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Expected value of first Zagreb connection index in random cyclooctatetraene chain, random polyphenyls chain, and random chain network.

ABSTRACT: The Zagreb connection indices are the known topological descriptors of the graphs that are constructed from the connection cardinality (degree of given nodes lying at a distance 2) presented in 1972 to determine the total electron energy of the alternate hydrocarbons. For a long time, these connection indices did not receive much research attention. Ali and Trinajstić [Mol. Inform. 37, Art. No. 1800008, 2018] examined the Zagreb connection indices and found that they compared to basic Zagreb indices and that they provide a finer value for the correlation coefficient for the 13 physico-chemical characteristics of the octane isomers. This article acquires the formulae of expected values of the first Zagreb connection index of a random cyclooctatetraene chain, a random polyphenyls chain, and a random chain network with l number of octagons, hexagons, and pentagons, respectively. The article presents extreme and average values of all the above random chains concerning a set of special chains, including the meta-chain, the ortho-chain, and the para-chain.

SUBMITTER: Raza Z

PROVIDER: S-EPMC9846538 | biostudies-literature | 2022

REPOSITORIES: biostudies-literature

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Expected value of first Zagreb connection index in random cyclooctatetraene chain, random polyphenyls chain, and random chain network.

Raza Zahid Z Akhter Shehnaz S Shang Yilun Y

Frontiers in chemistry 20230104

The Zagreb connection indices are the known topological descriptors of the graphs that are constructed from the connection cardinality (degree of given nodes lying at a distance 2) presented in 1972 to determine the total electron energy of the alternate hydrocarbons. For a long time, these connection indices did not receive much research attention. Ali and Trinajstić [Mol. Inform. 37, Art. No. 1800008, 2018] examined the Zagreb connection indices and found that they compared to basic Zagreb ind ...[more]

PMID: 36688029

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Project description:ObjectivesOperators performing fetal growth scans are usually aware of the gestational age of the pregnancy, which may lead to expected-value bias when performing biometric measurements. We aimed to evaluate the incidence of expected-value bias in routine fetal growth scans and assess its impact on standard biometric measurements.MethodsWe collected prospectively full-length video recordings of routine ultrasound growth scans coupled with operator eye tracking. Expected value was defined as the gestational age at the time of the scan, based on the estimated due date that was established at the dating scan. Expected-value bias was defined as occurring when the operator looked at the measurement box on the screen during the process of caliper adjustment before saving a measurement. We studied the three standard biometric planes on which measurements of head circumference (HC), abdominal circumference (AC) and femur length (FL) are obtained. We evaluated the incidence of expected-value bias and quantified the impact of biased measurements.ResultsWe analyzed 272 third-trimester growth scans, performed by 16 operators, during which a total of 1409 measurements (354 HC, 703 AC and 352 FL; including repeat measurements) were obtained. Expected-value bias occurred in 91.4% of the saved standard biometric plane measurements (85.0% for HC, 92.9% for AC and 94.9% for FL). The operators were more likely to adjust the measurements towards the expected value than away from it (47.7% vs 19.7% of measurements; P < 0.001). On average, measurements were corrected by 2.3 ± 5.6, 2.4 ± 10.4 and 3.2 ± 10.4 days of gestation towards the expected gestational age for the HC, AC, and FL measurements, respectively. Additionally, we noted a statistically significant reduction in measurement variance once the operator was biased (P = 0.026). Comparing the lowest and highest possible estimated fetal weight (using the smallest and largest biased HC, AC and FL measurements), we noted that the discordance, in percentage terms, was 10.1% ± 6.5%, and that in 17% (95% CI, 12-21%) of the scans, the fetus could be considered as small-for-gestational age or appropriate-for-gestational age if using the smallest or largest possible measurements, respectively. Similarly, in 13% (95% CI, 9-16%) of scans, the fetus could be considered as large-for-gestational age or appropriate-for-gestational age if using the largest or smallest possible measurements, respectively.ConclusionsDuring routine third-trimester growth scans, expected-value bias frequently occurs and significantly changes standard biometric measurements obtained. © 2019 the Authors. Ultrasound in Obstetrics & Gynecology published by John Wiley & Sons Ltd on behalf of the International Society of Ultrasound in Obstetrics and Gynecology.

Dataset Information

Expected value of first Zagreb connection index in random cyclooctatetraene chain, random polyphenyls chain, and random chain network.

Publications

Expected value of first Zagreb connection index in random cyclooctatetraene chain, random polyphenyls chain, and random chain network.

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