Universal patterns of inequality

Probability distributions of money, income, and energy consumption per capita are studied for ensembles of economic agents. The principle of entropy maximization for partitioning of a limited resource gives exponential distributions for the investigated variables. A non-equilibrium difference of money temperatures between different systems generates net fluxes of money and population. To describe income distribution, a stochastic process with additive and multiplicative components is introduced. The resultant distribution interpolates between exponential at the low end and power law at the high end, in agreement with the empirical data for USA. We show that the increase of income inequality in USA originates primarily from the increase of the income fraction going to the upper tail, which now exceeds 20% of the total income. Analyzing the data from the World Resources Institute, we find that the distribution of energy consumption per capita around the world can be approximately described by the exponential function. Comparing the data for 1990, 2000, and 2005, we discuss the effect of globalization on the inequality of energy consumption.Comment: Accepted to New Journal of Physics. 27 pages (IOP preprint style), 8 figures. V.2: Updated figs. 3 and 8, many references added, all text edited. V.3: Minor changes, last 3 references added. V.4: Minor stylistic changes and reference updates in proof

Satisfiability Modulo Theory based Methodology for Floorplanning in VLSI Circuits

This paper proposes a Satisfiability Modulo Theory based formulation for floorplanning in VLSI circuits. The proposed approach allows a number of fixed blocks to be placed within a layout region without overlapping and at the same time minimizing the area of the layout region. The proposed approach is extended to allow a number of fixed blocks with ability to rotate and flexible blocks (with variable width and height) to be placed within a layout without overlap. Our target in all cases is reduction in area occupied on a chip which is of vital importance in obtaining a good circuit design. Satisfiability Modulo Theory combines the problem of Boolean satisfiability with domains such as convex optimization. Satisfiability Modulo Theory provides a richer modeling language than is possible with pure Boolean SAT formulas. We have conducted our experiments on MCNC and GSRC benchmark circuits to calculate the total area occupied, amount of deadspace and the total CPU time consumed while placing the blocks without overlapping. The results obtained shows clearly that the amount of dead space or wasted space is reduced if rotation is applied to the blocks.Comment: 8 pages,5 figure

A study of the personal income distribution in Australia

We analyze the data on personal income distribution from the Australian Bureau of Statistics. We compare fits of the data to the exponential, log-normal, and gamma distributions. The exponential function gives a good (albeit not perfect) description of 98% of the population in the lower part of the distribution. The log-normal and gamma functions do not improve the fit significantly, despite having more parameters, and mimic the exponential function. We find that the probability density at zero income is not zero, which contradicts the log-normal and gamma distributions, but is consistent with the exponential one. The high-resolution histogram of the probability density shows a very sharp and narrow peak at low incomes, which we interpret as the result of a government policy on income redistribution.Comment: 7 pages, 4 figures, Proceedings of the Econophysics Colloquium, Canberra, 14-18 November 200

On the Stability of Electrostatic Orbits

We analyze the stability of two charged conducting spheres orbiting each other. Due to charge polarization, the electrostatic force between the two spheres deviates significantly from $1/r^2$ as they come close to each other. As a consequence, there exists a critical angular momentum, $L_c$, with a corresponding critical radius $r_c$. For $L > L_c$ two circular orbits are possible: one at $r > r_c$ that is stable and the other at $r < r_c$ that is unstable. This critical behavior is analyzed as a function of the charge and the size ratios of the two spheres.Comment: Added references, corrected typos, clarified languag

Problems Associated with Menstruation among School Going Adolescent Girls and Their Health-Seeking Behavior

Introduction: Start of menstruation among adolescent girls is a major concern, which leads to stress and physical conditions. Objectives: To find menstruation-related problems among the school-going adolescent girls and to assess their health-seeking behavior in relation to these problems.Methodology: A descriptive cross-sectional study was conducted from September 2013 to December 2013 in a government higher secondary school of Pooth Khurd village in North West Delhi, near rural residential health training center of Maulana Azad Medical College. All adolescent girls who gave consent (196 girls) from class 7 to 10 of the selected government higher secondary school were included in the study. A predesigned, pretested, semi-structured questionnaire was used. One of the investigators explained the questions to the respondents. The data was entered in MS-Excel and analyzed using SPSS version 17. Chi-square test and Fischer’s exact test have been used for comparison between proportions. “P” value less than 0.05 is considered to be statistically significant.Results: The mean age of the study participants was 15.31 (±1.35) years, with a range from 13 to 19 years. The mean age of menarche was 13.24 years, minimum reported age of onset of menarche was 10 years and maximum was 16 years. Out of 196 girls, 191 (97.4%) girls have attained menarche, while 57 (29.8%) girls complained of menstrual cycle-related problems, either in the form of irregular menstruation (47) or a current missing period in 10 girls.The school girls also experience a lot of somatic complaints during or just a day prior to onset of menstruation. It was found that a great number (21) of girls expressed their inability to perform simple daily activities owing to painful menstruation along with attending school and playing outdoor games.Only 28 girls (14.7%) would discuss menstrual problems with their mother who most of the time simply advises them to take rest. It was found that only few of them (14%) consult a doctor and few girls told they take self-medication (17.3%) during their painful menstruation

Studies of complex systems in condensed matter physics and economics

This dissertation reports the study of complex systems from two very different fields. The dissertation is divided into two parts. The first part involves study of angular magnetoresistance in quasi-one-dimensional organic conductors and graphene bilayers (chapter 2 and 3). The second part is devoted to the modeling and empirical study of personal income distribution (chapter 4 and 5). First, we study the effect of crystal superstructures, produced by orientational ordering of the ReO4 and ClO4 anions in the quasi-one-dimensional organic conductors (TMTSF)2ReO4 and (TMTSF)2ClO4, on the angular magnetoresistance oscillations (AMRO) observed in these materials. Folding of the Brillouin zone due to anion ordering generates effective tunneling amplitudes between distant chains. These amplitudes cause multiple peaks in interlayer conductivity for the magnetic field orientations along the rational crystallographic directions (the Lebed magic angles). Different wave vectors of the anion ordering in (TMTSF)2ReO4 and (TMTSF)2ClO4 result in the odd and even Lebed angles, as observed experimentally. When a strong magnetic field is applied parallel to the layers and perpendicular the chains and exceeds a certain threshold, the interlayer tunneling between different branches of the folded electron spectrum becomes possible, and interlayer conductivity should increase sharply. This effect can be utilized to probe the anion ordering gaps in (TMTSF)2ClO4 and (TMTSF)4ReO4. An application of this effect to kappa-(ET)2Cu(NCS)2 is also briefly discussed. Next, we study AMRO in graphene bilayers. We calculate the interlayer conductivity and investigate the effects of a parallel magnetic field on the low energy bands of graphene bilayer. Next, we analyze the data on personal income distribution from the Australian Bureau of Statistics. We compare fits of the data to the exponential, log-normal, and gamma distributions. The exponential function gives a good (albeit not perfect) description of 98% of the population in the lower part of the distribution. The log-normal and gamma functions do not improve the fit significantly, despite having more parameters, and mimic the exponential function. We find that the probability density at zero income is not zero, which contradicts the log-normal and gamma distributions, but is consistent with the exponential one. The high-resolution histogram of the probability density shows a very sharp and narrow peak at low incomes, which we interpret as the result of a government policy on income redistribution. We also analyze data on individual income from Internal Revenue Service and University of Maryland. Finally, we discuss a model which captures the two-class structure of income distribution in the USA

Expressing linear equality constraints in feedforward neural networks

We seek to impose linear, equality constraints in feedforward neural networks. As top layer predictors are usually nonlinear, this is a difficult task if we seek to deploy standard convex optimization methods and strong duality. To overcome this, we introduce a new saddle-point Lagrangian with auxiliary predictor variables on which constraints are imposed. Elimination of the auxiliary variables leads to a dual minimization problem on the Lagrange multipliers introduced to satisfy the linear constraints. This minimization problem is combined with the standard learning problem on the weight matrices. From this theoretical line of development, we obtain the surprising interpretation of Lagrange parameters as additional, penultimate layer hidden units with fixed weights stemming from the constraints. Consequently, standard minimization approaches can be used despite the inclusion of Lagrange parameters -- a very satisfying, albeit unexpected, discovery. Examples ranging from multi-label classification to constrained autoencoders are envisaged in the future