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Asim Ghosh

Publications and source records attributed to Asim Ghosh.

At least 19 recordsLinked to original sources
arXiv2026

Normalized fractional Hirsch Index and Modified Pareto Law

The Hirsch index (introduced in 2005) has been a very successful scientometric author-level measure for the publication impact inequalities among the authors. However, it does not have any upper bound and statistically it grows in proportion to the square root of the number of publications by the author. Social scientists, on the other hand, measure the economic performance of different countries (having different wealth amounts and populations etc.) using inequality indices like the Gini index (since 1912) etc., which are normalized quantities (independent of the country's total wealth or the population size). We show here that a normalized fractional Hirsch index, giving the fraction of total citations earned by fraction of those successful papers published by the author, can even indicate that typically about $14\%$ of the top cited papers earn about $86\%$ of citations for very successful scientists (like the 95 Nobel Laureates considered here). This is similar to Pareto's 80-20 law (since 1896) and agrees more precisely with those observed for self-organized sandpile models, where typically $86\%$ of the avalanche masses are dissipated through $14\%$ of the largest avalanches as the piles approach their respective self-organized critical points.

physics.soc-ph↗
arXiv2026

Relations Between the Inequality Indices Gini, Pietra and Kolkata: Theory and Data Analysis

We study relations between three inequality indices, namely the Gini ($g$), Pietra ($p$) and Kolkata ($k$) introduced in 1912, 1915 and 2014 respectively and all are derived from the Lorenz function $L(x)$ introduced in 1905. The Kolkata index (which corresponds to a fixed point of the complementary Lorenz function $L_c(x) \equiv 1-L(x)$) gives the fraction $k$ of wealth possessed by the richest $1-k$ fraction of people ($k$ = 0.8 corresponds to Pareto's 80-20 law from 1896). We show rigorously that while the Pietra index value $p$ should be greater than or equal to $2k-1$, the Robin Hood index should strictly be equal to the excess wealth fraction $2k-1$ possessed by the richest $1-k$ fraction of people. Our numerical data analysis for US IRS Income data (1983-2022), Bollywood (India) movie income data (1999-2024) and the citation inequalities across the publications by forty Nobel Laureates (2020-2025) in Economics, Physics, Chemistry and Medicine clearly show that $p/(2k-1)$ is always greater than unity but the deviation is never more than five percent. Assuming some simple analytic form for the Lorenz function, we also derived the relations $k = (1/2) + (3/8)g$ for small $g$ values and $p/g = 3/4$. However, by considering the Lorenz function appropriate for the generalized Pareto power law distribution, we obtain an extended range ($1_+ < p/g \leq e/2$) that captures most of the empirical data.

physics.soc-ph↗
arXiv2026

The Pareto principle in Sports and Economics in view of Runs Scored by Batters in the Indian Premier League

The analysis of income and wealth inequality is often constrained by the lack of reliable data. In this work, we introduce a proxy-based approach in which sports performance data are used to mimic economic distributions. In particular, the total runs scored by a batter in a single T20 season are treated as an analogue of annual income, while the cumulative runs scored across all seasons are taken to represent individual wealth. Using run distributions from the Indian Premier League (IPL), we explore how inequality evolves and estimate its upper limits in the absence of policy intervention. Our findings indicate that inequality derived from seasonal runs closely resembles the highest levels of income inequality observed in real-world data. In addition, the distribution of cumulative runs evolves over time and gradually approaches a limiting value consistent with global patterns of wealth inequality, in line with the Pareto principle. Overall, this study shows that proxy systems can capture essential features of economic inequality and offer a useful way to understand its inherent limits.

physics.soc-ph↗
arXiv2025

Does Excellence Correspond to Universal Inequality Level?

We study the inequality of citations received for different publications of various researchers and Nobel laureates in Physics, Chemistry, Medicine and Economics using Google Scholar data from 2012 to 2024. Citation distributions are found to be highly unequal, with even greater disparity among Nobel laureates. Measures of inequality, such as the Gini and Kolkata indices, emerge as useful indicators for distinguishing Nobel laureates from others. Such high inequality corresponds to growing critical fluctuations, suggesting that excellence aligns with an imminent (self-organized dynamical) critical point. Additionally, Nobel laureates exhibit systematically lower values of the Tsallis--Pareto parameter \( b \) and Shannon entropy, indicating more structured citation distributions. We also analyze the inequality in Olympic medal tallies across countries and find similar levels of disparity. Our results suggest that inequality measures can serve as proxies for competitiveness and excellence.

physics.soc-ph↗
arXiv2024

Signature of maturity in cryptocurrency volatility

We study the fluctuations, particularly the inequality of fluctuations, in cryptocurrency prices over the last ten years. We calculate the inequality in the price fluctuations through different measures, such as the Gini and Kolkata indices, and also the $Q$ factor (given by the ratio between the highest value and the average value) of these fluctuations. We compare the results with the equivalent quantities in some of the more prominent national currencies and see that while the fluctuations (or inequalities in such fluctuations) for cryptocurrencies were initially significantly higher than national currencies, over time the fluctuation levels of cryptocurrencies tend towards the levels characteristic of national currencies. We also compare similar quantities for a few prominent stock prices.

physics.soc-ph↗
arXiv2024

Q-factor: A measure of competition between the topper and the average in percolation and in SOC

We define the $Q$-factor in the percolation problem as the quotient of the size of the largest cluster and the average size of all clusters. As the occupation probability $p$ is increased, the $Q$-factor for the system size $L$ grows systematically to its maximum value $Q_{max}(L)$ at a specific value $p_{max}(L)$ and then gradually decays. Our numerical study of site percolation problems on the square, triangular and the simple cubic lattices exhibits that the asymptotic values of $p_{max}$ though close, are distinctly different from the corresponding percolation thresholds of these lattices. We have also shown using the scaling analysis that at $p_{max}$ the value of $Q_{max}(L)$ diverges as $L^d$ ($d$ denoting the dimension of the lattice) as the system size approaches to their asymptotic limit. We have further extended this idea to the non-equilibrium systems such as the sandpile model of self-organized criticality. Here, the $Q(ρ,L)$-factor is the quotient of the size of the largest avalanche and the cumulative average of the sizes of all the avalanches; $ρ$ being the drop density of the driving mechanism. This study has been prompted by some observations in Sociophysics.

cond-mat.stat-mech↗
arXiv2023

Do Successful Researchers Reach the Self-Organized Critical Point?

The index of success of the researchers is now mostly measured using the Hirsch index ($h$). Our recent precise demonstration, that statistically $h \sim \sqrt {N_c} \sim \sqrt {N_p}$, where $N_p$ and $N_c$ denote respectively the total number of publications and total citations for the researcher, suggests that average number of citations per paper ($N_c/N_p$), and hence $h$, are statistical numbers (Dunbar numbers) depending on the community or network to which the researcher belongs. We show here, extending our earlier observations, that the indications of success are not reflected by the total citations $N_c$, rather by the inequalities among citations from publications to publications. Specifically, we show that for very successful authors, the yearly variations in the Gini index ($g$, giving the average inequality of citations for the publications) and the Kolkata index ($k$, giving the fraction of total citations received by the top $1 - k$ fraction of publications; $k = 0.80$ corresponds to Pareto's 80/20 law) approach each other to $g = k \simeq 0.82$, signaling a precursor for the arrival of (or departure from) the Self-Organized Critical (SOC) state of his/her publication statistics. Analyzing the citation statistics (from Google Scholar) of thirty successful scientists throughout their recorded publication history, we find that the $g$ and $k$ for very successful among them (mostly Nobel Laureates, highest rank Stanford Cite-Scorers, and a few others) reach and hover just above (and then) below that $g = k \simeq 0.82$ mark, while for others they remain below that mark. We also find that all the lower (than the SOC mark 0.82) values of $k$ and $g$ fit a linear relationship $k = 1/2 + cg$, with $c = 0.39$.

cs.DL↗
arXiv2023

Kinetic Models of Wealth Distribution Having Extreme Inequality: Numerical Study of Their Stability Against Random Exchanges

In view of some persistent recent reports on a singular kind of growth of the world wealth inequality, where a finite (often handful) number of people tend to possess more than the wealth of the planet's 50\% population, we explore here if the kinetic exchange models of the market can ever capture such features where a significant fraction of wealth can concentrate in the hands of a countable few when the market size $N$ tends to infinity. One already existing example of such a kinetic exchange model is the Chakraborti or Yard-Sale model, where (in absence of tax redistribution etc) the entire wealth condenses in the hand of one (for any value of $N$), and the market dynamics stops. With tax redistribution etc, its steady state dynamics have been shown to have remarkable applicability in many cases of our extremely unequal world. We show here that another kinetic exchange model (called here the Banerjee model) has intriguing intrinsic dynamics, by which only ten rich traders or agents possess about 99.98\% of the total wealth in the steady state (without any tax etc like external manipulation) for any large value of $N$. We will discuss in some detail the statistical features of this model using Monte Carlo simulations. We will also show, if the traders each have a non-vanishing probability $f$ of following random exchanges, then these condensations of wealth (100\% in the hand of one agent in the Chakraborti model, or about 99.98\% in the hands ten agents in the Banerjee model) disappear in the large $N$ limit. We will also see that due to the built-in possibility of random exchange dynamics in the earlier proposed Goswami-Sen model, where the exchange probability decreases with an inverse power of the wealth difference of the pair of traders, one did not see any wealth condensation phenomena.

physics.soc-ph↗
arXiv2023

Scaling and Kinetic Exchange Like Behavior of Hirsch Index and Total Citation Distributions: Scopus-CiteScore Data Analysis

We analyze the data distributions $f(h)$, $f(N_c$) and $f(N_p)$ of the Hirsch index $(h)$, total citations ($N_c$) and total number of papers ($N_p$) of the top scoring 120,000 authors (scientists) from the Stanford cite-score (or c-score) 2022 list and their corresponding $h$ ($3 \le h \le 284$), $N_c (1009 \le N_c \le 428620$) and $N_p$ ($3\le N_p \le 3791$) statistics from the Scopus data. For reasons explained in the text, we divided the data of these top scorers (c-scores in the range 5.6125 to 3.3461) into six successive equal-sized Groups of 20,000 authors or scientists. We tried to fit, in each Group, $f(h)$, $f(Nc)$ and $f(Np)$ with Gamma distributions, viewing them as the ``wealth distributions'' in the fixed saving-propensity kinetic exchange models and found $f(h) \sim h^{γ_h} \mathrm{exp} (-h/T_h)$ with fitting noise level or temperature level ($T_h$) and average value of $h$, and the power $γ_h$ determined by the ``citation saving propensity'' in each Group. We further showed that using some earlier proposed power law scaling like $h = D_c N_c^{α_c}$ (or $h = D_p N_p^{α_p}$) with $α_c = 1/2 = α_p$, we can derive the observed $f(h)$ from the observed $f(N_c)$ or $f(N_p)$, with $D_c = 0.5$, but $D_p$ depending on the Group considered. This observation suggests that the average citations per paper ($N_c/N_p$) in each group ($= (D_p/D_c)^2 =4D_p^2$) vary (from 58 to 29) with the c-score range of the six Groups considered here, implying different effective Dunbar-like coordination numbers of the scientists belonging to different groups or networks.

physics.soc-ph↗
arXiv2023

Sandpile Universality in Social Inequality: Gini and Kolkata Measures

Social inequalities are ubiquitous and evolve towards a universal limit. Herein, we extensively review the values of inequality measures, namely the Gini ($g$) index and the Kolkata ($k$) index, two standard measures of inequality used in the analysis of various social sectors through data analysis. The Kolkata index, denoted as $k$, indicates the proportion of the `wealth' owned by $(1-k)$ fraction of the `people'. Our findings suggest that both the Gini index and the Kolkata index tend to converge to similar values (around $g=k \approx 0.87$, starting from the point of perfect equality, where $g=0$ and $k=0.5$) as competition increases in different social institutions, such as markets, movies, elections, universities, prize winning, battle fields, sports (Olympics), etc., under conditions of unrestricted competition (no social welfare or support mechanism). In this review, we present the concept of a generalized form of Pareto's 80/20 law ($k=0.80$), where the coincidence of inequality indices is observed. The observation of this coincidence is consistent with the precursor values of the $g$ and $k$ indices for the self-organized critical (SOC) state in self-tuned physical systems such as sand piles. These results provide quantitative support for the view that interacting socioeconomic systems can be understood within the framework of SOC, which has been hypothesized for many years. These findings suggest that the SOC model can be extended to capture the dynamics of complex socioeconomic systems and help us better understand their behavior.

physics.soc-ph↗
arXiv2022

Scaling Behavior of the Hirsch Index for Failure Avalanches, Percolation Clusters and Paper Citations

A popular measure for citation inequalities of individual scientists has been the Hirsch index ($h$). If for any scientist the number $n_c$ of citations is plotted against the serial number $n_p$ of the paper having those many citations (when the papers are ordered from highest cited to lowest) then $h$ corresponds to the nearest lower integer value of $n_p$ below the fixed point of the non-linear citation function (or given by $n_c = h = n_p$ if both $n_p$ and $n_c$ are dense set of integers near the $h$ value). The same index can be estimated (from $h=s=n_{s}$) for the avalanche or cluster of size ($s$) distributions ($n_s$) in elastic fiber bundle or percolation models. Another such inequality index, called the Kolkata index ($k$) says that $(1-k)$ fraction of papers attract $k$ fraction of citations ($k=0.80$ corresponds to the 80-20 law of Pareto). We find, for stress ($σ$), lattice occupation probability ($p$) or Kolkata index ($k$) near the bundle failure threshold ($σ_c$) or percolation threshold ($p_c$) or critical value of Kolkata index $k_c$, good fit to Widom-Stauffer like scaling $h/[\sqrt{N}/log N]$ = $f(\sqrt{N}[σ_c -σ]^α)$, $h/[\sqrt{N}/log N]=f(\sqrt{N}|p_c -p|^α)$ or $h/[\sqrt{N_c}/log N_c]=f(\sqrt{N_c}|k_c -k|^α)$ respectively, with asymptotically defined scaling function $f$, for systems of size $N$ (total number of fibers or lattice sites) or $N_c$ (total number of citations), and $α$ denoting the appropriate scaling exponent. We also show that if the number ($N_m$) of members of parliaments or national assemblies of different countries (with population $N$) is identified as their respective $h-$index, then the data fit the scaling relation $N_m \sim \sqrt N /log N$, resolving a major recent controversy.

physics.soc-ph↗
arXiv2022

Evolutionary Dynamics of Social Inequality and Coincidence of Gini and Kolkata indices under Unrestricted Competition

Social inequalities are ubiquitous and here we show that the values of the Gini ($g$) and Kolkata ($k$) indices, two generic inequality indices, approach each other (starting from $g = 0$ and $k = 0.5$ for equality) as the competitions grow in various social institutions like markets, universities, elections, etc. It is further showed that these two indices become equal and stabilize at a value (at $g = k \simeq 0.87$) under unrestricted competitions. We propose to view this coincidence of inequality indices as a generalized version of the (more than a) century old 80-20 law of Pareto. Furthermore, the coincidence of the inequality indices noted here is very similar to the ones seen before for self-organized critical (SOC) systems. The observations here, therefore, stand as a quantitative support towards viewing interacting socio-economic systems in the framework of SOC, an idea conjectured for years.

physics.soc-ph↗
arXiv2022

Success of Social Inequality Measures in Predicting Critical or Failure Points in Some Models of Physical Systems

Statistical physicists and social scientists both study extensively some characteristic features of the unequal distributions of energy, cluster or avalanche sizes and of income, wealth etc among the particles (or sites) and population respectively. While physicists concentrate on the self-similar (fractal) structure (and the characteristic exponents) of the largest (percolating) cluster or avalanche, social scientists study the inequality indices like Gini and Kolkata etc given by the non-linearity of the Lorenz function representing the cumulative fraction of the wealth possessed by different fraction of the population. We review here, using results from earlier publications and some new numerical as well as analytical results, how the above-mentioned social inequality indices, when extracted from the unequal distributions of energy (in kinetic exchange models), cluster sizes (in percolation models) or avalanche sizes (in self-organized critical or fiber bundle models) can help in a major way in providing precursor signals for an approaching critical point or imminent failure point. Extensive numerical and some analytical results have been discussed.

physics.soc-ph↗
arXiv2021

Kinetic Exchange Income Distribution Models with Saving Propensities: Inequality Indices and Self-Organised Poverty Level

We report the numerical results for the steady state income or wealth distribution $P(m)$ and the resulting inequality measures (Gini $g$ and Kolkata $k$ indices) in the kinetic exchange models of market dynamics. We study the variations of $P(m)$ and of the indices $g$ and $k$ with the saving propensity $λ$ of the agents, with two different kinds of trade (kinetic exchange) dynamics. In the first case, the exchange occurs between randomly chosen pairs of agents and in the next, one of the agents in the chosen pair is the poorest of all and the other agent is randomly picked up from the rest of the population (where, in the steady state, a self-organized poverty level or SOPL appears). These studies have also been made for two different kinds of saving behaviors. One, where each agent has the same value of $λ$ (constant over time) and the other where $λ$ for each agent can take two values (0 and 1), changing randomly over a fraction of time $ρ(<1)$ of choosing $λ= 1$. We find that the inequality decreases with increasing savings ($λ$); inequality indices ($g$ and $k$) decrease and SOPL increases with increasing $λ$, indicating possible applications in economic policy making.

physics.soc-ph↗
arXiv2021

Limiting Value of the Kolkata Index for Social Inequality and a Possible Social Constant

Based on some analytic structural properties of the Gini and Kolkata indices for social inequality, as obtained from a generic form of the Lorenz function, we make a conjecture that the limiting (effective saturation) value of the above-mentioned indices is about 0.865. This, together with some more new observations on the citation statistics of individual authors (including Nobel laureates), suggests that about $14\%$ of people or papers or social conflicts tend to earn or attract or cause about $86\%$ of wealth or citations or deaths respectively in very competitive situations in markets, universities or wars. This is a modified form of the (more than a) century old $80-20$ law of Pareto in economy (not visible today because of various welfare and other strategies) and gives an universal value ($0.86$) of social (inequality) constant or number.

physics.soc-ph↗
arXiv2017

Tracking Urban Human Activity from Mobile Phone Calling Patterns

Timings of human activities are marked by circadian clocks which in turn are entrained to different environmental signals. In an urban environment the presence of artificial lighting and various social cues tend to disrupt the natural entrainment with the sunlight. However, it is not completely understood to what extent this is the case. Here we exploit the large-scale data analysis techniques to study the mobile phone calling activity of people in large cities to infer the dynamics of urban daily rhythms. From the calling patterns of about 1,000,000 users spread over different cities but lying inside the same time-zone, we show that the onset and termination of the calling activity synchronizes with the east-west progression of the sun. We also find that the onset and termination of the calling activity of users follows a yearly dynamics, varying across seasons, and that its timings are entrained to solar midnight. Furthermore, we show that the average mid-sleep time of people living in urban areas depends on the age and gender of each cohort as a result of biological and social factors.

physics.soc-ph↗
arXiv2017

Peer relations with mobile phone data: Best friends and family formation

Earlier attempts to investigate the changes of the role of friendship in different life stages have failed due to lack of data. We close this gap by using a large data set of mobile phone calls from a European country in 2007, to study how the people's call patterns to their close social contacts are associated with age and gender of the callers. We hypothesize that (i) communication with peers, defined as callers of similar age, will be most important during the period of family formation and that (ii) the importance of best friends defined as same-sex callers of exactly the same age, will be stronger for women than for men. Results show that the frequency of phone calls with the same-sex peers in this population turns out to be relatively stable through life for both men and women. In line with the first hypothesis, there was a significant increase in the length of the phone calls for callers between ages 30 to 40 years. Partly in line with the second hypothesis, the increase in phone calls turned out to be particularly pronounced among females, although there were only minor gender differences in call frequencies. Furthermore, women tended to have long phone conversations with their same-age female friend, and also with somewhat older peers. In sum, we provide evidence from big data for the adult life stages at which peers are most important, and suggest that best friends appear to have a niche of their own in human sociality.

physics.soc-ph↗
arXiv2017

Network of families in a contemporary population: regional and cultural assortativity

Using a large dataset with individual-level demographic information of 60,000 families in contemporary Finland, we analyse the variation and cultural assortativity in a network of families. Families are considered as vertices and unions between males and females who have a common child and belong to different families are considered as edges in such a network of families. The sampled network is a collection of many disjoint components with the largest connected component being dominated by families rooted in one specific region. We characterize the network in terms of the basic structural properties and then explore the network transitivity and assortativity with regards to regions of origin and linguistic identity. Transitivity is seen to result from linguistic homophily in the network. Overall, our results demonstrate that geographic proximity and language strongly influence the structuring of network.

physics.soc-ph↗