Minimum-weight triangulation is NP-hard

A triangulation of a planar point set S is a maximal plane straight-line graph with vertex set S. In the minimum-weight triangulation (MWT) problem, we are looking for a triangulation of a given point set that minimizes the sum of the edge lengths. We prove that the decision version of this problem is NP-hard. We use a reduction from PLANAR-1-IN-3-SAT. The correct working of the gadgets is established with computer assistance, using dynamic programming on polygonal faces, as well as the beta-skeleton heuristic to certify that certain edges belong to the minimum-weight triangulation.Comment: 45 pages (including a technical appendix of 13 pages), 28 figures. This revision contains a few improvements in the expositio

On a Linear Program for Minimum-Weight Triangulation

Minimum-weight triangulation (MWT) is NP-hard. It has a polynomial-time constant-factor approximation algorithm, and a variety of effective polynomial- time heuristics that, for many instances, can find the exact MWT. Linear programs (LPs) for MWT are well-studied, but previously no connection was known between any LP and any approximation algorithm or heuristic for MWT. Here we show the first such connections: for an LP formulation due to Dantzig et al. (1985): (i) the integrality gap is bounded by a constant; (ii) given any instance, if the aforementioned heuristics find the MWT, then so does the LP.Comment: To appear in SICOMP. Extended abstract appeared in SODA 201

Retrospective Comparison of Non-Skin-Sparing Mastectomy and Skin-Sparing Mastectomy with Immediate Breast Reconstruction

Background. We compared Skin-sparing mastectomy (SSM) with immediate breast reconstruction and Non-skin-sparing mastectomy (NSSM), various types of incision in SSM. Method. Records of 202 consecutive breast cancer patients were reviewed retrospectively. Also in the SSM, three types of skin incision were used. Type A was a periareolar incision with a lateral extension, type B was a periareolar incision and axillary incision, and type C included straight incisions, a small elliptical incision (base line of nipple) within areolar complex and axillary incision. Results. Seventy-three SSMs and 129 NSSMs were performed. The mean follow-up was 30.0 (SSM) and 41.1 (NSSM) months. Respective values for the two groups were: mean age 47.0 and 57; seven-year cumulative local disease-free survival 92.1% and 95.2%; post operative skin necrosis 4.1% and 3.1%. In the SSM, average areolar diameter in type A & B was 35.4 mm, 43.0 mm in type C and postoperative nipple-areolar plasty was performed 61% in type A & B, 17% in type C, respectively. Conclusion. SSM for early breast cancer is associated with low morbidity and oncological safety that are as good as those of NSSM. Also in SSM, Type C is far superior as regards cost and cosmetic outcomes

Publishing and sharing multi-dimensional image data with OMERO

Imaging data are used in the life and biomedical sciences to measure the molecular and structural composition and dynamics of cells, tissues, and organisms. Datasets range in size from megabytes to terabytes and usually contain a combination of binary pixel data and metadata that describe the acquisition process and any derived results. The OMERO image data management platform allows users to securely share image datasets according to specific permissions levels: data can be held privately, shared with a set of colleagues, or made available via a public URL. Users control access by assigning data to specific Groups with defined membership and access rights. OMERO’s Permission system supports simple data sharing in a lab, collaborative data analysis, and even teaching environments. OMERO software is open source and released by the OME Consortium at www.openmicroscopy.org

琉球列島におけるソテツ(ソテツ科) の小羽片形態の地理的変異

Sixteen populations of Cycas revoluta（Cycadaceae）, covering almost all distribution areas on the Ryukyu Islands and Kyushu, Japan, were examined to determine geographical differences in leaflet morphology. We assessed four morphological characteristics of leaflets and applied one-way analysis of variance（ANOVA）to test thedifference in each morphological character. Cluster analysis based on four morphological properties resulted in two clear major clusters comprising northerly and southerly populations that were demarcated north of Yorontou and south of Tokunoshima Islands, respectively. Northern cycads tended to have leaflet margins with shallow recurving and narrower leaflet lamina width, while the southern populations had deeply recurved leaflet margins and wider leaflet lamina width. The morphological differentiation may imply intraspecific differentiation.琉球列島から九州にかけて分布するソテツ（Cycas revoluta Thunb.）の自生地16 集団を対象にして，小羽片の形態の地理的な分化を検証した。小羽片の横断面における小羽片の幅と厚さ，中肋の厚さ，小羽片の縁の巻き込みの高さの4 形質を測定してクラスター解析にかけたところ，北方型と南方型の2 つのグループに分かれた。北方型には主に与論島以北の集団が含まれ，南方型には主に徳之島以南の集団が含まれる。ただし，この境界にある徳之島は南方型に，沖永良部島は北方型に含まれる。これには，小羽片の幅と縁の巻き込みの高さに南北間で違いがあることが寄与しており，とくに縁の巻き込みの高さは，南側で大きく巻き込む傾向が見られた

Robustness and Stability of the Gene Regulatory Network Involved in DV Boundary Formation in the Drosophila Wing

Gene regulatory networks have been conserved during evolution. The Drosophila wing and the vertebrate hindbrain share the gene network involved in the establishment of the boundary between dorsal and ventral compartments in the wing and adjacent rhombomeres in the hindbrain. A positive feedback-loop between boundary and non-boundary cells and mediated by the activities of Notch and Wingless/Wnt-1 leads to the establishment of a Notch dependent organizer at the boundary. By means of a Systems Biology approach that combines mathematical modeling and both in silico and in vivo experiments in the Drosophila wing primordium, we modeled and tested this regulatory network and present evidence that a novel property, namely refractoriness to the Wingless signaling molecule, is required in boundary cells for the formation of a stable dorsal-ventral boundary. This new property has been validated in vivo, promotes mutually exclusive domains of Notch and Wingless activities and confers stability to the dorsal-ventral boundary. A robustness analysis of the regulatory network complements our results and ensures its biological plausibility

Efficacy and safety of single-dose ivermectin in mild-to-moderate COVID-19: the double-blind, randomized, placebo-controlled CORVETTE-01 trial

BackgroundTo investigate whether ivermectin inhibits SARS-CoV-2 proliferation in patients with mild-to-moderate COVID-19 using time to a negative COVID-19 reverse transcription-polymerase chain reaction (RT-PCR) test.MethodsCORVETTE-01 was a double-blind, randomized, placebo-controlled study (August 2020–October 2021) conducted in Japan. Overall, 248 patients diagnosed with COVID-19 using RT-PCR were assessed for eligibility. A single oral dose of ivermectin (200  μg/kg) or placebo was administered under fasting. The primary outcome was time to a negative COVID-19 RT-PCR test result for SARS-CoV-2 nucleic acid, assessed using stratified log-rank test and Cox regression models.ResultsOverall, 112 and 109 patients were randomized to ivermectin and placebo, respectively; 106 patients from each group were included in the full analysis set (male [%], mean age: 68.9%, 47.9 years [ivermectin]; 62.3%, 47.5 years [placebo]). No significant difference was observed in the occurrence of negative RT-PCR tests between the groups (hazard ratio, 0.96; 95% confidence interval [CI] 0.70–1.32; p = 0.785). Median (95% CI) time to a negative RT-PCR test was 14.0 (13.0–16.0) and 14.0 (12.0–16.0) days for ivermectin and placebo, respectively; 82.1% and 84% of patients achieved negative RT-PCR tests, respectively.ConclusionIn patients with COVID-19, single-dose ivermectin was ineffective in decreasing the time to a negative RT-PCR test.Clinical Trial RegistrationClinicalTrials.gov, NCT04703205

Neuronal Deletion of Caspase 8 Protects against Brain Injury in Mouse Models of Controlled Cortical Impact and Kainic Acid-Induced Excitotoxicity

system. mice demonstrated superior survival, reduced seizure severity, less apoptosis, and reduced caspase 3 processing. Uninjured aged knockout mice showed improved learning and memory, implicating a possible role for caspase 8 in cognitive decline with aging.Neuron-specific deletion of caspase 8 reduces brain damage and improves post-traumatic functional outcomes, suggesting an important role for this caspase in pathophysiology of acute brain trauma