An optimal network for passenger traffic

The optimal solution of an inter-city passenger transport network has been studied using Zipf's law for the city populations and the Gravity law describing the fluxes of inter-city passenger traffic. Assuming a fixed value for the cost of transport per person per kilometer we observe that while the total traffic cost decreases, the total wiring cost increases with the density of links. As a result the total cost to maintain the traffic distribution is optimal at a certain link density which vanishes on increasing the network size. At a finite link density the network is scale-free. Using this model the air-route network of India has been generated and an one-to-one comparison of the nodal degree values with the real network has been made.Comment: 5 pages, 4 figure

Scale-free network on a vertical plane

A scale-free network is grown in the Euclidean space with a global directional bias. On a vertical plane, nodes are introduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodes which are below it using the attachment probability: $\pi_i(t) \sim k_i(t)\ell^{\alpha}$. Our numerical results indicate that the directed scale-free network for $\alpha=0$ belongs to a different universality class compared to the isotropic scale-free network. For $\alpha < \alpha_c$ the degree distribution is stretched exponential in general which takes a pure exponential form in the limit of $\alpha \to -\infty$. The link length distribution is calculated analytically for all values of $\alpha$.Comment: 4 pages, 4 figure

Review of Viola, L.A. (2020) The closure of the international system: how institutions create political equalities and hierarchies

History and International Relation

Naked Singularity Explosion

It is known that the gravitational collapse of a dust ball results in naked singularity formation from an initial density profile which is physically reasonable. In this paper, we show that explosive radiation is emitted during the formation process of the naked singularity.Comment: 6 pages, 3 figures, Accepted for Publication in Phys. Rev. D as a Rapid Communicatio

Role of Initial Data in Higher Dimensional Quasi-Spherical Gravitational Collapse

We study the gravitational collapse in ($n+2$)-D quasi-spherical Szekeres space-time (which possess no killing vectors) with dust as the matter distribution. Instead of choosing the radial coordinate `$r$' as the initial value for the scale factor $R$, we consider a power function of $r$ as the initial scale for the radius $R$. We examine the influence of initial data on the formation of singularity in gravitational collapse.Comment: 7 Latex Pages, RevTex Style, No figure

Persistence in a Stationary Time-series

We study the persistence in a class of continuous stochastic processes that are stationary only under integer shifts of time. We show that under certain conditions, the persistence of such a continuous process reduces to the persistence of a corresponding discrete sequence obtained from the measurement of the process only at integer times. We then construct a specific sequence for which the persistence can be computed even though the sequence is non-Markovian. We show that this may be considered as a limiting case of persistence in the diffusion process on a hierarchical lattice.Comment: 8 pages revte

Higher dimensional inhomogeneous dust collapse and cosmic censorship

We investigate the occurrence and nature of a naked singularity in the gravitational collapse of an inhomogeneous dust cloud described by higher dimensional Tolman-Bondi space-times. The naked singularities are found to be gravitationally strong in the sense of Tipler. Higher dimensions seem to favour black holes rather than naked singularities.Comment: 15 pages, LaTeX, 1 figure, 2 table

U.S. stock market interaction network as learned by the Boltzmann Machine

We study historical dynamics of joint equilibrium distribution of stock returns in the U.S. stock market using the Boltzmann distribution model being parametrized by external fields and pairwise couplings. Within Boltzmann learning framework for statistical inference, we analyze historical behavior of the parameters inferred using exact and approximate learning algorithms. Since the model and inference methods require use of binary variables, effect of this mapping of continuous returns to the discrete domain is studied. The presented analysis shows that binarization preserves market correlation structure. Properties of distributions of external fields and couplings as well as industry sector clustering structure are studied for different historical dates and moving window sizes. We found that a heavy positive tail in the distribution of couplings is responsible for the sparse market clustering structure. We also show that discrepancies between the model parameters might be used as a precursor of financial instabilities.Comment: 15 pages, 17 figures, 1 tabl

Higher dimensional dust collapse with a cosmological constant

The general solution of the Einstein equation for higher dimensional (HD) spherically symmetric collapse of inhomogeneous dust in presence of a cosmological term, i.e., exact interior solutions of the Einstein field equations is presented for the HD Tolman-Bondi metrics imbedded in a de Sitter background. The solution is then matched to exterior HD Scwarschild-de Sitter. A brief discussion on the causal structure singularities and horizons is provided. It turns out that the collapse proceed in the same way as in the Minkowski background, i.e., the strong curvature naked singularities form and that the higher dimensions seem to favor black holes rather than naked singularities.Comment: 7 Pages, no figure

Anomalous Transport from Kubo Formulae

Chiral anomalies have profound impact on the transport properties of relativistic fluids. In four dimensions there are different types of anomalies, pure gauge and mixed gauge-gravitational anomalies. They give rise to two new non-dissipative transport coefficients, the chiral magnetic conductivity and the chiral vortical conductivity. They can be calculated from the microscopic degrees of freedom with the help of Kubo formulae. We review the calculation of the anomalous transport coefficients via Kubo formulae with a particular emphasis on the contribution of the mixed gauge-gravitational anomaly.Comment: 36 pages, 4 figures, 1 table; to appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Yee; v2 small changes in introduction, added references; v3 corrected eq. (21) and added eq. (77), added reference