882 research outputs found
Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains
Existing approaches for multivariate functional principal component analysis
are restricted to data on the same one-dimensional interval. The presented
approach focuses on multivariate functional data on different domains that may
differ in dimension, e.g. functions and images. The theoretical basis for
multivariate functional principal component analysis is given in terms of a
Karhunen-Lo\`eve Theorem. For the practically relevant case of a finite
Karhunen-Lo\`eve representation, a relationship between univariate and
multivariate functional principal component analysis is established. This
offers an estimation strategy to calculate multivariate functional principal
components and scores based on their univariate counterparts. For the resulting
estimators, asymptotic results are derived. The approach can be extended to
finite univariate expansions in general, not necessarily orthonormal bases. It
is also applicable for sparse functional data or data with measurement error. A
flexible R-implementation is available on CRAN. The new method is shown to be
competitive to existing approaches for data observed on a common
one-dimensional domain. The motivating application is a neuroimaging study,
where the goal is to explore how longitudinal trajectories of a
neuropsychological test score covary with FDG-PET brain scans at baseline.
Supplementary material, including detailed proofs, additional simulation
results and software is available online.Comment: Revised Version. R-Code for the online appendix is available in the
.zip file associated with this article in subdirectory "/Software". The
software associated with this article is available on CRAN (packages funData
and MFPCA
Spin Correlations in the Two-Dimensional Spin-5/2 Heisenberg Antiferromagnet Rb2MnF4
We report a neutron scattering study of the instantaneous spin correlations
in the two-dimensional spin S=5/2 square-lattice Heisenberg antiferromagnet
Rb_2MnF_4. The measured correlation lengths are quantitatively described, with
no adjustable parameters, by high-temperature series expansion results and by a
theory based on the quantum self-consistent harmonic approximation. Conversely,
we find that the data, which cover the range from about 1 to 50 lattice
constants, are outside of the regime corresponding to renormalized classical
behavior of the quantum non-linear sigma model. In addition, we observe a
crossover from Heisenberg to Ising critical behavior near the Neel temperature;
this crossover is well described by a mean-field model with no adjustable
parameters.Comment: 8 pages, LaTeX, with 6 included EPS figures, submitted to EPJ
The Square-Lattice Heisenberg Antiferromagnet at Very Large Correlation Lengths
The correlation length of the square-lattice spin-1/2 Heisenberg
antiferromagnet is studied in the low-temperature (asymptotic-scaling) regime.
Our novel approach combines a very efficient loop cluster algorithm --
operating directly in the Euclidean time continuum -- with finite-size scaling.
This enables us to probe correlation lengths up to
lattice spacings -- more than three orders of magnitude larger than any
previous study. We resolve a conundrum concerning the applicability of
asymptotic-scaling formulae to experimentally- and numerically-determined
correlation lengths, and arrive at a very precise determination of the
low-energy observables. Our results have direct implications for the
zero-temperature behavior of spin-1/2 ladders.Comment: 12 pages, RevTeX, plus two Postscript figures. Some minor
modifications for final submission to Physical Review Letters. (accepted by
PRL
Correlation Lengths in Quantum Spin Ladders
Analytic expressions for the correlation length temperature dependences are
given for antiferromagnetic spin-1/2 Heisenberg ladders using a finite-size
non-linear sigma-model approach. These calculations rely on identifying three
successive crossover regimes as a function of temperature. In each of these
regimes, precise and controlled approximations are formulated. The analytical
results are found to be in excellent agreement with Monte Carlo simulations for
the Heisenberg Hamiltonian.Comment: 5 pages LaTeX using RevTeX, 3 encapsulated postscript figure
Inhomogeneity Induces Resonance Coherence Peaks in Superconducting BSCCO
In this paper we analyze, using scanning tunneling spectroscopy, the density
of electronic states in nearly optimally doped BSCCO in zero field. Focusing on
the superconducting gap, we find patches of what appear to be two different
phases in a background of some average gap, one with a relatively small gap and
sharp large coherence peaks and one characterized by a large gap with broad
weak coherence peaks. We compare these spectra with calculations of the local
density of states for a simple phenomenological model in which a 2 xi_0 * 2
xi_0 patch with an enhanced or supressed d-wave gap amplitude is embedded in a
region with a uniform average d-wave gap.Comment: 4 pages, 3 figure
Area evolution, bulk viscosity and entropy principles for dynamical horizons
We derive from Einstein equation an evolution law for the area of a trapping
or dynamical horizon. The solutions to this differential equation show a causal
behavior. Moreover, in a viscous fluid analogy, the equation can be interpreted
as an energy balance law, yielding to a positive bulk viscosity. These two
features contrast with the event horizon case, where the non-causal evolution
of the area and the negative bulk viscosity require teleological boundary
conditions. This reflects the local character of trapping horizons as opposed
to event horizons. Interpreting the area as the entropy, we propose to use an
area/entropy evolution principle to select a unique dynamical horizon and time
slicing in the Cauchy evolution of an initial marginally trapped surface.Comment: Some references added, 5 pages, Phys. Rev. D, in pres
Periodic Coherence Peak Height Modulations in Superconducting BSCCO
In this paper we analyze, using scanning tunneling spectroscopy (STS), the
local density of electronic states (LDOS) in nearly optimally doped BSCCO in
zero field. We see both dispersive and non-dispersive spatial LDOS modulations
as a function of energy in our samples. Moreover, a spatial map of the
superconducting coherence peak heights shows the same structure as the low
energy LDOS. This suggests that these non-dispersive LDOS modulations originate
from an underlying charge-density modulation which interacts with
superconductivity.Comment: 8 pages, 5 figures with 15 total eps file
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