On well-covered triangulations: Part I

AbstractA graph G is said to be well-covered if every maximal independent set of vertices has the same cardinality. A planar (simple) graph in which each face is a triangle is called a triangulation. It is the aim of this paper to prove that there are no 5-connected planar well-covered triangulations

Rainbow domination and related problems on some classes of perfect graphs

Let $k \in \mathbb{N}$ and let $G$ be a graph. A function $f: V(G) \rightarrow 2^{[k]}$ is a rainbow function if, for every vertex $x$ with $f(x)=\emptyset$, $f(N(x)) =[k]$. The rainbow domination number $\gamma_{kr}(G)$ is the minimum of $\sum_{x \in V(G)} |f(x)|$ over all rainbow functions. We investigate the rainbow domination problem for some classes of perfect graphs

The Firefighter Problem: A Structural Analysis

We consider the complexity of the firefighter problem where b>=1 firefighters are available at each time step. This problem is proved NP-complete even on trees of degree at most three and budget one (Finbow et al.,2007) and on trees of bounded degree b+3 for any fixed budget b>=2 (Bazgan et al.,2012). In this paper, we provide further insight into the complexity landscape of the problem by showing that the pathwidth and the maximum degree of the input graph govern its complexity. More precisely, we first prove that the problem is NP-complete even on trees of pathwidth at most three for any fixed budget b>=1. We then show that the problem turns out to be fixed parameter-tractable with respect to the combined parameter "pathwidth" and "maximum degree" of the input graph

Challenging the Perceptions of Human Tendon Allografts: Influence of Donor Age, Sex, Height, and Tendon on Biomechanical Properties

Background: The use of allograft tendons has increased for primary and revision anterior cruciate ligament reconstruction, but allograft supply is currently limited to a narrow range of tendons and donors up to the age of 65 years. Expanding the range of donors and tendons could help offset an increasing clinical demand. Purpose: To investigate the effects of donor age, sex, height, and specific tendon on the mechanical properties of a range of human lower leg tendons. Study Design: Descriptive laboratory study. Methods: Nine tendons were retrieved from 39 fresh-frozen human cadaveric lower legs (35 donors [13 female, 22 male]; age, 49-99 years; height, 57-85 inches [145-216 cm]) including: Achilles tendon, tibialis posterior and anterior, fibularis longus and brevis, flexor and extensor hallucis longus, plantaris, and flexor digitorum longus. Tendons underwent tensile loading to failure measuring cross-sectional area (CSA), maximum load, strain at failure, ultimate tensile strength, and elastic modulus. Results from 332 tendons were analyzed using mixed-effects linear regression, accounting for donor age, sex, height, and weight. Results: Mechanical properties were significantly different among tendons and were substantially greater than the effects of donor characteristics. Significant effects of donor sex, age, and height were limited to specific tendons: Achilles tendon, tibialis posterior, and tibialis anterior. All other tendons were unaffected. The Achilles tendon was most influenced by donor variables: greater CSA in men (β = 15.45 mm2; Šidák adjusted P < .0001), decreased maximum load with each year of increased age (β = −17.20 N per year; adjusted P = .0253), and increased CSA (β = 1.92 mm2 per inch; adjusted P < .0001) and maximum load (β = 86.40 N per inch; adjusted P < .0001) with each inch of increased height. Conclusion: Mechanical properties vary significantly across different human tendons. The effects of donor age, sex, and height are relatively small, are limited to specific tendons, and affect different tendons uniquely. The findings indicate that age negatively affected only the Achilles tendon (maximum load) and challenge the exclusion of donors aged >65 years across all tendon grafts. Clinical Relevance: The findings support including a broader range of tendons for use as allografts for anterior cruciate ligament reconstruction and reviewing the current exclusion criterion of donors aged >65 years

Characterizing Hepatitis C Virus–Specific CD4+ T Cells Following Viral‐Vectored Vaccination, Directly Acting Antivirals, and Spontaneous Viral Cure

BACKGROUND AND AIMS: Induction of functional helper CD4+ T cells is the hallmark of a protective immune response against hepatitis C virus (HCV), associated with spontaneous viral clearance. Heterologous prime/boost viral vectored vaccination has demonstrated induction of broad and polyfunctional HCV-specific CD8+ T cells in healthy volunteers; however, much less is known about CD4+ T-cell subsets following vaccination. APPROACH AND RESULTS: We analyzed HCV-specific CD4+ T-cell populations using major histocompatibility complex class II tetramers in volunteers undergoing HCV vaccination with recombinant HCV adenoviral/modified vaccinia Ankara viral vectors. Peptide-specific T-cell responses were tracked over time, and functional (proliferation and cytokine secretion) and phenotypic (cell surface and intranuclear) markers were assessed using flow cytometry. These were compared to CD4+ responses in 10 human leukocyte antigen-matched persons with HCV spontaneous resolution and 21 chronically infected patients treated with directly acting antiviral (DAA) therapy. Vaccination induced tetramer-positive CD4+ T cells that were highest 1-4 weeks after boosting (mean, 0.06%). Similar frequencies were obtained for those tracked following spontaneous resolution of disease (mean, 0.04%). In addition, the cell-surface phenotype (CD28, CD127) memory subset markers and intranuclear transcription factors, as well as functional capacity of peptide-specific CD4+ T-cell responses characterized after vaccination, are comparable to those following spontaneous viral resolution. In contrast, helper responses in chronic infection were infrequently detected and poorly functional and did not consistently recover following HCV cure. CONCLUSIONS: Helper CD4+ T-cell phenotype and function following HCV viral vectored vaccination resembles "protective memory" that is observed following spontaneous clearance of HCV. DAA cure does not promote resurrection of exhausted CD4+ T-cell memory in chronic infection

A Novel Unsupervised Method to Identify Genes Important in the Anti-viral Response: Application to Interferon/Ribavirin in Hepatitis C Patients

Background: Treating hepatitis C with interferon/ribavirin results in a varied response in terms of decrease in viral titer and ultimate outcome. Marked responders have a sharp decline in viral titer within a few days of treatment initiation, whereas in other patients there is no effect on the virus (poor responders). Previous studies have shown that combination therapy modifies expression of hundreds of genes in vitro and in vivo. However, identifying which, if any, of these genes have a role in viral clearance remains challenging. Aims: The goal of this paper is to link viral levels with gene expression and thereby identify genes that may be responsible for early decrease in viral titer. Methods: Microarrays were performed on RNA isolated from PBMC of patients undergoing interferon/ribavirin therapy. Samples were collected at pre-treatment (day 0), and 1, 2, 7, 14 and 28 days after initiating treatment. A novel method was applied to identify genes that are linked to a decrease in viral titer during interferon/ribavirin treatment. The method uses the relationship between inter-patient gene expression based proximities and inter-patient viral titer based proximities to define the association between microarray gene expression measurements of each gene and viral-titer measurements. Results: We detected 36 unique genes whose expressions provide a clustering of patients that resembles viral titer based clustering of patients. These genes include IRF7, MX1, OASL and OAS2, viperin and many ISG's of unknown function. Conclusion: The genes identified by this method appear to play a major role in the reduction of hepatitis C virus during the early phase of treatment. The method has broad utility and can be used to analyze response to any group of factors influencing biological outcome such as antiviral drugs or anti-cancer agents where microarray data are available. © 2007 Brodsky et al

An improved measurement of muon antineutrino disappearance in MINOS

We report an improved measurement of muon anti-neutrino disappearance over a distance of 735km using the MINOS detectors and the Fermilab Main Injector neutrino beam in a muon anti-neutrino enhanced configuration. From a total exposure of 2.95e20 protons on target, of which 42% have not been previously analyzed, we make the most precise measurement of the anti-neutrino "atmospheric" delta-m squared = 2.62 +0.31/-0.28 (stat.) +/- 0.09 (syst.) and constrain the anti-neutrino atmospheric mixing angle >0.75 (90%CL). These values are in agreement with those measured for muon neutrinos, removing the tension reported previously.Comment: 5 pages, 4 figures. In submission to Phys.Rev.Let

First measurement of neutrino oscillation parameters using neutrinos and antineutrinos by NOvA.

The NOvA experiment has seen a 4.4σ signal of ν[over ¯]_{e} appearance in a 2&nbsp;GeV ν[over ¯]_{μ} beam at a distance of 810&nbsp;km. Using 12.33×10^{20} protons on target delivered to the Fermilab NuMI neutrino beamline, the experiment recorded 27 ν[over ¯]_{μ}→ν[over ¯]_{e} candidates with a background of 10.3 and 102 ν[over ¯]_{μ}→ν[over ¯]_{μ} candidates. This new antineutrino data are combined with neutrino data to measure the parameters |Δm_{32}^{2}|=2.48_{-0.06}^{+0.11}×10^{-3}  eV^{2}/c^{4} and sin^{2}θ_{23} in the ranges from (0.53-0.60) and (0.45-0.48) in the normal neutrino mass hierarchy. The data exclude most values near δ_{CP}=π/2 for the inverted mass hierarchy by more than 3σ and favor the normal neutrino mass hierarchy by 1.9σ and θ_{23} values in the upper octant by 1.6σ

Observation of seasonal variation of atmospheric multiple-muon events in the NOvA Near Detector

Using two years of data from the NOvA Near Detector at Fermilab, we report a seasonal variation of cosmic ray induced multiple-muon (Nμ≥2) event rates which has an opposite phase to the seasonal variation in the atmospheric temperature. The strength of the seasonal multiple-muon variation is shown to increase as a function of the muon multiplicity. However, no significant dependence of the strength of the seasonal variation of the multiple-muon variation is seen as a function of the muon zenith angle, or the spatial or angular separation between the correlated muons