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 H30α\alpha Radio Recombination Line in MWC349A

We used the Submillimeter Array to map the angular distribution of the H30$\alpha$ 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 $1 kms$. The two strongest maser components (called high velocity components) at velocities near -14 and $32 kms$ 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 $v \sim r^{-1/2}$, 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