An algorithm for partitioning parameterized 45-degree polygons into parameterized trapezoids is proposed in this article. The algorithm is based on the plane-sweep technique and can handle polygons with complicated constraints. The input to the algorithm consists of the contour of a parameterized polygon to be partitioned and a set of constraints for parameters of the contour. The algorithm uses horizontal cuts only and generates a number of nonoverlapping trapezoids whose union is the original parameterized polygon. Processing of constraints and coordinates that contain first-order multiple-variable polynomials has been made possible by incorporating the JaCoP constraint programming library. The proposed algorithm has been implemented in Java programming language and can be used as the basis to build the trapezoidal corner stitching data structure for parameterized VLSI layout masks.
Longest-path routing problems, which can arise in the design of high-performance printed circuit boards (PCBs), have been proven to be NP-hard. In this article, we propose a constraint programming (CP) formulation and a mixed integer linear programming (MILP) formulation to gridded longest-path routing problems; each of which may contain obstacles. After a longest-path routing problem has been transformed into a CP problem, a CP solver can be used to find optimal solutions. On the other hand, parallel MILP solvers can be used to find optimal solutions after the longest-path routing problem has been transformed into an MILP problem. Also, suboptimal solutions can be generated in exchange for reduced execution time. The proposed formulation methods can also be used to solve shortest-path routing problems. Experimental results show that more than 3,700x speed-up can be achieved by using a parallel MILP solver with 16 threads in solving formulated longest-path routing problems. The execution time can be further reduced if a computer containing more processer cores is available. 1
Psoriasis is a chronic inflammatory skin disease. Metabolic syndrome and cardiovascular disease, such as hypertension, stroke, diabetes mellitus, and hyperlipidemia, are more frequent among psoriatic patients and they experience increased morbidity and mortality than the normal population. Therefore, psoriasis and its comorbidities are important issues, especially in the geriatric population.Many studies have revealed that psoriasis has a bimodal onset of distribution. The first peak occurs in the early 30s and the second in the early 60s. [1][2][3] reported that approximately 4.9% of patients started suffering from this disease at over 60 years of age, which they defined as elderly-onset psoriasis. Previous studies in different countries showed different clinical characteristics of psoriasis between the early-and late-onset populations. 5 In Taiwan, the elderly (>65 years) account for approximately 14.9% of the total population. The incidence of psoriasis is approximately 0.24% within this group, 6 which means that nearly 10 000 elderly patients have psoriasis. With such a large case number of geriatric patients with psoriasis, further research and updated treatment guidelines on elderly psoriasis is warranted. There is a scarcity of reports regarding elderly psoriasis in Asia. 4,7 This study aimed to evaluate the clinical characteristics and disease courses in a geriatric population, and to analyze the differences between the earlyversus elderly-onset patients in this age group.
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