Regularity of prime ideals

We answer several natural questions which arise from a recent paper of McCullough and Peeva providing counterexamples to the Eisenbud\u2013Goto Regularity Conjecture. We give counterexamples using Rees algebras, and also construct counterexamples that do not rely on the Mayr\u2013Meyer construction. Furthermore, examples of prime ideals for which the difference between the maximal degree of a minimal generator and the maximal degree of a minimal first syzygy can be made arbitrarily large are given. Using a result of Ananyan-Hochster we show that there exists an upper bound on regularity of prime ideals in terms of the multiplicity alone

Dimension of the Torelli group for Out(F_n)

Let T_n be the kernel of the natural map from Out(F_n) to GL(n,Z). We use combinatorial Morse theory to prove that T_n has an Eilenberg-MacLane space which is (2n-4)-dimensional and that H_{2n-4}(T_n,Z) is not finitely generated (n at least 3). In particular, this recovers the result of Krstic-McCool that T_3 is not finitely presented. We also give a new proof of the fact, due to Magnus, that T_n is finitely generated.Comment: 27 pages, 9 figure

Risk factors for heart failure in patients with type 2 diabetes mellitus and stage 4 chronic kidney disease treated with bardoxolone methyl

Background: A phase 3 randomized clinical trial was designed to test whether bardoxolone methyl, a nuclear factor erythroid-2–related factor 2 (Nrf2) activator, slows progression to end-stage renal disease in patients with stage 4 chronic kidney disease and type 2 diabetes mellitus. The trial was terminated because of an increase in heart failure in the bardoxolone methyl group; many of the events were clinically associated with fluid retention.<p></p> Methods and Results: We randomized 2,185 patients with type 2 diabetes mellitus (T2DM) and stage 4 chronic kidney disease (CKD) (estimated glomerular filtration rate 15 to <30 mL min−1 1.73 m−2) to once-daily bardoxolone methyl (20 mg) or placebo. We used classification and regression tree analysis to identify baseline factors predictive of heart failure or fluid overload events. Elevated baseline B-type natriuretic peptide and previous hospitalization for heart failure were identified as predictors of heart failure events; bardoxolone methyl increased the risk of heart failure by 60% in patients with these risk factors. For patients without these baseline characteristics, the risk for heart failure events among bardoxolone methyl– and placebo-treated patients was similar (2%). The same risk factors were also identified as predictors of fluid overload and appeared to be related to other serious adverse events.<p></p> Conclusions: Bardoxolone methyl contributed to events related to heart failure and/or fluid overload in a subpopulation of susceptible patients with an increased risk for heart failure at baseline. Careful selection of participants and vigilant monitoring of the study drug will be required in any future trials of bardoxolone methyl to mitigate the risk of heart failure and other serious adverse events.<p></p&gt

Maximal quadratic modules on *-rings

We generalize the notion of and results on maximal proper quadratic modules from commutative unital rings to $\ast$-rings and discuss the relation of this generalization to recent developments in noncommutative real algebraic geometry. The simplest example of a maximal proper quadratic module is the cone of all positive semidefinite complex matrices of a fixed dimension. We show that the support of a maximal proper quadratic module is the symmetric part of a prime $\ast$-ideal, that every maximal proper quadratic module in a Noetherian $\ast$-ring comes from a maximal proper quadratic module in a simple artinian ring with involution and that maximal proper quadratic modules satisfy an intersection theorem. As an application we obtain the following extension of Schm\" udgen's Strict Positivstellensatz for the Weyl algebra: Let $c$ be an element of the Weyl algebra $\mathcal{W}(d)$ which is not negative semidefinite in the Schr\" odinger representation. It is shown that under some conditions there exists an integer $k$ and elements $r_1,...,r_k \in \mathcal{W}(d)$ such that $\sum_{j=1}^k r_j c r_j^\ast$ is a finite sum of hermitian squares. This result is not a proper generalization however because we don't have the bound $k \le d$.Comment: 11 page

Defining forgiveness: Christian clergy and general population perspectives.

The lack of any consensual definition of forgiveness is a serious weakness in the research literature (McCullough, Pargament &amp; Thoresen, 2000). As forgiveness is at the core of Christianity, this study returns to the Christian source of the concept to explore the meaning of forgiveness for practicing Christian clergy. Comparisons are made with a general population sample and social science definitions of forgiveness to ensure that a shared meaning of forgiveness is articulated. Anglican and Roman Catholic clergy (N = 209) and a general population sample (N = 159) completed a postal questionnaire about forgiveness. There is agreement on the existence of individual differences in forgiveness. Clergy and the general population perceive reconciliation as necessary for forgiveness while there is no consensus within psychology. The clergy suggests that forgiveness is limitless and that repentance is unnecessary while the general population suggests that there are limits and that repentance is necessary. Psychological definitions do not conceptualize repentance as necessary for forgiveness and the question of limits has not been addressed although within therapy the implicit assumption is that forgiveness is limitless.</p

Developing autonomous learning in first year university students using perspectives from positive psychology

Autonomous learning is a commonly occurring learning outcome from university study, and it is argued that students require confidence in their own abilities to achieve this. Using approaches from positive psychology, this study aimed to develop confidence in first‐year university students to facilitate autonomous learning. Psychological character strengths were assessed in 214 students on day one at university. Two weeks later their top three strengths were given to them in study skills modules as part of a psycho‐educational intervention designed to increase their self‐efficacy and self‐esteem. The impact of the intervention was assessed against a control group of 40 students who had not received the intervention. The results suggested that students were more confident after the intervention, and that levels of autonomous learning increased significantly compared to the controls. Character strengths were found to be associated with self‐efficacy, self‐esteem and autonomous learning in ways that were theoretically meaningful

Cyclic Statistics In Three Dimensions

While 2-dimensional quantum systems are known to exhibit non-permutation, braid group statistics, it is widely expected that quantum statistics in 3-dimensions is solely determined by representations of the permutation group. This expectation is false for certain 3-dimensional systems, as was shown by the authors of ref. [1,2,3]. In this work we demonstrate the existence of ``cyclic'', or $Z_n$, {\it non-permutation group} statistics for a system of n > 2 identical, unknotted rings embedded in $R^3$. We make crucial use of a theorem due to Goldsmith in conjunction with the so called Fuchs-Rabinovitch relations for the automorphisms of the free product group on n elements.Comment: 13 pages, 1 figure, LaTex, minor page reformattin

XO-3b: A Massive Planet in an Eccentric Orbit Transiting an F5V Star

We report the discovery of a massive (Mpsini = 13.02 +/- 0.64 Mjup; total mass 13.25 +/- 0.64 Mjup), large (1.95 +/- 0.16 Rjup) planet in a transiting, eccentric orbit (e = 0.260 +/- 0.017) around a 10th magnitude F5V star in the constellation Camelopardalis. We designate the planet XO-3b, and the star XO-3, also known as GSC 03727-01064. The orbital period of XO-3b is 3.1915426 +/- 0.00014 days. XO-3 lacks a trigonometric distance; we estimate its distance to be 260 +/- 23 pc. The radius of XO-3 is 2.13 +/- 0.21 Rsun, its mass is 1.41 +/- 0.08 Msun, its vsini = 18.54 +/- 0.17 km/s, and its metallicity is [Fe/H] = -0.177 +/- 0.027. This system is unusual for a number of reasons. XO-3b is one of the most massive planets discovered around any star for which the orbital period is less than 10 days. The mass is near the deuterium burning limit of 13 Mjup, which is a proposed boundary between planets and brown dwarfs. Although Burrows et al. (2001) propose that formation in a disk or formation in the interstellar medium in a manner similar to stars is a more logical way to differentiate planets and brown dwarfs, our current observations are not adequate to address this distinction. XO-3b is also unusual in that its eccentricity is large given its relatively short orbital period. Both the planetary radius and the inclination are functions of the spectroscopically determined stellar radius. Analysis of the transit light curve of XO-3b suggests that the spectroscopically derived parameters may be over estimated. Though relatively noisy, the light curves favor a smaller radius in order to better match the steepness of the ingress and egress. The light curve fits imply a planetary radius of 1.25 +/- 0.15 Rjup, which would correspond to a mass of 12.03 +/- 0.46 Mjup.Comment: 26 pages, 10 figures. Accepted by ApJ. Current version has several small corrections as a result of a bug in the fitting softwar