A simple proof for visibility paths in simple polygons

The purpose of this note is to give a simple proof for a necessary and sufficient condition for visibility paths in simple polygons. A visibility path is a curve such that every point inside a simple polygon is visible from at least one point on the path. This result is essential for finding the shortest watchman route inside a simple polygon specially when the route is restricted to curved paths

Query-points visibility constraint minimum link paths in simple polygons

We study the query version of constrained minimum link paths between two points inside a simple polygon $P$ with $n$ vertices such that there is at least one point on the path, visible from a query point. The method is based on partitioning $P$ into a number of faces of equal link distance from a point, called a link-based shortest path map (SPM). Initially, we solve this problem for two given points $s$, $t$ and a query point $q$. Then, the proposed solution is extended to a general case for three arbitrary query points $s$, $t$ and $q$. In the former, we propose an algorithm with $O(n)$ preprocessing time. Extending this approach for the latter case, we develop an algorithm with $O(n^3)$ preprocessing time. The link distance of a $q$-$visible$ path between $s$, $t$ as well as the path are provided in time $O(\log n)$ and $O(m+\log n)$, respectively, for the above two cases, where $m$ is the number of links

Complexity Growth Following Multiple Shocks

In this paper by making use of the "Complexity=Action" proposal, we study the complexity growth after shock waves in holographic field theories. We consider both double black hole-Vaidya and AdS-Vaidya with multiple shocks geometries. We find that the Lloyd's bound is respected during the thermalization process in each of these geometries and at the late time, the complexity growth saturates to the value which is proportional to the energy of the final state. We conclude that the saturation value of complexity growth rate is independent of the initial temperature and in the case of thermal initial state, the rate of complexity is always less than the value for the vacuum initial state such that considering multiple shocks it gets more smaller. Our results indicate that by increasing the temperature of the initial state, the corresponding rate of complexity growth starts far from final saturation rate value.Comment: 19 pages, 3 figs, Ref.s adde

Striped Circle Visual Acuity Chart; A Novel Visual Acuity Chart Based on the Landolt-C Chart

Measurement of Visual Acuity (VA) has been used for eye examinations under various clinical conditions. In addition, because of changes in VA with a range of eye diseases, its measurement is used to screen, diagnose, and evaluate response to treatment in numerous eye diseases and predict the patient's visual function. VA and the likelihood of astigmatism could be evaluated simultaneously using a newly designed Stripped Circle (SC) VA chart. This chart has been  developed based on the standard VA measurement scale chart, and the Landolt-C (LC) VA chart and all the standards for a VA chart design were implemented during its development. However, to publicize the clinical application of this VA measurement chart, further studies are required to evaluate its sensitivity, specificity, and repeatability compared with a similar standard VA chart

KINEMATIC AND KINETIC COMPARISONS BElWEEN SPOT, CROSSOVER AND UPWARD JUMP THROWINGS IN HANDBALL

Throwing is one of the most important skills in handball in which two basic factors are of importance with regard to the efficiency of shots Le. accuracy and velocity. A 2Dimensional analysis of different throws Le. on the spot, with a cross-over step, and with upward jump has been undertaken. Eighteen high-performance handball players took part in this study. The average values of basic parameters of physical characteristics of subjects were: 80.2 ± 6.1 Kg (body mass), 184.8 ± 4 cm (body height), and 19.79 ± 0.63 years of age. The main aim of present study was to establish a valuable kinematic and kinetic comparison between different types of throws in handball. Statistically significant differences were found between maximal ban velocity during throws with cross-over step and ball velocity during other analyzed throws. In addition to the high velocity in this throw, the energy and power consumptions were also higher in magnitude comparing with other throws. The results obtained by this study agreed well with the results reported by other researchers

Striped Circle Visual Acuity Chart; A Novel Visual Acuity Chart Based on the Landolt-C Chart

Measurement of Visual Acuity (VA) has been used for eye examinations under various clinical conditions. In addition, because of changes in VA with a range of eye diseases, its measurement is used to screen, diagnose, and evaluate response to treatment in numerous eye diseases and predict the patient's visual function. VA and the likelihood of astigmatism could be evaluated simultaneously using a newly designed Stripped Circle (SC) VA chart. This chart has been  developed based on the standard VA measurement scale chart, and the Landolt-C (LC) VA chart and all the standards for a VA chart design were implemented during its development. However, to publicize the clinical application of this VA measurement chart, further studies are required to evaluate its sensitivity, specificity, and repeatability compared with a similar standard VA chart