Intensity of focused waves near turning points.

A wave near an isolated turning point is typically assumed to have an Airy function profile with respect to the separation distance. This description is incomplete, however, and is insufficient to describe the behavior of more realistic wave fields that are not simple plane waves. Asymptotic matching to a prescribed incoming wave field generically introduces a phase front curvature term that changes the characteristic wave behavior from the Airy function to that of the hyperbolic umbilic function. This function, which is one of the seven classic "elementary" functions from catastrophe theory along with the Airy function, can be understood intuitively as the solution for a linearly focused Gaussian beam propagating in a linearly varying density profile, as we show. The morphology of the caustic lines that govern the intensity maxima of the diffraction pattern as one alters the density length scale of the plasma, the focal length of the incident beam, and also the injection angle of the incident beam are presented in detail. This morphology includes a Goos-Hänchen shift and focal shift at oblique incidence that do not appear in a reduced ray-based description of the caustic. The enhancement of the intensity swelling factor for a focused wave compared to the typical Airy solution is highlighted, and the impact of a finite lens aperture is discussed. Collisional damping and finite beam waist are included in the model and appear as complex components to the arguments of the hyperbolic umbilic function. The observations presented here on the behavior of waves near turning points should aid the development of improved reduced wave models to be used, for example, in designing modern nuclear fusion experiments.

Exactly unitary discrete representations of the metaplectic transform for linear-time algorithms.

The metaplectic transform (MT), a generalization of the Fourier transform sometimes called the linear canonical transform, is a tool used ubiquitously in modern optics, for example, when calculating the transformations of light beams in paraxial optical systems. The MT is also an essential ingredient of the geometrical-optics modeling of caustics that we recently proposed. In particular, this application relies on the near-identity MT (NIMT); however, the NIMT approximation used so far is not exactly unitary and leads to numerical instability. Here, we develop a discrete MT that is exactly unitary, and approximate it to obtain a discrete NIMT that is also unitary and can be computed in linear time. We prove that the discrete NIMT converges to the discrete MT when iterated, thereby allowing the NIMT to compute MTs that are not necessarily near-identity. We then demonstrate the new algorithms with a series of examples.

Pseudo-differential representation of the metaplectic transform and its application to fast algorithms.

The metaplectic transform (MT), also known as the linear canonical transform, is a unitary integral mapping that is widely used in signal processing and can be viewed as a generalization of the Fourier transform. For a given function $ \psi $ψ on an $ {N} $N-dimensional continuous space $ {\textbf q} $q, the MT of $ \psi $ψ is parameterized by a rotation (or more generally, a linear symplectic transformation) of the $ 2{N} $2N-dimensional phase space $ ({\textbf q},{\textbf p}) $(q,p), where $ {\textbf p} $p is the wavevector space dual to $ {\textbf q} $q. Here, we derive a pseudo-differential form of the MT. For small-angle rotations, or near-identity transformations of the phase space, it readily yields asymptotic differential representations of the MT, which are easy to compute numerically. Rotations by larger angles are implemented as successive applications of $ {K} \gg 1 $K≫1 small-angle MTs. The algorithm complexity scales as $ {O}({K}{{N}^3}{{N}_p}) $O(KN3Np), where $ {{N}_p} $Np is the number of grid points. Here, we present a numerical implementation of this algorithm and discuss how to mitigate the associated numerical instabilities.

Linear unilateral hamartomatous basal cell naevus with glandular and follicular differentiation.

Mosaicisms are characterized by genetic or functional differences between > or = 2 cell lines in one person, derived from a single zygote. Of the various clinical patterns of cutaneous mosaicism, linear lesions following Blaschko's lines are probably the most commonly encountered, Several cases of multiple basal cell carcinomas or basaloid hamartomatous lesions distributed in a segmentary distribution and following Blaschko's lines have been described. The various terms of 'linear unilateral basal cell naevus with comedones', 'linear unilateral basaloid follicular hamartoma', 'linear unilateral basal cell naevus', and 'basal-cell and linear unilateral adnexal hamartoma' have been used to define this apparently heterogeneous group of disorders. We report a 66-year-old woman with a linear unilateral lesion that appeared during puberty and that histologically showed an adnexal hamartomatous lesion with multiple superficial and nodular basal cell carcinomas. Focal areas of glandular and follicular differentiation were also noted. Molecular studies from these lesions ruled out loss of heterozygosity or mutations in patched gene.

[The congenital absence of the femur. A report of 2 cases]. / Ausencia congénita de fémur. Informe de dos casos.

We present two patients with congenital femoral absence, in six year period, in two hospitals of Minatitlán, Veracruz, Mexico. The first case is a six-year-old male. He begin to walk at four year old. The second case is a twelve-month female, who the walk is not started. Furthermore, she have another muscle-skeletal malformations. None of the have received surgical treatment. We give information about of several classifications of femoral congenital malformations.

Comparative study of diagnostic testing for feline leukemia virus infection.

Results of commercially available diagnostic test kits and commercial laboratory test results were compared for ability to detect FeLV antigen. Results of the immunofluorescent antibody (IFA) test were compared with test kit ELISA results and with results of a system in which samples were applied to an absorbent material, dried, sent to a laboratory, eluted, and assayed by a plate ELISA. Test kits were generally highly sensitive and specific, compared with the IFA test performed at a commercial laboratory. Feline heterophile antibody, specific for mouse immunoglobulin, was detected in approximately 0.14 to 0.57% of the cat population. Test kits B, E, and D contain reagents that correct for antimouse antibodies. During 1989 and 1990, 2,229 feline serum samples were tested for FeLV antigen (gsa p27); positive ELISA results were obtained for 204 (9%) of the samples. Results for 32 (1.4%) samples were interpreted as equivocal (color development slightly exceeded that of the negative control, but was much less than that of the positive control). Collectively, the data indicate that when testing serum or saliva, a negative test result may be a good predictor that a cat is not infected. In populations of cats in which FeLV prevalence is low, a positive test result may not be reliable and thus, a confirmatory test should be performed.

Sensitivity, specificity, and predictive values of ClinEase-Virastat saliva test for feline leukemia virus infection.

Detection of virus in saliva using a commercial enzyme-linked immunosorbent assay (ELISA), ClinEase-VirastatR, was compared to evidence of FeLV infection by the indirect immunofluorescent antibody assay (IFA) and plasma ELISA. The sensitivity and specificity of the saliva ELISA were derived by comparison to IFA and plasma ELISA in 103 cats from a large colony in New York State. The sensitivity of the saliva test in relation to IFA and plasma ELISA was approximately 100% and 93%, respectively. The specificity of the saliva ELISA in relation to IFA and plasma ELISA was approximately 85% and 92%, respectively. This test appears to be particularly suitable as a screening test for FeLV infection, especially in populations where the expected prevalence is low. Because of its high sensitivity, the saliva test has a high negative predictive value, particularly in populations where the disease is rare. Since the specificity is moderate, however, the predictive value of a positive test will be poorest in cats originating from places where the infection is rare (e.g. single cat households, or free roaming cats), and better among cats from environments having a high prevalence of FeLV (e.g. multiple-cat households).

False-positive reactions associated with anti-mouse activity in serotests for feline leukemia virus antigen.

False-positive reactions were observed in commercial test kits designed to detect FeLV infections in cats. The false-positive reactions were associated with heterophilic antibody in cat serum directed primarily against mouse immunoglobulins. Of 2,830 sera tested, 579 were considered FeLV positive or equivocal via ELISA; of these, 10 were found that did not have FeLV antigen but did have anti-mouse antibody. With 95% confidence, 0.14% to 0.57% of cats would have such false-positive reactions in ELISA, because one in 283 (0.35%) cats had anti-mouse antibodies.

Sensitivity and specificity of blood test kits for feline leukemia virus antigen.

Enzyme-linked immunosorbent assay (ELISA) test kits have been used widely to diagnose FeLV infection. Several companies have licensed such kits, but because these test kits are designed somewhat differently, a demonstration of their relative merits was needed. Differences in the sensitivity and specificity of 7 commercial test kits were determined by testing sera that induce false-negative (limiting dilution of FeLV group specific antigen, p27), and false-positive (cat anti-mouse antibody) test results. Among the panels of sera used in this study, significant differences in test kit sensitivity were not observed, but differences in specificity were identified. An interim report of these studies, supplied to the manufacturers, prompted changes in some of the kits, resulting in improved specificities. Generally, FeLV test kits are now more efficient in accurately detecting p27 in blood, serum, or plasma of cats. Nevertheless, some kits still lack specificity attributable to reagents supplied by the manufacturer.