<Emphasis Type="Bold">A Reliable Solver of Regular-Grid Travelling Salesman Problems: Double Threshold Accepting for Schedule Planning Optimisation with Unified Pattern of Normalised Threshold Values</Emphasis>

The threshold accepting (TA) method is a meta-heuristic algorithm to solve optimisation problems. Like the simulatedannealing (SA) method, the result of TA does not guarantee to converge to the global optimum within the truncated computer time. A double TA is proposed to overcome this problem and is applied to regular-grid travelling salesman problems (TSPs). It is discovered that with a proper selection of threshold values in a double TA, the empirical result shows that it always converges to the optimal solution in the regular-grid TSPs. The experiment is performed on 18 cases ranging from 16 to 441 points (cities) and each case is executed 100 times. They all converge to the optimal solution within the specified limit of the number of function evaluations. The pattern of the normalised threshold values is identical for all 18 cases. The pattern is in the shape of a natural cubic spline and can be constructed by eight control points. The threshold values in 18 cases are classified into three groups. In each particular group, although the pattern and size of the normalised threshold values is the same, the scale of the pattern is different for each case in the group. The scale is termed cap and can be obtained from the cap function of positive changes of the cost function in the steps of moves from a suboptimal tour to a global optimal tour. Empirically, our method is shown to be superior to the simulated annealing method in terms of the reliability of obtaining a global optimum within the truncated computer time.     

Predictive value of p63, ki‐67, and survivin expression in oral leukoplakia: A tissue microarray study

The aim of this study was to analyze the immunohistochemical expression of survivin, ki‐67, and p63 in oral leukoplakic lesions, histopathologically differentiated into dysplastic and nondysplastic. A tissue microarray containing 57 samples of biopsies from clinically classified lesions, such as leukoplakia, was immunolabeled for survivin, ki‐67, and p63. Samples were scored for percentage of positively stained. Scores were designated as follows: low = less than 25% of positive cells; and high = more than 25% of positive cells. On performing histopathological diagnosis, 20 dysplastic lesions and 37 nondysplastic lesions were seen, in which female patients (56.1%) were predominant with an average age of 58.27 years. The study showed a high expression of 37.5% for survivin, 43.7% for ki‐67, and 88.2% for p63 in dysplastic lesions. However, there was a high expression of 16.7% for survivin, 16.7% for ki‐67, and 92% for p63 in nondysplastic lesions. There is a positive correlation of expression among the three antibodies. In the association of immunoreactivity, in both dysplastic and nondysplastic lesions, increased expression of survivin reflects on the increased expression of ki‐67, and there is an overexpression of p63. In leukoplakia, the expression of survivin associated with that of ki‐67 reinforces the assumption that all these lesions are potentially malignant, regardless of histopathology; and the overexpression of p63 may indicate carcinogenic potential. These findings may help in the treatment of patients with this type of lesion.