Generalized Pearson Distributions and Related Characterization Problems

This paper is concerned with a Rodrigues' formula for generating new classes of polynomials. The associated density functions belong to the family of generalized Pearson curves, which extends the classical Pearson family. Various properties of these polynomials (degree, orthogonality ...) are investigated and then exploited to derive several related results, especially characterizations, in probability.     

Multispectral imaging using multiple-bandpass filters

We present a method for multispectral imaging. This method uses color CCD cameras with a multiple-bandpass filter, which modifies the spectral response of the cameras used and enables concurrent acquisition of multiple images at defined spectral bands. We experimentally demonstrate methodological feasibility using two color CCD cameras and a polychroic mirror to simultaneously capture eight spectral bands. We discuss how the method developed is well suited for multispectral applications of transient phenomena or for real-time measurements.     

Complete-angle projection diffuse optical tomography by use of early photons

We present the first, to our knowledge, experimental images of complex-shaped phantoms embedded in diffuse media by use of optical tomography. Imaging is based on a complete-angle projection tomographic technique that utilizes transmitted early photons. Results are contrasted with measurements obtained at later gates as well as pseudocontinuous-wave data. The scanning system developed employs noncontact illumination and detection technologies that allow for high spatial sampling of transmitted photons. Combining this system with complete-angle illumination is found to be an important strategy toward improved imaging performance, resulting in a better-posed inversion problem. The appropriateness of reconstruction algorithms similar to those employed in x-ray computed tomography are showcased, and suggestions for model improvements are provided.     

Novel methodology for 3D reconstruction of carotid arteries and plaque characterization based upon magnetic resonance imaging carotid angiography data

In this study, we present a novel methodology that allows reliable segmentation of the magnetic resonance images (MRIs) for accurate fully automated three-dimensional (3D) reconstruction of the carotid arteries and semiautomated characterization of plaque type. Our approach uses active contours to detect the luminal borders in the time-of-flight images and the outer vessel wall borders in the T(1)-weighted images. The methodology incorporates the connecting components theory for the automated identification of the bifurcation region and a knowledge-based algorithm for the accurate characterization of the plaque components. The proposed segmentation method was validated in randomly selected MRI frames analyzed offline by two expert observers. The interobserver variability of the method for the lumen and outer vessel wall was -1.60%±6.70% and 0.56%±6.28%, respectively, while the Williams Index for all metrics was close to unity. The methodology implemented to identify the composition of the plaque was also validated in 591 images acquired from 24 patients. The obtained Cohen's k was 0.68 (0.60-0.76) for lipid plaques, while the time needed to process an MRI sequence for 3D reconstruction was only 30 s. The obtained results indicate that the proposed methodology allows reliable and automated detection of the luminal and vessel wall borders and fast and accurate characterization of plaque type in carotid MRI sequences. These features render the currently presented methodology a useful tool in the clinical and research arena.     

Imager that combines near-infrared diffusive light and ultrasound

We introduce an imaging technique that combines complementary features of ultrasound and near-infrared diffusive light imaging. We achieve the combined technology experimentally by mounting an ultrasound array together with multiple laser source and optical detector fibers upon a hand-held probe. The technique is demonstrated with tissue phantoms wherein both acoustic and optical sensors image the volume underneath the probe. Coregistration of acoustic and optical images is achieved with an accuracy of 0.27+/-0.20cm, approximately half of the image pixel size of our prototype. Accurate determination of target optical absorption is also achieved by use of image segmentation on the ultrasound reconstruction. The combined technique may provide improved breast-cancer detection sensitivity and specificity.     

Reconstruction of thermally quenched glow curves in quartz

The experimentally measured thermoluminescence (TL) glow curves of quartz samples are influenced by the presence of the thermal quenching effect, which involves a variation of the luminescence efficiency as a function of temperature. The real shape of the thermally unquenched TL glow curves is completely unknown. In the present work an attempt is made to reconstruct these unquenched glow curves from the quenched experimental data, and for two different types of quartz samples. The reconstruction is based on the values of the thermal quenching parameter W (activation energy) and C (a dimensionless constant), which are known from recent experimental work on these two samples. A computerized glow-curve deconvolution (CGCD) analysis was performed twice for both the reconstructed and the experimental TL glow curves. Special attention was paid to check for consistency between the results of these two independent CGCD analyses. The investigation showed that the reconstruction attempt was successful, and it is concluded that the analysis of reconstructed TL glow curves can provide improved values of the kinetic parameters E, s for the glow peaks of quartz. This also leads to a better evaluation of the half-lives of electron trapping levels used for dosimetry and luminescence dating.     

Ultrafast Photophysics of Regioisomeric Triphenylamine Dyes Having Dipolar D-π-A-A and Octupolar D-(π-A-A)3 Character with a Benzothiazole Unit in Matched or Mismatched Orientation

Benzothiazole is among prominent electron-withdrawing heteroarene moieties used in a variety of π-conjugated molecules. Its relative orientation with respect to the principal dipole vector(s) of chromophores derived thereof is crucial, affecting photophysical and nonlinear optical properties. Here we compare the photophysics and ultrafast dynamics of dipolar and octupolar molecules comprising a triphenylamine electron-donating core, ethynylene π-conjugated linker(s) and benzothiazole acceptor(s) having the matched or mismatched orientation (with respect to the direction of intramolecular charge transfer), while a carbaldehyde group is attached as an auxiliary acceptor. Among chromophores without the auxiliary acceptor, stronger fluorescence solvatochromism and faster excited state dynamics are exhibited for the derivatives with the mismatched geometry. On the contrary, introduction of the auxiliary acceptor to the benzothiazole unit enhances the intramolecular charge transfer ICT (featuring ultrafast dynamics of the excited state) for the matched geometry. The data confirm the crucial role of the relative orientation of asymmetric heteroaromatic unit (regioisomeric effect) in dipolar as well as in multipolar molecules in tuning linear and nonlinear optical properties as well as excited state dynamics.     

On the area of the intersection of disks in the plane

Let C₁,…, C_n and C′₁,…, C′_n be two collections of equal disks in the plane, with centers c₁,…, c_n and c′₁,…, c′_n. According to a well-known conjecture of Klee and Wagon (1991), if |c_i − c_j| ≥ |c′_i − c′_j| for all i, j, then Area(∩_i C_i) ≤ Area(∩_i C′_i).

We prove this statement in the special case when there is a continuous contraction of {c₁,…, c_n} onto {c′₁,…, c′_n}.