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Relevant bibliographies by topics / Base invariance, scale invariance, Benford

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Academic literature on the topic 'Base invariance, scale invariance, Benford'

Author: Grafiati

Published: 24 April 2022

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Journal articles on the topic "Base invariance, scale invariance, Benford"

1

Burgos, Andrea, and Andrés Santos. "The Newcomb–Benford law: Scale invariance and a simple Markov process based on it." American Journal of Physics 89, no. 9 (2021): 851–61. http://dx.doi.org/10.1119/10.0004957.

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SHAO, LIJING, and BO-QIANG MA. "FIRST DIGIT DISTRIBUTION OF HADRON FULL WIDTH." Modern Physics Letters A 24, no. 40 (2009): 3275–82. http://dx.doi.org/10.1142/s0217732309031223.

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A phenomenological law, called Benford's law, states that the occurrence of the first digit, i.e. 1, 2,…, 9, of numbers from many real world sources is not uniformly distributed, but instead favors smaller ones according to a logarithmic distribution. We investigate, for the first time, the first digit distribution of the full widths of mesons and baryons in the well-defined science domain of particle physics systematically, and find that they agree excellently with the Benford distribution. We also discuss several general properties of Benford's law, i.e. the law is scale-invariant, base-inva

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Ryder, Peter. "The Relationship Between the Newcomb-Benford Law and the Distribution of Rational Numbers." Zeitschrift für Naturforschung A 64, no. 9-10 (2009): 615–17. http://dx.doi.org/10.1515/zna-2009-9-1012.

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The Newcomb-Benford law, also known as Benford’s law or the first-digit law, applies to many tabulated sets of real-world data. It states that the probability that the first significant digit is n, (n ∈ {1,2,3,4,5,6,7,8,9}) is given by log(1+ 1/n). The law has been verified empirically with widely differing data sets. In the present paper it is shown that it does not necessarily follow from the requirement of scale invariance alone, as has been claimed. This condition is necessary, but not sufficient. In addition, it is necessary to consider the properties of certain finite subsets of the set

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4

Rescorla, Leslie A., Akhgar Ghassabian, Masha Y. Ivanova, Vincent WV Jaddoe, Frank C. Verhulst, and Henning Tiemeier. "Structure, longitudinal invariance, and stability of the Child Behavior Checklist 1½–5’s Diagnostic and Statistical Manual of Mental Disorders–Autism Spectrum Disorder scale: Findings from Generation R (Rotterdam)." Autism 23, no. 1 (2017): 223–35. http://dx.doi.org/10.1177/1362361317736201.

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Although the Child Behavior Checklist 1½–5’s 12-item Diagnostic and Statistical Manual of Mental Disorders-Autism Spectrum Problems Scale (formerly called Pervasive Developmental Problems scale) has been used in several studies as an autism spectrum disorder screener, the base rate and stability of its items and its measurement model have not been previously studied. We therefore examined the structure, longitudinal invariance, and stability of the Child Behavior Checklist 1½–5’s Diagnostic and Statistical Manual of Mental Disorders-Autism Spectrum Problems Scale in the diverse Generation R (R

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de Jong, Jurjen, Jos de Bruijne, and Joris De Ridder. "Benford’s law in the Gaia universe." Astronomy & Astrophysics 642 (October 2020): A205. http://dx.doi.org/10.1051/0004-6361/201937256.

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Context. Benford’s law states that for scale- and base-invariant data sets covering a wide dynamic range, the distribution of the first significant digit is biased towards low values. This has been shown to be true for wildly different datasets, including financial, geographical, and atomic data. In astronomy, earlier work showed that Benford’s law also holds for distances estimated as the inverse of parallaxes from the ESA HIPPARCOS mission. Aims. We investigate whether Benford’s law still holds for the 1.3 billion parallaxes contained in the second data release of Gaia (Gaia DR2). In contras

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Trigueros, Rubén, Noelia Navarro-Gómez, José M. Aguilar-Parra, and Adolfo J. Cangas. "Factorial Structure and Measurement Invariance of the Acceptance and Action Questionnaire-Stigma (AAQ-S) in Spain." International Journal of Environmental Research and Public Health 17, no. 2 (2020): 658. http://dx.doi.org/10.3390/ijerph17020658.

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The objective of the present study was to validate and adapt the Acceptance and Action Questionnaire-Stigma (AAQ-S) to the Spanish context. Method: The study included the participation of 1212 subjects, with an average age of 17.12 years old. Results: The confirmatory factorial analysis revealed a number of adequate fit indices for the new version of the scale χ2/df = 3.24; Comparative Fit Index = 0.96; Incremental Fit Index = 0.96; Root Mean Square Error of Approximation = 0.060; Standardized Root Mean Square Residual = 0.035, in which the factorial structures displayed gender invariance. The

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7

Napoli, Mariateresa, Bassam Bamieh, and Mohammed Dahleh. "Optimal Control of Arrays of Microcantilevers." Journal of Dynamic Systems, Measurement, and Control 121, no. 4 (1999): 686–90. http://dx.doi.org/10.1115/1.2802535.

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In this paper we will present a model for an array of microcantilevers that are used in Atomic Force Microscopy and nano-scale manufacturing. The microcantilevers are connected to each other through a common base, and are individually actuated. The sensors are also integrated on each microcantilever. We consider the problem of controlling a tightly packed array of identical microcantilevers that are dynamically coupled. This system is an example of a spatially-invariant system with a distributed array of sensors and actuators. We exploit the spatial invariance of the problem to design optimal

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8

Ma, Yong-Feng, Szymon P. Malinowski, Katarzyna Karpińska, Hermann E. Gerber, and Wojciech Kumala. "Scaling Analysis of Temperature and Liquid Water Content in the Marine Boundary Layer Clouds during POST." Journal of the Atmospheric Sciences 74, no. 12 (2017): 4075–92. http://dx.doi.org/10.1175/jas-d-17-0015.1.

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AbstractThe authors have analyzed the scaling behavior of marine boundary layer (MBL) clouds using high-resolution temperature (T) and liquid water content (LWC) fluctuations from aircraft measurements collected over the Pacific Ocean during the Physics of Stratocumulus Top (POST) research campaign in summer of 2008. As an extension of the past studies for scale-invariant properties of MBL clouds, the authors studied the variability of scaling exponents with height. The results showed that both LWC and T have two distinct scaling regimes: the first one displays scale invariance over a range fr

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Kopaneva, Victoria, Leonid Kostenko, and Tetyana Symonenko. "DEVELOPMENT OF MATHEMATICAL FUNDAMENTALS OF SOCIAL COMMUNICATIONS." Scientific journal “Library Science. Record Studies. Informology”, no. 1 (April 23, 2021): 42–49. http://dx.doi.org/10.32461/2409-9805.1.2021.229853.

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The purpose of the article is to generalize the patterns of phenomena and processes of social communications and to develop on this basis their unified mathematical model. The methodology is a systematic, infometric, and synergetic approaches to the development of mathematical principles of socialcommunication. The first one (systematic) is to generalize the empirical patterns of scaling in librarianship, linguistics, and science. The second one (infometric) is to obtain an analytical description of the quantitative relationship between the subjects and objects of social communications, the th

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Fressengeas, Claude, Benoît Beausir, Christophe Kerisit, et al. "On the evaluation of dislocation densities in pure tantalum from EBSD orientation data." Matériaux & Techniques 106, no. 6 (2018): 604. http://dx.doi.org/10.1051/mattech/2018058.

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We analyze measurements of dislocation densities carried out independently by several teams using three different methods on orientation maps obtained by Electron Back Scattered Diffraction on commercially pure tantalum samples in three different microstructural states. The characteristic aspects of these three methods: the Kernel average method, the Dillamore method and the determination of the lattice curvature-induced Nye’s tensor component fields are reviewed and their results are compared. One of the main features of the uncovered dislocation density distributions is their strong heteroge

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Book chapters on the topic "Base invariance, scale invariance, Benford"

1

Berger, Arno, and Theodore P. Hill. "Scale-, Base-, and Sum-lnvariance." In An Introduction to Benford's Law. Princeton University Press, 2015. http://dx.doi.org/10.23943/princeton/9780691163062.003.0005.

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This chapter establishes and illustrates three basic invariance properties of the Benford distribution that are instrumental in demonstrating whether or not certain datasets are Benford, and that also prove helpful for predicting which empirical data are likely to follow Benford's law closely. These are the scale-invariance property, base-invariance property, and sum-invariance property.

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"5. Scale-, Base-, and Sum-Invariance." In An Introduction to Benford's Law. Princeton University Press, 2015. http://dx.doi.org/10.1515/9781400866588-006.

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3

Hoyle, David. "Benfordʼs Law in the Natural Sciences." In Benford's Law. Princeton University Press, 2015. http://dx.doi.org/10.23943/princeton/9780691147611.003.0016.

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This chapter focuses on the occurrence of Benford's law within the natural sciences, emphasizing that Benford's law is to be expected within many scientific data sets. This is a consequence of the reasonable assumption that a particular scientific process is scale invariant, or nearly scale invariant. The chapter reviews previous work from many fields showing a number of data sets that conform to Benford's law. In each case the underlying scale invariance, or mechanism that leads to scale invariance, is identified. Having established that Benford's law is to be expected for many data sets in the natural sciences, the second half of the chapter highlights generic potential applications of Benford's law. Finally, direct applications of Benford's law are highlighted, whereby the Benford distribution is used in a constructive way rather than simply assessing an already existing data set.

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