8,598 research outputs found
The Measure of a Measurement
While finite non-commutative operator systems lie at the foundation of
quantum measurement, they are also tools for understanding geometric iterations
as used in the theory of iterated function systems (IFSs) and in wavelet
analysis. Key is a certain splitting of the total Hilbert space and its
recursive iterations to further iterated subdivisions. This paper explores some
implications for associated probability measures (in the classical sense of
measure theory), specifically their fractal components.
We identify a fractal scale in a family of Borel probability measures
on the unit interval which arises independently in quantum information
theory and in wavelet analysis. The scales we find satisfy and , some . We identify these
scales by considering the asymptotic properties of
where are dyadic subintervals, and .Comment: 18 pages, 3 figures, and reference
Harmonic analysis of iterated function systems with overlap
In this paper we extend previous work on IFSs without overlap. Our method
involves systems of operators generalizing the more familiar Cuntz relations
from operator algebra theory, and from subband filter operators in signal
processing.Comment: 37 page
Construction of Parseval wavelets from redundant filter systems
We consider wavelets in L^2(R^d) which have generalized multiresolutions.
This means that the initial resolution subspace V_0 in L^2(R^d) is not singly
generated. As a result, the representation of the integer lattice Z^d
restricted to V_0 has a nontrivial multiplicity function. We show how the
corresponding analysis and synthesis for these wavelets can be understood in
terms of unitary-matrix-valued functions on a torus acting on a certain vector
bundle. Specifically, we show how the wavelet functions on R^d can be
constructed directly from the generalized wavelet filters.Comment: 34 pages, AMS-LaTeX ("amsproc" document class) v2 changes minor typos
in Sections 1 and 4, v3 adds a number of references on GMRA theory and
wavelet multiplicity analysis; v4 adds material on pages 2, 3, 5 and 10, and
two more reference
Global energetic neutral atom (ENA) measurements and their association with the Dst index
We present a new global magnetospheric index that measures the intensity of the Earth\u27s ring current through energetic neutral atoms (ENAs). We have named it the Global Energetic Neutral Index (GENI), and it is derived from ENA measurements obtained by the Imaging Proton Spectrometer (IPS), part of the Comprehensive Energetic Particle and Pitch Angle Distribution (CEPPAD) experiment on the POLAR satellite. GENI provides a simple orbit-independent global sum of ENAs measured with IPS. Actual ENA measurements for the same magnetospheric state look different when seen from different points in the POLAR orbit. In addition, the instrument is sensitive to weak ion populations in the polar cap, as well as cosmic rays. We have devised a method for removing the effects of cosmic rays and weak ion fluxes, in order to produce an image of “pure” ENA counts. We then devised a method of normalizing the ENA measurements to remove the orbital bias effect. The normalized data were then used to produce the GENI. We show, both experimentally and theoretically the approximate proportionality between the GENI and the Dst index. In addition we discuss possible implications of this relation. Owing to the high sensitivity of IPS to ENAs, we can use these data to explore the ENA/Dst relationship not only during all phases of moderate geomagnetic storms, but also during quiescent ring current periods
The Mystery Deepens: Spitzer Observations of Cool White Dwarfs
We present 4.5m and 8m photometric observations of 18 cool white
dwarfs obtained with the Spitzer Space Telescope. Our observations demonstrate
that four white dwarfs with T_eff< 6000 K show slightly depressed mid-infrared
fluxes relative to white dwarf models. In addition, another white dwarf with a
peculiar optical and near-infrared spectral energy distribution (LHS 1126) is
found to display significant flux deficits in Spitzer observations. These
mid-infrared flux deficits are not predicted by the current white dwarf models
including collision induced absorption due to molecular hydrogen. We postulate
that either the collision induced absorption calculations are incomplete or
there are other unrecognized physical processes occuring in cool white dwarf
atmospheres. The spectral energy distribution of LHS 1126 surprisingly fits a
Rayleigh-Jeans spectrum in the infrared, mimicking a hot white dwarf with
effective temperature well in excess of 10 K. This implies that the source
of this flux deficit is probably not molecular absorption but some other
process.Comment: 17 pages, 4 figures, ApJ in press, 10 May 200
Sub-Audible Speech Recognition Based upon Electromyographic Signals
Method and system for processing and identifying a sub-audible signal formed by a source of sub-audible sounds. Sequences of samples of sub-audible sound patterns ("SASPs") for known words/phrases in a selected database are received for overlapping time intervals, and Signal Processing Transforms ("SPTs") are formed for each sample, as part of a matrix of entry values. The matrix is decomposed into contiguous, non-overlapping two-dimensional cells of entries, and neural net analysis is applied to estimate reference sets of weight coefficients that provide sums with optimal matches to reference sets of values. The reference sets of weight coefficients are used to determine a correspondence between a new (unknown) word/phrase and a word/phrase in the database
Essential selfadjointness of the graph-Laplacian
We study the operator theory associated with such infinite graphs as
occur in electrical networks, in fractals, in statistical mechanics, and even
in internet search engines. Our emphasis is on the determination of spectral
data for a natural Laplace operator associated with the graph in question. This
operator will depend not only on , but also on a prescribed
positive real valued function defined on the edges in . In electrical
network models, this function will determine a conductance number for each
edge. We show that the corresponding Laplace operator is automatically
essential selfadjoint. By this we mean that is defined on the dense
subspace (of all the real valued functions on the set of vertices
with finite support) in the Hilbert space . The
conclusion is that the closure of the operator is selfadjoint in
, and so in particular that it has a unique spectral resolution,
determined by a projection valued measure on the Borel subsets of the infinite
half-line. We prove that generically our graph Laplace operator
will have continuous spectrum. For a given infinite graph
with conductance function , we set up a system of finite graphs with
periodic boundary conditions such the finite spectra, for an ascending family
of finite graphs, will have the Laplace operator for as its limit.Comment: 50 pages with TOC and figure
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