Arc Operads and Arc Algebras

Several topological and homological operads based on families of projectively weighted arcs in bounded surfaces are introduced and studied. The spaces underlying the basic operad are identified with open subsets of a compactification due to Penner of a space closely related to Riemann's moduli space. Algebras over these operads are shown to be Batalin-Vilkovisky algebras, where the entire BV structure is realized simplicially. Furthermore, our basic operad contains the cacti operad up to homotopy, and it similarly acts on the loop space of any topological space. New operad structures on the circle are classified and combined with the basic operad to produce geometrically natural extensions of the algebraic structure of BV algebras, which are also computed.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper15.abs.htm

Subclasses of Normal Helly Circular-Arc Graphs

A Helly circular-arc model M = (C,A) is a circle C together with a Helly family \A of arcs of C. If no arc is contained in any other, then M is a proper Helly circular-arc model, if every arc has the same length, then M is a unit Helly circular-arc model, and if there are no two arcs covering the circle, then M is a normal Helly circular-arc model. A Helly (resp. proper Helly, unit Helly, normal Helly) circular-arc graph is the intersection graph of the arcs of a Helly (resp. proper Helly, unit Helly, normal Helly) circular-arc model. In this article we study these subclasses of Helly circular-arc graphs. We show natural generalizations of several properties of (proper) interval graphs that hold for some of these Helly circular-arc subclasses. Next, we describe characterizations for the subclasses of Helly circular-arc graphs, including forbidden induced subgraphs characterizations. These characterizations lead to efficient algorithms for recognizing graphs within these classes. Finally, we show how do these classes of graphs relate with straight and round digraphs.Comment: 39 pages, 13 figures. A previous version of the paper (entitled Proper Helly Circular-Arc Graphs) appeared at WG'0

Evaluation of Hybrid Arc and Volumetric-Modulated Arc Therapy Treatment Plans for Fractionated Stereotactic Intracranial Radiotherapy.

PURPOSE: The study was aimed to compare hybrid arc and volumetric-modulated arc therapy treatment plans for fractionated stereotactic radiotherapy of brain tumors. METHODS: Treatment plans of 22 patients were studied. Hybrid arc and volumetric-modulated arc therapy plans were generated using Brainlab iPlanDose and Varian Eclipse treatment planning systems, respectively, with 6 MV photon beams on a Varian TrueBeam STx linear accelerator (Palo Alto, CA). Prescription dose was 54 Gy. The fractionation was 1.8 Gy per fraction and 30 fractions in total, or 2 Gy per fraction and 27 fractions in total. Planning target volume ranged from 2.4 to 28.6 cm RESULTS: Conformity indexes of hybrid arc and volumetric-modulated arc therapy plans are 1.10 ± 0.10 and 1.14 ± 0.07, respectively ( P = .4); gradient indexes are 5.02 ± 1.20 and 5.64 ± 1.28, respectively ( P = .0001); homogeneity indexes are 1.02 ± 0.01 and 1.05 ± 0.01, respectively ( P = .0001); brainstem maximum doses are 53.87 ± 1.63 Gy and 54.06 ± 3.17 Gy, respectively ( P = .1); and optic chiasm maximum doses are 53.86 ± 1.28 Gy and 53.95 ± 1.81, respectively ( P = .4). The monitor unit efficiencies of hybrid arc and volumetric-modulated arc therapy plans are 2.57 ± 0.25 MU/cGy and 2.68 ± 0.24 MU/cGy, respectively ( P = .2). The differences of conformity index, gradient index, and homogeneity index between hybrid arc and volumetric-modulated arc therapy plans are small: 0.08 ± 0.05, 0.65 ± 0.46, and 0.02 ± 0.01, respectively. The maximum doses in organs at risks are similar between hybrid arc and volumetric-modulated arc therapy plans. Hybrid arc and volumetric-modulated arc therapy plans, which have similar monitor unit efficiencies, present similar dosimetric results in the fractionated intracranial radiotherapy

Motion studies of cathode roots in high current arcs using an optical fibre array based imaging system

This paper presents an integrated portable measurement system for the study of high speed and high temperature unsteady plasma flows such as those found in the vicinity of high current switching arcs. The system permits direct and non-intrusive measurement of arc light emission images with a capture rate of 1 million images per second (1MHz), and 8 bit intensity resolution. Novel software techniques are reported to measure arc trajectories. Results are presented on single high current (2kA) discharge events where the electrode and arc runner surfaces are investigated using 3D laser scanning methods; such that the position of the arc roots on the runner can be correlated to the measured trajectories. The results show evidence of the cathode arc root stepping along the arc runners, and regions of where the arc runner is eroded by a stationary arc

Large optical conductivity of Dirac semimetal Fermi arc surfaces states

Fermi arc surface states, a hallmark of topological Dirac semimetals, can host carriers that exhibit unusual dynamics distinct from that of their parent bulk. Here we find that Fermi arc carriers in intrinsic Dirac semimetals possess a strong and anisotropic light matter interaction. This is characterized by a large Fermi arc optical conductivity when light is polarized transverse to the Fermi arc; when light is polarized along the Fermi arc, Fermi arc optical conductivity is significantly muted. The large surface spectral weight is locked to the wide separation between Dirac nodes and persists as a large Drude weight of Fermi arc carriers when the system is doped. As a result, large and anisotropic Fermi arc conductivity provides a novel means of optically interrogating the topological surfaces states of Dirac semimetals.Comment: 8 pages, 3 figure