The Newcomb-Benford Law in Its Relation to Some Common Distributions

An often reported, but nevertheless persistently striking observation, formalized as the Newcomb-Benford law (NBL), is that the frequencies with which the leading digits of numbers occur in a large variety of data are far away from being uniform. Most spectacular seems to be the fact that in many data the leading digit 1 occurs in nearly one third of all cases. Explanations for this uneven distribution of the leading digits were, among others, scale- and base-invariance. Little attention, however, found the interrelation between the distribution of the significant digits and the distribution of the observed variable. It is shown here by simulation that long right-tailed distributions of a random variable are compatible with the NBL, and that for distributions of the ratio of two random variables the fit generally improves. Distributions not putting most mass on small values of the random variable (e.g. symmetric distributions) fail to fit. Hence, the validity of the NBL needs the predominance of small values and, when thinking of real-world data, a majority of small entities. Analyses of data on stock prices, the areas and numbers of inhabitants of countries, and the starting page numbers of papers from a bibliography sustain this conclusion. In all, these findings may help to understand the mechanisms behind the NBL and the conditions needed for its validity. That this law is not only of scientific interest per se, but that, in addition, it has also substantial implications can be seen from those fields where it was suggested to be put into practice. These fields reach from the detection of irregularities in data (e.g. economic fraud) to optimizing the architecture of computers regarding number representation, storage, and round-off errors

The leading digit distribution of the worldwide Illicit Financial Flows

Benford's law states that in data sets from different phenomena leading digits tend to be distributed logarithmically such that the numbers beginning with smaller digits occur more often than those with larger ones. Particularly, the law is known to hold for different types of financial data. The Illicit Financial Flows (IFFs) exiting the developing countries are frequently discussed as hidden resources which could have been otherwise properly utilized for their development. We investigate here the distribution of the leading digits in the recent data on estimates of IFFs to look for the existence of a pattern as predicted by Benford's law and establish that the frequency of occurrence of the leading digits in these estimates does closely follow the law.Comment: 13 pages, 10 figures, 6 tables, additional data analyi

Heat generation and transfer in automotive dry clutch engagement

Dynamic behaviour of automotive dry clutches depends on the frictional characteristics of the contact between the friction lining material, the flywheel, and the pressure plate during the clutch engagement process. During engagement due to high interfacial slip and relatively high contact pressures, generated friction gives rise to contact heat, which affects the material behaviour and the associated frictional characteristics. In practice excess interfacial slipping and generated heat during torque transmission can result in wear of the lining, thermal distortion of the friction disc, and reduced useful life of the clutch. This paper provides measurement of friction lining characteristics for dry clutches for new and worn state under representative operating conditions pertaining to interfacial slipping during clutch engagement, applied contact pressures, and generated temperatures. An analytical thermal partitioning network model of the clutch assembly, incorporating the flywheel, friction lining, and the pressure plate is presented, based upon the principle of conservation of energy. The results of the analysis show a higher coefficient of friction for the new lining material which reduces the extent of interfacial slipping during clutch engagement, thus reducing the frictional power loss and generated interfacial heating. The generated heat is removed less efficiently from worn lining. This might be affected by different factors observed such as the reduced lining thickness and the reduction of density of the material but mainly because of poorer thermal conductivity due to the depletion of copper particles in its microstructure as the result of wear. The study integrates frictional characteristics, microstructural composition, mechanisms of heat generation, effect of lining wear, and heat transfer in a fundamental manner, an approach not hitherto reported in literature

Universal Ecological Patterns in College Basketball Communities

The rank abundance of common and rare species within ecological communities is remarkably consistent from the tropics to the tundra. This invariant patterning provides one of ecology's most enduring and unified tenets: most species rare and a few very common. Increasingly, attention is focused upon elucidating biological mechanisms that explain these species abundance distributions (SADs), but these evaluations remain controversial. We show that college basketball wins generate SADs just like those observed in ecological communities. Whereas college basketball wins are structured by competitive interactions, the result produces a SAD pattern indistinguishable from random wins. We also show that species abundance data for tropical trees exhibits a significant-digit pattern consistent with data derived from complex structuring forces. These results cast doubt upon the ability of SAD analysis to resolve ecological mechanism, and their patterning may reflect statistical artifact as much as biological processes

Genome-Wide Interaction Analyses between Genetic Variants and Alcohol Consumption and Smoking for Risk of Colorectal Cancer

Genome-wide association studies (GWAS) have identified many genetic susceptibility loci for colorectal cancer (CRC). However, variants in these loci explain only a small proportion of familial aggregation, and there are likely additional variants that are associated with CRC susceptibility. Genome-wide studies of gene-environment interactions may identify variants that are not detected in GWAS of marginal gene effects. To study this, we conducted a genome-wide analysis for interaction between genetic variants and alcohol consumption and cigarette smoking using data from the Colon Cancer Family Registry (CCFR) and the Genetics and Epidemiology of Colorectal Cancer Consortium (GECCO). Interactions were tested using logistic regression. We identified interaction between CRC risk and alcohol consumption and variants in the 9q22.32/HIATL1 (Pinteraction = 1.76×10−8; permuted pvalue 3.51x10-8) region. Compared to non-/occasional drinking light to moderate alcohol consumption was associated with a lower risk of colorectal cancer among individuals with rs9409565 CT genotype (OR, 0.82 [95% CI, 0.74±0.91]; P = 2.1×10−4) and TT genotypes (OR,0.62 [95% CI, 0.51±0.75]; P = 1.3×10−6) but not associated among those with the CC genotype (p = 0.059). No genome-wide statistically significant interactions were observed for smoking. If replicated our suggestive finding of a genome-wide significant interaction between genetic variants and alcohol consumption might contribute to understanding colorectal cancer etiology and identifying subpopulations with differential susceptibility to the effect of alcohol on CRC risk

Fitness, training, and the growth hormone-->insulin-like growth factor I axis in prepubertal girls.

We recently demonstrated that a brief endurance type training program led to increases in thigh muscle mass and peak oxygen uptake (VO(2)) in prepubertal girls. In this study, we examined the effect of training on the GH-->insulin-like growth factor I (GH-->IGF-I) axis, a system known to be involved both in the process of growth and development and in the response to exercise. Healthy girls (mean age 9.17 +/- 0.10 yr old) volunteered for the study and were randomized to control (n = 20) and training groups (n = 19) for 5 weeks. Peak VO(2), thigh muscle volume, and blood samples [for IGF-I, IGF-binding proteins (IGFBP)-1 to -6, and GHBP] were measured. At baseline, IGF-I was significantly correlated with both peak VO(2) (r = 0.44, P < 0.02) and muscle volume (r = 0.58, P < 0.004). IGFBP-1 was negatively correlated with muscle volume (r = -0.71, P < 0.0001), as was IGFBP-2. IGFBP-4 and -5 were significantly correlated with muscle volume. We found a threshold value of body mass index percentile (by age) of about 71, above which systematic changes in GHBP, IGFBP-1, and peak VO(2) per kilogram were noted, suggesting decreases in the following: 1) GH function, 2) insulin sensitivity, and 3) fitness. Following the training intervention, IGF-I increased in control (19.4 +/- 9.6%, P < 0.05) but not trained subjects, and both IGFBP-3 and GHBP decreased in the training group (-4.2 +/- 3.1% and -9.9 +/- 3.8%, respectively, P < 0.05). Fitness in prepubertal girls is associated with an activated GH-->IGF-I axis, but, paradoxically, early in a training program, children first pass through what appears to be a neuroendocrine state more consistent with catabolism