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

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

Effectiveness of manual therapies: the UK evidence report

<p>Abstract</p> <p>Background</p> <p>The purpose of this report is to provide a succinct but comprehensive summary of the scientific evidence regarding the effectiveness of manual treatment for the management of a variety of musculoskeletal and non-musculoskeletal conditions.</p> <p>Methods</p> <p>The conclusions are based on the results of systematic reviews of randomized clinical trials (RCTs), widely accepted and primarily UK and United States evidence-based clinical guidelines, plus the results of all RCTs not yet included in the first three categories. The strength/quality of the evidence regarding effectiveness was based on an adapted version of the grading system developed by the US Preventive Services Task Force and a study risk of bias assessment tool for the recent RCTs.</p> <p>Results</p> <p>By September 2009, 26 categories of conditions were located containing RCT evidence for the use of manual therapy: 13 musculoskeletal conditions, four types of chronic headache and nine non-musculoskeletal conditions. We identified 49 recent relevant systematic reviews and 16 evidence-based clinical guidelines plus an additional 46 RCTs not yet included in systematic reviews and guidelines.</p> <p>Additionally, brief references are made to other effective non-pharmacological, non-invasive physical treatments.</p> <p>Conclusions</p> <p>Spinal manipulation/mobilization is effective in adults for: acute, subacute, and chronic low back pain; migraine and cervicogenic headache; cervicogenic dizziness; manipulation/mobilization is effective for several extremity joint conditions; and thoracic manipulation/mobilization is effective for acute/subacute neck pain. The evidence is inconclusive for cervical manipulation/mobilization alone for neck pain of any duration, and for manipulation/mobilization for mid back pain, sciatica, tension-type headache, coccydynia, temporomandibular joint disorders, fibromyalgia, premenstrual syndrome, and pneumonia in older adults. Spinal manipulation is not effective for asthma and dysmenorrhea when compared to sham manipulation, or for Stage 1 hypertension when added to an antihypertensive diet. In children, the evidence is inconclusive regarding the effectiveness for otitis media and enuresis, and it is not effective for infantile colic and asthma when compared to sham manipulation.</p> <p>Massage is effective in adults for chronic low back pain and chronic neck pain. The evidence is inconclusive for knee osteoarthritis, fibromyalgia, myofascial pain syndrome, migraine headache, and premenstrual syndrome. In children, the evidence is inconclusive for asthma and infantile colic.</p

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

Partial molar volumes of l-serine and l-threonine in aqueous ammonium sulfate solutions at (278.15, 288.15, 298.15, and 308.15) k

In this study, the partial molar volumes of l-serine and l-threonine in aqueous solutions of ammonium sulfate at (0.0, 0.1, 0.3, 0.7, and 1.0) mol·kg-1 are reported between 278.15 and 308.15 K. Transfer volumes and hydration numbers were obtained, which are larger in l-serine than in l-threonine. Dehydration of the amino acids is observed, rising with the temperature and salt molality. The data suggest that interactions between ions and charged/hydrophilic groups are predominant, and by applying the McMillan and Mayer formalism, it was concluded that they are mainly pair wise. The combination of the data presented in this study with solubility and molecular dynamics data suggests a stronger interaction of the ammonium cation with the zwitterionic centers of the amino acids when compared to the interactions of those centers with the sulfate anion