Merging KK-means with hierarchical clustering for identifying general-shaped groups

Clustering partitions a dataset such that observations placed together in a group are similar but different from those in other groups. Hierarchical and $K$-means clustering are two approaches but have different strengths and weaknesses. For instance, hierarchical clustering identifies groups in a tree-like structure but suffers from computational complexity in large datasets while $K$-means clustering is efficient but designed to identify homogeneous spherically-shaped clusters. We present a hybrid non-parametric clustering approach that amalgamates the two methods to identify general-shaped clusters and that can be applied to larger datasets. Specifically, we first partition the dataset into spherical groups using $K$-means. We next merge these groups using hierarchical methods with a data-driven distance measure as a stopping criterion. Our proposal has the potential to reveal groups with general shapes and structure in a dataset. We demonstrate good performance on several simulated and real datasets.Comment: 16 pages, 1 table, 9 figures; accepted for publication in Sta

Does monetary policy have differential state-level effects? an empirical evaluation

The paper examines whether monetary policy has similar effects across major states in the Indian polity. Impulse response functions from an estimated Structural Vector Auto Regression (SVAR) reveal two sets of states: a core of states that respond to monetary policy in a significant fashion vis-à-vis others whose response is less significant. The paper attempts to trace the reasons for the differential response of these two sets of states in terms of financial deepening and differential industry mix.monetary policy; regional effect; optimum currency area

Planar Two-particle Coulomb Interaction: Classical and Quantum Aspects

The classical and quantum aspects of planar Coulomb interactions have been studied in detail. In the classical scenario, Action Angle Variables are introduced to handle relativistic corrections, in the scheme of time-independent perturbation theory. Complications arising due to the logarithmic nature of the potential are pointed out. In the quantum case, harmonic oscillator approximations are considered and effects of the perturbations on the excited (oscillator) states have been analysed. In both the above cases, the known 3+1-dimensional analysis is carried through side by side, for a comparison with the 2+1-dimensional (planar) results.Comment: LaTex, Figures on request, e-mail:<[email protected]

Observation of the Faraday effect via beam deflection in a longitudinal magnetic field

We report the observation of the magnetic field induced circular differential deflection of light at the interface of a Faraday medium. The difference in the angles of refraction or reflection between the two circular polarization components is a function of the magnetic field strength and the Verdet constant. The reported phenomena permit the observation of the Faraday effect not via polarization rotation in transmission, but via changes in the propagation direction in refraction or in reflection. An unpolarized light beam is predicted to split into its two circular polarization components. The light deflection arises within a few wavelengths at the interface and is therefore independent of pathlength

Low-Mass X-Ray Binaries, Millisecond Radio Pulsars, and the Cosmic Star Formation Rate

We report on the implications of the peak in the cosmic star-formation rate (SFR) at redshift z ~ 1.5 for the resulting population of low-mass X-ray binaries(LMXB) and for that of their descendants, the millisecond radio pulsars (MRP). Since the evolutionary timescales of LMXBs, their progenitors, and their descendants are thought be significant fractions of the time-interval between the SFR peak and the present epoch, there is a lag in the turn-on of the LMXB population, with the peak activity occurring at z ~ 0.5 - 1.0. The peak in the MRP population is delayed further, occurring at z < 0.5. We show that the discrepancy between the birthrate of LMXBs and MRPs, found under the assumption of a stead-state SFR, can be resolved for the population as a whole when the effects of a time-variable SFR are included. A discrepancy may persist for LMXBs with short orbital periods, although a detailed population synthesis will be required to confirm this. Further, since the integrated X-ray luminosity distribution of normal galaxies is dominated by X-ray binaries, it should show strong luminosity evolution with redshift. In addition to an enhancement near the peak (z ~ 1.5) of the SFR due to the prompt turn-on of the relatively short-lived massive X-ray binaries and young supernova remnants, we predict a second enhancement by a factor ~10 at a redshift between ~ 0.5 and ~ 1 due to the delayed turn-on of the LMXB population. Deep X-ray observations of galaxies out to z ~ 1 by AXAF will be able to observe this enhancement, and, by determining its shape as a function of redshift, will provide an important new method for constraining evolutionary models of X-ray binaries.Comment: 13 pages, including 1 figure. Accepted for publication in ApJ Letter

On the orientational ordering of long rods on a lattice

We argue that a system of straight rigid rods of length k on square lattice with only hard-core interactions shows two phase transitions as a function of density, rho, for k >= 7. The system undergoes a phase transition from the low-density disordered phase to a nematic phase as rho is increased from 0, at rho = rho_c1, and then again undergoes a reentrant phase transition from the nematic phase to a disordered phase at rho = rho_c2 < 1.Comment: epl.cl

Warm stellar matter with neutrino trapping

The properties of hybrid stars formed by hadronic and quark matter in beta-equilibrium at fixed entropies are described by appropriate equations of state (EOS) in the framework of relativistic mean-field theory. In this work we include the possibility of neutrino trapped EOS and compare the star properties with the ones obtained after deleptonization, when neutrinos have already diffused out. We use the nonlinear Walecka model for the hadron matter with two different sets for the hyperon couplings and the MIT Bag and the Nambu-Jona-Lasinio models for the quark matter. The phase transition to a deconfined quark phase is investigated. Depending on the model and the parameter set used, the mixed phase may or may not exist in the EOS at high densities. The star properties are calculated for each equation of state. The maximum mass stellar configurations obtained within the NJL have larger masses than the ones obtained within the Bag model. The Bag model predicts a mixed phase in the interior of the most massive stable stars while, depending on the hyperon couplings, the NJL model predicts a mixed phase or pure quark matter. Comparing with neutrino free stars, the maximum allowed baryonic masses for protoneutron stars are $\sim 0.4 M_\odot$ larger for the Bag model and $\sim 0.1 M_\odot$ larger for the NJL model when neutrino trapping is imposed.Comment: 8 pages, 8 figures, 1 tabl