFC Editor, January 2016. http://dx.doi.org/10.17487/rfc7680.

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Zwart, P. H., R. W. Grosse-Kunstleve, and P. D. Adams. Exploring Metric Symmetry. Office of Scientific and Technical Information (OSTI), July 2006. http://dx.doi.org/10.2172/926901.

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Carver, Gary P. A metric America:. Gaithersburg, MD: National Institute of Standards and Technology, 1992. http://dx.doi.org/10.6028/nist.ir.4858.

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Benham, Elizabeth. NIST Metric Recipes. Gaithersburg, MD: National Institute of Standards and Technology, 2023. http://dx.doi.org/10.6028/nist.sp.1290.

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Psenak, P., and H. Johnston. OSPF Reverse Metric. Edited by K. Talaulikar. RFC Editor, December 2022. http://dx.doi.org/10.17487/rfc9339.

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None, None. EERE GPRA2003 metric estimates. Office of Scientific and Technical Information (OSTI), July 2003. http://dx.doi.org/10.2172/1216530.

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Cowlin, Shannon, Donna Heimiller, Jordan Macknick, Margaret Mann, Jacquelyn Pless, and David Munoz. Multi-Metric Sustainability Analysis. Office of Scientific and Technical Information (OSTI), December 2014. http://dx.doi.org/10.2172/1167056.

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Manadhata, Pratyusa, and Jeannette M. Wing. An Attack Surface Metric. Fort Belvoir, VA: Defense Technical Information Center, July 2005. http://dx.doi.org/10.21236/ada457096.

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