The Gorenstein and complete intersection properties of associated graded rings

Let I be an m-primary ideal of a Noetherian local ring (R,m). We consider the Gorenstein and complete intersection properties of the associated graded ring G(I) and the fiber cone F(I) of I as reflected in their defining ideals as homomorphic images of polynomial rings over R/I and R/m respectively. In case all the higher conormal modules of I are free over R/I, we observe that: (i) G(I) is Cohen-Macaulay iff F(I) is Cohen- Macaulay, (ii) G(I) is Gorenstein iff both F(I) and R/I are Gorenstein, and (iii) G(I) is a relative complete intersection iff F(I) is a relative complete intersection. In case R/I is Gorenstein, we give a necessary and sufficient condition for G(I) to be Gorenstein in terms of residuation of powers of I with respect to a reduction J of I with \mu(J) = dim R and the reduction number r of I with respect to J. We prove that G(I) is Gorenstein iff J:I^{r-i} = J + I^{i+1}, for i = 0, ...,r-1. If (R,m) is a Gorenstein local ring and I \subseteq m is an ideal having a reduction J with reduction number r such that \mu(J) = ht(I) = g > 0, we prove that the extended Rees algebra R[It, t^-1}] is quasi-Gorenstein with \a-invariant a if and only if J^n:I^r = I^{n+a-r+g-1} for every integer n

The Menstrual Cycle and Performance Feedback Alter Gender Differences in Competitive Choices

Economic experiments have shown that in mixed gender groups women are more reluctant than men to choose tournaments when given the choice between piece rate and winner-take-all tournament style compensation. These gender difference experiments have all relied on a framework where subjects were not informed of their abilities relative to potential competitors. We replicate these findings with math and word tasks, and then show that feedback about relative performance moves high ability females towards more competitive compensation schemes, moves low ability men towards less competitive schemes such as piece rate and group pay, and removes the average gender difference in compensation choices. We also examine between and within-subjects differences in choices for females across the menstrual cycle. We find women's relative reluctance to choose tournaments comes mostly from women in the low hormone phase of their menstrual cycle. Women in the high hormone phase are substantially more willing to compete than women in the low phase, though still somewhat less willing to compete than men. There are no significant differences between the choices of any of these groups after they receive relative performance feedback.competition, tournaments, gender, hormones, menstruation, feedback

Off-shell Currents and Color-Kinematics Duality

We elaborate on the color-kinematics duality for off-shell diagrams in gauge theories coupled to matter, by investigating the scattering process $gg\to ss, q\bar q, gg$, and show that the Jacobi relations for the kinematic numerators of off-shell diagrams, built with Feynman rules in axial gauge, reduce to a color-kinematics violating term due to the contributions of sub-graphs only. Such anomaly vanishes when the four particles connected by the Jacobi relation are on their mass shell with vanishing squared momenta, being either external or cut particles, where the validity of the color-kinematics duality is recovered. We discuss the role of the off-shell decomposition in the direct construction of higher-multiplicity numerators satisfying color-kinematics identity in four as well as in $d$ dimensions, for the latter employing the Four Dimensional Formalism variant of the Four Dimensional Helicity scheme. We provide explicit examples for the QCD process $gg\to q\bar{q}g$.Comment: Accepted version for publication in PLB. Manuscript extended: 19 pages, 15 figures; C/K duality for tree-level amplitudes in dimensional regularization added; references added; title modifie

On 2-transitive sets of equiangular lines

All finite sets of equiangular lines spanning finite-dimensional unitary spaces are determined for which the action on the lines of the set-stabilizer in the unitary group is 2-transitive with a regular normal subgroup

Forebrain Origins of Glutamatergic Innervation to the Rat Paraventricular Nucleus of the Hypothalamus: Differential Inputs to the Anterior Versus Posterior Subregions

The hypothalamic paraventricular nucleus (PVN) regulates numerous homeostatic systems and functions largely under the influence of forebrain inputs. Glutamate is a major neurotransmitter in forebrain, and glutamate neurosignaling in the PVN is known to mediate many of its functions. Previous work showed that vesicular glutamate transporters (VGluTs; specific markers for glutamatergic neurons) are expressed in forebrain sites that project to the PVN; however, the extent of this presumed glutamatergic innervation to the PVN is not clear. In the present study retrograde FluoroGold (FG) labeling of PVN-projecting neurons was combined with in situ hybridization for VGluT1 and VGluT2 mRNAs to identify forebrain regions that provide glutamatergic innervation to the PVN and its immediate surround in rats, with special consideration for the sources to the anterior versus posterior PVN. VGluT1 mRNA colocalization with retrogradely labeled FG neurons was sparse. VGluT2 mRNA colocalization with FG neurons was most abundant in the ventromedial hypothalamus after anterior PVN FG injections, and in the lateral, posterior, dorsomedial, and ventromedial hypothalamic nuclei after posterior PVN injections. Anterograde tract tracing combined with VGluT2 immunolabeling showed that 1) ventromedial nucleus-derived glutamatergic inputs occur in both the anterior and posterior PVN; 2) posterior nucleus-derived glutamatergic inputs occur predominantly in the posterior PVN; and 3) medial preoptic nucleus-derived inputs to the PVN are not glutamatergic, thereby corroborating the innervation pattern seen with retrograde tracing. The results suggest that PVN subregions are influenced by varying amounts and sources of forebrain glutamatergic regulation, consistent with functional differentiation of glutamate projections. J. Comp. Neurol. 519:1301–1319, 2011. © 2010 Wiley-Liss, Inc

Ro 15-4513 Antagonizes Alcohol-Induced Sedation in Mice Through aß¿2-type GABA(A) Receptors

Peer reviewedPublisher PD

High-energy collision of black holes in higher dimensions

We compute the gravitational wave energy E_(rad) radiated in head-on collisions of equal-mass, nonspinning black holes in up to (D=8)-dimensional asymptotically flat spacetimes for boost velocities v up to about 90% of the speed of light. We identify two main regimes: weak radiation at velocities up to about 40% of the speed of light, and exponential growth of E_(rad) with v at larger velocities. Extrapolation to the speed of light predicts a limit of 12.9% (10.1, 7.7, 5.5, 4.5)% of the total mass that is lost in gravitational waves in D=4 (5, 6, 7, 8) spacetime dimensions. In agreement with perturbative calculations, we observe that the radiation is minimal for small but finite velocities, rather than for collisions starting from rest. Our computations support the identification of regimes with super-Planckian curvature outside the black-hole horizons reported by Okawa, Nakao, and Shibata [Phys. Rev. D 83, 121501(R) (2011)]

News From The Gamma Cephei Planetary System

The Gamma Cephei planetary system is one of the most interesting systems due to several reasons: 1.) it is the first planet candidate detected by precise radial velocity (RV) measurements that was discussed in the literature (Campbell et al. 1988); 2.) it is a tight binary system with a ~ 20AU; and 3.) the planet host star is an evolved K-type star. In Hatzes et al. (2003) we confirmed the presence of the planetary companion with a minimum mass of 1.7 M_Jup at 2 AU. In this paper we present additional eight years of precise RV data from the Harlan J. Smith 2.7 m Telescope and its Tull Coude spectrograph at McDonald Observatory. The 900 d signal, that is interpreted as the presence of the giant planetary companion, is strongly confirmed by adding the new data. We present an updated orbital solution for the planet, which shows that the planet is slightly more massive and the orbit more circular than previous results have suggested. An intensive high-cadence week of RV observations in 2007 revealed that Gamma Cep A is a multi-periodic pulsator. We discuss this issue within the context of searching for additional planets in this system.Comment: Part of PlanetsbeyondMS/2010 proceedings http://arxiv.org/html/1011.660