Algorithms for Computing Closest Points for Segments

Given a set $P$ of $n$ points and a set $S$ of $n$ segments in the plane, we consider the problem of computing for each segment of $S$ its closest point in $P$. The previously best algorithm solves the problem in $n^{4/3}2^{O(\log^*n)}$ time [Bespamyatnikh, 2003] and a lower bound (under a somewhat restricted model) $\Omega(n^{4/3})$ has also been proved. In this paper, we present an $O(n^{4/3})$ time algorithm and thus solve the problem optimally (under the restricted model). In addition, we also present data structures for solving the online version of the problem, i.e., given a query segment (or a line as a special case), find its closest point in $P$. Our new results improve the previous work.Comment: Accepted to STACS 202

Effect of treated length on performance of full scale turbofan inlet noise suppressors

Two inlet noise suppressors containing wall treatment plus three treated rings were tested on a fan in an outdoor noise facility. Sound power attenuations were measured for three treated lengths of each suppressor. The noise reduction from the segment of liner closest to the fan, which contained a segment of wall treatment downstream of the splitter rings, was greater than the reduction from either of the other segments. The decibel attenuations of the ringed liner segments were linear with liner length as predicted by theory. The acoustic attenuation of the wall treatment was considerably greater than expected for available theory. This inordinate effectiveness of the wall treatment strongly suggests the possibility of using no-ring inlet suppressors when the required noise reduction is moderate. The decibel attenuations were higher than predicted above 2000 hertz, and the two suppressors behaved similarly despite the prediction of different behavior

Proximity problems on line segments spanned by points

AbstractFinding the closest or farthest line segment (line) from a point are fundamental proximity problems. Given a set S of n points in the plane and another point q, we present optimal O(nlogn) time, O(n) space algorithms for finding the closest and farthest line segments (lines) from q among those spanned by the points in S. We further show how to apply our techniques to find the minimum (maximum) area triangle with a vertex at q and the other two vertices in S∖{q} in optimal O(nlogn) time and O(n) space. Finally, we give an O(nlogn) time, O(n) space algorithm to find the kth closest line from q and show how to find the k closest lines from q in O(nlogn+k) time and O(n+k) space

Automatic segmentation of the left ventricle cavity and myocardium in MRI data

A novel approach for the automatic segmentation has been developed to extract the epi-cardium and endo-cardium boundaries of the left ventricle (lv) of the heart. The developed segmentation scheme takes multi-slice and multi-phase magnetic resonance (MR) images of the heart, transversing the short-axis length from the base to the apex. Each image is taken at one instance in the heart's phase. The images are segmented using a diffusion-based filter followed by an unsupervised clustering technique and the resulting labels are checked to locate the (lv) cavity. From cardiac anatomy, the closest pool of blood to the lv cavity is the right ventricle cavity. The wall between these two blood-pools (interventricular septum) is measured to give an approximate thickness for the myocardium. This value is used when a radial search is performed on a gradient image to find appropriate robust segments of the epi-cardium boundary. The robust edge segments are then joined using a normal spline curve. Experimental results are presented with very encouraging qualitative and quantitative results and a comparison is made against the state-of-the art level-sets method

Probabilistic Analysis of a Greedy Heuristic for Euclidean Matching

Given a collection of n points in the plane, the Euclidean matching problem is the task of decomposing the collection into matched pairs connected by line segments in such a way as to minimize the sum of all the segment lengths. The greedy heuristic provides an approximate solution to the Euclidean matching problem by successively matching the two closest unmatched points. We study the behavior of Gn, the sum of the lengths of the segments produced by the greedy heuristic

Average Structures of a Single Knotted Ring Polymer

Two types of average structures of a single knotted ring polymer are studied by Brownian dynamics simulations. For a ring polymer with N segments, its structure is represented by a 3N -dimensional conformation vector consisting of the Cartesian coordinates of the segment positions relative to the center of mass of the ring polymer. The average structure is given by the average conformation vector, which is self-consistently defined as the average of the conformation vectors obtained from a simulation each of which is rotated to minimize its distance from the average conformation vector. From each conformation vector sampled in a simulation, 2N conformation vectors are generated by changing the numbering of the segments. Among the 2N conformation vectors, the one closest to the average conformation vector is used for one type of the average structure. The other type of the averages structure uses all the conformation vectors generated from those sampled in a simulation. In thecase of the former average structure, the knotted part of the average structure is delocalized for small N and becomes localized as N is increased. In the case of the latter average structure, the average structure changes from a double loop structure for small N to a single loop structure for large N, which indicates the localization-delocalization transition of the knotted part.Comment: 15 pages, 19 figures, uses jpsj2.cl

Evidence of Fragmenting Dust Particles from Near-Simultaneous Optical and Near-IR Photometry and Polarimetry of Comet 73P/Schwassmann-Wachmann 3

We report imaging polarimetry of segments B and C of the Jupiter-family Comet 73P/Schwassmann-Wachmann 3 in the I and H bandpasses at solar phase angles of approximately 35 and 85deg. The level of polarization was typical for active comets, but larger than expected for a Jupiter-family comet. The polarimetric color was slightly red (dP/dL = +1.2 +/- 0.4) at a phase angle of ~ 35deg and either neutral or slightly blue at a phase angle of ~ 85deg. Observations during the closest approach from 2006 May 11-13 achieved a resolution of 35 km at the nucleus. Both segments clearly depart from a 1/rho surface brightness for the first 50 - 200 km from the nucleus. Simulations of radiation driven dust dynamics can reproduce some of the observed coma morphology, but only with a wide distribution of initial dust velocities (at least a factor of 10) for a given grain radius. Grain aggregate breakup and fragmentation are able to reproduce the observed profile perpendicular to the Sun-Comet axis, but fit the observations less well along this axis (into the tail). The required fragmentation is significant, with a reduction in the mean grain aggregate size by about a factor of 10. A combination of the two processes could possibly explain the surface brightness profile of the comet.Comment: 40 pages including 11 figure