Gaussian processes for classification: mean field algorithms:mean-field algorithms

We derive a mean field algorithm for binary classification with Gaussian processes which is based on the TAP approach originally proposed in Statistical Physics of disordered systems. The theory also yields an approximate leave-one-out estimator for the generalization error which is computed with no extra computational cost. We show that from the TAP approach, it is possible to derive both a simpler 'naive' mean field theory and support vector machines (SVM) as limiting cases. For both mean field algorithms and support vectors machines, simulation results for three small benchmark data sets are presented. They show 1. that one may get state of the art performance by using the leave-one-out estimator for model selection and 2. the built-in leave-one-out estimators are extremely precise when compared to the exact leave-one-out estimate. The latter result is a taken as a strong support for the internal consistency of the mean field approach.

Resonant gradient force on atom interacting with laser field

The gradient force, as a function of position and velocity, is derived for a two-level atom interacting with a standing-wave laser field. Basing on optical Bloch equations, the numerical solutions for the gradient force f_(|_;n) (n = 0, 1, 2, 3, 4, ...) pointing in the direction of the transverse of the laser beam are given. It is shown the higher order gradient force plays important role at strong intensity (G = 64), the contribution of them can not be neglected.

Quantification of visual field loss in age-related macular degeneration

Presentation Purpose:To determine methods of quantifying the sensitivity loss in the central 10o visual field in a cross section of patients at various stages of age-related macular degeneration (AMD). Methods:Standard and short-wavelength automated perimetry (SAP and SWAP) visual fields were collected using program 10-2 of the Humphrey Field Analyzer, in 44 eyes of 27 patients with AMD and 41 eyes of 22 normal subjects. Stereoscopic fundus photographs were graded by two independent observers and the stage of disease determined. Global indices were compared for their ability to delineate the normal visual field from early stages of AMD and to differentiate between stages. Results:Mean Deviation (MD) and Pattern Standard Deviation (PSD) varied significantly with stage of disease in SAP (both p<0.001) and SWAP (both p<0.001), but post-hoc analysis revealed overlap of functional values between stages. Global indices of focal loss, PSD and local spatial variability (LSV) were the most sensitive to detecting differences between normal subjects and early stage AMD patients, in SAP and SWAP, respectively. Overall, defects were confined to the central 5°. SWAP defects were consistently greater in depth and area than those in SAP. The most vulnerable region of the 10° field to sensitivity loss with increasing stage of AMD was the central 1°, in which the sensitivity decline was -4.8dB per stage in SAP and -4.9dB per stage in SWAP. Based on the pattern deviation defect maps, a severity index of AMD visual field loss was derived. Threshold variability was considerably increased in late stage AMD eyes. Conclusions:Global indices of focal loss were more sensitive to the detection of early stage AMD from normal. The sensitivity decline with advancing stage of AMD was greater in SWAP compared to SAP, however the trend was not strong across all stages of disease. The less commonly used index LSV represents relatively statistically unmanipulated summary measure of focal loss. A new severity index is described which is sensitive to visual field change in AMD, measures visual field defects on a continuous scale and may serve as a useful measure of functional change in AMD in longitudinal studies. Keywords: visual fields • age-related macular degeneration • perimetry

Relationships between fundus image quantification and visual field status in age-related macular degeneration

Presentation Purpose:To relate structural change to functional change in age-related macular degeneration (AMD) in a cross-sectional population using fundus imaging and the visual field status. Methods:10 degree standard and SWAP visual fields and other standard functional clinical measures were acquired in 44 eyes of 27 patients at various stages of AMD, as well as fundus photographs. Retro-mode SLO images were captured in a subset of 29 eyes of 19 of the patients. Drusen area, measured by automated drusen segmentation software (Smith et al. 2005) was correlated with visual field data. Visual field defect position was compared to the position of the imaged drusen and deposits using custom software. Results:The effect of AMD stage on drusen area within the 6000µm was significant (One-way ANOVA: F = 17.231, p < 0.001), however the trend was not strong across all stages. There were significant linear relationships between visual field parameters and drusen area. The mean deviation (MD) declined by 3.00dB and 3.92dB for each log % drusen area for standard perimetry and SWAP, respectively. The visual field parameters of focal loss displayed the strongest correlations with drusen area. The number of pattern deviation (PD) defects increased by 9.30 and 9.68 defects per log % drusen area for standard perimetry and SWAP, respectively. Weaker correlations were found between drusen area and visual acuity, contrast sensitivity, colour vision and reading speed. 72.6% of standard PD defects and 65.2% of SWAP PD defects coincided with retinal signs of AMD on fundus photography. 67.5% of standard PD defects and 69.7% of SWAP PD defects coincided with deposits on retro-mode images. Conclusions:Perimetry exhibited a stronger relationship with drusen area than other measures of visual function. The structure-function relationship between visual field parameters and drusen area was linear. Overall the indices of focal loss had a stronger correlation with drusen area in SWAP than in standard perimetry. Visual field defects had a high coincidence proportion with retinal manifestations of AMD.Smith R.T. et al. (2005) Arch Ophthalmol 123:200-206.

Side detection of strong radiation-mode out-coupling from blazed FBGs in single-mode and multimode fibers

We report on the effective side detection of radiation-mode out-coupling from blazed fiber Bragg gratings (BFBGs) fabricated in single-mode fiber (SMF) and multimode fiber (MMF). The far-field radiation power distribution from BFBGs have been measured achieving a high spatial-spectral resolution (0.17 mm/nm). We have also investigated comparatively the transmission-loss characteristics of BFBGs in both fiber types, fabricated using phase-mask and holographic inscription techniques. Our results reveal clearly that the radiation out-coupling from BFBGs is significantly stronger and spectrally more confined in MMF than in SMF.