Total Number Of Arcs Research Articles

Path planning of a mobile robot among curved obstacles through tangent drawing and trapezoidal decomposition

Most of the previous studies on mobile robot path planning consider the obstacles as polygons. However, the complex shaped obstacles should be considered as curves rather than polygons, since the latter may result in non-optimal paths. Three new algorithms are proposed for finding the shortest path of a mobile robot among curved obstacles: TAD which uses a tangent drawing method, TRAD which uses trapezoidal decomposition, and TAD-TRAD which uses a combination of the TAD and the TRAD algorithms. The time complexities of the TAD algorithm, the TRAD algorithm, and the TAD-TRAD algorithm are O(n3logn), O(nlogn), and O(n(logn)2) respectively, where n is the total number of arcs in all the obstacles. The TAD and the TAD-TRAD algorithms compute an optimal shortest path, whereas the TRAD algorithm computes an approximate shortest path, among curved obstacles. The TAD algorithm has a lower time complexity than existing algorithms which are implemented for the computation of the optimal shortest path. The TRAD algorithm has a lower time complexity than existing algorithms which compute an approximate shortest path and the TAD-TRAD algorithm has a lower time complexity than existing algorithms which compute an optimal shortest path. The experimental comparison of the TAD, TRAD, and TAD-TRAD algorithms on 200 randomly generated problems shows that the TAD-TRAD algorithm has the least running time. Moreover, the TAD-TRAD algorithm computes an optimal path using a lesser number of tangents and with lesser time complexity when experimental comparisons are performed with existing algorithms in the literature.

Could the Jawless Flattening-Filter-Free Double-Mlc Layer Machine Reduce Low-Dose Regions Compared to Conventional Linear Accelerator for Large-Field Pelvic and Abdominal IMRT/VMAT Cases?

For large-field static IMRT/VMAT treatment plans for pelvic & abdominal targets, multi-leaf collimator (MLC) leakage is a dominant factor that contributes to low-dose regions, and is related to maximum jaw opening and/or multiple isocenters, and field-size dependent MLC leakage. The goal of this study was to evaluate the impact of jawless flattening-filter-free (FFF) double-MLC machine recently introduced in the clinic on low-dose regions for large-field pelvic & abdominal targets and to compare its delivery efficiency with conventional linear accelerators using total monitor unit (MU) as a metric. Ten challenging clinical pelvic & abdominal cases were retrospectively selected and treatment plans were generated using commercial treatment planning software for the jaw-less FFF double-MLC layer machine, and these research plans were comparable to clinical plans in terms of target coverage and Organ-at-Risk (OAR) doses. Prescription dose was 45Gy in 25 fx in all but 3 replanned cases. The cases were all large-field IMRT/VMAT cases with the median target size of 1713 cm3 (max=2269 cm3, SD=505 cm3). To minimize any subjective bias, static IMRT or VMAT techniques with the same arcs or gantry angles, which were identical to the clinical plans, were used for dose calculation. After achieving comparable target coverage as well as OAR doses, low-dose regions (10%, 20%, & 30% of prescription dose) and total MU were compared between two different plans. Target coverages were found to be over 95% with the median values of 96.3% for clinical plans and 97.3% for this study, and doses for various OARs were mostly comparable between clinical plans and this study. The median total MU was 684(SD=227) for the clinical plans and 878(SD=287) for this study. The higher MU for this study was related to the limitation of maximum field size for the jawless double-MLC layer machine; two isocenters had to be used for three cases due to the limited maximum field size of 28cm. Since the separation of two isocenters for the jawless machine should be within 8cm apart, total number of arcs or fields for the jawless machine were twice as that of clinical plans for three out of 10 clinical cases. The median value of low-dose region (10% of prescription dose) was 48.4% (SD=11.8%) for clinical plans vs. 48.6% (SD=11.7%) for this study, and the ratios of low-dose regions (10%, 20%, & 30%) between clinical plans and this study were 1.03(SD=0.04), 1.01(SD=0.03), and 0.97(SD=0.07), respectively. The comparable low-dose regions for this study resulted from the double-MLC layer features, which shows the extremely low measured MLC leakage rate of 0.1% For large-field static IMRT/VMAT cases, low-dose regions (10%, 20%, & 30% of prescription dose) for the jawless FFF double-MLC layer machine were comparable to those of conventional machines.

Project Scheduling in AND–OR Graphs: A Generalization of Dijkstra's Algorithm

The paper considers a project scheduling problem in weighted directed graphs in which arcs represent operations while nodes are identified with starting and finishing endpoints of the operations; arc lengths represent operation durations. The graphs have two types of nodes—AND-nodes and OR-nodes. The problem is to find the earliest starting times for all operations. This problem generalizes the shortest path problem and the critical path problem. The complexity of the suggested algorithm is O(p′ p) where p′ is the number of arcs entering the AND-nodes and p is the total number of arcs.

Chapter 2 - WITHDRAWN: Search

This book has been removed at request of the author.

On the Theory of the Striated Fuse-Wire Disintegration

The multiple arcing observed in h.b.c. fuses having a wire element, which results in a striated fulgurite, is explained. Experimental evidence shows that the number of possbe arcs is larger than the actual number determined from the number of the streaks The energy consumed by multiple arcing of striation is only a small faction ofthe total arc energy. The dynamic axial forces of arcs on each side of a molten wire section interact with the dynamic-pinch force on this section. As a result, the total number of arcs is given by the equilibrium of these forces. This theory can explain known expermental relationships of the modulus of striation versus the wire diameter. Also, the pressure shock wave measurements give some support of the theory.