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Journal articles on the topic 'Metric'

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Published: 4 June 2021
Last updated: 6 September 2023

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1

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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2

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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4

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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5

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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7

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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10

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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11

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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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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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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14

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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16

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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17

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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18

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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19

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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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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21

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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22

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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23

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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Pongsriiam, Prapanpong, and Imchit Termwuttipong. "Remarks on Ultrametrics and Metric-Preserving Functions." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/163258.

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Functions whose composition with every metric is a metric are said to be metric-preserving. In this paper, we investigate a variation of the concept of metric-preserving functions where metrics are replaced by ultrametrics.
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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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Wu, Hsien-Chung. "Convergence in Fuzzy Semi-Metric Spaces." Mathematics 6, no. 9 (September 17, 2018): 170. http://dx.doi.org/10.3390/math6090170.

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The convergence using the fuzzy semi-metric and dual fuzzy semi-metric is studied in this paper. The infimum type of dual fuzzy semi-metric and the supremum type of dual fuzzy semi-metric are proposed in this paper. Based on these two types of dual fuzzy semi-metrics, the different types of triangle inequalities can be obtained. We also study the convergence of these two types of dual fuzzy semi-metrics.
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Li, Changqing, Yanlan Zhang, and Jing Zhang. "On statistical convergence in fuzzy metric spaces." Journal of Intelligent & Fuzzy Systems 39, no. 3 (October 7, 2020): 3987–93. http://dx.doi.org/10.3233/jifs-200148.

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The idea of statistical convergence, which was first introduced by Fast and Steinhaus independently in 1951, has become one of the most active area of research in the field of mathematics. Recently, it has been applied to the realm of metrics by several authors and some useful results have been obtained. However, the existence of non-completable fuzzy metric spaces, in the sense of George and Veeramani, demonstrates that the theory of fuzzy metrics seem to be richer than that of metrics. In view of this, we attempt to generalize this convergence to the realm of fuzzy metrics. Firstly, we introduce the concept of sts-convergence in fuzzy metric spaces. Then we characterize those fuzzy metric spaces in which all convergent sequences are sts-convergent. Finally, we study sts-Cauchy sequences in fuzzy metric spaces and sts-completeness of fuzzy metric spaces.
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Zhu, Yifan, Lu Chen, Yunjun Gao, Baihua Zheng, and Pengfei Wang. "DESIRE." Proceedings of the VLDB Endowment 15, no. 10 (June 2022): 2121–33. http://dx.doi.org/10.14778/3547305.3547317.

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Similarity search finds similar objects for a given query object based on a certain similarity metric. Similarity search in metric spaces has attracted increasing attention, as the metric space can accommodate any type of data and support flexible distance metrics. However, a metric space only models a single data type with a specific similarity metric. In contrast, a multi-metric space combines multiple metric spaces to simultaneously model a variety of data types and a collection of associated similarity metrics. Thus, a multi-metric space is capable of performing similarity search over any combination of metric spaces. Many studies focus on indexing a single metric space, while only a few aims at indexing multi-metric space to accelerate similarity search. In this paper, we propose DESIRE, an efficient dynamic cluster-based forest index for similarity search in multi-metric spaces. DESIRE first selects high-quality centers to cluster objects into compact regions, and then employs B + -trees to effectively index distances between centers and corresponding objects. To support dynamic scenarios, efficient update strategies are developed. Further, we provide filtering techniques to accelerate similarity queries in multi-metric spaces. Extensive experiments on four real datasets demonstrate the superior efficiency and scalability of our proposed DESIRE compared with the state-of-the-art multi-metric space indexes.
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Lopez, Victor Emmanuel Pierre, and Lawrence Dale Thomas. "Metric for Structural Complexity Assessment of Space Systems Modeled Using the System Modeling Language." Aerospace 9, no. 10 (October 17, 2022): 612. http://dx.doi.org/10.3390/aerospace9100612.

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A complexity metric is proposed for the quantification of system complexity using information about the composition of a system and its interactions depicted in a System Modelling Language (SysML) model. The proposed metric is adapted from the complexity metric developed for design structure matrix (DSM) applications and was modified to allow the metric to be applied at different decomposition levels and to accommodate the inclusion of external interactions. The metric was applied to three case studies: a Mars lander, a CubeSat and a spacecraft thermal control system. The proposed metric attributed a higher amount of complexity due to the interactions compared to the DSM metric. This variance resulted in instances where the results differed for the two metrics. Despite these differences, both metrics behaved similarly to changes in component or interaction complexity.
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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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Chang, Yu-Tzu, and Dan N. Stone. "Why does decomposed audit proposal readability differ by audit firm size? A Coh-Metrix approach." Managerial Auditing Journal 34, no. 8 (September 2, 2019): 895–923. http://dx.doi.org/10.1108/maj-02-2018-1789.

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Purpose This paper aims to introduce the emerging artificial-intelligence-based readability metrics (Coh-Metrix) to examine the effects of firm size on audit proposal readability. Design/methodology/approach Coh-Metrix readability measures use emerging computation linguistics technology to better assess document readability. These metrics measure co-relations of words, sentences and paragraphs on multi-dimensions rather than adopting the unidimensional “bag of words” approach that examines words in isolation. Using eight Coh-Metrix orthogonal principal component factors, the authors analyze the Chang and Stone (2019) data set comprised of 370 hand-collected audit proposals submitted by audit firms for the US state and local governments’ audit service contracts. Findings Audit firm size has a significant impact on the readability of audit proposals. Specifically, as measured by the traditional readability metric, the proposals from smaller firms are more readable than those submitted by larger firms. Furthermore, decomposed readability metrics indicate that smaller firm proposals evidence stronger (deep) text cohesion, whereas larger firm proposals evidence a stronger narrative structure and higher connectivity (relational indicators) among proposal elements. Unlike the traditional readability metric, however, the emergent readability metrics are uncorrelated with auditor selection. Research limitations/implications Work remains to develop and validate Coh-Metrix measures that are specific to the context of accounting and auditing practice. Future research can use emerging readability measures to examine various textual features (e.g. text cohesion) in finance or accounting related documents. Practical implications The results provide practitioners with insight into the proposal writing strategies and practices of larger and smaller firms. In addition, the results highlight the differing audit firm selection outcomes from traditional and Coh-Metrix readability metrics. Originality/value This study introduces new data and holistic readability measures to the auditing literature.
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33

Othman, Khadija Ben, Oliver Von Shtawzen, Ahmad Khaldi, and Rozina Ali. "On Neutrosophic Metric Spaces Generated By Classical Metrics." Galoitica: Journal of Mathematical Structures and Applications 7, no. 1 (2023): 36–42. http://dx.doi.org/10.54216/gjmsa.070104.

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This paper is dedicated to study the concept of symbolic neutrosophic metric spaces and refined neutrosophic metric spaces (X(I),d) which are generated by classical metrics, where many elementary properties will be discussed in terms of theorems and examples. Also, we study the topological properties of neutrosophic open balls, closed balls, and their topological metric complements, with many related examples that clarify the validity of our work.
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34

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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35

Masárová, Renáta. "Fréchet Metric for Space of Binary Coded Software." Research Papers Faculty of Materials Science and Technology Slovak University of Technology 22, no. 35 (December 1, 2014): 17–21. http://dx.doi.org/10.2478/rput-2014-0030.

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Abstract As stated in (7), binary coded computer programs can be shown as a metric space. Therefore, they can be measured by metric in a sense of metric space theory. This paper presents the proof that Fréchet metric is a metric on the space of all sequences of elements M={0,1t} Therefore, it is usable to build a system of software metrics based on the metric space theory
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36

Gursky, Matthew J., and Jeffrey Streets. "A formal Riemannian structure on conformal classes and the inverse Gauss curvature flow." Geometric Flows 4, no. 1 (January 1, 2019): 30–50. http://dx.doi.org/10.1515/geofl-2019-0003.

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Abstract We define a formal Riemannian metric on a given conformal class of metrics with signed curvature on a closed Riemann surface. As it turns out this metric is the well-known Mabuchi-Semmes-Donaldson metric of Kähler geometry in a different guise. The metric has many interesting properties, and in particular we show that the classical Liouville energy is geodesically convex. This suggests a different approach to the uniformization theorem by studying the negative gradient flow of the normalized Liouville energy with respect to this metric, a new geometric flow whose principal term is the inverse of the Gauss curvature. We prove long time existence of solutions with arbitrary initial data and weak convergence to constant scalar curvature metrics by exploiting the metric space structure.
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37

Xie, Ying Hong, and Cheng Dong Wu. "Study on the Comparison of Two Metrics Used in the Fields of Object Tracking." Applied Mechanics and Materials 483 (December 2013): 419–22. http://dx.doi.org/10.4028/www.scientific.net/amm.483.419.

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The paper researches on the comparison of two metrics methods under Riemannian metric and under Log-Euclidean metric respectively. Firstly, Experiments are done for comparing the distance and mean values worked out under the two metrics. And the time required for computing under these two metrics is also shown. Lastly, the two methods are applied to the field of image tracking. The performance of the two methods is compared, and the time required for tracking each frame is gained. Experiments results show that the two methods can gain similar distance and mean values, and similar tracking results, while the time required under Log-Euclidean metric is less than under Riemannian metric.
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38

ALKURDI, TALEB, SANDER C. HILLE, and ONNO VAN GAANS. "ON METRIZATION OF UNIONS OF FUNCTION SPACES ON DIFFERENT INTERVALS." Journal of the Australian Mathematical Society 92, no. 3 (June 2012): 281–97. http://dx.doi.org/10.1017/s1446788712000365.

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AbstractThis paper investigates a class of metrics that can be introduced on the set consisting of the union of continuous functions defined on different intervals with values in a fixed metric space, where the union ranges over a family of intervals. Its definition is motivated by the Skorohod metric(s) on càdlàg functions. We show what is essential in transferring the ideas employed in the latter metric to our setting and obtain a general construction for metrics in our case. Next, we define the metric space where elements are sequences of functions from the above mentioned set. We provide conditions that ensure separability and completeness of the constructed metric spaces.
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39

Shen, Zhongmin. "On a Class of Landsberg Metrics in Finsler Geometry." Canadian Journal of Mathematics 61, no. 6 (December 1, 2009): 1357–74. http://dx.doi.org/10.4153/cjm-2009-064-9.

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Abstract In this paper, we study a long existing open problem on Landsberg metrics in Finsler geometry. We consider Finsler metrics defined by a Riemannian metric and a 1-form on a manifold. We show that a regular Finsler metric in this form is Landsbergian if and only if it is Berwaldian. We further show that there is a two-parameter family of functions, ɸ = ɸ(s), for which there are a Riemannian metric 𝜶 and a 1-form ᵦ on a manifold M such that the scalar function F = 𝜶ɸ(ᵦ/𝜶) on TM is an almost regular Landsberg metric, but not a Berwald metric.
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Gutiérrez-Reina, Daniel, Vishal Sharma, Ilsun You, and Sergio Toral. "Dissimilarity Metric Based on Local Neighboring Information and Genetic Programming for Data Dissemination in Vehicular Ad Hoc Networks (VANETs)." Sensors 18, no. 7 (July 17, 2018): 2320. http://dx.doi.org/10.3390/s18072320.

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This paper presents a novel dissimilarity metric based on local neighboring information and a genetic programming approach for efficient data dissemination in Vehicular Ad Hoc Networks (VANETs). The primary aim of the dissimilarity metric is to replace the Euclidean distance in probabilistic data dissemination schemes, which use the relative Euclidean distance among vehicles to determine the retransmission probability. The novel dissimilarity metric is obtained by applying a metaheuristic genetic programming approach, which provides a formula that maximizes the Pearson Correlation Coefficient between the novel dissimilarity metric and the Euclidean metric in several representative VANET scenarios. Findings show that the obtained dissimilarity metric correlates with the Euclidean distance up to 8.9% better than classical dissimilarity metrics. Moreover, the obtained dissimilarity metric is evaluated when used in well-known data dissemination schemes, such as p-persistence, polynomial and irresponsible algorithm. The obtained dissimilarity metric achieves significant improvements in terms of reachability in comparison with the classical dissimilarity metrics and the Euclidean metric-based schemes in the studied VANET urban scenarios.
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41

Miyachi, Hideki, Ken'ichi Ohshika, and Athanase Papadopoulos. "Tangent spaces of the Teichmüller space of the torus with Thurston's weak metric." Annales Fennici Mathematici 47, no. 1 (January 21, 2022): 325–34. http://dx.doi.org/10.54330/afm.113702.

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In this paper, we show that the analogue of Thurston's asymmetric metric on the Teichmüller space of flat structures on the torus is weak Finsler and we give a geometric description of its unit circle at each point in the tangent space to Teichmüller space. We then introduce a family of weak Finsler metrics which interpolate between Thurston's asymmetric metric and the Teichmüller metric of the torus (which coincides with the hyperbolic metric). We describe the unit tangent circles of the metrics in this family.
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42

Sajib, AH, AZM Shafiullah, and AH Sumon. "An Alternative Algorithm for Classification Based on Robust Mahalanobis Distance." Dhaka University Journal of Science 61, no. 1 (May 27, 2013): 81–85. http://dx.doi.org/10.3329/dujs.v61i1.15101.

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This study considers the classification problem for binary output attribute when input attributes are drawn from multivariate normal distribution, in both clean and contaminated case. Classical metrics are affected by the outliers, while robust metrics are computationally inefficient. In order to achieve robustness and computational efficiency at the same time, we propose a new robust distance metric for K-Nearest Neighbor (KNN) method. We call our proposed metric Alternative Robust Mahalanobis Distance (ARMD) metric. Thus KNN using ARMD is alternative KNN method. The classical metrics use non robust estimate (mean) as the building block. To construct the proposed ARMD metric, we replace non robust estimate (mean) by its robust counterpart median. Thus, we developed ARMD metric for alternative KNN classification technique. Our simulation studies show that the proposed alternative KNN method gives better results in case of contaminated data compared to the classical KNN. The performance of our method is similar to classical KNN using the existing robust metric. The major advantage of proposed method is that it requires less computing time compared to classical KNN that using existing robust metric. Dhaka Univ. J. Sci. 61(1): 81-85, 2013 (January) DOI: http://dx.doi.org/10.3329/dujs.v61i1.15101
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43

Grigorenko, Olga, and Alexander Šostak. "Fuzzy Metrics in Terms of Fuzzy Relations." Mathematics 11, no. 16 (August 15, 2023): 3528. http://dx.doi.org/10.3390/math11163528.

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In this paper, we study the concept of fuzzy metrics from the perspective of fuzzy relations. Specifically, we analyze the commonly used definitions of fuzzy metrics. We begin by noting that crisp metrics can be uniquely characterized by linear order relations. Further, we explore the criteria that crisp relations must satisfy in order to determine a crisp metric. Subsequently, we extend these conditions to obtain a fuzzy metric and investigate the additional axioms involved. Additionally, we introduce the definition of an extensional fuzzy metric or E-d-metric, which is a fuzzification of the expression d(x,y)=t. Thus, we examine fuzzy metrics from both the linear order and from the equivalence relation perspectives, where one argument is a value d(x,y) and the other is a number within the range [0,+∞).
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44

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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45

Doucha, Michal. "Metric topological groups: their metric approximation and metric ultraproducts." Groups, Geometry, and Dynamics 12, no. 2 (June 4, 2018): 615–36. http://dx.doi.org/10.4171/ggd/450.

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46

Hussain, Nawab, Jamal Rezaei Roshan, Vahid Parvaneh, and Abdul Latif. "A Unification ofG-Metric, Partial Metric, andb-Metric Spaces." Abstract and Applied Analysis 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/180698.

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Using the concepts ofG-metric, partial metric, andb-metric spaces, we define a new concept of generalized partialb-metric space. Topological and structural properties of the new space are investigated and certain fixed point theorems for contractive mappings in such spaces are obtained. Some examples are provided here to illustrate the usability of the obtained results.
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47

BOWDITCH, BRIAN H. "Median and injective metric spaces." Mathematical Proceedings of the Cambridge Philosophical Society 168, no. 1 (July 27, 2018): 43–55. http://dx.doi.org/10.1017/s0305004118000555.

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AbstractWe describe a construction which associates to any median metric space a pseudometric satisfying the binary intersection property for closed balls. Under certain conditions, this implies that the resulting space is, in fact, an injective metric space, bilipschitz equivalent to the original metric. In the course of doing this, we derive a few other facts about median metrics, and the geometry of CAT(0) cube complexes. One motivation for the study of such metrics is that they arise as asymptotic cones of certain naturally occurring spaces.
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48

Lu, Guoxiang. "A Class of New Metrics forn-Dimensional Unit Hypercube." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/942687.

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We study the metric on then-dimensional unit hypercube. We introduce a class of new metrics for the space, which is information theoretically motivated and has close relation to Jensen-Shannon divergence. These metrics are obtained by discussing a functionFDα(P,Q)with the parameterα. We come to the conclusion that the sufficient and necessary condition of the function being a metric is0<α≤1/2. Finally, by computing basic examples of codons, we show some numerical comparison of the new metrics to the former metric.
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49

Zohrehvand, M., and H. Maleki. "On general (α,β)-metrics of Landsberg type." International Journal of Geometric Methods in Modern Physics 13, no. 06 (June 15, 2016): 1650085. http://dx.doi.org/10.1142/s0219887816500857.

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In this paper, we study a class of Finsler metrics, which are defined by a Riemannian metric [Formula: see text] and a one-form [Formula: see text]. They are called general [Formula: see text]-metrics. We have proven that, every Landsberg general [Formula: see text]-metric is a Berwald metric, under a certain condition. This shows that the hunting for an unicorn, one of the longest standing open problem in Finsler geometry, cannot be successful in the class of general [Formula: see text]-metrics.
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Taş, Nihal, and Nihal Yılmaz Özgür. "On ParametricS-Metric Spaces and Fixed-Point Type Theorems for Expansive Mappings." Journal of Mathematics 2016 (2016): 1–6. http://dx.doi.org/10.1155/2016/4746732.

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We introduce the notion of a parametricS-metric space as generalization of a parametric metric space. Using some expansive mappings, we prove a fixed-point theorem on a parametricS-metric space. It is important to obtain new fixed-point theorems on a parametricS-metric space because there exist some parametricS-metrics which are not generated by any parametric metric. We expect that many mathematicians will study various fixed-point theorems using new expansive mappings (or contractive mappings) in a parametricS-metric space.
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