RAM-Efficient External Memory Sorting

In recent years a large number of problems have been considered in external memory models of computation, where the complexity measure is the number of blocks of data that are moved between slow external memory and fast internal memory (also called I/Os). In practice, however, internal memory time often dominates the total running time once I/O-efficiency has been obtained. In this paper we study algorithms for fundamental problems that are simultaneously I/O-efficient and internal memory efficient in the RAM model of computation.Comment: To appear in Proceedings of ISAAC 2013, getting the Best Paper Awar

Energy levels and radiative rates for transitions in Fe V, Co VI and Ni VII

Energy levels, Land\'{e} $g$-factors and radiative lifetimes are reported for the lowest 182 levels of the 3d$^4$, 3d$^3$4s and 3d$^3$4p configurations of Fe~V, Co~VI and Ni~VII. Additionally, radiative rates ($A$-values) have been calculated for the E1, E2 and M1 transitions among these levels. The calculations have been performed in a quasi-relativistic approach (QR) with a very large {\em configuration interaction} (CI) wavefunction expansion, which has been found to be necessary for these ions. Our calculated energies for all ions are in excellent agreement with the available measurements, for most levels. Discrepancies among various calculations for the radiative rates of E1 transitions in Fe~V are up to a factor of two for stronger transitions ($f \geq 0.1$), and larger (over an order of magnitude) for weaker ones. The reasons for these discrepancies have been discussed and mainly are due to the differing amount of CI and methodologies adopted. However, there are no appreciable discrepancies in similar data for M1 and E2 transitions, or the $g$-factors for the levels of Fe~V, the only ion for which comparisons are feasible.Comment: This paper of 78 pages including 9 Tables will appear in ADNDT (2016

Cumulative effect of Weibel-type instabilities in counterstreaming plasmas with non-Maxwellian anisotropies

Counterstreaming plasma structures are widely present in laboratory experiments and astrophysical systems, and they are investigated either to prevent unstable modes arising in beam-plasma experiments or to prove the existence of large scale magnetic fields in astrophysical objects. Filamentation instability arises in a counterstreaming plasma and is responsible for the magnetization of the plasma. Filamentationally unstable mode is described by assuming that each of the counterstreaming plasmas has an isotropic Lorentzian (kappa) distribution. In this case, the filamentation instability growth rate can reach a maximum value markedly larger than that for a a plasma with a Maxwellian distribution function. This behaviour is opposite to what was observed for the Weibel instability growth rate in a bi-kappa plasma, which is always smaller than that obtained for a bi-Maxwellian plasma. The approach is further generalized for a counterstreaming plasma with a bi-kappa temperature anisotropy. In this case, the filamentation instability growth rate is enhanced by the Weibel effect when the plasma is hotter in the streaming direction, and the growth rate becomes even larger. These effects improve significantly the efficiency of the magnetic field generation, and provide further support for the potential role of the Weibel-type instabilities in the fast magnetization scenarios

Experimental Signatures of Anomaly Induced DCC Formation

We discuss characteristic experimental signatures related to the formation of domains of disoriented chiral condensate (DCC) triggered by the axial anomaly in relativistic heavy ion collisions. We predict that the enhancement of the fraction of neutral pions compared to all pions depends on the angle of emission with respect to the scattering plane and is concentrated at small transverse momentum and small rapidity in the center-of-mass frame. The anisotropy with respect to the reaction plane is also observable in the inclusive photon distribution.Comment: 11 pages, 4 figures, REVTEX, discussion on photon distribution added, one figure adde

Interferometry of direct photons in Pb+Pb collisions at 158 AGeV

We present final results from the WA98 experiment which provide first measurements of Bose-Einstein correlations of direct photons in ultrarelativistic heavy ion collisions. Invariant interferometric radii were extracted in the range $100<K_T<300$ MeV/c and compared to interferometric radii of charged pions. The yield of direct photons for $100<p_T<300$ MeV/c was extracted from the correlation strength parameter and compared to the yield of direct photons measured in WA98 at higher $p_T$ with the statistical subtraction method, and to predictions of a fireball model.Comment: 4 pages, 3 figures, proceedings for Quark Matter 200

Energy levels and radiative rates for transitions in Cr-like Co IV and Ni V

We report calculations of energy levels and radiative rates ($A$-values) for transitions in Cr-like Co IV and Ni V. The quasi-relativistic Hartree-Fock (QRHF) code is adopted for calculating the data although GRASP (general-purpose relativistic atomic structure package) and flexible atomic code (FAC) have also been employed for comparison purposes. No radiative rates are available in the literature to compare with our results, but our calculated energies are in close agreement with those compiled by NIST for a majority of the levels. However, there are discrepancies for a few levels of up to 3\%. The $A$-values are listed for all significantly contributing E1, E2 and M1 transitions, and the corresponding lifetimes reported, although unfortunately no previous theoretical or experimental results exist to compare with our data.Comment: The paper will appear in ADNDT (2016) and in October 2015 on the we

Electron Impact Excitation Cross Sections for Hydrogen-Like Ions

We present cross sections for electron-impact-induced transitions n --> n' in hydrogen-like ions C 5+, Ne 9+, Al 12+, and Ar 17+. The cross sections are computed by Coulomb-Born with exchange and normalization (CBE) method for all transitions with n < n' < 7 and by convergent close-coupling (CCC) method for transitions with n 2s and 1s --> 2p are presented as well. The CCC and CBE cross sections agree to better than 10% with each other and with earlier close-coupling results (available for transition 1 --> 2 only). Analytical expression for n --> n' cross sections and semiempirical formulae are discussed.Comment: RevTeX, 5 pages, 13 PostScript figures, submitted to Phys. Rev.

A tight lower bound instance for k-means++ in constant dimension

The k-means++ seeding algorithm is one of the most popular algorithms that is used for finding the initial $k$ centers when using the k-means heuristic. The algorithm is a simple sampling procedure and can be described as follows: Pick the first center randomly from the given points. For $i > 1$, pick a point to be the $i^{th}$ center with probability proportional to the square of the Euclidean distance of this point to the closest previously $(i-1)$ chosen centers. The k-means++ seeding algorithm is not only simple and fast but also gives an $O(\log{k})$ approximation in expectation as shown by Arthur and Vassilvitskii. There are datasets on which this seeding algorithm gives an approximation factor of $\Omega(\log{k})$ in expectation. However, it is not clear from these results if the algorithm achieves good approximation factor with reasonably high probability (say $1/poly(k)$). Brunsch and R\"{o}glin gave a dataset where the k-means++ seeding algorithm achieves an $O(\log{k})$ approximation ratio with probability that is exponentially small in $k$. However, this and all other known lower-bound examples are high dimensional. So, an open problem was to understand the behavior of the algorithm on low dimensional datasets. In this work, we give a simple two dimensional dataset on which the seeding algorithm achieves an $O(\log{k})$ approximation ratio with probability exponentially small in $k$. This solves open problems posed by Mahajan et al. and by Brunsch and R\"{o}glin.Comment: To appear in TAMC 2014. arXiv admin note: text overlap with arXiv:1306.420