25,615 research outputs found
On the Assouad dimension of self-similar sets with overlaps
It is known that, unlike the Hausdorff dimension, the Assouad dimension of a
self-similar set can exceed the similarity dimension if there are overlaps in
the construction. Our main result is the following precise dichotomy for
self-similar sets in the line: either the \emph{weak separation property} is
satisfied, in which case the Hausdorff and Assouad dimensions coincide; or the
\emph{weak separation property} is not satisfied, in which case the Assouad
dimension is maximal (equal to one).
In the first case we prove that the self-similar set is Ahlfors regular, and
in the second case we use the fact that if the \emph{weak separation property}
is not satisfied, one can approximate the identity arbitrarily well in the
group generated by the similarity mappings, and this allows us to build a
\emph{weak tangent} that contains an interval. We also obtain results in higher
dimensions and provide illustrative examples showing that the
`equality/maximal' dichotomy does not extend to this setting.Comment: 24 pages, 2 figure
Frequency-Domain Stochastic Modeling of Stationary Bivariate or Complex-Valued Signals
There are three equivalent ways of representing two jointly observed
real-valued signals: as a bivariate vector signal, as a single complex-valued
signal, or as two analytic signals known as the rotary components. Each
representation has unique advantages depending on the system of interest and
the application goals. In this paper we provide a joint framework for all three
representations in the context of frequency-domain stochastic modeling. This
framework allows us to extend many established statistical procedures for
bivariate vector time series to complex-valued and rotary representations.
These include procedures for parametrically modeling signal coherence,
estimating model parameters using the Whittle likelihood, performing
semi-parametric modeling, and choosing between classes of nested models using
model choice. We also provide a new method of testing for impropriety in
complex-valued signals, which tests for noncircular or anisotropic second-order
statistical structure when the signal is represented in the complex plane.
Finally, we demonstrate the usefulness of our methodology in capturing the
anisotropic structure of signals observed from fluid dynamic simulations of
turbulence.Comment: To appear in IEEE Transactions on Signal Processin
A Pre-Protostellar Core in L1551. II. State of Dynamical and Chemical Evolution
Both analytic and numerical radiative transfer models applied to high
spectral resolution CS and N2H+ data give insight into the evolutionary state
of L1551 MC. This recently discovered pre-protostellar core in L1551 appears to
be in the early stages of dynamical evolution. Line-of-sight infall velocities
of >0.1km/s are needed in the outer regions of L1551 MC to adequately fit the
data. This translates to an accretion rate of ~ 1e-6 Msun/yr, uncertain to
within a factor of 5 owing to unknown geometry. The observed dynamics are not
due to spherically symmetric gravitational collapse and are not consistent with
the standard model of low-mass star formation. The widespread, fairly uniform
CS line asymmetries are more consistent with planar infall. There is modest
evidence for chemical depletion in the radial profiles of CS and C18O
suggesting that L1551 MC is also chemically young. The models are not very
sensitive to chemical evolution. L1551 MC lies within a quiescent region of
L1551 and is evidence for continued star formation in this evolved cloud.Comment: 27 pages, 7 figures, ApJ accepte
A Contracting, Turbulent, Starless Core in the Serpens Cluster
We present combined single-dish and interferometric CS(2--1) and N2H+(1--0)
observations of a compact core in the NW region of the Serpens molecular cloud.
The core is starless according to observations from optical to millimeter
wavelengths and its lines have turbulent widths and ``infall asymmetry''. Line
profile modeling indicates supersonic inward motions v_in>0.34 km/s over an
extended region L>12000AU. The high infall speed and large extent exceeds the
predictions of most thermal ambipolar diffusion models and points to a more
dynamical process for core formation. A short (dynamic) timescale, ~1e5
yr=L/v_in, is also suggested by the low N2H+ abundance ~1e-10.Comment: 11 pages including 2 figures. Accepted for publication in the
Astrophysical Journal Letter
A Power Variance Test for Nonstationarity in Complex-Valued Signals
We propose a novel algorithm for testing the hypothesis of nonstationarity in
complex-valued signals. The implementation uses both the bootstrap and the Fast
Fourier Transform such that the algorithm can be efficiently implemented in
O(NlogN) time, where N is the length of the observed signal. The test procedure
examines the second-order structure and contrasts the observed power variance -
i.e. the variability of the instantaneous variance over time - with the
expected characteristics of stationary signals generated via the bootstrap
method. Our algorithmic procedure is capable of learning different types of
nonstationarity, such as jumps or strong sinusoidal components. We illustrate
the utility of our test and algorithm through application to turbulent flow
data from fluid dynamics
SMA Imaging of the Maser Emission from the H30 Radio Recombination Line in MWC349A
We used the Submillimeter Array to map the angular distribution of the
H30 recombination line (231.9 GHz) in the circumstellar region of the
peculiar star MWC349A. The resolution was 1\farcs2, but because of high
signal-to-noise ratio we measured the positions of all maser components to
accuracies better than 0\farcs01, at a velocity resolution of . The
two strongest maser components (called high velocity components) at velocities
near -14 and are separated by 0\farcs048 \pm 0\farcs001 (60 AU)
along a position angle of 102 \pm 1\arcdeg. The distribution of maser
emission at velocities between and beyond these two strongest components were
also provided. The continuum emission lies at the center of the maser
distribution to within 10 mas. The masers appear to trace a nearly edge-on
rotating disk structure, reminiscent of the water masers in Keplerian rotation
in the nuclear accretion disk of the galaxy NGC4258. However, the maser
components in MWC349A do not follow a simple Keplerian kinematic prescription
with , but have a larger power law index. We explore the
possibility that the high velocity masers trace spiral density or shock waves.
We also emphasize caution in the interpretation of relative centroid maser
positions where the maser is not clearly resolved in position or velocity, and
we present simulations that illustrate the range of applicability of the
centroiding method.Comment: 23 pages with 9 figures (two of these figures are vertically aligned
as Figure 4) submitted to the Astrophysical Journa
Dosimetric impact of gastrointestinal air column in radiation treatment of pancreatic cancer
OBJECTIVE:
Dosimetric evaluation of air column in gastrointestinal (GI) structures in intensity modulated radiation therapy (IMRT) of pancreatic cancer.
METHODS:
Nine sequential patients were retrospectively chosen for dosimetric analysis of air column in the GI apparatus in pancreatic cancer using cone beam CT (CBCT). The four-dimensional CT (4DCT) was used for target and organs at risk (OARs) and non-coplanar IMRT was used for treatment. Once a week, these patients underwent CBCT for air filling, isocentre verification and dose calculations retrospectively.
RESULTS:
Abdominal air column variation was as great as ±80% between weekly CBCT and 4DCT. Even with such a large air column in the treatment path for pancreatic cancer, changes in anteroposterior dimension were minimal (2.8%). Using IMRT, variations in air column did not correlate dosimetrically with large changes in target volume. An average dosimetric deviation of mere -3.3% and a maximum of -5.5% was observed.
CONCLUSION:
CBCT revealed large air column in GI structures; however, its impact is minimal for target coverage. Because of the inherent advantage of segmentation in IMRT, where only a small fraction of a given beam passes through the air column, this technique might have an advantage over 3DCRT in treating upper GI malignancies where the daily air column can have significant impact. Advances in knowledge: Radiation treatment of pancreatic cancer has significant challenges due to positioning, imaging of soft tissues and variability of air column in bowels. The dosimetric impact of variable air column is retrospectively studied using CBCT. Even though, the volume of air column changes by ± 80%, its dosimetric impact in IMRT is minimum
Effect of silver content on the structure and antibacterial activity of silver-doped phosphate-based glasses
Staphylococcus aureus can cause a range of diseases, such as osteomyelitis, as well as colonize implanted medical devices. In most instances the organism forms biofilms that not only are resistant to the body's defense mechanisms but also display decreased susceptibilities to antibiotics. In the present study, we have examined the effect of increasing silver contents in phosphate-based glasses to prevent the formation of S. aureus biofilms. Silver was found to be an effective bactericidal agent against S. aureus biofilms, and the rate of silver ion release (0.42 to 1.22 µg·mm–2·h–1) from phosphate-based glass was found to account for the variation in its bactericidal effect. Analysis of biofilms by confocal microscopy indicated that they consisted of an upper layer of viable bacteria together with a layer (20 µm) of nonviable cells on the glass surface. Our results showed that regardless of the silver contents in these glasses (10, 15, or 20 mol%) the silver exists in its +1 oxidation state, which is known to be a highly effective bactericidal agent compared to that of silver in other oxidation states (+2 or +3). Analysis of the glasses by 31P nuclear magnetic resonance imaging and high-energy X-ray diffraction showed that it is the structural rearrangement of the phosphate network that is responsible for the variation in silver ion release and the associated bactericidal effectiveness. Thus, an understanding of the glass structure is important in interpreting the in vitro data and also has important clinical implications for the potential use of the phosphate-based glasses in orthopedic applications to deliver silver ions to combat S. aureus biofilm infections
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