35,421 research outputs found
Some remarks on the isoperimetric problem for the higher eigenvalues of the Robin and Wentzell Laplacians
We consider the problem of minimising the th eigenvalue, , of
the (-)Laplacian with Robin boundary conditions with respect to all domains
in of given volume . When , we prove that the second
eigenvalue of the -Laplacian is minimised by the domain consisting of the
disjoint union of two balls of equal volume, and that this is the unique domain
with this property. For and , we prove that in many cases a
minimiser cannot be independent of the value of the constant in the
boundary condition, or equivalently of the volume . We obtain similar
results for the Laplacian with generalised Wentzell boundary conditions .Comment: 16 page
Measurement of retinal vessel widths from fundus images based on 2-D modeling
Changes in retinal vessel diameter are an important sign of diseases such as hypertension, arteriosclerosis and diabetes mellitus. Obtaining precise measurements of vascular widths is a critical and demanding process in automated retinal image analysis as the typical vessel is only a few pixels wide. This paper presents an algorithm to measure the vessel diameter to subpixel accuracy. The diameter measurement is based on a two-dimensional difference of Gaussian model, which is optimized to fit a two-dimensional intensity vessel segment. The performance of the method is evaluated against Brinchmann-Hansen's half height, Gregson's rectangular profile and Zhou's Gaussian model. Results from 100 sample profiles show that the presented algorithm is over 30% more precise than the compared techniques and is accurate to a third of a pixel
Optic nerve head segmentation
Reliable and efficient optic disk localization and segmentation are important tasks in automated retinal screening. General-purpose edge detection algorithms often fail to segment the optic disk due to fuzzy boundaries, inconsistent image contrast or missing edge features. This paper presents an algorithm for the localization and segmentation of the optic nerve head boundary in low-resolution images (about 20 /spl mu//pixel). Optic disk localization is achieved using specialized template matching, and segmentation by a deformable contour model. The latter uses a global elliptical model and a local deformable model with variable edge-strength dependent stiffness. The algorithm is evaluated against a randomly selected database of 100 images from a diabetic screening programme. Ten images were classified as unusable; the others were of variable quality. The localization algorithm succeeded on all bar one usable image; the contour estimation algorithm was qualitatively assessed by an ophthalmologist as having Excellent-Fair performance in 83% of cases, and performs well even on blurred image
Quantitative study of molecular N_2 trapped in disordered GaN:O films
The structure of disordered GaN:O films grown by ion-assisted deposition is
investigated using x-ray absorption near-edge spectroscopy and Raman
spectroscopy. It is found that between 4 and 21 % of the nitrogen in the films
is in the form of molecular N_2 that interacts only weakly with the surrounding
matrix. The anion to cation ratio in the GaN:O host remains close to unity, and
there is a close correlation between the N_2 fraction, the level of oxygen
impurities, and the absence of short-range order in the GaN:O matrix.Comment: 5 pages, 3 figure
Photoionization of the Ne-like Si4+ ion in ground and metastable states in the 110–184-eV photon energy range
We present measurements of the absolute photoionization cross section of the neonlike Si4+ ion over the 110–184 eV photon energy range. The measurements were performed using two independent merged-beam setups at the super-ACO and ASTRID synchrotron-radiation facilities, respectively. Signals produced in the photoionization of the 2p subshell of the Si4+ ion both from the 2p6 1S0 ground state and the 2p53s 3P0,2 metastable levels were observed. Calculations of the 2p photoionization cross sections were carried out using a multi-configuration Dirac-Fock code. They give results in good agreement with the measured spectra. Comparison with other available theoretical results is also presented
Particle Swarm Optimization and gravitational wave data analysis: Performance on a binary inspiral testbed
The detection and estimation of gravitational wave (GW) signals belonging to
a parameterized family of waveforms requires, in general, the numerical
maximization of a data-dependent function of the signal parameters. Due to
noise in the data, the function to be maximized is often highly multi-modal
with numerous local maxima. Searching for the global maximum then becomes
computationally expensive, which in turn can limit the scientific scope of the
search. Stochastic optimization is one possible approach to reducing
computational costs in such applications. We report results from a first
investigation of the Particle Swarm Optimization (PSO) method in this context.
The method is applied to a testbed motivated by the problem of detection and
estimation of a binary inspiral signal. Our results show that PSO works well in
the presence of high multi-modality, making it a viable candidate method for
further applications in GW data analysis.Comment: 13 pages, 5 figure
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