Asim Ghosh

Universality of citation distributions for academic institutions and journals

Citations measure the importance of a publication, and may serve as a proxy for its popularity and quality of its contents. Here we study the distributions of citations to publications from individual academic institutions for a single year. The average number of citations have large variations between different institutions across the world, but the probability distributions of citations for individual institutions can be rescaled to a common form by scaling the citations by the average number of citations for that institution. We find this feature seems to be universal for a broad selection of institutions irrespective of the average number of citations per article. A similar analysis for citations to publications in a particular journal in a single year reveals similar results. We find high absolute inequality for both these sets, Gini coefficients being around 0.66 and 0.58 for institutions and journals respectively. We also find that the top 25% of the articles hold about 75% of the total citations for institutions and the top 29% of the articles hold about 71% of the total citations for journals.

Inequality in societies, academic institutions and science journals: Gini and k-indices

Abstract Social inequality is traditionally measured by the Gini-index ( g ). The g -index takes values from 0 to 1 where g = 0 represents complete equality and g = 1 represents complete inequality. Most of the estimates of the income or wealth data indicate the g value to be widely dispersed across the countries of the world: g values typically range from 0.30 to 0.65 at a particular time (year). We estimated similarly the Gini-index for the citations earned by the yearly publications of various academic institutions and the science journals. The ISI web of science data suggests remarkably strong inequality and universality ( g = 0.70 ± 0.07 ) across all the universities and institutions of the world, while for the journals we find g = 0.65 ± 0.15 for any typical year. We define a new inequality measure, namely the k -index, saying that the cumulative income or citations of ( 1 − k ) fraction of people or papers exceed those earned by the fraction ( k ) of the people or publications respectively. We find, while the k -index value for income ranges from 0.60 to 0.75 for income distributions across the world, it has a value around 0.75 ± 0.05 for different universities and institutions across the world and around 0.77 ± 0.10 for the science journals. Apart from above indices, we also analyze the same institution and journal citation data by measuring Pietra index and median index.

Measuring social inequality with quantitative methodology: Analytical estimates and empirical data analysis by Gini and k indices

Social inequality manifested across different strata of human existence can be quantified in several ways. Here we compute non-entropic measures of inequality such as Lorenz curve, Gini index and the recently introduced k index analytically from known distribution functions. We characterize the distribution functions of different quantities such as votes, journal citations, city size, etc. with suitable fits, compute their inequality measures and compare with the analytical results. A single analytic function is often not sufficient to fit the entire range of the probability distribution of the empirical data, and fit better to two distinct functions with a single crossover point. Here we provide general formulas to calculate these inequality measures for the above cases. We attempt to specify the crossover point by minimizing the gap between empirical and analytical evaluations of measures. Regarding the k index as an ‘extra dimension’, both the lower and upper bounds of the Gini index are obtained as a function of the k index. This type of inequality relations among inequality indices might help us to check the validity of empirical and analytical evaluations of those indices.

Continuous transition of social efficiencies in the stochastic-strategy minority game.

We show that in a variant of the minority game problem, the agents can reach a state of maximum social efficiency, where the fluctuation between the two choices is minimum, by following a simple stochastic strategy. By imagining a social scenario where the agents can only guess about the number of excess people in the majority, we show that as long as the guessed value is sufficiently close to the reality, the system can reach a state of full efficiency or minimum fluctuation. A continuous transition to less efficient condition is observed when the guessed value becomes worse. Hence, people can optimize their guess for excess population to optimize the period of being in the majority state. We also consider the situation where a finite fraction of agents always decide completely randomly (random trader) as opposed to the rest of the population who follow a certain strategy (chartist). For a single random trader the system becomes fully efficient with majority-minority crossover occurring every 2 days on average. For just two random traders, all the agents have equal gain with arbitrarily small fluctuations.

Sex differences in social focus across the life cycle in humans.

Age and gender are two important factors that play crucial roles in the way organisms allocate their social effort. In this study, we analyse a large mobile phone dataset to explore the way life history influences human sociality and the way social networks are structured. Our results indicate that these aspects of human behaviour are strongly related to age and gender such that younger individuals have more contacts and, among them, males more than females. However, the rate of decrease in the number of contacts with age differs between males and females, such that there is a reversal in the number of contacts around the late 30s. We suggest that this pattern can be attributed to the difference in reproductive investments that are made by the two sexes. We analyse the inequality in social investment patterns and suggest that the age- and gender-related differences we find reflect the constraints imposed by reproduction in a context where time (a form of social capital) is limited.

Communication with Family and Friends across the Life Course

Each stage of the human life course is characterised by a distinctive pattern of social relations. We study how the intensity and importance of the closest social contacts vary across the life course, using a large database of mobile communication from a European country. We first determine the most likely social relationship type from these mobile phone records by relating the age and gender of the caller and recipient to the frequency, length, and direction of calls. We then show how communication patterns between parents and children, romantic partner, and friends vary across the six main stages of the adult family life course. Young adulthood is dominated by a gradual shift of call activity from parents to close friends, and then to a romantic partner, culminating in the period of early family formation during which the focus is on the romantic partner. During middle adulthood call patterns suggest a high dependence on the parents of the ego, who, presumably often provide alloparental care, while at this stage female same-gender friendship also peaks. During post-reproductive adulthood, individuals and especially women balance close social contacts among three generations. The age of grandparenthood brings the children entering adulthood and family formation into the focus, and is associated with a realignment of close social contacts especially among women, while the old age is dominated by dependence on their children.

Invariant features of spatial inequality in consumption: The case of India

We study the distributional features and inequality of consumption expenditure across India, for different states, castes, religion and urban–rural divide. We find that even though the aggregate measures of inequality are fairly diversified across states, the consumption distributions show near identical statistics, once properly normalized. This feature is seen to be robust with respect to variations in sociological and economic factors. We also show that state-wise inequality seems to be positively correlated with growth which is in accord with the traditional idea of Kuznets’ curve. We present a brief model to account for the invariance found empirically and show that better but riskier technology draws can create a positive correlation between inequality and growth.

Inequality measures in kinetic exchange models of wealth distributions

In this paper, we study the inequality indices for some models of wealth exchange. We calculated Gini index and newly introduced k-index and compare the results with reported empirical data available for different countries. We have found lower and upper bounds for the indices and discuss the efficiencies of the models. Some exact analytical calculations are given for a few cases. We also exactly compute the quantities for Gamma and double Gamma distributions.

Zipf's law in city size from a resource utilization model

We study a resource utilization scenario characterized by intrinsic fitness. To describe the growth and organization of different cities, we consider a model for resource utilization where many restaurants compete, as in a game, to attract customers using an iterative learning process. Results for the case of restaurants with uniform fitness are reported. When fitness is uniformly distributed, it gives rise to a Zipf law for the number of customers. We perform an exact calculation for the utilization fraction for the case when choices are made independent of fitness. A variant of the model is also introduced where the fitness can be treated as an ability to stay in the business. When a restaurant loses customers, its fitness is replaced by a random fitness. The steady state fitness distribution is characterized by a power law, while the distribution of the number of customers still follows the Zipf law, implying the robustness of the model. Our model serves as a paradigm for the emergence of Zipf law in city size distribution.

Econophysics Research in India in the last two Decades

We discuss here researches on econophysics done in India in the last two decades. The term ‘econophysics’ was formally coined in India (Kolkata) in 1995. Since then many research papers, books, reviews, etc., have been written by scientists. Many institutions are now involved in this research field and many conferences are being organized here. In this article we give an account (of papers, books, reviews, papers in proceedings volumes, etc.) of this research from India.