Parallel Mapper

The construction of Mapper has emerged in the last decade as a powerful and effective topological data analysis tool that approximates and generalizes other topological summaries, such as the Reeb graph, the contour tree, split, and joint trees. In this paper, we study the parallel analysis of the construction of Mapper. We give a provably correct parallel algorithm to execute Mapper on multiple processors and discuss the performance results that compare our approach to a reference sequential Mapper implementation. We report the performance experiments that demonstrate the efficiency of our method

Modeling of Covalent Bonding in Solids by Inversion of Cohesive Energy Curves

We provide a systematic test of empirical theories of covalent bonding in solids using an exact procedure to invert ab initio cohesive energy curves. By considering multiple structures of the same material, it is possible for the first time to test competing angular functions, expose inconsistencies in the basic assumption of a cluster expansion, and extract general features of covalent bonding. We test our methods on silicon, and provide the direct evidence that the Tersoff-type bond order formalism correctly describes coordination dependence. For bond-bending forces, we obtain skewed angular functions that favor small angles, unlike existing models. As a proof-of-principle demonstration, we derive a Si interatomic potential which exhibits comparable accuracy to existing models.Comment: 4 pages revtex (twocolumn, psfig), 3 figures. Title and some wording (but no content) changed since original submission on 24 April 199

Order-N Density-Matrix Electronic-Structure Method for General Potentials

A new order-N method for calculating the electronic structure of general (non-tight-binding) potentials is presented. The method uses a combination of the ``purification''-based approaches used by Li, Nunes and Vanderbilt, and Daw, and a representation of the density matrix based on ``travelling basis orbitals''. The method is applied to several one-dimensional examples, including the free electron gas, the ``Morse'' bound-state potential, a discontinuous potential that mimics an interface, and an oscillatory potential that mimics a semiconductor. The method is found to contain Friedel oscillations, quantization of charge in bound states, and band gap formation. Quantitatively accurate agreement with exact results is found in most cases. Possible advantages with regard to treating electron-electron interactions and arbitrary boundary conditions are discussed.Comment: 13 pages, REVTEX, 7 postscript figures (not quite perfect

The Theory of the Interleaving Distance on Multidimensional Persistence Modules

In 2009, Chazal et al. introduced $\epsilon$-interleavings of persistence modules. $\epsilon$-interleavings induce a pseudometric $d_I$ on (isomorphism classes of) persistence modules, the interleaving distance. The definitions of $\epsilon$-interleavings and $d_I$ generalize readily to multidimensional persistence modules. In this paper, we develop the theory of multidimensional interleavings, with a view towards applications to topological data analysis. We present four main results. First, we show that on 1-D persistence modules, $d_I$ is equal to the bottleneck distance $d_B$. This result, which first appeared in an earlier preprint of this paper, has since appeared in several other places, and is now known as the isometry theorem. Second, we present a characterization of the $\epsilon$-interleaving relation on multidimensional persistence modules. This expresses transparently the sense in which two $\epsilon$-interleaved modules are algebraically similar. Third, using this characterization, we show that when we define our persistence modules over a prime field, $d_I$ satisfies a universality property. This universality result is the central result of the paper. It says that $d_I$ satisfies a stability property generalizing one which $d_B$ is known to satisfy, and that in addition, if $d$ is any other pseudometric on multidimensional persistence modules satisfying the same stability property, then $d\leq d_I$. We also show that a variant of this universality result holds for $d_B$, over arbitrary fields. Finally, we show that $d_I$ restricts to a metric on isomorphism classes of finitely presented multidimensional persistence modules.Comment: Major revision; exposition improved throughout. To appear in Foundations of Computational Mathematics. 36 page

SUMER Observations Confirm the Dynamic Nature of the Quiet Solar Outer Atmosphere: The Inter-network Chromosphere

On 12 March 1996 we obtained observations of the quiet Sun with the SUMER instrument. The observa- tions were sequences of 15-20 second exposures of ultraviolet emission line profiles and of the neighboring continua. These data contain signatures of the dynamics of the solar chromosphere that are uniquely useful because of wavelength coverage, moderate signal-to-noise ratios, and image stability. The dominant observed phenomenon is an oscillatory behavior that is analogous to the 3 minute oscillations seen in Ca II lines. The oscillations appear to be coherent over 3-8". At any time they occur over approx. 50 % of the area studied, and they appear as large perturbations in the intensities of lines and continua. The oscillations are most clearly seen in intensity variations in the UV (lambda > 912 A) continua, and they are also seen in the intensities and velocities of chromospheric lines of C I, N I and O I. Intensity brightenings are accompanied by blueshifts of typically 5 km s$^{-1}$. Phase differences between continuum and line intensities also indicate the presence of upward propagating waves. Three minute intensity oscillations are occasionally seen in second spectra (C II 1335), but never in third spectra (C III and Si III). Third spectra and He I 584 show oscillations in velocity that are not simply related to the 3 minute oscillations. The continuum intensity variations are consistent with recent simulations of chromospheric dynamics (Carlsson & Stein 1994) while the line observations indicate that important ingredients are missing at higher layers in the simulations. The data show that time variations are crucial for our understanding of the chromosphere itself and for the spectral features formed there.Comment: 8 pages, 3 figs, AASTeX, Accepted for publication in APJ letter

Collective vibrational states with fast iterative QRPA method

An iterative method we previously proposed to compute nuclear strength functions is developed to allow it to accurately calculate properties of individual nuclear states. The approach is based on the quasi-particle-random-phase approximation (QRPA) and uses an iterative non-hermitian Arnoldi diagonalization method where the QRPA matrix does not have to be explicitly calculated and stored. The method gives substantial advantages over conventional QRPA calculations with regards to the computational cost. The method is used to calculate excitation energies and decay rates of the lowest lying 2+ and 3- states in Pb, Sn, Ni and Ca isotopes using three different Skyrme interactions and a separable gaussian pairing force.Comment: 10 pages, 11 figure