Association of Changes in Cardiovascular Health Metrics and Risk of Subsequent Cardiovascular Disease and Mortality

Background The extent to which change in cardiovascular health (CVH) in midlife reduces risk of subsequent cardiovascular disease and mortality is unclear. Methods and Results CVH was computed at 2 ARIC (Atherosclerosis Risk in Communities) study visits in 1987 to 1989 and 1993 to 1995, using 7 metrics (smoking, body mass index, total cholesterol, blood glucose, blood pressure, physical activity, and diet), each classified as poor, intermediate, and ideal. Overall CVH was classified as poor, intermediate, and ideal to correspond to 0 to 2, 3 to 4, and 5 to 7 metrics at ideal levels. There 10 038 participants, aged 44 to 66 years that were eligible. From the first to the second study visit, there was an improvement in overall CVH for 17% of participants and a decrease in CVH for 21% of participants. At both study visits, 28%, 27%, and 6% had poor, intermediate, and ideal overall CVH, respectively. Compared with those with poor CVH at both visits, the risk of cardiovascular disease (hazard ratio [HR], 0.26; 95% CI, 0.20–0.34) and mortality (HR, 0.35; 95% CI, 0.29–0.44) was lowest in those with ideal CVH at both measures. Improvement from poor to intermediate/ideal CVH was also associated with a lower risk of cardiovascular disease (HR, 0.67; 95% CI, 0.59–0.75) and mortality (HR, 0.80; 95% CI, 0.72–0.89). Conclusions Improvement in CVH or stable ideal CVH, compared with those with poor CVH over time, is associated with a lower risk of incident cardiovascular disease and all‐cause mortality. The change in smoking status and cholesterol may have accounted for a large part of the observed association.

Generalized Newton complementary duals of monomial ideals

Given a monomial ideal in a polynomial ring over a field, we define the generalized Newton complementary dual of the given ideal. We show good properties of such duals including linear quotients and isomorphism between the special fiber rings. We construct the cellular free resolutions of duals of strongly stable ideals generated in the same degree. When the base ideal is generated in degree two, we provide an explicit description of cellular free resolution of the dual of a compatible generalized stable ideal.

Macaulay-like marked bases

We define marked sets and bases over a quasi-stable ideal [Formula: see text] in a polynomial ring on a Noetherian [Formula: see text]-algebra, with [Formula: see text] a field of any characteristic. The involved polynomials may be non-homogeneous, but their degree is bounded from above by the maximum among the degrees of the terms in the Pommaret basis of [Formula: see text] and a given integer [Formula: see text]. Due to the combinatorial properties of quasi-stable ideals, these bases behave well with respect to homogenization, similarly to Macaulay bases. We prove that the family of marked bases over a given quasi-stable ideal has an affine scheme structure, is flat and, for large enough [Formula: see text], is an open subset of a Hilbert scheme. Our main results lead to algorithms that explicitly construct such a family. We compare our method with similar ones and give some complexity results.

Note on Primitive Ideals of Enveloping Algebras in Prime Characteristic

Let [Formula: see text] be a restricted Lie algebra over an algebraically closed field F of characteristic p > 0, [Formula: see text] the center of the universal enveloping algebra [Formula: see text] of [Formula: see text]. In this note, we study primitive ideals of [Formula: see text]. The following results are included: (1) The ideal of [Formula: see text] generated by the central character ideal associated with any irreducible [Formula: see text]-module has finite co-dimension in [Formula: see text]. Furthermore, the co-dimension is no less than [Formula: see text], where [Formula: see text] is the maximal dimension of irreducible [Formula: see text]-modules. (2) Each annihilator ideal of irreducible [Formula: see text]-modules of maximal dimension is generated by the corresponding central character ideal in [Formula: see text]. (3) Each G-stable ideal in [Formula: see text] for [Formula: see text] contains nonzero fixed points under the action of G, where G is a connected reductive algebraic group. Additionally, the arguments on ideals help us to give an alternative description of the Azumaya locus in the Zassenhaus variety without using the normality of the Zassenhaus variety.

An introduction to argumentation semantics

This paper presents an overview on the state of the art of semantics for abstract argumentation, covering both some of the most influential literature proposals and some general issues concerning semantics definition and evaluation. As to the former point, the paper reviews Dung's original notions of complete, grounded, preferred, and stable semantics, as well as subsequently proposed notions like semi-stable, ideal, stage, and CF2 semantics, considering both the extension-based and the labelling-based approaches with respect to their definitions. As to the latter point, the paper presents an extensive set of general properties for semantics evaluation and analyzes the notions of argument justification and skepticism. The final part of the paper is focused on the discussion of some relationships between semantics properties and domain-specific requirements.