New cutting-planes for the time-and/or precedence-constrained ATSP and directed VRP

In this paper, we introduce five classes of new valid cutting planes for the precedence-constrained (PC) and/or time-window-constrained (TW) Asymmetric Travelling Salesman Problems (ATSPs) and directed Vehicle Routing Problems (VRPs). We show that all five classes of new inequalities are facet-defining for the directed VRP-TW, under reasonable conditions and the assumption that vehicles are identical. Similar proofs can be developed for the VRP-PC. As ATSP-TW and PC-ATSP can be formulated as directed identical-vehicle VRP-TW and PC-VRP, respectively, this provides a link to study the polyhedral combinatorics for the ATSP-TW and PC-ATSP. The first four classes of these new cutting planes are cycle-breaking inequalities that are lifted from the well-known D^-_k and D⁺_k inequalities (see Grötschel and Padberg in Polyhedral theory. The traveling salesman problem: a guided tour of combinatorial optimization, Wiley, New York, 1985). The last class of new cutting planes, the TW ₂ inequalities, are infeasible-path elimination inequalities. Separation of these constraints will also be discussed. We also present prelimanry numerical results to demonstrate the strengh of these new cutting planes.

The relationship between native vegetation and in-stream salinity: An Australian case study

The Glenelg-Hopkins area is a large regional watershed (2.6 million ha) in southwest Victoria that has been extensively cleared for agriculture. In-stream electrical conductivity (EC) in relation to remnant native vegetation is examined from the headwaters to the upper extent of the estuary of the Glenelg River. Five water quality gauging stations were selected. Their contributing subcatchments represent a continuum of disturbance. Proportions of native vegetation ranged from ∼100% at the headwaters of the river to ∼30% at the furthest downstream gauge station. The relationship between remnant vegetation and in-stream EC was examined using aggregated and non-aggregated land use statistics over a period of 22 years from three land use maps. Increased proportions of native vegetation were significantly negatively correlated with in-stream EC and were consistent across all scenarios investigated.

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.