A system of ODEs for a Perturbation of a Minimal Mass Soliton

We study soliton solutions to a nonlinear Schrodinger equation with a saturated nonlinearity. Such nonlinearities are known to possess minimal mass soliton solutions. We consider a small perturbation of a minimal mass soliton, and identify a system of ODEs similar to those from Comech and Pelinovsky (2003), which model the behavior of the perturbation for short times. We then provide numerical evidence that under this system of ODEs there are two possible dynamical outcomes, which is in accord with the conclusions of Pelinovsky, Afanasjev, and Kivshar (1996). For initial data which supports a soliton structure, a generic initial perturbation oscillates around the stable family of solitons. For initial data which is expected to disperse, the finite dimensional dynamics follow the unstable portion of the soliton curve.Comment: Minor edit

Atmospheric sources of trace element contamination in cultivated urban areas: A review

Producing food in cities has garnered increasing attention over the past decade. Although there are ecological and social benefits, cultivated urban areas (CUAs) also bear contamination hazards, including from trace elements (TEs). Trace element contamination has been studied extensively in CUAs, but atmospheric sources remain understudied and poorly understood. A brief discussion is offered on atmospheric particulate deposition processes in cities and their implications for urban food production. Available findings are discussed and contrasted. Existing research assesses atmospheric deposition indirectly or otherwise lacks controls for other TE contaminants. There is little to no engagement with methodological guidelines from the atmospheric sciences, which reduces confidence in the findings so far attained. Suggestions are delineated to combine techniques used in the atmospheric sciences with the robust methodologies already generated by studies on TE contamination in CUAs, such as isotope and TE ratios analyses

The performance of solarscan : an automated dermoscopy image analysis instrument for the diagnosis of primary melanoma

Objective To describe the diagnostic performance of SolarScan (Polartechnics Ltd, Sydney, Australia), an automated instrument for the diagnosis of primary melanoma.Design Images from a data set of 2430 lesions (382 were melanomas; median Breslow thickness, 0.36 mm) were divided into a training set and an independent test set at a ratio of approximately 2:1. A diagnostic algorithm (absolute diagnosis of melanoma vs benign lesion and estimated probability of melanoma) was developed and its performance described on the test set. High-quality clinical and dermoscopy images with a detailed patient history for 78 lesions (13 of which were melanomas) from the test set were given to various clinicians to compare their diagnostic accuracy with that of SolarScan.Setting Seven specialist referral centers and 2 general practice skin cancer clinics from 3 continents. Comparison between clinician diagnosis and SolarScan diagnosis was by 3 dermoscopy experts, 4 dermatologists, 3 trainee dermatologists, and 3 general practitioners.Patients Images of the melanocytic lesions were obtained from patients who required either excision or digital monitoring to exclude malignancy.Main Outcome Measures Sensitivity, specificity, the area under the receiver operator characteristic curve, median probability for the diagnosis of melanoma, a direct comparison of SolarScan with diagnoses performed by humans, and interinstrument and intrainstrument reproducibility.Results The melanocytic-only diagnostic model was highly reproducible in the test set and gave a sensitivity of 91% (95% confidence interval [CI], 86%-96%) and specificity of 68% (95% CI, 64%-72%) for melanoma. SolarScan had comparable or superior sensitivity and specificity (85% vs 65%) compared with those of experts (90% vs 59%), dermatologists (81% vs 60%), trainees (85% vs 36%; P =.06), and general practitioners (62% vs 63%). The intraclass correlation coefficient of intrainstrument repeatability was 0.86 (95% CI, 0.83-0.88), indicating an excellent repeatability. There was no significant interinstrument variation (P = .80).Conclusions SolarScan is a robust diagnostic instrument for pigmented or partially pigmented melanocytic lesions of the skin. Preliminary data suggest that its performance is comparable or superior to that of a range of clinician groups. However, these findings should be confirmed in a formal clinical trial.<br /