Dimension and rank for mapping class groups

We study the large scale geometry of the mapping class group, MCG. Our main result is that for any asymptotic cone of MCG, the maximal dimension of locally compact subsets coincides with the maximal rank of free abelian subgroups of MCG. An application is an affirmative solution to Brock-Farb's Rank Conjecture which asserts that MCG has quasi-flats of dimension N if and only if it has a rank N free abelian subgroup. We also compute the maximum dimension of quasi-flats in Teichmuller space with the Weil-Petersson metric.Comment: Incorporates referee's suggestions. To appear in Annals of Mathematic

Ethics Education in the First Year: An Experiment

Bundy presents an account of the University of California at Berkeley\u27s School of Law\u27s experiment with teaching the required professional responsibility course in the first year. During this experiment, the faculty members involved in the course developed a strong set of teaching materials and a strong commitment to teaching from those materials

Interferon β-1a in relapsing multiple sclerosis: four-year extension of the European IFNβ-1a Dose-C omparison Study

Background: Multiple sclerosis (MS) is a chronic disease requiring long-term monitoring of treatment. Objective: To assess the four-year clinical efficacy of intramuscular (IM) IFNb-1a in patients with relapsing MS from the European IFNb-1a Dose-C omparison Study. Methods: Patients who completed 36 months of treatment (Part 1) of the European IFNb-1a Dose-C omparison Study were given the option to continue double-blind treatment with IFNb-1a 30 mcg or 60 mcg IM once weekly (Part 2). Analyses of 48-month data were performed on sustained disability progression, relapses, and neutralizing antibody (NA b) formation. Results: O f 608/802 subjects who completed 36 months of treatment, 493 subjects continued treatment and 446 completed 48 months of treatment and follow-up. IFNb-1a 30 mcg and 60 mcg IM once weekly were equally effective for up to 48 months. There were no significant differences between doses over 48 months on any of the clinical endpoints, including rate of disability progression, cumulative percentage of patients who progressed (48 and 43, respectively), and annual relapse rates; relapses tended to decrease over 48 months. The incidence of patients who were positive for NAbs at any time during the study was low in both treatment groups. Conclusion: C ompared with 60-mcg IM IFNb-1a once weekly, a dose of 30 mcg IM IFNb-1a once weekly maintains the same clinical efficacy over four years

Modified Chaplygin Gas and Solvable F-essence Cosmologies

The Modified Chaplygin Gas (MCG) model belongs to the class of a unified models of dark energy and dark matter. In this paper, we have modeled MCG in the framework of f-essence cosmology. By constructing an equation connecting the MCG and the f-essence, we solve it to obtain explicitly the pressure and energy density of MCG. As special cases, we obtain both positive and negative pressure solutions for suitable choices of free parameters. We also calculate the state parameter which describes the phantom crossing.Comment: 12 pages, (Invited Review), accepted for publication in "Astrophysics and Space Science" DOI: 10.1007/s10509-011-0870-

Adding ROS Scavengers to Cold K\u3csup\u3e+\u3c/sup\u3e Cardioplegia Reduces Superoxide Emission During 2 h Global Cold Cardiac Ischemia

We reported that the combination of reactive oxygen species (ROS) quenchers Mn(III) tetrakis (4-benzoic acid) porphyrin (MnTBAP), catalase, and glutathione (MCG) given before 2 hours cold ischemia better protected cardiac mitochondria against cold ischemia and warm reperfusion (IR)-induced damage than MnTBAP alone. Here, we hypothesize that high K+ cardioplegia (CP) plus MCG would provide added protection of mitochondrial bioenergetics and cardiac function against IR injury. Using fluorescence spectrophotometry, we monitored redox balance, ie reduced nicotinamide adenine dinucleotide and flavin adenine dinucleotide (NADH/FAD), superoxide (O2 •−), and mitochondrial Ca2+ (m[Ca2+]) in the left ventricular free wall. Guinea pig isolated hearts were perfused with either Krebs Ringer’s (KR) solution, CP, or CP + MCG, before and during 27°C perfusion followed immediately by 2 hours of global ischemia at 27°C. Drugs were washed out with KR at the onset of 2 hours 37°C reperfusion. After 120 minutes warm reperfusion, myocardial infarction was lowest in the CP + MCG group and highest in the KR group. Developed left ventricular pressure recovery was similar in CP and CP + MCG and was better than in the KR group. O2 •−, m[Ca2+], and NADH/FAD were significantly different between the treatment and KR groups. O2 •− was lower in CP + MCG than in the CP group. This study suggests that CP and ROS quenchers act in parallel to improve mitochondrial function and to provide protection against IR injury at 27°C

On the Location and Composition of the Dust in the MCG-6-30-15 Warm Absorber

Hubble Space Telescope images of MCG-6-30-15 show a dust lane crossing the galaxy just below the nucleus. In this paper, we argue that this dust lane is responsible for the observed reddening of the nuclear emission and the Fe I edge hinted at in the Chandra spectrum of MCG-6-30-15. We further suggest that the gas within the dust lane can comprise much of the low ionization component (i.e., the one contributing the O VII edge) of the observed warm absorber. Moreover, placing the warm absorbing material at such distances (hundreds of pc) can account for the small outflow velocities of the low ionization absorption lines as well as the constancy of the O VIII edge. Photoionization models of a dusty interstellar gas cloud (with a column appropriate for the reddening toward MCG-6-30-15) using a toy Seyfert 1 spectral energy distribution show that it is possible to obtain a significant O VII edge (\tau~0.2) if the material is ~150 pc from the ionizing source. For MCG-6-30-15, such a distance is consistent with the observed dust lane. The current data on MCG-6-30-15 is unable to constrain the dust composition within the warm absorber. Astronomical silicate is a viable candidate, but there are indications of a very low O abundance in the dust, which is inconsistent with a silicate origin. If true, this may indicate that there were repeated cycles of grain destruction and growth from shocks in the interstellar medium of MCG-6-30-15. Pure iron grains are an unlikely dust constituent due to the limit on their abundance in the Galaxy, yet they cannot be ruled out. The high column densities inferred from the highly ionized zone of the warm absorber implies that this gas is dust-free.Comment: 7 pages, 3 Figures, A&A accepte