Global Income Inequality and Savings: A Data Science Perspective

A society or country with income equally distributed among its people is truly a fiction! The phenomena of socioeconomic inequalities have been plaguing mankind from times immemorial. We are interested in gaining an insight about the co-evolution of the countries in the inequality space, from a data science perspective. For this purpose, we use the time series data for Gini indices of different countries, and construct the equal-time cross-correlation matrix. We then use this to construct a similarity matrix and generate a map with the countries as different points generated through a multi-dimensional scaling technique. We also produce a similar map of different countries using the time series data for Gross Domestic Savings (% of GDP). We also pose a different, yet significant, question: Can higher savings moderate the income inequality? In this paper, we have tried to address this question through another data science technique - linear regression, to seek an empirical linkage between the income inequality and savings, mainly for relatively small or closed economies. This question was inspired from an existing theoretical model proposed by Chakraborti-Chakrabarti (2000), based on the principle of kinetic theory of gases. We tested our model empirically using Gini index and Gross Domestic Savings, and observed that the model holds reasonably true for many economies of the world.Comment: 8 pages, 6 figures. IEEE format. Accepted for publication in 5th IEEE DSAA 2018 conference at Torino, Ital

Discrete Data Assimilation in the Lorenz and 2D Navier--Stokes Equations

Consider a continuous dynamical system for which partial information about its current state is observed at a sequence of discrete times. Discrete data assimilation inserts these observational measurements of the reference dynamical system into an approximate solution by means of an impulsive forcing. In this way the approximating solution is coupled to the reference solution at a discrete sequence of points in time. This paper studies discrete data assimilation for the Lorenz equations and the incompressible two-dimensional Navier--Stokes equations. In both cases we obtain bounds on the time interval h between subsequent observations which guarantee the convergence of the approximating solution obtained by discrete data assimilation to the reference solution

Comments on F-maximization and R-symmetry in 3D SCFTs

We report preliminary results on the recently proposed F-maximization principle in 3D SCFTs. We compute numerically in the large-N limit the free energy on the three-sphere of an N=2 Chern-Simons-Matter theory with a single adjoint chiral superfield which is known to exhibit a pattern of accidental symmetries associated to chiral superfields that hit the unitarity bound and become free. We observe that the F-maximization principle produces a U(1) R-symmetry consistent with previously obtained bounds but inconsistent with a postulated Seiberg-like duality. Potential modifications of the principle associated to the decoupling fields do not appear to be sufficient to account for the observed violations.Comment: 17 pages, 3 figures; v2 a reference has been added, a missing factor of 2 has been corrected in eq (3.3) and the numerical results have been accordingly updated. The new results do not show any obvious signs of violation of previously obtained bounds. A potential disagreement with a postulated Seiberg-like duality is note

An entropic approach to local realism and noncontextuality

For any Bell locality scenario (or Kochen-Specker noncontextuality scenario), the joint Shannon entropies of local (or noncontextual) models define a convex cone for which the non-trivial facets are tight entropic Bell (or contextuality) inequalities. In this paper we explore this entropic approach and derive tight entropic inequalities for various scenarios. One advantage of entropic inequalities is that they easily adapt to situations like bilocality scenarios, which have additional independence requirements that are non-linear on the level of probabilities, but linear on the level of entropies. Another advantage is that, despite the nonlinearity, taking detection inefficiencies into account turns out to be very simple. When joint measurements are conducted by a single detector only, the detector efficiency for witnessing quantum contextuality can be arbitrarily low.Comment: 12 pages, 8 figures, minor mistakes correcte

Numerical Evidence that the Perturbation Expansion for a Non-Hermitian PT\mathcal{PT}-Symmetric Hamiltonian is Stieltjes

Recently, several studies of non-Hermitian Hamiltonians having $\mathcal{PT}$ symmetry have been conducted. Most striking about these complex Hamiltonians is how closely their properties resemble those of conventional Hermitian Hamiltonians. This paper presents further evidence of the similarity of these Hamiltonians to Hermitian Hamiltonians by examining the summation of the divergent weak-coupling perturbation series for the ground-state energy of the $\mathcal{PT}$-symmetric Hamiltonian $H=p^2+{1/4}x^2+i\lambda x^3$ recently studied by Bender and Dunne. For this purpose the first 193 (nonzero) coefficients of the Rayleigh-Schr\"odinger perturbation series in powers of $\lambda^2$ for the ground-state energy were calculated. Pad\'e-summation and Pad\'e-prediction techniques recently described by Weniger are applied to this perturbation series. The qualitative features of the results obtained in this way are indistinguishable from those obtained in the case of the perturbation series for the quartic anharmonic oscillator, which is known to be a Stieltjes series.Comment: 20 pages, 0 figure