scholarly journals Corrected Evolutive Kendall’s τ Coefficients for Incomplete Rankings with Ties: Application to Case of Spotify Lists

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1828
Author(s):  
Francisco Pedroche ◽  
J. Alberto Conejero
Keyword(s):  
Group Decision ◽  
Industrial Applications ◽  
The Other ◽  
Kendall’S Tau ◽  
Kendall's Tau ◽  
On Demand ◽  
Wide Range ◽  
Kendall’S Τ ◽  
Internet Streaming ◽  
Grant Proposals

Mathematical analysis of rankings is essential for a wide range of scientific, public, and industrial applications (e.g., group decision-making, organizational methods, R&D sponsorship, recommender systems, voter systems, sports competitions, grant proposals rankings, web searchers, Internet streaming-on-demand media providers, etc.). Recently, some methods for incomplete aggregate rankings (rankings in which not all the elements are ranked) with ties, based on the classic Kendall’s tau coefficient, have been presented. We are interested in ordinal rankings (that is, we can order the elements to be the first, the second, etc.) allowing ties between the elements (e.g., two elements may be in the first position). We extend a previous coefficient for comparing a series of complete rankings with ties to two new coefficients for comparing a series of incomplete rankings with ties. We make use of the newest definitions of Kendall’s tau extensions. We also offer a theoretical result to interpret these coefficients in terms of the type of interactions that the elements of two consecutive rankings may show (e.g., they preserve their positions, cross their positions, and they are tied in one ranking but untied in the other ranking, etc.). We give some small examples to illustrate all the newly presented parameters and coefficients. We also apply our coefficients to compare some series of Spotify charts, both Top 200 and Viral 50, showing the applicability and utility of the proposed measures.

scholarly journals Automatic Evaluation of Information Ordering: Kendall's Tau

2006 ◽  
Vol 32 (4) ◽  
pp. 471-484 ◽  
Author(s):  
Mirella Lapata
Keyword(s):  
Evaluation Method ◽  
Rank Correlation ◽  
Automatic Evaluation ◽  
Text Generation ◽  
Kendall’S Tau ◽  
Kendall's Tau ◽  
Kendall’S Τ ◽  
Multidocument Summarization

This article considers the automatic evaluation of information ordering, a task underlying many text-based applications such as concept-to-text generation and multidocument summarization. We propose an evaluation method based on Kendall's τ, a metric of rank correlation. The method is inexpensive, robust, and representation independent. We show that Kendall's τ correlates reliably with human ratings and reading times.

A Rank-Free Method of Calculating Kendall's Tau

1997 ◽  
Vol 81 (2) ◽  
pp. 655-658
Author(s):  
Manuel Martinez-Pons
Keyword(s):  
Original Method ◽  
General Treatment ◽  
Alternative Methods ◽  
Paired Comparisons ◽  
Kendall’S Tau ◽  
Data Set ◽  
Kendall's Tau ◽  
Kendall’S Τ

A rank-free method of calculating Kendall's τ is described. Derived from Daniels' 1944 general treatment of correlation, it is based on the signs of all possible paired comparisons in a data set. Unlike the 1975 alternative methods of Cooper and those of 1977 by Stuart, it allows for ties and thus yields the same coefficient as that of Kendall's original method. The execution is simpler, however, because it does not require ranking of data.

scholarly journals Multiple Ordinal Correlation Based on Kendall’s Tau Measure: A Proposal

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1616
Author(s):  
Juan M. Muñoz-Pichardo ◽  
Emilio D. Lozano-Aguilera ◽  
Antonio Pascual-Acosta ◽  
Ana M. Muñoz-Reyes
Keyword(s):  
Ordinal Data ◽  
Experimental Studies ◽  
Joint Analysis ◽  
Correlation Measure ◽  
Kendall’S Tau ◽  
Social Survey ◽  
Kendall's Tau ◽  
Research Fields ◽  
Bivariate Correlation ◽  
Wide Range

The joint analysis of various ordinal variables is necessary in many experimental studies within research fields such as sociology and psychology. Therefore, the necessary measures of multiple ordinal dependence must be easy to interpret and facilitate the interpretation of multivariate models that fit ordinal data. The main objective of this article is to propose a multiple ordinal correlation measure based on a bivariate correlation measure: Kendall’s tau. A sample version of the measure is proposed for its estimation. Furthermore, a confidence interval and a multiple ordinal independence test are proposed. The measure is applied to various simulations, covering a wide range of multiple ordinal dependency scenarios, in order to illustrate the adequacy of the measure and the proposed inferential techniques. Finally, the measure is applied to a real-world study based on a social survey of the levels of life satisfaction and the happiness index of a population.

Kendall's “Tau” Coefficient as an Index of Similarity in Comparisons of Plant or Animal Communities

1963 ◽  
Vol 95 (6) ◽  
pp. 568-575 ◽  
Author(s):  
A. W. Ghent
Keyword(s):  
Soil Fauna ◽  
Rank Correlation ◽  
Special Problem ◽  
The Other ◽  
Confidence Limits ◽  
Kendall’S Tau ◽  
Kendall's Tau ◽  
Animal Communities ◽  
Graph Form ◽  
Zero Frequency

AbstractComparisons of ecologic communities are often limited to presentations of frequency lists in tabular or bar-graph form. Kendall's “Tau” coefficient is appropriate as a measure of rank correlation between such numerical profiles. A special problem arises where species in one community are absent from the other. Such species may either be assigned zero frequency and last-place ranking in the community where they are absent, or they may be dropped from both rankings, depending on which method yields the more conservative correlation. Tau has the same limits (± 1) as the familiar product-moment correlation coefficient. Moreover, as a nonparametric statistic it is free of considerations of distribution. Comparisons between soil-fauna communities from the Quetico-Superior forest area are used to illustrate the method. The problems of tied rankings, variance and significance of Tau, confidence limits for Tau, and the significance of a difference between Tau coefficients, are also considered.

scholarly journals Controlling Angular Distortion in Manual Metal Arc Welding of Austenitic Stainless Steels Using Back-step Technique

2018 ◽  
Vol 26 (2) ◽  
pp. 311-319
Author(s):  
Abdul Sameea Jasim Abdul Zehra Jilabi
Keyword(s):  
Stainless Steels ◽  
Nuclear Power ◽  
Elevated Temperatures ◽  
Austenitic Stainless Steels ◽  
Industrial Applications ◽  
The Other ◽  
Angular Distortion ◽  
Mma Welding ◽  
Other Hand ◽  
Wide Range

Nowadays, austenitic stainless steels (A.S.S.) have many industrial applications in the fields of chemical and petrochemical processing, marine, medicine, water treatment, petroleum refining, food and drinks processing, nuclear power generation etc. The secret behind this wide range of applications is the fact that A.S.S. have great corrosion resistance, high strength and scale resistance at elevated temperatures, good ductility at low temperatures approached to absolute zero in addition to notable weldability. On the other hand, manual metal arc (MMA) is probably the most common process used for the welding of A.S.S. Unfortunately, MMA welding of A.S.S. could be associated with considerable distortion. Uncontrolled or excessive distortion usually increases the cost of the production process due to the high expense of rectification or replacing the weldment by a non-distorted one. MMA welding of A.S.S. was carried out using the back-step technique with various bead lengths, and without using this technique for comparison. Results have showed that the angular distortion was a function of the bead length in the back-step welding of A.S.S. The angular distortion decreased by (14.32%) when the back-step technique was used with a (60 mm) length for each bead, and by (41.08%) when the bead length was (40 mm). On the other hand, it increased by (25%) when the back-step technique was done with a (30 mm) length for each bead.

2D Color-Intensity Representation of Ultrasonic Thickness Gauge Measurements

2020 ◽  
pp. 1192-1198
Author(s):  
M.S. Mohammad ◽  
Tibebe Tesfaye ◽  
Kim Ki-Seong
Keyword(s):  
Cost Effective ◽  
The Other ◽  
Thickness Gauge ◽  
Color Intensity ◽  
Digital Readout ◽  
Flat Surfaces ◽  
Video Cameras ◽  
Wide Range ◽  
Cost Effective Alternative ◽  
Ultrasonic Thickness

Ultrasonic thickness gauges are easy to operate and reliable, and can be used to measure a wide range of thicknesses and inspect all engineering materials. Supplementing the simple ultrasonic thickness gauges that present results in either a digital readout or as an A-scan with systems that enable correlating the measured values to their positions on the inspected surface to produce a two-dimensional (2D) thickness representation can extend their benefits and provide a cost-effective alternative to expensive advanced C-scan machines. In previous work, the authors introduced a system for the positioning and mapping of the values measured by the ultrasonic thickness gauges and flaw detectors (Tesfaye et al. 2019). The system is an alternative to the systems that use mechanical scanners, encoders, and sophisticated UT machines. It used a camera to record the probe’s movement and a projected laser grid obtained by a laser pattern generator to locate the probe on the inspected surface. In this paper, a novel system is proposed to be applied to flat surfaces, in addition to overcoming the other limitations posed due to the use of the laser projection. The proposed system uses two video cameras, one to monitor the probe’s movement on the inspected surface and the other to capture the corresponding digital readout of the thickness gauge. The acquired images of the probe’s position and thickness gauge readout are processed to plot the measured data in a 2D color-coded map. The system is meant to be simpler and more effective than the previous development.

Substituent Effects on the Thermal Decomposition of Phosphate Esters on Ferrous Surfaces

2019 ◽  
Author(s):  
James Ewen ◽  
Carlos Ayestaran Latorre ◽  
Arash Khajeh ◽  
Joshua Moore ◽  
Joseph Remias ◽  
...  
Keyword(s):  
Thermal Decomposition ◽  
Film Formation ◽  
Substituent Effects ◽  
Vapour Phase ◽  
Industrial Applications ◽  
Phosphate Esters ◽  
Antiwear Additives ◽  
Formation Mechanisms ◽  
Phosphate Ester ◽  
Wide Range

<p>Phosphate esters have a wide range of industrial applications, for example in tribology where they are used as vapour phase lubricants and antiwear additives. To rationally design phosphate esters with improved tribological performance, an atomic-level understanding of their film formation mechanisms is required. One important aspect is the thermal decomposition of phosphate esters on steel surfaces, since this initiates film formation. In this study, ReaxFF molecular dynamics simulations are used to study the thermal decomposition of phosphate esters with different substituents on several ferrous surfaces. On Fe<sub>3</sub>O<sub>4</sub>(001) and α-Fe(110), chemisorption interactions between the phosphate esters and the surfaces occur even at room temperature, and the number of molecule-surface bonds increases as the temperature is increased from 300 to 1000 K. Conversely, on hydroxylated, amorphous Fe<sub>3</sub>O<sub>4</sub>, most of the molecules are physisorbed, even at high temperature. Thermal decomposition rates were much higher on Fe<sub>3</sub>O<sub>4</sub>(001) and particularly α-Fe(110) compared to hydroxylated, amorphous Fe<sub>3</sub>O<sub>4</sub>. This suggests that water passivates ferrous surfaces and inhibits phosphate ester chemisorption, decomposition, and ultimately film formation. On Fe<sub>3</sub>O<sub>4</sub>(001), thermal decomposition proceeds mainly through C-O cleavage (to form surface alkyl and aryl groups) and C-H cleavage (to form surface hydroxyls). The onset temperature for C-O cleavage on Fe<sub>3</sub>O<sub>4</sub>(001) increases in the order: tertiary alkyl < secondary alkyl < primary linear alkyl ≈ primary branched alkyl < aryl. This order is in agreement with experimental observations for the thermal stability of antiwear additives with similar substituents. The results highlight surface and substituent effects on the thermal decomposition of phosphate esters which should be helpful for the design of new molecules with improved performance.</p>

PLATINUM

Alloy Digest ◽  
1970 ◽  
Vol 19 (11) ◽  
Keyword(s):  
Corrosion Resistance ◽  
High Temperature ◽  
Heat Treating ◽  
Industrial Applications ◽  
High Melting ◽  
High Melting Point ◽  
White Metal ◽  
Temperature Performance ◽  
Wide Range ◽  
Corrosion And Oxidation

Abstract PLATINUM is a soft, ductile, white metal which can be readily worked either hot or cold. It has a wide range of industrial applications because of its excellent corrosion and oxidation resistance and its high melting point. This datasheet provides information on composition, physical properties, hardness, elasticity, and tensile properties. It also includes information on high temperature performance and corrosion resistance as well as forming, heat treating, machining, and joining. Filing Code: Pt-1. Producer or source: Matthey Bishop Inc..

p-Sulfonic acid calix[n]arene catalyzed synthesis of bioactive heterocycles: A review

2020 ◽  
Vol 24 ◽  
Author(s):  
Bubun Banerjee ◽  
Gurpreet Kaur ◽  
Navdeep Kaur
Keyword(s):  
Supramolecular Chemistry ◽  
Sulfonic Acid ◽  
Catalytic Efficiency ◽  
The Other ◽  
Reaction Conditions ◽  
Metal Free ◽  
Bioactive Scaffolds ◽  
Wide Range ◽  
Efficient Alternative ◽  
Bioactive Heterocycles

: Metal-free organocatalysts are becoming an important tool for the sustainable developments of various bioactive heterocycles. On the other hand, during last two decades, calix[n]arenes have been gaining considerable attention due to their wide range of applicability in the field of supramolecular chemistry. Recently, sulfonic acid functionalized calix[n] arenes are being employed as an efficient alternative catalyst for the synthesis of various bioactive scaffolds. In this review we have summarized the catalytic efficiency of p-sulfonic acid calix[n]arenes for the synthesis of diverse biologically promising scaffolds under various reaction conditions. There is no such review available in the literature showing the catalytic applicability of p-sulfonic acid calix[n]arenes. Therefore, we strongly believe that this review will surely attract those researchers who are interested about this fascinating organocatalyst.

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