6,944 research outputs found
The Theory of the Interleaving Distance on Multidimensional Persistence Modules
In 2009, Chazal et al. introduced -interleavings of persistence
modules. -interleavings induce a pseudometric on (isomorphism
classes of) persistence modules, the interleaving distance. The definitions of
-interleavings and 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,
is equal to the bottleneck distance . 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 -interleaving relation on multidimensional
persistence modules. This expresses transparently the sense in which two
-interleaved modules are algebraically similar. Third, using this
characterization, we show that when we define our persistence modules over a
prime field, satisfies a universality property. This universality result
is the central result of the paper. It says that satisfies a stability
property generalizing one which is known to satisfy, and that in
addition, if is any other pseudometric on multidimensional persistence
modules satisfying the same stability property, then . We also show
that a variant of this universality result holds for , over arbitrary
fields. Finally, we show that 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
Giant Monopole Resonances and nuclear incompressibilities studied for the zero-range and separable pairing interactions
Background: Following the 2007 precise measurements of monopole strengths in
tin isotopes, there has been a continuous theoretical effort to obtain a
precise description of the experimental results. Up to now, there is no
satisfactory explanation of why the tin nuclei appear to be significantly
softer than 208Pb.
Purpose: We determine the influence of finite-range and separable pairing
interactions on monopole strength functions in semi-magic nuclei.
Methods: We employ self-consistently the Quasiparticle Random Phase
Approximation on top of spherical Hartree-Fock-Bogolyubov solutions. We use the
Arnoldi method to solve the linear-response problem with pairing.
Results: We found that the difference between centroids of Giant Monopole
Resonances measured in lead and tin (about 1 MeV) always turns out to be
overestimated by about 100%. We also found that the volume incompressibility,
obtained by adjusting the liquid-drop expression to microscopic results, is
significantly larger than the infinite-matter incompressibility.
Conclusions: The zero-range and separable pairing forces cannot induce
modifications of monopole strength functions in tin to match experimental data.Comment: 11 RevTeX pages, 16 figures, 1 table, extended versio
PGS14 CORRELATION BETWEEN DIFFERENT PRODUCTIVITY VARIABLES OBTAINED FROM THE WPAI-GERD QUESTIONNAIRE
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
Correlation studies of fission fragment neutron multiplicities
We calculate neutron multiplicities from fission fragments with specified
mass numbers for events having a specified total fragment kinetic energy. The
shape evolution from the initial compound nucleus to the scission
configurations is obtained with the Metropolis walk method on the
five-dimensional potential-energy landscape, calculated with the
macroscopic-microscopic method for the three-quadratic-surface shape family.
Shape-dependent microscopic level densities are used to guide the random walk,
to partition the intrinsic excitation energy between the two proto-fragments at
scission, and to determine the spectrum of the neutrons evaporated from the
fragments. The contributions to the total excitation energy of the resulting
fragments from statistical excitation and shape distortion at scission is
studied. Good agreement is obtained with available experimental data on neutron
multiplicities in correlation with fission fragments from U(n,f). At higher neutron energies a superlong fission mode appears which
affects the dependence of the observables on the total fragment kinetic energy.Comment: 12 pages, 10 figure
A New Multi-Resource cumulatives Constraint with Negative Heights
This paper presents a new cumulatives constraint which generalizes the original cumulative constraint in different ways. The two most important aspects consist in permitting multiple cumulative resources as well as negative heights for the resource consumption of the tasks. This allows modeling in an easy way new scheduling and planning problems. The introduction of negative heights has forced us to come up with new propagation algorithms and to revisit existing ones. The first propagation algorithm is derived from an idea called sweep which is extensively used in computational geometry; the second algorithm is based on a combination of sweep and constructive disjunction, while the last is a generalization of task intervals to this new context. A real-life timetabling problem originally motivated this constraint which was implemented within the SICStus finite domain solver and evaluated against different problem patterns
Reappraising the Spite Lithium Plateau: Extremely Thin and Marginally Consistent with WMAP
The lithium abundance in 62 halo dwarfs is determined from accurate
equivalent widths reported in the literature and an improved infrared flux
method (IRFM) temperature scale. The Li abundance of 41 plateau stars (those
with Teff > 6000 K) is found to be independent of temperature and metallicity,
with a star-to-star scatter of only 0.06 dex over a broad range of temperatures
(6000 K < Teff < 6800 K) and metallicities (-3.4 < [Fe/H] < -1), thus imposing
stringent constraints on depletion by mixing and production by Galactic
chemical evolution. We find a mean Li plateau abundance of A(Li) = 2.37 dex
(7Li/H = 2.34 X 10^{-10}), which, considering errors of the order of 0.1 dex in
the absolute abundance scale, is just in borderline agreement with the
constraints imposed by the theory of primordial nucleosynthesis and WMAP data
(2.51 < A(Li)[WMAP] < 2.66 dex).Comment: ApJ Letters, in pres
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
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