On the complexity of Generalized Chromatic Polynomials

J. Makowsky and B. Zilber (2004) showed that many variations of graph colorings, called CP-colorings in the sequel, give rise to graph polynomials. This is true in particular for harmonious colorings, convex colorings, mcct-colorings, and rainbow colorings, and many more. N. Linial (1986) showed that the chromatic polynomial �(G;X) is #P-hard to evaluate for all but three values X = 0, 1, 2, where evaluation is in P. This dichotomy includes evaluation at real or complex values, and has the further property that the set of points for which evaluation is in P is finite. We investigate how the complexity of evaluating univariate graph polynomials that arise from CPcolorings varies for different evaluation points. We show that for some CP-colorings (harmonious, convex) the complexity of evaluation follows a similar pattern to the chromatic polynomial. However, in other cases (proper edge colorings, mcct-colorings, H-free colorings) we could only obtain a dichotomy for evaluations at non-negative integer points. We also discuss some CP-colorings where we only have very partial results

The modeling of contaminant flow during proposed treatment of U.S. Department of Energy low-level radioactive mixed wastes

Estimations of waste materials throughput and the potential radiological and chemical releases resulting from the proposed treatment of US Department of Energy (DOE) low-level mixed wastes (LLMWs) were used to support analyses of risks and costs associated with various waste management alternatives outlined in the Office of Environmental Management Programmatic Environmental Impact Statement (EM PEIS). The modeling of material flow and contaminant releases through a consolidated waste management flowchart was performed by the WASTE{_}MGMT computational model developed by Argonne National Laboratory. This paper (1) briefly describes the process used to model estimated material and contaminant flow through the proposed treatment scenarios for the EM PEIS, (2) discusses the key site- and/or waste-stream-dependent factors involved in the determination of radiological and chemical emissions, and (3) explains the assumptions used to integrate the available LLMW database with the computational model

Effect of the molecular structure of the polymer and nucleation on the optical properties of polypropylene homo- and copolymers.

Two soluble nucleating agents were used to modify the optical properties of nine PP homo- and random copolymers. The ethylene content of the polymers changed between 0 and 5.3 wt%. Chain regularity was characterized by the stepwise isothermal segregation technique (SIST), while optical properties by the measurement of the haze of injection molded samples. Crystallization and melting characteristics were determined by differential scanning calorimetry (DSC). The analysis of the results proved that lamella thickness and change in crystallinity influence haze only slightly. A model was introduced which describes quantitatively the dependence of nucleation efficiency and haze on the concentration of the nucleating agent. The model assumes that the same factors influence the peak temperature of crystallization and optical properties. The analysis of the results proved that the assumption is valid under the same crystallization conditions. The parameters of the model depend on the molecular architecture of the polymer. Chain regularity determines supermolecular structure and thus the dependence of optical properties on nucleation

Antiinflammatory Therapy with Canakinumab for Atherosclerotic Disease

Background: Experimental and clinical data suggest that reducing inflammation without affecting lipid levels may reduce the risk of cardiovascular disease. Yet, the inflammatory hypothesis of atherothrombosis has remained unproved. Methods: We conducted a randomized, double-blind trial of canakinumab, a therapeutic monoclonal antibody targeting interleukin-1β, involving 10,061 patients with previous myocardial infarction and a high-sensitivity C-reactive protein level of 2 mg or more per liter. The trial compared three doses of canakinumab (50 mg, 150 mg, and 300 mg, administered subcutaneously every 3 months) with placebo. The primary efficacy end point was nonfatal myocardial infarction, nonfatal stroke, or cardiovascular death. RESULTS: At 48 months, the median reduction from baseline in the high-sensitivity C-reactive protein level was 26 percentage points greater in the group that received the 50-mg dose of canakinumab, 37 percentage points greater in the 150-mg group, and 41 percentage points greater in the 300-mg group than in the placebo group. Canakinumab did not reduce lipid levels from baseline. At a median follow-up of 3.7 years, the incidence rate for the primary end point was 4.50 events per 100 person-years in the placebo group, 4.11 events per 100 person-years in the 50-mg group, 3.86 events per 100 person-years in the 150-mg group, and 3.90 events per 100 person-years in the 300-mg group. The hazard ratios as compared with placebo were as follows: in the 50-mg group, 0.93 (95% confidence interval [CI], 0.80 to 1.07; P = 0.30); in the 150-mg group, 0.85 (95% CI, 0.74 to 0.98; P = 0.021); and in the 300-mg group, 0.86 (95% CI, 0.75 to 0.99; P = 0.031). The 150-mg dose, but not the other doses, met the prespecified multiplicity-adjusted threshold for statistical significance for the primary end point and the secondary end point that additionally included hospitalization for unstable angina that led to urgent revascularization (hazard ratio vs. placebo, 0.83; 95% CI, 0.73 to 0.95; P = 0.005). Canakinumab was associated with a higher incidence of fatal infection than was placebo. There was no significant difference in all-cause mortality (hazard ratio for all canakinumab doses vs. placebo, 0.94; 95% CI, 0.83 to 1.06; P = 0.31). Conclusions: Antiinflammatory therapy targeting the interleukin-1β innate immunity pathway with canakinumab at a dose of 150 mg every 3 months led to a significantly lower rate of recurrent cardiovascular events than placebo, independent of lipid-level lowering. (Funded by Novartis; CANTOS ClinicalTrials.gov number, NCT01327846.

MUSIC AND THE ACT OF SONG IN DANTE’S ‘PURGATORIO’ AND ‘PARADISO’

The present paper explores the relation between the vernacular words used to designate the Act of Song, and the inscribed texts of the Sung Music itself, by considering a set of key cases first in Purgatory and then in Paradise. It focuses on important moments of structural and literary transition, at the same time as showing how sung sacred texts relate to each other (and to other kinds of passages) in important functional ways. I examine how song works in five key moments of the protagonist’s journey: the exit from the final terrace of the Purgatorial mountain, and the opening of the vision of the Procession of the Books of the Bible, as well as Carlo Martello’s famous citation of the first ode of the Convivio, which I link to the sacred “Osanna” sung by the souls of the third heaven. Finally, I analyze the (sung) relationship between the angel Gabriel and the Virgin Mary, both in their descent to the eighth heaven and then in their “eternal home” in the Empyrean