Statistical Properties of Height of Japanese Schoolchildren

We study height distributions of Japanese schoolchildren based on the statictical data which are obtained from the school health survey by the ministry of education, culture, sports, science and technology, Japan . From our analysis, it has been clarified that the distribution of height changes from the lognormal distribution to the normal distribution in the periods of puberty.Comment: 2 pages, 2 figures, submitted to J. Phys. Soc. Jpn.; resubmitted to J. Phys. Soc. Jpn. after some revisio

A triangle model of criminality

This paper is concerned with a quantitative model describing the interaction of three sociological species, termed as owners, criminals and security guards, and denoted by X, Y and Z respectively. In our model, Y is a predator of the species X, and so is Z with respect to Y . Moreover, Z can also be thought of as a predator of X, since this last population is required to bear the costs of maintaining Z. We propose a system of three ordinary differential equations to account for the time evolution of X(t), Y (t) and Z(t) according to our previous assumptions. Out of the various parameters that appear in that system, we select two of them, denoted by H, and h, which are related with the efficiency of the security forces as a control parameter in our discussion. To begin with, we consider the case of large and constant owners population, which allows us to reduce (3)–(5) to a bidimensional system for Y (t) and Z(t). As a preliminary step, this situation is first discussed under the additional assumption that Y (t) + Z(t) is constant. A bifurcation study is then performed in terms of H and h, which shows the key role played by the rate of casualties in Y and Z, that results particularly in a possible onset of bistability. When the previous restriction is dropped, we observe the appearance of oscillatory behaviours in the full two-dimensional system. We finally provide a exploratory study of the complete model (3)–(5), where a number of bifurcations appear as parameter H changes, and the corresponding solutions behaviours are described

The statistical laws of popularity: Universal properties of the box office dynamics of motion pictures

Are there general principles governing the process by which certain products or ideas become popular relative to other (often qualitatively similar) competitors? To investigate this question in detail, we have focused on the popularity of movies as measured by their box-office income. We observe that the log-normal distribution describes well the tail (corresponding to the most successful movies) of the empirical distributions for the total income, the income on the opening week, as well as, the weekly income per theater. This observation suggests that popularity may be the outcome of a linear multiplicative stochastic process. In addition, the distributions of the total income and the opening income show a bimodal form, with the majority of movies either performing very well or very poorly in theaters. We also observe that the gross income per theater for a movie at any point during its lifetime is, on average, inversely proportional to the period that has elapsed after its release. We argue that (i) the log-normal nature of the tail, (ii) the bimodal form of the overall gross income distribution, and (iii) the decay of gross income per theater with time as a power law, constitute the fundamental set of {\em stylized facts} (i.e., empirical "laws") that can be used to explain other observations about movie popularity. We show that, in conjunction with an assumption of a fixed lower cut-off for income per theater below which a movie is withdrawn from a cinema, these laws can be used to derive a Weibull distribution for the survival probability of movies which agrees with empirical data. The connection to extreme-value distributions suggests that popularity can be viewed as a process where a product becomes popular by avoiding failure (i.e., being pulled out from circulation) for many successive time periods. We suggest that these results may apply to popularity in general.Comment: 14 pages, 11 figure

Mister Mary Somerville: Husband and Secretary

Mary Somerville’s life as a mathematician and savant in nineteenth-century Great Britain was heavily influenced by her gender; as a woman, her access to the ideas and resources developed and circulated in universities and scientific societies was highly restricted. However, her engagement with learned institutions was by no means nonexistent, and although she was 90 before being elected a full member of any society (Società Geografica Italiana, 1870), Somerville (Figure 1) nevertheless benefited from the resources and social networks cultivated by such institutions from as early as 1812. A key intermediary between Somerville and these societies was her husband, Dr. William Somerville, whose mediation was vital to her access to knowledge and her subsequent career as a scientific author. In this paper we will consider how spousal cooperation enabled the overcoming of gendered barriers to scientific institutions in the nineteenth century

Agent-based Social Psychology: from Neurocognitive Processes to Social Data

Moral Foundation Theory states that groups of different observers may rely on partially dissimilar sets of moral foundations, thereby reaching different moral valuations. The use of functional imaging techniques has revealed a spectrum of cognitive styles with respect to the differential handling of novel or corroborating information that is correlated to political affiliation. Here we characterize the collective behavior of an agent-based model whose inter individual interactions due to information exchange in the form of opinions are in qualitative agreement with experimental neuroscience data. The main conclusion derived connects the existence of diversity in the cognitive strategies and statistics of the sets of moral foundations and suggests that this connection arises from interactions between agents. Thus a simple interacting agent model, whose interactions are in accord with empirical data on conformity and learning processes, presents statistical signatures consistent with moral judgment patterns of conservatives and liberals as obtained by survey studies of social psychology.Comment: 11 pages, 4 figures, 2 C codes, to appear in Advances in Complex System

A mathematical model of a criminal-prone society

Criminals are common to all societies. To fight against them the community takes different security measures as, for example, to bring about a police. Thus, crime causes a depletion of the common wealth not only by criminal acts but also because the cost of hiring a police force. In this paper, we present a mathematical model of a criminal-prone self-protected society that is divided into socio-economical classes. We study the effect of a non-null crime rate on a free-of-criminals society which is taken as a reference system. As a consequence, we define a criminal-prone society as one whose free-of-criminals steady state is unstable under small perturbations of a certain socio-economical context. Finally, we compare two alternative strategies to control crime: (i) enhancing police efficiency, either by enlarging its size or by updating its technology, against (ii) either reducing criminal appealing or promoting social classes at ris

Prevalence of Obesity and the Relationship between the Body Mass Index and Body Fat: Cross-Sectional, Population-Based Data

Background: Anthropometric measures such as the body mass index (BMI) and waist circumference are widely used as convenient indices of adiposity, yet there are limitations in their estimates of body fat. We aimed to determine the prevalence of obesity using criteria based on the BMI and waist circumference, and to examine the relationship between the BMI and body fat.Methodology/Principal Findings: This population-based, cross-sectional study was conducted as part of the Geelong Osteoporosis Study. A random sample of 1,467 men and 1,076 women aged 20&ndash;96 years was assessed 2001&ndash;2008. Overweight and obesity were identified according to BMI (overweight 25.0&ndash;29.9 kg/m2; obesity 30.0 kg/m2) and waist circumference (overweight men 94.0–101.9 cm; women 80.0–87.9 cm; obesity men 102.0 cm, women $88.0 cm); body fat mass was assessed using dual energy X-ray absorptiometry; height and weight were measured and lifestyle factors documented by self-report. According to the BMI, 45.1% (95%CI 42.4&ndash;47.9) of men and 30.2% (95%CI 27.4&ndash;33.0) of women were overweight and a further 20.2% (95%CI 18.0&ndash;22.4) of men and 28.6% (95%CI 25.8&ndash;31.3) of women were obese. Using waist circumference, 27.5% (95%CI 25.1&ndash;30.0) of men and 23.3% (95%CI 20.8&ndash;25.9) of women were overweight, and 29.3% (95%CI 26.9&ndash;31.7) of men and 44.1% (95%CI 41.2&ndash;47.1) of women, obese. Both criteria indicate that approximately 60% of the population exceeded recommended thresholds for healthy body habitus. There was no consistent pattern apparent between BMI and energy intake. Compared with women, BMI overestimated adiposity in men, whose excess weight was largely attributable to muscular body builds and greater bone mass. BMI also underestimated adiposity in the elderly. Regression models including gender, age and BMI explained 0.825 of the variance in percent body fat.Conclusions/Significance: As the BMI does not account for differences in body composition, we suggest that gender- and age-specific thresholds should be considered when the BMI is used to indicate adiposity.<br /

A study of orientational ordering in a fluid of dipolar Gay-Berne molecules using density-functional theory

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