Journal articles: 'Metrics'

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Pentecost, Michael J. "Metrics, Metrics, Metrics." Journal of the American College of Radiology 13, no. 6 (June 2016): 628–29. http://dx.doi.org/10.1016/j.jacr.2016.03.002.

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Jekl, Jan, and Jiří Jánský. "Security Challenges and Economic-Geographical Metrics for Analyzing Safety to Achieve Sustainable Protection." Sustainability 14, no. 22 (November 16, 2022): 15161. http://dx.doi.org/10.3390/su142215161.

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In this article, we aim to develop the theoretical background for the possible application of Economic-Geographical metrics in the field of population protection. We deal with various options for analyzing the availability of “safety” for citizens using studied metrics. Among others, we apply well-known metrics such as the Gini coefficient, Hoover index and even establish their generalizations. We develop a theoretical background and evaluate our findings on generated and actual data. We find that the metrics used can have an opposite interpretation depending on the scenario we are considering. We also discover that some scenarios demand a modification to the usual metric. We conclude that Economic-Geographical metrics give valuable tools to address specific security challenges. Metric’s generalizations could serve as a potent tool for other authors working in the field of population protection. Nevertheless, we must keep in mind that metrics also have drawbacks.

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Hoffman, Robert R., Peter A. Hancock, and Jeffrey M. Bradshaw. "Metrics, Metrics, Metrics, Part 2: Universal Metrics?" IEEE Intelligent Systems 25, no. 6 (November 2010): 93–97. http://dx.doi.org/10.1109/mis.2010.147.

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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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Hoffman, R. R., M. Marx, and P. Hancock. "Metrics, Metrics, Metrics: Negative Hedonicity." IEEE Intelligent Systems 23, no. 2 (March 2008): 69–73. http://dx.doi.org/10.1109/mis.2008.31.

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Mennucci, Andrea C. G. "Designing metrics; the delta metric for curves." ESAIM: Control, Optimisation and Calculus of Variations 25 (2019): 59. http://dx.doi.org/10.1051/cocv/2018044.

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In the first part, we revisit some key notions. Let M be a Riemannian manifold. Let G be a group acting on M. We discuss the relationship between the quotient M∕G, “horizontality” and “normalization”. We discuss the distinction between path-wise invariance and point-wise invariance and how the former positively impacts the design of metrics, in particular for the mathematical and numerical treatment of geodesics. We then discuss a strategy to design metrics with desired properties. In the second part, we prepare methods to normalize some standard group actions on the curve; we design a simple differential operator, called the delta operator, and compare it to the usual differential operators used in defining Riemannian metrics for curves. In the third part we design two examples of Riemannian metrics in the space of planar curves. These metrics are based on the “delta” operator; they are “modular”, they are composed of different terms, each associated to a group action. These are “strong” metrics, that is, smooth metrics on the space of curves, that is defined as a differentiable manifolds, modeled on the standard Sobolev space H2. These metrics enjoy many important properties, including: metric completeness, geodesic completeness, existence of minimal length geodesics. These metrics properly project on the space of curves up to parameterization; the quotient space again enjoys the above properties.

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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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Rhodes, Frank. "Metric subgraphs of the chamfer metrics and the Melter-Tomescu path generated metrics." Discrete Mathematics 147, no. 1-3 (December 1995): 197–209. http://dx.doi.org/10.1016/0012-365x(94)00238-e.

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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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ROD GOVER, A., and F. LEITNER. "A SUB-PRODUCT CONSTRUCTION OF POINCARÉ–EINSTEIN METRICS." International Journal of Mathematics 20, no. 10 (October 2009): 1263–87. http://dx.doi.org/10.1142/s0129167x09005753.

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Given any two Einstein (pseudo-)metrics, with scalar curvatures suitably related, we give an explicit construction of a Poincaré–Einstein (pseudo-)metric with conformal infinity the conformal class of the product of the initial metrics. We show that these metrics are equivalent to ambient metrics for the given conformal structure. The ambient metrics have holonomy that agrees with the conformal holonomy. In the generic case the ambient metric arises directly as a product of the metric cones over the original Einstein spaces. In general the conformal infinity of the Poincaré metric we construct is not Einstein, and so this describes a class of non-conformally Einstein metrics for which the (Fefferman–Graham) obstruction tensor vanishes.

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Fu, Wen Qing, Sheng Gang Li, Harish Garg, Heng Liu, Ahmed Mostafa Khalil, and Jingjing Zhao. "An Easy-to-Understand Method to Construct Desired Distance-Like Measures." Complexity 2021 (July 8, 2021): 1–15. http://dx.doi.org/10.1155/2021/5571546.

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Metrics and their weaker forms are used to measure the difference between two data (or other things). There are many metrics that are available but not desired by a practitioner. This paper recommends in a plausible reasoning manner an easy-to-understand method to construct desired distance-like measures: to fuse easy-to-obtain (or easy to be coined by practitioners) pseudo-semi-metrics, pseudo-metrics, or metrics by making full use of well-known t-norms, t-conorms, aggregation operators, and similar operators (easy to be coined by practitioners). The simple reason to do this is that data for a real world problem are sometimes from multiagents. A distance-like notion, called weak interval-valued pseudo-metrics (briefly, WIVP-metrics), is defined by using known notions of pseudo-semi-metrics, pseudo-metrics, and metrics; this notion is topologically good and shows precision, flexibility, and compatibility than single pseudo-semi-metrics, pseudo-metrics, or metrics. Propositions and detailed examples are given to illustrate how to fabricate (including using what “material”) an expected or demanded WIVP-metric (even interval-valued metric) in practical problems, and WIVP-metric and its special cases are characterized by using axioms. Moreover, some WIVP-metrics pertinent to quantitative logic theory or interval-valued fuzzy graphs are constructed, and fixed point theorems and common fixed point theorems in weak interval-valued metric spaces are also presented. Topics and strategies for further study are also put forward concretely and clearly.

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CASE, JEFFREY S. "SMOOTH METRIC MEASURE SPACES AND QUASI-EINSTEIN METRICS." International Journal of Mathematics 23, no. 10 (October 2012): 1250110. http://dx.doi.org/10.1142/s0129167x12501108.

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Smooth metric measure spaces have been studied from the two different perspectives of Bakry–Émery and Chang–Gursky–Yang, both of which are closely related to work of Perelman on the Ricci flow. These perspectives include a generalization of the Ricci curvature and the associated quasi-Einstein metrics, which include Einstein metrics, conformally Einstein metrics, gradient Ricci solitons and static metrics. In this paper, we describe a natural perspective on smooth metric measure spaces from the point of view of conformal geometry and show how it unites these earlier perspectives within a unified framework. We offer many results and interpretations which illustrate the unifying nature of this perspective, including a natural variational characterization of quasi-Einstein metrics as well as some interesting families of examples of such metrics.

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Kornev, R. A. "Computable metrics above the standard real metric." Sibirskie Elektronnye Matematicheskie Izvestiya 18, no. 1 (April 13, 2021): 377–92. http://dx.doi.org/10.33048/semi.2021.18.027.

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Vallin. "MORE ON THE METRIC SPACE OF METRICS." Real Analysis Exchange 21, no. 2 (1995): 739. http://dx.doi.org/10.2307/44152685.

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Bogachev, V. I., A. N. Doledenok, and S. V. Shaposhnikov. "Weighted Zolotarev metrics and the Kantorovich metric." Doklady Mathematics 95, no. 2 (March 2017): 113–17. http://dx.doi.org/10.1134/s1064562417020028.

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Case, Jeffrey S. "Sharp metric obstructions for quasi-Einstein metrics." Journal of Geometry and Physics 64 (February 2013): 12–30. http://dx.doi.org/10.1016/j.geomphys.2012.10.006.

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Zage, Wayne M., Dolores M. Zage, and Cathy Wilburn. "Avoiding metric monsters: A design metrics approach." Annals of Software Engineering 1, no. 1 (December 1995): 43–55. http://dx.doi.org/10.1007/bf02249045.

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Kaur, Sandeep. "Software Metrics and Metric Tools A Review." International Journal on Recent and Innovation Trends in Computing and Communication 3, no. 4 (2015): 2076–79. http://dx.doi.org/10.17762/ijritcc2321-8169.150468.

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Faran, V, James J. "Hermitian Finsler metrics and the Kobayashi metric." Journal of Differential Geometry 31, no. 3 (1990): 601–25. http://dx.doi.org/10.4310/jdg/1214444630.

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Isah, Ahmed. "METRICS AND METRIC SPACES OF SOFT MULTISETS." FUDMA JOURNAL OF SCIENCES 7, no. 1 (February 28, 2023): 188–92. http://dx.doi.org/10.33003/fjs-2023-0701-1275.

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The theory of Soft set found applications in so many fields including multiset theory to obtain soft multisets. These theories together with some of their properties were presented. Moreover, considering the various applications of metric spaces in various fields; Metrics and metric spaces of soft multisets with some of their attributes were introduced. However, it was discovered that only pseudo-metric spaces could favorably be formulated. Moreover, soft multiset ordering was also presented.

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Gregori, Valentín, Juan-José Miñana, and David Miravet. "A Duality Relationship Between Fuzzy Partial Metrics and Fuzzy Quasi-Metrics." Mathematics 8, no. 9 (September 12, 2020): 1575. http://dx.doi.org/10.3390/math8091575.

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In 1994, Matthews introduced the notion of partial metric and established a duality relationship between partial metrics and quasi-metrics defined on a set X. In this paper, we adapt such a relationship to the fuzzy context, in the sense of George and Veeramani, by establishing a duality relationship between fuzzy quasi-metrics and fuzzy partial metrics on a set X, defined using the residuum operator of a continuous t-norm ∗. Concretely, we provide a method to construct a fuzzy quasi-metric from a fuzzy partial one. Subsequently, we introduce the notion of fuzzy weighted quasi-metric and obtain a way to construct a fuzzy partial metric from a fuzzy weighted quasi-metric. Such constructions are restricted to the case in which the continuous t-norm ∗ is Archimedean and we show that such a restriction cannot be deleted. Moreover, in both cases, the topology is preserved, i.e., the topology of the fuzzy quasi-metric obtained coincides with the topology of the fuzzy partial metric from which it is constructed and vice versa. Besides, different examples to illustrate the exposed theory are provided, which, in addition, show the consistence of our constructions comparing it with the classical duality relationship.

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Bēts, Raivis, and Alexander Šostak. "Fuzzy Approximating Metrics, Approximating Parametrized Metrics and Their Relations with Fuzzy Partial Metrics." Mathematics 11, no. 15 (July 27, 2023): 3313. http://dx.doi.org/10.3390/math11153313.

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We generalize the concept of a fuzzy metric by introducing its approximating counterpart in order to make it more appropriate for the study of some problems related to combinatorics on words. We establish close relations between fuzzy approximating metrics in the case of special t-norms and approximating parametrized metrics, discuss some relations between fuzzy approximating metrics and fuzzy partial metrics, as well as showing some possible applications of approximating parametrized metrics in the problems of combinatorics on words.

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CHEN, GUANGZU, and XINYUE CHENG. "AN IMPORTANT CLASS OF CONFORMALLY FLAT WEAK EINSTEIN FINSLER METRICS." International Journal of Mathematics 24, no. 01 (January 2013): 1350003. http://dx.doi.org/10.1142/s0129167x13500031.

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In this paper, we study conformally flat (α, β)-metrics in the form F = αϕ(β/α), where α is a Riemannian metric and β is a 1-form on a C∞ manifold M. We prove that if ϕ = ϕ(s) is a polynomial in s, the conformally flat weak Einstein (α, β)-metric must be either a locally Minkowski metric or a Riemannian metric. Moreover, we prove that conformally flat (α, β)-metrics with isotropic S-curvature are also either locally Minkowski metrics or Riemannian metrics.

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Liu, Huaifu, and Xiaohuan Mo. "On Projectively Flat Finsler Warped Product Metrics of Constant Flag Curvature." Journal of Geometric Analysis 31, no. 11 (May 24, 2021): 11471–92. http://dx.doi.org/10.1007/s12220-021-00690-5.

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AbstractIn this paper, we study locally projectively flat Finsler metrics of constant flag curvature. We find equations that characterize these metrics by warped product. Using the obtained equations, we manufacture new locally projectively flat Finsler warped product metrics of vanishing flag curvature. These metrics contain the metric introduced by Berwald and the spherically symmetric metric given by Mo-Zhu.

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M. Taaffe, Kevin, Robert William Allen, and Lindsey Grigg. "Performance metrics analysis for aircraft maintenance process control." Journal of Quality in Maintenance Engineering 20, no. 2 (May 6, 2014): 122–34. http://dx.doi.org/10.1108/jqme-07-2012-0022.

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Purpose – Performance measurements or metrics are that which measure a company's performance and behavior, and are used to help an organization achieve and maintain success. Without the use of performance metrics, it is difficult to know whether or not the firm is meeting requirements or making desired improvements. During the course of this study with Lockheed Martin, the research team was tasked with determining the effectiveness of the site's existing performance metrics that are used to help an organization achieve and maintain success. Without the use of performance metrics, it is difficult to know whether or not the firm is meeting requirements or making desired improvements. The paper aims to discuss these issues. Design/methodology/approach – Research indicates that there are five key elements that influence the success of a performance metric. A standardized method of determining whether or not a metric has the right mix of these elements was created in the form of a metrics scorecard. Findings – The scorecard survey was successful in revealing good metric use, as well as problematic metrics. In the quality department, the Document Rejects metric has been reworked and is no longer within the executive's metric deck. It was also recommended to add root cause analysis, and to quantify and track the cost of non-conformance and the overall cost of quality. In total, the number of site wide metrics has decreased from 75 to 50 metrics. The 50 remaining metrics are undergoing a continuous improvement process in conjunction with the use of the metric scorecard tool developed in this research. Research limitations/implications – The metrics scorecard should be used site-wide for an assessment of all metrics. The focus of this paper is on the metrics within the quality department. Practical implications – Putting a quick and efficient metrics assessment technique in place was critical. With the leadership and participation of Lockheed Martin, this goal was accomplished. Originality/value – This paper presents the process of metrics evaluation and the issues that were encountered during the process, including insights that would not have been easily documented without this mechanism. Lockheed Martin Company has used results from this research. Other industries could also apply the methods proposed here.

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Tayebi, Akbar. "On generalized 4-th root metrics of isotropic scalar curvature." Mathematica Slovaca 68, no. 4 (August 28, 2018): 907–28. http://dx.doi.org/10.1515/ms-2017-0154.

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AbstractBy an interesting physical perspective and a suitable contraction of the Riemannian curvature tensor in Finsler geometry, Akbar-Zadeh introduced the notion of scalar curvature for the Finsler metrics. A Finsler metric is called of isotropic scalar curvature if the scalar curvature depends on the position only. In this paper, we study the class of generalized 4-th root metrics. These metrics generalize 4-th root metrics which are used in Biology as ecological metrics. We find the necessary and sufficient condition under which a generalized 4-th root metric is of isotropic scalar curvature. Then, we find the necessary and sufficient condition under which the conformal change of a generalized 4-th root metric is of isotropic scalar curvature. Finally, we characterize the Bryant metrics of isotropic scalar curvature.

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Grigorenko, Olga, Juan Jose Miñana, Alexander Šostak, and Oscar Valero. "On t-Conorm Based Fuzzy (Pseudo)metrics." Axioms 9, no. 3 (July 8, 2020): 78. http://dx.doi.org/10.3390/axioms9030078.

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We present an alternative approach to the concept of a fuzzy (pseudo)metric using t-conorms instead of t-norms and call them t-conorm based fuzzy (pseudo)metrics or just CB-fuzzy (pseudo)metrics. We develop the basics of the theory of CB-fuzzy (pseudo)metrics and compare them with “classic” fuzzy (pseudo)metrics. A method for construction CB-fuzzy (pseudo)metrics from ordinary metrics is elaborated and topology induced by CB-fuzzy (pseudo)metrics is studied. We establish interrelations between CB-fuzzy metrics and modulars, and in the process of this study, a particular role of Hamacher t-(co)norm in the theory of (CB)-fuzzy metrics is revealed. Finally, an intuitionistic version of a CB-fuzzy metric is introduced and applied in order to emphasize the roles of t-norms and a t-conorm in this context.

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Spivey, Alvin, and Anthony Vodacek. "Multiscale Fourier Landscape Pattern Indices For Landscape Ecology." Journal of Landscape Ecology 11, no. 2 (November 1, 2018): 5–30. http://dx.doi.org/10.2478/jlecol-2018-0004.

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Abstract A factor analysis of 67 landscape pattern metrics was performed to quantify the ability of landscape pattern metrics to explain land cover pattern, and to report individual landscape pattern metric values that are statistically independent. This land cover pattern is measured from 7.68 x 7.68 [km] GeoTiff image tiles of the conterminous United States Geological Survey (USGS) 1992 National Land Cover Dataset (NCLD). Using factor analysis to rank independent landscape pattern information, each landscape pattern metric produces the explanatory power of that landscape pattern metric amongst the other 66 landscape pattern metrics—any landscape pattern metrics that report similar values contribute redundant information. The metrics that contribute the most information are Jackson’s Contagion statistic (P005), typically contributing to 97 % of the explained variability; the Fourier Metric of Fragmentation (FMF), typically contributing to 65 % of the explained variability; and average LCLU class lacunarity (TLAC), typically contributing to 62 % of the explained variability. Two other Fourier-based landscape pattern metrics we tested, the Least Squares Fourier Transform Fractal Dimension Estimation (LsFT) and the Fourier Metric of Proportion (FMP), contributed 50 % and 12 % to the explained variability, respectively. In addition, the values reported by each of the Fourier metrics are revealed to be relatively independent amongst commonly used landscape pattern metrics and are thus demonstrated to be appropriate for explaining general landscape pattern variability.

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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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Rusu, Cătălin V., and Răzvan V. Florian. "A New Class of Metrics for Spike Trains." Neural Computation 26, no. 2 (February 2014): 306–48. http://dx.doi.org/10.1162/neco_a_00545.

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The distance between a pair of spike trains, quantifying the differences between them, can be measured using various metrics. Here we introduce a new class of spike train metrics, inspired by the Pompeiu-Hausdorff distance, and compare them with existing metrics. Some of our new metrics (the modulus-metric and the max-metric) have characteristics that are qualitatively different from those of classical metrics like the van Rossum distance or the Victor and Purpura distance. The modulus-metric and the max-metric are particularly suitable for measuring distances between spike trains where information is encoded in bursts, but the number and the timing of spikes inside a burst do not carry information. The modulus-metric does not depend on any parameters and can be computed using a fast algorithm whose time depends linearly on the number of spikes in the two spike trains. We also introduce localized versions of the new metrics, which could have the biologically relevant interpretation of measuring the differences between spike trains as they are perceived at a particular moment in time by a neuron receiving these spike trains.

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AYDIN, Fatih. "Uzaklık Metriklerinin Performansı Üzerine Ampirik Bir Çalışma." Afyon Kocatepe University Journal of Sciences and Engineering 23, no. 6 (December 22, 2023): 1445–57. http://dx.doi.org/10.35414/akufemubid.1325843.

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Metrics are used to measure the distance, similarity, or dissimilarity between two points in a metric space. Metric learning algorithms perform the finding task of data points that are closest or furthest to a query point in m-dimensional metric space. Some metrics take into account the assumption that the whole dimensions are of equal importance, and vice versa. However, this assumption does not incorporate a number of real-world problems that classification algorithms tackle. In this research, the existing information gain, the information gain ratio, and some well-known conventional metrics have been compared by each other. The 1-Nearest Neighbor algorithm taking these metrics as its meta-parameter has been applied to forty-nine benchmark datasets. Only the accuracy rate criterion has been employed in order to quantify the performance of the metrics. The experimental results show that each metric is successful on datasets corresponding to its own domain. In other words, each metric is favorable on datasets overlapping its own assumption. In addition, there also exists incompleteness in classification tasks for metrics just like there is for learning algorithms.

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Abbott, Alison, David Cyranoski, Nicola Jones, Brendan Maher, Quirin Schiermeier, and Richard Van Noorden. "Metrics: Do metrics matter?" Nature 465, no. 7300 (June 2010): 860–62. http://dx.doi.org/10.1038/465860a.

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Kwan, Chiman, and Bence Budavari. "A New Blind Video Quality Metric for Assessing Different Turbulence Mitigation Algorithms." Electronics 10, no. 18 (September 16, 2021): 2277. http://dx.doi.org/10.3390/electronics10182277.

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Although many algorithms have been proposed to mitigate air turbulence in optical videos, there do not seem to be consistent blind video quality assessment metrics that can reliably assess different approaches. Blind video quality assessment metrics are necessary because many videos containing air turbulence do not have ground truth. In this paper, a simple and intuitive blind video quality assessment metric is proposed. This metric can reliably and consistently assess various turbulent mitigation algorithms for optical videos. Experimental results using more than 10 videos in the literature show that the proposed metrics correlate well with human subjective evaluations. Compared with an existing blind video metric and two other blind image quality metrics, the proposed metrics performed consistently better.

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Kreizenbeck, Karma L., Erin E. Hughes, F. Marc Stewart, Thomas David Brown, Eric Y. Chen, John M. Corman, Thomas Curry, et al. "Regional initiative to define, collect, and report value metrics in cancer care." Journal of Clinical Oncology 32, no. 30_suppl (October 20, 2014): 25. http://dx.doi.org/10.1200/jco.2014.32.30_suppl.25.

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25 Background: In the context of numerous national initiatives aimed at measuring quality and value in cancer care, the Hutchinson Institute for Cancer Outcomes Research, in partnership with local healthcare delivery organizations, patient advocacy groups, payers, and policymakers launched a regional, stakeholder-driven initiative to define 3-5 “value-based metrics” for cancer care for Washington State. Methods: Representatives from major cancer care delivery organizations, patient advocacy groups, payers, and policymakers were invited to participate in a day-long Value Summit. Attendees were tasked with identifying metrics that considered both costs and outcomes. Trained facilitators helped participants identify metrics for 9 domains: appropriate use of effective therapies, adherence to best practices, survival, comprehensive disease management, efficiency of care, hospice/palliative care, patient and family satisfaction with care, patient reported outcomes/preferences and safety. After the initial list was generated, attendees were then asked to rank the metrics on the basis of feasibility to collect, clinical relevance, ability to act on, meaningfulness to multiple stakeholders, and willingness to report statewide. Attendees were then asked to participate in 3 domain-specific facilitated breakout sessions to prioritize the top metrics for each domain. Breakout sessions reported top metrics for a final group prioritization exercise. Following the Summit, attendees provided feedback on the final rankings. The metrics were then presented at a Town Hall style meeting for public comment. Results: Over 70 participants, representing 20 different organizations, identified 750 unique metrics from 9 domains. The prioritization process yielded 3 areas of interest, with 2 specific metrics within each: end of life and palliative care (metric 1, metric 2); adherence to best practices (metric 3, metric 4); and coordinated and efficient care (metric 5, metric 6). Follow-up surveys of Summit attendees and the Town Hall forum showed widespread support for these metrics Conclusions: Using an iterative, transparent, multi-stakeholder process, it is feasible build regional consensus around value metrics in cancer care.

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Adewumi, Misra, and Damaševičius. "A Complexity Metrics Suite for Cascading Style Sheets." Computers 8, no. 3 (July 10, 2019): 54. http://dx.doi.org/10.3390/computers8030054.

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We perform a theoretical and empirical analysis of a set of Cascading Style Sheets (CSS) document complexity metrics. The metrics are validated using a practical framework that demonstrates their viability. The theoretical analysis is performed using the Weyuker’s properties−a widely adopted approach to conducting empirical validations of metrics proposals. The empirical analysis is conducted using visual and statistical analysis of distribution of metric values, Cliff’s delta, Chi-square and Liliefors statistical normality tests, and correlation analysis on our own dataset of CSS documents. The results show that five out of the nine metrics (56%) satisfy Weyuker’s properties except for the Number of Attributes Defined per Rule Block (NADRB) metric, which satisfies six out of nine (67%) properties. In addition, the results from the statistical analysis show good statistical distribution characteristics (only the Number of Extended Rule Blocks (NERB) metric exceeds the rule-of-thumb threshold value of the Cliff’s delta). The correlation between the metric values and the size of the CSS documents is insignificant, suggesting that the presented metrics are indeed complexity rather than size metrics. The practical application of the presented CSS complexity metric suite is to assess the risk of CSS documents. The proposed CSS complexity metrics suite allows identification of CSS files that require immediate attention of software maintenance personnel.

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McNamara, Sara. "HOW TO MAXIMIZE THE REACH OF YOUR PUBLISHED WORK." Innovation in Aging 3, Supplement_1 (November 2019): S224. http://dx.doi.org/10.1093/geroni/igz038.823.

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Abstract Part 2 of this symposium will discuss how to maximize the reach and impact of your published work. Researchers are under increasing pressure to demonstrate the impact of their work. First, it is important to clearly articulate the translational impact of your work in the Discussion of your manuscript and briefly in the Abstract. In addition, it is important to know how to increase visibility of your manuscript because university administrators and funding agencies rely heavily on numerical metrics for decision-making. This presentation will look at the needs that metrics serve and provide an overview of how the dominant metric, the Impact Factor, is determined (along with a discussion of the metric’s flaws). The value of newer methodologies and alternative metrics (Altmetrics) will also be discussed. The presentation will also cover practical steps for how researchers can increase the reach and potential impact of their work.

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COUNSELL, S., T. HALL, and D. BOWES. "A THEORETICAL AND EMPIRICAL ANALYSIS OF THREE SLICE-BASED METRICS FOR COHESION." International Journal of Software Engineering and Knowledge Engineering 20, no. 05 (August 2010): 609–36. http://dx.doi.org/10.1142/s0218194010004888.

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Sound empirical research suggests that we should analyze software metrics from a theoretical and practical perspective. This paper describes the result of an investigation into the respective merits of two cohesion-based metrics for program slicing. The Tightness and Overlap metrics were those originally proposed by Weiser for the procedural paradigm. We compare and contrast these two metrics with a third metric for the OO paradigm first proposed by Counsell et al. based on Hamming Distance and based on a matrix-based notation. We theoretically validated the three metrics using the properties of Kitchenham and then empirically validated the same three metrics; some revealing properties of the metrics were found as a result. In particular, that the OO-based metric was the most stable of the three; module length was not a confounding factor for the Hamming Distance-based metric; it was however for the two slice-based metrics supporting previous work by Meyers and Binkley. The number of module slices however, was found to be an even stronger influence on the values of the two slice-based metrics, whose near perfect correlation with each other suggests that they may be measuring the same software attribute. We calculated and then compared the three metrics using first, a set of manufactured, pre-determined modules as a preliminary analysis and second, approximately nine thousand functions from the modules of multiple versions of the Barcode system, used previously by Meyers and Binkley in their empirical study. The over-arching message of the research is that a combination of theoretical and empirical analysis can help significantly in comparing the viability and indeed choice of a metric or set of metrics. More specifically, although cohesion is a subjective measure, there are certain properties of a metric that are less desirable than others and it is these 'relative' features that distinguish metrics, make their comparison possible and their value more evident.

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Zohrehvand, Mosayeb. "Projective change between G.R.C. exponential metrics and Randers metrics." Annals of the Alexandru Ioan Cuza University - Mathematics 70, no. 1 (2024): 17–29. http://dx.doi.org/10.47743/anstim.2024.00002.

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In this paper, we find the necessary and sufficient conditions under which two classes of (α, β)-metrics, i.e. generalized Randers change (G.R.C.) exponential metric F = α exp(β/α) + ϵβ and Randers metric F˜ = ˜α + β˜ are projectively related. Note that α and ˜α are Riemannian metrics, β and β˜ are 1-forms on a manifold M with dimension n > 2 and ϵ ̸= 0 is a constant. Furthermore, we study this projective relation when F has special curvature properties.

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Chen, Guangzu, Lihong Liu, and Qisen Jiang. "An important class of conformally flat weak Einstein cubic (α,β)-metrics." International Journal of Geometric Methods in Modern Physics 16, no. 07 (July 2019): 1950113. http://dx.doi.org/10.1142/s0219887819501135.

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The theory of cubic metrics plays an important role in the theory of space-time structure, gravitation and unified gauge field theories. In this paper, we study conformally flat weak Einstein cubic [Formula: see text]-metrics. We prove that such metrics must be either locally Minkowski metric or Riemannian metric.

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Esra Sengelen, Sevim, and Zhongmin Shen. "Randers Metrics of Constant Scalar Curvature." Canadian Mathematical Bulletin 56, no. 3 (September 1, 2013): 615–20. http://dx.doi.org/10.4153/cmb-2011-187-1.

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Abstract.Randers metrics are a special class of Finsler metrics. Every Randers metric can be expressed in terms of a Riemannian metric and a vector field via Zermelo navigation. In this paper, we show that a Randers metric has constant scalar curvature if the Riemannian metric has constant scalar curvature and the vector field is homothetic

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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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Nath, Pravin. "Taking measure: the link between metrics and marketing’s exploitative and explorative capabilities." European Journal of Marketing 54, no. 7 (May 23, 2020): 1549–80. http://dx.doi.org/10.1108/ejm-01-2018-0050.

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Purpose While metrics are becoming increasingly important for marketing’s relevance, there is also a need to understand how they, as enablers of learning, affect marketing’s adaptive capabilities that ensure its long-term success. Therefore, this study aims to test the association of marketing and financial metrics use and the metric-based orientations of training and compensation, with two key marketing routines – exploitation, i.e. the perfecting of existing activities while allowing for incremental adaptations and exploration or experimentation accompanied by radical adaptation. Design/methodology/approach The study gathers data from 205 managers and uses partial least squares structural equation modeling to test the hypothesized relationships. Findings Marketing metrics encourage both forms of marketing adaptation. Financial metrics use discourages exploration. Market orientation and long-term orientation strengthen (weaken) the positive (negative) relationship between marketing (financial) metrics use and marketing exploration. Metric-based training is more positively associated with both adaptive capabilities than a metric-based compensation orientation, albeit weakly. Research limitations/implications The study’s central proposition – that different metrics or metric orientations are associated with distinct types of knowledge, interpretations, mindsets, motivations and cultural contexts – provides a deeper theoretical understanding of the pathways by which a metric emphasis affects marketing adaptation. Practical implications Marketing managers should emphasize marketing metrics and training more than compensation, to promote marketing exploitation/exploration, while exercising caution in overstressing financial metrics given their negative association with exploration. This latter negative relationship can be weakened (as can the positive one between marketing metrics and exploration be strengthened) with increased market orientation and long-term orientation. Originality/value This study addresses the research gap regarding the relationship between metrics as a configurational element of marketing organization and marketing adaptation.

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Kushwaha, Ramdayal Singh, and Gauree Shanker. "On the ℒ-duality of a Finsler space with exponential metric αeβ/α." Acta Universitatis Sapientiae, Mathematica 10, no. 1 (August 1, 2018): 167–77. http://dx.doi.org/10.2478/ausm-2018-0014.

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Abstract The (α, β)-metrics are the most studied Finsler metrics in Finsler geometry with Randers, Kropina and Matsumoto metrics being the most explored metrics in modern Finsler geometry. The ℒ-dual of Randers, Kropina and Matsumoto space have been introduced in [3, 4, 5], also in recent the ℒ-dual of a Finsler space with special (α, β)-metric and generalized Matsumoto spaces have been introduced in [16, 17]. In this paper, we find the ℒ-dual of a Finsler space with an exponential metric αeβ/α, where α is Riemannian metric and β is a non-zero one form.

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Hakuta, Keisuke. "Construction of metrics on the set of elliptic curves over a finite field." Publications de l'Institut Math?matique (Belgrade) 109, no. 123 (2021): 125–41. http://dx.doi.org/10.2298/pim2123125h.

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We consider metrics on the set of elliptic curves in short Weierstrass form over a finite field of characteristic greater than three. The metrics have been first found by Mishra and Gupta (2008). Vetro (2011) constructs other metrics which are independent on the choice of a generator of the multiplicative group of the underlying finite field, whereas the metrics found by Mishra and Gupta, are dependent on the choice of a generator of the multiplicative group of the underlying finite field. Hakuta (2015, 2018) constructs metrics on the set of non-supersingular elliptic curves in shortWeierstrass form over a finite field of characteristic two and three, respectively. The aim of this paper is to point out that the metric found by Mishra and Gupta is in fact not a metric. We also construct new metrics which are slightly modified versions of the metric found by Mishra and Gupta.

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Zhong, Yiwen, Kun Song, ShengKai Lv, and Peng He. "An Empirical Study of Software Metrics Diversity for Cross-Project Defect Prediction." Mathematical Problems in Engineering 2021 (November 28, 2021): 1–11. http://dx.doi.org/10.1155/2021/3135702.

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Cross-project defect prediction (CPDP) is a mainstream method estimating the most defect-prone components of software with limited historical data. Several studies investigate how software metrics are used and how modeling techniques influence prediction performance. However, the software’s metrics diversity impact on the predictor remains unclear. Thus, this paper aims to assess the impact of various metric sets on CPDP and investigate the feasibility of CPDP with hybrid metrics. Based on four software metrics types, we investigate the impact of various metric sets on CPDP in terms of F-measure and statistical methods. Then, we validate the dominant performance of CPDP with hybrid metrics. Finally, we further verify the CPDP-OSS feasibility built with three types of metrics (orient-object, semantic, and structural metrics) and challenge them against two current models. The experimental results suggest that the impact of different metric sets on the performance of CPDP is significantly distinct, with semantic and structural metrics performing better. Additionally, trials indicate that it is helpful for CPDP to increase the software’s metrics diversity appropriately, as the CPDP-OSS improvement is up to 53.8%. Finally, compared with two baseline methods, TCA+ and TDSelector, the optimized CPDP model is viable in practice, and the improvement rate is up to 50.6% and 25.7%, respectively.

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Müller, Alfred. "Integral Probability Metrics and Their Generating Classes of Functions." Advances in Applied Probability 29, no. 2 (June 1997): 429–43. http://dx.doi.org/10.2307/1428011.

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We consider probability metrics of the following type: for a class of functions and probability measures P, Q we define A unified study of such integral probability metrics is given. We characterize the maximal class of functions that generates such a metric. Further, we show how some interesting properties of these probability metrics arise directly from conditions on the generating class of functions. The results are illustrated by several examples, including the Kolmogorov metric, the Dudley metric and the stop-loss metric.

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Müller, Alfred. "Integral Probability Metrics and Their Generating Classes of Functions." Advances in Applied Probability 29, no. 02 (June 1997): 429–43. http://dx.doi.org/10.1017/s000186780002807x.

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We consider probability metrics of the following type: for a class of functions and probability measures P, Q we define A unified study of such integral probability metrics is given. We characterize the maximal class of functions that generates such a metric. Further, we show how some interesting properties of these probability metrics arise directly from conditions on the generating class of functions. The results are illustrated by several examples, including the Kolmogorov metric, the Dudley metric and the stop-loss metric.

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Stephens, Simon, and Padraig Gallagher. "Metrics, metrics, metrics: the emergence of technological universities in Ireland." Quality Assurance in Education 30, no. 1 (October 11, 2021): 19–31. http://dx.doi.org/10.1108/qae-04-2021-0060.

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Purpose This paper aims to explore the experiences, attitudes and expectations of higher education managers in relation to the increased use of metrics. Specifically, the authors examine a system of metrics which was introduced as part of the process for establishing Technological Universities in Ireland. Design/methodology/approach A total of 12 managers were interviewed. The authors present data from the interviews in which the authors explore: the previous use of metrics; the impacts of the introduction of metrics; and the future use of metrics. A mix of narrative structuring and thematic analysis is used. Findings The introduction of metrics evokes a mixed reaction from the managers. The metrics allow performance in a range of activities to be measured, assessed and benchmarked. However, there are both direct and indirect impacts of the transition to a metric-based system, which the authors explore using six themes. Originality/value The authors apply the Academics Responding to Change model proposed by Trowler (1998) as the theoretical lens. This helps to capture the complex mix of direct and indirect effects that metrics can have on activities both at an individual and institutional level.

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Zhu, Hongmei. "On general (α, β)-metrics with vanishing Douglas curvature." International Journal of Mathematics 26, no. 09 (August 2015): 1550076. http://dx.doi.org/10.1142/s0129167x15500767.

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In this paper, we study a class of Finsler metrics called general (α, β)-metrics, which are defined by a Riemannian metric α and a 1-form β. We find an equation which is necessary and sufficient condition for such Finsler metric to be a Douglas metric. By solving this equation, we obtain all of general (α, β)-metrics with vanishing Douglas curvature under certain condition. Many new non-trivial examples are explicitly constructed.

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Journal articles on the topic 'Metrics'

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