Untangling polygons and graphs

Untangling is a process in which some vertices of a planar graph are moved to obtain a straight-line plane drawing. The aim is to move as few vertices as possible. We present an algorithm that untangles the cycle graph C_n while keeping at least \Omega(n^{2/3}) vertices fixed. For any graph G, we also present an upper bound on the number of fixed vertices in the worst case. The bound is a function of the number of vertices, maximum degree and diameter of G. One of its consequences is the upper bound O((n log n)^{2/3}) for all 3-vertex-connected planar graphs.Comment: 11 pages, 3 figure

Partial molar volumes of organic solutes in water. XXIII. Cyclic ketones at T = (298 to 573) K and pressures up to 30 MPa

Density data for dilute aqueous solutions of four cyclic ketones (cyclopentanone, cyclohexanone, cycloheptanone, and cyclohexane-1,4-dione) are presented together with standard molar volumes (partial molar volumes at infinite dilution) calculated from the experimental data. The measurements were performed at temperatures from T = 298 K up to T = 573 K. Experimental pressures were close to the saturated vapor pressure of water, and (15 and 30) MPa. The data were obtained using a high-temperature high-pressure flow vibrating-tube densimeter. Experimental standard molar volumes were correlated as a function of temperature and pressure using an empirical polynomial function. Contributions of the molecular structural segments (methylene and carbonyl groups) to the standard molar volume were also evaluated and analyzed. © 2011 Elsevier Ltd. All rights reserved

The Radius of Metric Subregularity

There is a basic paradigm, called here the radius of well-posedness, which quantifies the "distance" from a given well-posed problem to the set of ill-posed problems of the same kind. In variational analysis, well-posedness is often understood as a regularity property, which is usually employed to measure the effect of perturbations and approximations of a problem on its solutions. In this paper we focus on evaluating the radius of the property of metric subregularity which, in contrast to its siblings, metric regularity, strong regularity and strong subregularity, exhibits a more complicated behavior under various perturbations. We consider three kinds of perturbations: by Lipschitz continuous functions, by semismooth functions, and by smooth functions, obtaining different expressions/bounds for the radius of subregularity, which involve generalized derivatives of set-valued mappings. We also obtain different expressions when using either Frobenius or Euclidean norm to measure the radius. As an application, we evaluate the radius of subregularity of a general constraint system. Examples illustrate the theoretical findings.Comment: 20 page

Enhanced photoluminescence extraction efficiency from a diamond photonic crystal via leaky modes

Two-dimensional photonic crystal can be exploited as the top part of a light source in order to increase its extraction efficiency. Here, we report on the room-temperature intrinsic photoluminescence (PL) behavior of a nanocrystalline diamond (NCD) layer with diamond columns prepared on the top and periodically ordered into the lattice with square symmetry. Angle-resolved far-field measurements in the Gamma-X crystal direction of broadband visible PL revealed up to six-fold enhancement of extraction efficiency as compared to a smooth NCD layer. A photonic band diagram above the lightcone derived from these measurements is in agreement with the diagram obtained from transmission measurements and simulation, suggesting that the enhancement is primarily due to light's coupling to leaky modes

Review of methods used by chiropractors to determine the site for applying manipulation

Background: With the development of increasing evidence for the use of manipulation in the management of musculoskeletal conditions, there is growing interest in identifying the appropriate indications for care. Recently, attempts have been made to develop clinical prediction rules, however the validity of these clinical prediction rules remains unclear and their impact on care delivery has yet to be established. The current study was designed to evaluate the literature on the validity and reliability of the more common methods used by doctors of chiropractic to inform the choice of the site at which to apply spinal manipulation. Methods: Structured searches were conducted in Medline, PubMed, CINAHL and ICL, supported by hand searches of archives, to identify studies of the diagnostic reliability and validity of common methods used to identify the site of treatment application. To be included, studies were to present original data from studies of human subjects and be designed to address the region or location of care delivery. Only English language manuscripts from peer-reviewed journals were included. The quality of evidence was ranked using QUADAS for validity and QAREL for reliability, as appropriate. Data were extracted and synthesized, and were evaluated in terms of strength of evidence and the degree to which the evidence was favourable for clinical use of the method under investigation. Results: A total of 2594 titles were screened from which 201 articles met all inclusion criteria. The spectrum of manuscript quality was quite broad, as was the degree to which the evidence favoured clinical application of the diagnostic methods reviewed. The most convincing favourable evidence was for methods which confirmed or provoked pain at a specific spinal segmental level or region. There was also high quality evidence supporting the use, with limitations, of static and motion palpation, and measures of leg length inequality. Evidence of mixed quality supported the use, with limitations, of postural evaluation. The evidence was unclear on the applicability of measures of stiffness and the use of spinal x-rays. The evidence was of mixed quality, but unfavourable for the use of manual muscle testing, skin conductance, surface electromyography and skin temperature measurement. Conclusions: A considerable range of methods is in use for determining where in the spine to administer spinal manipulation. The currently published evidence falls across a spectrum ranging from strongly favourable to strongly unfavourable in regard to using these methods. In general, the stronger and more favourable evidence is for those procedures which take a direct measure of the presumptive site of care– methods involving pain provocation upon palpation or localized tissue examination. Procedures which involve some indirect assessment for identifying the manipulable lesion of the spine–such as skin conductance or thermography–tend not to be supported by the available evidence.https://doi.org/10.1186/2045-709X-21-3

Orientational Effects and Random Mixing in 1‑Alkanol + Nitrile Mixtures

1-Alkanol + alkanenitrile or + benzonitrile systems have been investigated by means of the molar excess functionsenthalpies (Hm E ), isobaric heat capacities (Cp,m E ), volumes (Vm E ), and entropiesand using the Flory model and the concentration−concentration structure factor (SCC(0)) formalism. From the analysis of the experimental data available in the literature, it is concluded that interactions are mainly of dipolar type. In addition, large Hm E values contrast with rather low Vm E values, indicating the existence of strong structural effects. Hm E measurements have been used to evaluate the enthalpy of the hydroxyl−nitrile interactions (ΔHOH−CN). They are stronger in methanol systems and become weaker when the alcohol size increases. In solutions with a given short chain 1-alkanol (up to 1-butanol), the replacement of ethanenitrile by butanenitrile weakens the mentioned interactions. Application of the Flory model shows that orientational effects exist in methanol or 1- nonanol, or 1-decanol + ethanenitrile mixtures. In the former solution, this is due to the existence of interactions between unlike molecules. For mixtures including 1-nonanol or 1-decanol, the systems at 298.15 K are close to their UCST (upper critical solution temperature), and interactions between like molecules are dominant. Orientational effects also are encountered in methanol or ethanol + butanenitrile mixtures because self-association of the alcohol plays a more important role. Aromaticity effect seems to enhance orientational effects. For the remainder of the systems under consideration, the random mixing hypothesis is attained to a rather large extent. Results from the application of the SCC(0) formalism show that homocoordination is the dominant trend in the investigated solutions, and are consistent with those obtained from the Flory model