Inequality reversal: Effects of the savings propensity and correlated returns

In the last decade, a large body of literature has been developed to explain the universal features of inequality in terms of income and wealth. By now, it is established that the distributions of income and wealth in various economies show a number of statistical regularities. There are several models to explain such static features of inequality in a unifying framework, and the kinetic exchange models in particular provide one such framework. Here we focus on the dynamic features of inequality. In the process of development and growth, inequality in an economy in terms of income and wealth follows a particular pattern of rising in the initial stage followed by an eventual fall. This inverted U-shaped curve is known as the Kuznets Curve. We examine the possibilities of such behavior of an economy in the context of a generalized kinetic exchange model. It is shown that under some specific conditions, our model economy indeed shows inequality reversal.     

Effect of Savings on a Gas-Like Model Economy with Credit and Debt

In kinetic exchange models, agents make transactions based on well-established microscopic rules that give rise to macroscopic variables in analogy to statistical physics. These models have been applied to study processes such as income and wealth distribution, economic inequality sources, economic growth, etc., recovering well-known concepts in the economic literature. In this work, we apply ensemble formalism to a geometric agents model to study the effect of saving propensity in a system with money, credit, and debt. We calculate the partition function to obtain the total money of the system, with which we give an interpretation of the economic temperature in terms of the different payment methods available to the agents. We observe an interplay between the fraction of money that agents can save and their maximum debt. The system’s entropy increases as a function of the saved proportion, and increases even more when there is debt.     

Discretized kinetic theory on scale-free networks

The network of interpersonal connections is one of the possible heterogeneous factors which affect the income distribution emerging from micro-to-macro economic models. In this paper we equip our model discussed in [1, 2] with a network structure. The model is based on a system of n differential equations of the kinetic discretized-Boltzmann kind. The network structure is incorporated in a probabilistic way, through the introduction of a link density P(α) and of correlation coefficients P(β|α), which give the conditioned probability that an individual with α links is connected to one with β links. We study the properties of the equations and give analytical results concerning the existence, normalization and positivity of the solutions. For a fixed network with P(α) = c/α^q, we investigate numerically the dependence of the detailed and marginal equilibrium distributions on the initial conditions and on the exponent q. Our results are compatible with those obtained from the Bouchaud-Mezard model and from agent-based simulations, and provide additional information about the dependence of the individual income on the level of connectivity.     

An almost linear stochastic map related to the particle system models of social sciences

We propose a stochastic map model of economic dynamics. In the past decade, an array of observations in economics has been investigated in the econophysics literature, a major example being the universal features of inequality in terms of income and wealth. Another area of enquiry is the formation of opinion in a society. The model proposed attempts to produce positively skewed distributions and power law distributions as has been observed in the real data of income and wealth. Also, it shows a non-trivial phase transition in the opinion of a society (opinion formation). A number of physical models also generate similar results. In particular, kinetic exchange models have been successful especially in this regard. Therefore, we compare the results obtained from these two approaches and discuss a number of new features and drawbacks of this model.     

Molecular dynamics in concentrated sugar solutions and glasses: an NMR field cycling study

The frequency dependence of the proton longitudinal relaxation time in concentrated sugar in water solutions and glasses is compared with various theoretical models and used to derive correlation times characterizing the dynamic state of the water and sugar. It is shown that the water retains a high degree of molecular mobility even in the ‘sugar glass’, while the spectral density of the 3-dimensional glass lattice shows no evidence for a distribution of correlation times.     

From microscopic taxation and redistribution models to macroscopic income distributions

We present here a general framework, expressed by a system of nonlinear differential equations, suitable for the modeling of taxation and redistribution in a closed society. This framework allows one to describe the evolution of income distribution over the population and to explain the emergence of collective features based on knowledge of the individual interactions. By making different choices of the framework parameters, we construct different models, whose long-time behavior is then investigated. Asymptotic stationary distributions are found, which enjoy similar properties as those observed in empirical distributions. In particular, they exhibit power law tails of Pareto type and their Lorenz curves and Gini indices are consistent with some real world ones.     

An equilibrium-conserving taxation scheme for income from capital

Under conditions of market equilibrium, the distribution of capital income follows a Pareto power law, with an exponent that characterizes the given equilibrium. Here, a simple taxation scheme is proposed such that the post-tax capital income distribution remains an equilibrium distribution, albeit with a different exponent. This taxation scheme is shown to be progressive, and its parameters can be simply derived from (i) the total amount of tax that will be levied, (ii) the threshold selected above which capital income will be taxed and (iii) the total amount of capital income. The latter can be obtained either by using Piketty’s estimates of the capital/labor income ratio or by fitting the initial Pareto exponent. Both ways moreover provide a check on the amount of declared income from capital.     

Estimating income mobility using census data

This study uses the entropy method to overcome the problem with estimating income distribution dynamics in the absence of data that allow identifying and following up economic units over time. The axiomatic mobility approach (Shorrocks, 1976) [1] and the tools developed by Aebi et al. (1999) [2] were considered. This strategy assumes that income mobility between two time periods is governed by a first-order Markov process. In this context, the measurement of the dynamics of income distribution will be equivalent to fitting cell probabilities for contingency tables, where only marginal distributions are observed. Results suggest that Brazil has low intragenerational income mobility, indicating that its social framework is relatively rigid. In other words, the income class in which an individual is inserted will determine his/her future social position.     

Evidence for the Gompertz curve in the income distribution of Brazil 1978–2005

This work presents an empirical study of the evolution of the personal income distribution in Brazil. Yearly samples available from 1978 to 2005 were studied and evidence was found that the complementary cumulative distribution of personal income for 99% of the economically less favorable population is well represented by a Gompertz curve of the form G(x) = exp [exp (A-Bx)], where x is the normalized individual income. The complementary cumulative distribution of the remaining 1% richest part of the population is well represented by a Pareto power law distribution P(x) = βx^-α. This result means that similarly to other countries, Brazil’s income distribution is characterized by a well defined two class system. The parameters A, B, α, β were determined by a mixture of boundary conditions, normalization and fitting methods for every year in the time span of this study. Since the Gompertz curve is characteristic of growth models, its presence here suggests that these patterns in income distribution could be a consequence of the growth dynamics of the underlying economic system. In addition, we found out that the percentage share of both the Gompertzian and Paretian components relative to the total income shows an approximate cycling pattern with periods of about 4 years and whose maximum and minimum peaks in each component alternate at about every 2 years. This finding suggests that the growth dynamics of Brazil’s economic system might possibly follow a Goodwin-type class model dynamics based on the application of the Lotka-Volterra equation to economic growth and cycle.     

Regional changes in the distribution of foreign aid: An entropy approach

Foreign aid contributes significantly to the income levels and economic viability of many developing countries. This paper investigates the dispersion in the distribution of foreign aid using the Theil entropy measure of inequality. Results show that the inequality (dispersion) of foreign aid has increased substantially in recent years. The increased inequality in the total distribution of aid has been due to both increases in the regional inequality of aid and increases in the average inequality of aid within each region. As a result, the distribution of aid is becoming less alike between regions and between countries within regions.     

Two-dimensional models of expanding vacuum arc plasmas

Multifluid equations describing the plasma of vacuum arcs expanding anisotropically from a cathode spot are given and discussed. Some first and preliminary results from an approximate analytical integration of such a system of equations, based on the representation of all plasma parameters by asymptotic power series, are presented and evaluated. Though the dependence of the plasma parameters on the direction (angle ϑ) is weak, the inclusion of angular terms and angular equations changes some results significantly, compared with the experiences from usually 1-D models. While the basic radial dependence (r) of the terms ~r^-2k/5, k=0,1,2..., remains the same as in 1-D theories, we now get an angular dependence ~ϑ² of the parameters in a first approximation, with positive factors, i.e., a flattening of the whole plasma distribution. However, with analytical solutions of higher flexibility, cos-like distributions are possible as well. The final kinetic energy of the plasma ions in the case of Cu arc spots is caused by the electric field within the plasma (contributing approximately 27%), the ion pressure gradient (~24%), and the electron-ion friction (plasma resistivity, ~49%) in directions near to the discharge axis. Again, similar to the results from 1-D models. With an approach to the cathode surface (ϑ→π/2), the plasma flow becomes ambipolar. Finally, some further possibilities which are available with the help of this model are discussed     

About the modified Gaussian family of income distributions with applications to individual incomes

In a recent paper in this journal [Q. Guo, L. Gao, Distribution of individual incomes in China between 1992 and 2009, Physica A 391 (2012) 5139–5145], a new family of distributions for modeling individual incomes in China was proposed. This family is the so-called Modified Gaussian (MG) distribution, which depends on two parameters. The MG distribution shows a satisfactory fit for the individual income data between 1992 and 2009. However, for the practical use of this model with individual incomes, it is necessary to know its probabilistic and statistical properties, especially the corresponding inequality measures. In this paper, probabilistic functions and inequality measures of the MG distribution are obtained in closed form, including the normalizing constant, probability functions, moments, first-degree stochastic dominance conditions, relationships with other families of distributions and standard tools for inequality measurement (Lorenz and generalized Lorenz curves and Gini, Donaldson–Weymark–Kakwani and Pietra indices). Several methods for parameter estimation are also discussed. In order to illustrate all the previous formulations, we have fitted individual incomes of Spain for three years using the European community household panel survey, concluding a static pattern of inequality, since the Gini index and other inequality measures remain constant over the study period.     

Kinetic models for diffusion generated by an external force

Two kinetic models are used to study the homogeneous color diffusion problem in a dilute binary mixture. Both kinetic models incorporate a temperature dependence in the collision frequencies, which allows for the consideration of a general repulsive molecular interaction. The main transport properties as well as the velocity distribution functions are explicitly obtaines in terms of the field strength and the parameters characterizing the mixture. The results are illustrated for the two extreme cases of Maxwell molecules and hard spheres. A comparison between both models and with previous results derived from the Boltzmann equation for Maxwell molecules is carried out.     

Kinetic models for optimal control of wealth inequalities

We introduce and discuss optimal control strategies for kinetic models for wealth distribution in a simple market economy, acting to minimize the variance of the wealth density among the population. Our analysis is based on a finite time horizon approximation, or model predictive control, of the corresponding control problem for the microscopic agents’ dynamic and results in an alternative theoretical approach to the taxation and redistribution policy at a global level. It is shown that in general the control is able to modify the Pareto index of the stationary solution of the corresponding Boltzmann kinetic equation, and that this modification can be exactly quantified. Connections between previous Fokker–Planck based models for taxation-redistribution policies and the present approach are also discussed.     

Socioeconomic Patterns of Twitter User Activity

Stratifying behaviors based on demographics and socioeconomic status is crucial for political and economic planning. Traditional methods to gather income and demographic information, like national censuses, require costly large-scale surveys both in terms of the financial and the organizational resources needed for their successful collection. In this study, we use data from social media to expose how behavioral patterns in different socioeconomic groups can be used to infer an individual’s income. In particular, we look at the way people explore cities and use topics of conversation online as a means of inferring individual socioeconomic status. Privacy is preserved by using anonymized data, and abstracting human mobility and online conversation topics as aggregated high-dimensional vectors. We show that mobility and hashtag activity are good predictors of income and that the highest and lowest socioeconomic quantiles have the most differentiated behavior across groups.     

Single-particle space-momentum angle distribution effect on two-pion HBT correlation in high-energy heavy-ion collisions

We analyze the transverse momentum dependence of HBT radii in relativistic heavy-ion collisions using several source models.Results indicate that the single-particle space-momentum angle distribution plays an important role in the transverse momentum dependence of HBT radii.In a cylinder source,we use several formulas to describe the transverse momentum dependence of HBT radii and the single-particle space-momentum angle distribution.We also make a numerical connection between them in the transverse plane.     

The determination of the Coulomb energy of a nuclear system at the scission point upon fission

The dependence of the Coulomb energy of deformed nuclei on the shape and the nuclear matter density distribution is considered. For an ellipsoidal shape of the nucleus and a homogeneous distribution of nuclear matter, the result was obtained in a simple analytical form convenient for further use. Separate attention was paid to the consideration of a Fermi-like distribution of nuclear matter using different shapes of the nucleus that reflect several different kinds of collective motions. After these considerations, the dependence of the Coulomb energy of the fission products at the scission point of binary fission reactions on configurations, shapes and nuclear matter distributions was investigated. Calculation of the dependence of the shape of the nuclei deformation parameters at the scission point from their total kinetic energies was made in detail. Finally, the influence of shell effects on the mass yield of fission products is discussed. The text was submitted by the authors in English.     

Theil Entropy as a Non-Lineal Analysis for Spectral Inequality of Physiological Oscillations

Theil entropy is a statistical measure used in economics to quantify income inequalities. However, it can be applied to any data distribution including biological signals. In this work, we applied different spectral methods on heart rate variability signals and cellular calcium oscillations previously to Theil entropy analysis. The behavior of Theil entropy and its decomposable property was investigated using exponents in the range of [−1, 2], on the spectrum of synthetic and physiological signals. Our results suggest that the best spectral decomposition method to analyze the spectral inequality of physiological oscillations is the Lomb–Scargle method, followed by Theil entropy analysis. Moreover, our results showed that the exponents that provide more information to describe the spectral inequality in the tested signals were zero, one, and two. It was also observed that the intra-band component is the one that contributes the most to total inequality for the studied oscillations. More in detail, we found that in the state of mental stress, the inequality determined by the Theil entropy analysis of heart rate increases with respect to the resting state. Likewise, the same analytical approach shows that cellular calcium oscillations present on developing interneurons display greater inequality distribution when inhibition of a neurotransmitter system is in place. In conclusion, we propose that Theil entropy is useful for analyzing spectral inequality and to explore its origin in physiological signals.     

Analytical model of a corona discharge from a conical electrode under saturation

Exact partial solutions are found for the electric field distribution in the outer region of a stationary unipolar corona discharge from an ideal conical needle in the space-charge-limited current mode with allowance for the electric field dependence of the ion mobility. It is assumed that only the very tip of the cone is responsible for the discharge, i.e., that the ionization zone is a point. The solutions are obtained by joining the spherically symmetric potential distribution in the drift space and the self-similar potential distribution in the space-charge-free region. Such solutions are outside the framework of the conventional Deutsch approximation, according to which the space charge insignificantly influences the shape of equipotential surfaces and electric lines of force. The dependence is derived of the corona discharge saturation current on the apex angle of the conical electrode and applied potential difference. A simple analytical model is suggested that describes drift in the point-plane electrode geometry under saturation as a superposition of two exact solutions for the field potential. In terms of this model, the angular distribution of the current density over the massive plane electrode is derived, which agrees well with Warburg??s empirical law.     

Remarks on the Calculation of Eigenvalues and Generalized Eigenfunctions Using a Finite Dimensional Approximation for the Inscattering Part of the Boltzmann Collision Operator

From several points of view it is of advantage to know the properties of the collision operators in kinetic equations, e.g. in the well known Boltzmann equation, in particular for the purpose of solving eigenvalue problems. With regard to elastic, exciting and deexciting processes some attemps were recently made to investigate such operators in the Boltzmann equation describing the behaviour of electrons in weakly ionized plasmas. In the following we will prove that in the case of a finite dimensional inscattering operator the eigenvalues and the corresponding eigenfunctions can be represented explicitly. Finite dimensional operators were used successfully in special models to approximate the inscattering operators; they possess the property of compactness and are well suitable for analytical or numerical calculations. The representation has been obtained by solving an adequate linear equation system. The generalized eigenfunctions correspond to the normal solutions used by Case in the neutron transport theory. The regularization of the singular integrals which are necessary to obtain this solution will be given in detail. Further a velocity dependence of the collision frequency which need not be monotonous in the considered case and the dependence on the direction could be included.