6,331 research outputs found
Performing Nonlinear Blind Source Separation with Signal Invariants
Given a time series of multicomponent measurements x(t), the usual objective
of nonlinear blind source separation (BSS) is to find a "source" time series
s(t), comprised of statistically independent combinations of the measured
components. In this paper, the source time series is required to have a density
function in (s,ds/dt)-space that is equal to the product of density functions
of individual components. This formulation of the BSS problem has a solution
that is unique, up to permutations and component-wise transformations.
Separability is shown to impose constraints on certain locally invariant
(scalar) functions of x, which are derived from local higher-order correlations
of the data's velocity dx/dt. The data are separable if and only if they
satisfy these constraints, and, if the constraints are satisfied, the sources
can be explicitly constructed from the data. The method is illustrated by using
it to separate two speech-like sounds recorded with a single microphone.Comment: 8 pages, 3 figure
Blind Normalization of Speech From Different Channels
We show how to construct a channel-independent representation of speech that
has propagated through a noisy reverberant channel. This is done by blindly
rescaling the cepstral time series by a non-linear function, with the form of
this scale function being determined by previously encountered cepstra from
that channel. The rescaled form of the time series is an invariant property of
it in the following sense: it is unaffected if the time series is transformed
by any time-independent invertible distortion. Because a linear channel with
stationary noise and impulse response transforms cepstra in this way, the new
technique can be used to remove the channel dependence of a cepstral time
series. In experiments, the method achieved greater channel-independence than
cepstral mean normalization, and it was comparable to the combination of
cepstral mean normalization and spectral subtraction, despite the fact that no
measurements of channel noise or reverberations were required (unlike spectral
subtraction).Comment: 25 pages, 7 figure
Channel-Independent and Sensor-Independent Stimulus Representations
This paper shows how a machine, which observes stimuli through an
uncharacterized, uncalibrated channel and sensor, can glean machine-independent
information (i.e., channel- and sensor-independent information) about the
stimuli. First, we demonstrate that a machine defines a specific coordinate
system on the stimulus state space, with the nature of that coordinate system
depending on the device's channel and sensor. Thus, machines with different
channels and sensors "see" the same stimulus trajectory through state space,
but in different machine-specific coordinate systems. For a large variety of
physical stimuli, statistical properties of that trajectory endow the stimulus
configuration space with differential geometric structure (a metric and
parallel transfer procedure), which can then be used to represent relative
stimulus configurations in a coordinate-system-independent manner (and,
therefore, in a channel- and sensor-independent manner). The resulting
description is an "inner" property of the stimulus time series in the sense
that it does not depend on extrinsic factors like the observer's choice of a
coordinate system in which the stimulus is viewed (i.e., the observer's choice
of channel and sensor). This methodology is illustrated with analytic examples
and with a numerically simulated experiment. In an intelligent sensory device,
this kind of representation "engine" could function as a "front-end" that
passes channel/sensor-independent stimulus representations to a pattern
recognition module. After a pattern recognizer has been trained in one of these
devices, it could be used without change in other devices having different
channels and sensors.Comment: The results of a numerically simulated experiment, which illustrates
the proposed method, have been added to the version submitted on October 27,
2004. This paper has been accepted for publication in the Journal of Applied
Physics. For related papers, see http://www.geocities.com/dlevin2001
Using state space differential geometry for nonlinear blind source separation
Given a time series of multicomponent measurements of an evolving stimulus,
nonlinear blind source separation (BSS) seeks to find a "source" time series,
comprised of statistically independent combinations of the measured components.
In this paper, we seek a source time series with local velocity cross
correlations that vanish everywhere in stimulus state space. However, in an
earlier paper the local velocity correlation matrix was shown to constitute a
metric on state space. Therefore, nonlinear BSS maps onto a problem of
differential geometry: given the metric observed in the measurement coordinate
system, find another coordinate system in which the metric is diagonal
everywhere. We show how to determine if the observed data are separable in this
way, and, if they are, we show how to construct the required transformation to
the source coordinate system, which is essentially unique except for an unknown
rotation that can be found by applying the methods of linear BSS. Thus, the
proposed technique solves nonlinear BSS in many situations or, at least,
reduces it to linear BSS, without the use of probabilistic, parametric, or
iterative procedures. This paper also describes a generalization of this
methodology that performs nonlinear independent subspace separation. In every
case, the resulting decomposition of the observed data is an intrinsic property
of the stimulus' evolution in the sense that it does not depend on the way the
observer chooses to view it (e.g., the choice of the observing machine's
sensors). In other words, the decomposition is a property of the evolution of
the "real" stimulus that is "out there" broadcasting energy to the observer.
The technique is illustrated with analytic and numerical examples.Comment: Contains 14 pages and 3 figures. For related papers, see
http://www.geocities.com/dlevin2001/ . New version is identical to original
version except for URL in the bylin
Dramatically increased musculoskeletal ultrasound utilization from 2000 to 2009, especially by podiatrists in private offices
PURPOSE: Over the past two decades, musculoskeletal (MSK) ultrasound has emerged as an effective means of diagnosing MSK pathologies. However, some insurance providers have expressed concern about increased MSK ultrasound utilization, possibly facilitated by the low cost and ready availability of ultrasound technology. The purpose of this study was to document trends in MSK ultrasound utilization from 2000 to 2009 within the Medicare population.
METHODS: Source data were obtained from the CMS Physician/Supplier Procedure Summary Master Files from 2000 to 2009, and records were extracted for procedures for extremity nonvascular ultrasound. We analyzed annual volume by provider type using specialties, practice settings, and geographic regions where the studies were performed.
RESULTS: In 2000, Medicare reimbursed 56,254 MSK ultrasound studies, which increased to 233,964 in 2009 (+316%). Radiologists performed the largest number of MSK ultrasound studies in 2009, 91,022, an increase from 40,877 in 2000. Podiatrists utilized the next highest number of studies in 2009, 76,332, an increase from 3,920 in 2000. Overall, private office MSK ultrasound procedures increased from 19,372 in 2000 to 158,351 in 2009 (+717%). In 2009, podiatrists performed the largest number of private office procedures (75,544) and accounted for 51.5% of the total private office growth from 2000 to 2009. Radiologist private office procedures totaled 19,894 in 2009, accounting for 9.2% of the total private office MSK ultrasound growth.
CONCLUSIONS: The MSK ultrasound volume increase among nonradiologists, especially podiatrists, was far higher than that among radiologists from 2000 and 2009, with the highest growth in private offices. These findings raise concern for self-referral.
Copyright © 2012 American College of Radiology. Published by Elsevier Inc. All rights reserved
On the fundamental theorem of card counting with application to the game of trente et quarante
Abstract. A simplified proof of Thorp and Walden's fundamental theorem of card counting is presented, and a corresponding central limit theorem is established. Results are applied to the casino game of trente et quarante, which was studied by Poisson and De Morgan
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