Euclidean TSP with few inner points in linear space

Given a set of $n$ points in the Euclidean plane, such that just $k$ points are strictly inside the convex hull of the whole set, we want to find the shortest tour visiting every point. The fastest known algorithm for the version when $k$ is significantly smaller than $n$, i.e., when there are just few inner points, works in $O(k^{11\sqrt{k}} k^{1.5} n^{3})$ time [Knauer and Spillner, WG 2006], but also requires space of order $k^{c\sqrt{k}}n^{2}$. The best linear space algorithm takes $O(k! k n)$ time [Deineko, Hoffmann, Okamoto, Woeginer, Oper. Res. Lett. 34(1), 106-110]. We construct a linear space $O(nk^2+k^{O(\sqrt{k})})$ time algorithm. The new insight is extending the known divide-and-conquer method based on planar separators with a matching-based argument to shrink the instance in every recursive call. This argument also shows that the problem admits a quadratic bikernel.Comment: under submissio

Efficacy and safety of acupuncture for chronic pain caused by gonarthrosis: A study protocol of an ongoing multi-centre randomised controlled clinical trial [ISRCTN27450856]

BACKGROUND: Controlled clinical trials produced contradictory results with respect to a specific analgesic effect of acupuncture. There is a lack of large multi-centre acupuncture trials. The German Acupuncture Trial represents the largest multi-centre study of acupuncture in the treatment of chronic pain caused by gonarthrosis up to now. METHODS: 900 patients will be randomised to three treatment arms. One group receives verum acupuncture, the second sham acupuncture, and the third conservative standard therapy. The trial protocol is described with eligibility criteria, detailed information on the treatment definition, blinding, endpoints, safety evaluation, statistical methods, sample size determination, monitoring, legal aspects, and the current status of the trial. DISCUSSION: A critical discussion is given regarding the considerations about standardisation of the acupuncture treatment, the choice of the control group, and the blinding of patients and observers

Lawson criterion for ignition exceeded in an inertial fusion experiment

For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a positive thermodynamic feedback loop with rapidly increasing temperature. In inertially confined fusion, ignition is a state where the fusion plasma can begin "burn propagation" into surrounding cold fuel, enabling the possibility of high energy gain. While "scientific breakeven" (i.e., unity target gain) has not yet been achieved (here target gain is 0.72, 1.37 MJ of fusion for 1.92 MJ of laser energy), this Letter reports the first controlled fusion experiment, using laser indirect drive, on the National Ignition Facility to produce capsule gain (here 5.8) and reach ignition by nine different formulations of the Lawson criterion

Oncoplastic Breast Consortium consensus conference on nipple-sparing mastectomy.

Purpose Indications for nipple-sparing mastectomy (NSM) have broadened to include the risk reducing setting and locally advanced tumors, which resulted in a dramatic increase in the use of NSM. The Oncoplastic Breast Consortium consensus conference on NSM and immediate reconstruction was held to address a variety of questions in clinical practice and research based on published evidence and expert panel opinion. Methods The panel consisted of 44 breast surgeons from 14 countries across four continents with a background in gynecology, general or reconstructive surgery and a practice dedicated to breast cancer, as well as a patient advocate. Panelists presented evidence summaries relating to each topic for debate during the in-person consensus conference. The iterative process in question development, voting, and wording of the recommendations followed the modified Delphi methodology. Results Consensus recommendations were reached in 35, majority recommendations in 24, and no recommendations in the remaining 12 questions. The panel acknowledged the need for standardization of various aspects of NSM and immediate reconstruction. It endorsed several oncological contraindications to the preservation of the skin and nipple. Furthermore, it recommended inclusion of patients in prospective registries and routine assessment of patient-reported outcomes. Considerable heterogeneity in breast reconstruction practice became obvious during the conference. Conclusions In case of conflicting or missing evidence to guide treatment, the consensus conference revealed substantial disagreement in expert panel opinion, which, among others, supports the need for a randomized trial to evaluate the safest and most efficacious reconstruction techniques

Experimental confirmation of efficient island divertor operation and successful neoclassical transport optimization in Wendelstein 7-X

We present recent highlights from the most recent operation phases of Wendelstein 7-X, the most advanced stellarator in the world. Stable detachment with good particle exhaust, low impurity content, and energy confinement times exceeding 100 ms, have been maintained for tens of seconds. Pellet fueling allows for plasma phases with reduced ion-temperature-gradient turbulence, and during such phases, the overall confinement is so good (energy confinement times often exceeding 200 ms) that the attained density and temperature profiles would not have been possible in less optimized devices, since they would have had neoclassical transport losses exceeding the heating applied in W7-X. This provides proof that the reduction of neoclassical transport through magnetic field optimization is successful. W7-X plasmas generally show good impurity screening and high plasma purity, but there is evidence of longer impurity confinement times during turbulence-suppressed phases.EC/H2020/633053/EU/Implementation of activities described in the Roadmap to Fusion during Horizon 2020 through a Joint programme of the members of the EUROfusion consortium/ EUROfusio