2,151 research outputs found
Calculation of the Density of States Using Discrete Variable Representation and Toeplitz Matrices
A direct and exact method for calculating the density of states for systems
with localized potentials is presented. The method is based on explicit
inversion of the operator . The operator is written in the discrete
variable representation of the Hamiltonian, and the Toeplitz property of the
asymptotic part of the obtained {\it infinite} matrix is used. Thus, the
problem is reduced to the inversion of a {\it finite} matrix
Structured penalties for functional linear models---partially empirical eigenvectors for regression
One of the challenges with functional data is incorporating spatial
structure, or local correlation, into the analysis. This structure is inherent
in the output from an increasing number of biomedical technologies, and a
functional linear model is often used to estimate the relationship between the
predictor functions and scalar responses. Common approaches to the ill-posed
problem of estimating a coefficient function typically involve two stages:
regularization and estimation. Regularization is usually done via dimension
reduction, projecting onto a predefined span of basis functions or a reduced
set of eigenvectors (principal components). In contrast, we present a unified
approach that directly incorporates spatial structure into the estimation
process by exploiting the joint eigenproperties of the predictors and a linear
penalty operator. In this sense, the components in the regression are
`partially empirical' and the framework is provided by the generalized singular
value decomposition (GSVD). The GSVD clarifies the penalized estimation process
and informs the choice of penalty by making explicit the joint influence of the
penalty and predictors on the bias, variance, and performance of the estimated
coefficient function. Laboratory spectroscopy data and simulations are used to
illustrate the concepts.Comment: 29 pages, 3 figures, 5 tables; typo/notational errors edited and
intro revised per journal review proces
Phonon Localization in One-Dimensional Quasiperiodic Chains
Quasiperiodic long range order is intermediate between spatial periodicity
and disorder, and the excitations in 1D quasiperiodic systems are believed to
be transitional between extended and localized. These ideas are tested with a
numerical analysis of two incommensurate 1D elastic chains: Frenkel-Kontorova
(FK) and Lennard-Jones (LJ). The ground state configurations and the
eigenfrequencies and eigenfunctions for harmonic excitations are determined.
Aubry's "transition by breaking the analyticity" is observed in the ground
state of each model, but the behavior of the excitations is qualitatively
different. Phonon localization is observed for some modes in the LJ chain on
both sides of the transition. The localization phenomenon apparently is
decoupled from the distribution of eigenfrequencies since the spectrum changes
from continuous to Cantor-set-like when the interaction parameters are varied
to cross the analyticity--breaking transition. The eigenfunctions of the FK
chain satisfy the "quasi-Bloch" theorem below the transition, but not above it,
while only a subset of the eigenfunctions of the LJ chain satisfy the theorem.Comment: This is a revised version to appear in Physical Review B; includes
additional and necessary clarifications and comments. 7 pages; requires
revtex.sty v3.0, epsf.sty; includes 6 EPS figures. Postscript version also
available at
http://lifshitz.physics.wisc.edu/www/koltenbah/koltenbah_homepage.htm
Reconstructing the primordial power spectrum from the CMB
We propose a straightforward and model independent methodology for
characterizing the sensitivity of CMB and other experiments to wiggles,
irregularities, and features in the primordial power spectrum. Assuming that
the primordial cosmological perturbations are adiabatic, we present a function
space generalization of the usual Fisher matrix formalism, applied to a CMB
experiment resembling Planck with and without ancillary data. This work is
closely related to other work on recovering the inflationary potential and
exploring specific models of non-minimal, or perhaps baroque, primordial power
spectra. The approach adopted here, however, most directly expresses what the
data is really telling us. We explore in detail the structure of the available
information and quantify exactly what features can be reconstructed and at what
statistical significance.Comment: 43 pages Revtex, 23 figure
Analysis of Dynamic Brain Imaging Data
Modern imaging techniques for probing brain function, including functional
Magnetic Resonance Imaging, intrinsic and extrinsic contrast optical imaging,
and magnetoencephalography, generate large data sets with complex content. In
this paper we develop appropriate techniques of analysis and visualization of
such imaging data, in order to separate the signal from the noise, as well as
to characterize the signal. The techniques developed fall into the general
category of multivariate time series analysis, and in particular we extensively
use the multitaper framework of spectral analysis. We develop specific
protocols for the analysis of fMRI, optical imaging and MEG data, and
illustrate the techniques by applications to real data sets generated by these
imaging modalities. In general, the analysis protocols involve two distinct
stages: `noise' characterization and suppression, and `signal' characterization
and visualization. An important general conclusion of our study is the utility
of a frequency-based representation, with short, moving analysis windows to
account for non-stationarity in the data. Of particular note are (a) the
development of a decomposition technique (`space-frequency singular value
decomposition') that is shown to be a useful means of characterizing the image
data, and (b) the development of an algorithm, based on multitaper methods, for
the removal of approximately periodic physiological artifacts arising from
cardiac and respiratory sources.Comment: 40 pages; 26 figures with subparts including 3 figures as .gif files.
Originally submitted to the neuro-sys archive which was never publicly
announced (was 9804003
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