Farrell cohomology of low genus pure mapping class groups with punctures

In this paper, we calculate the p-torsion of the Farrell cohomology for low genus pure mapping class groups with punctures, where p is an odd prime. Here, `low genus' means g=1,2,3; and `pure mapping class groups with punctures' means the mapping class groups with any number of punctures, where the punctures are not allowed to be permuted. These calculations use our previous results about the periodicity of pure mapping class groups with punctures, as well as other cohomological tools. The low genus cases are interesting because we know that the high genus cases can be reduced to the low genus ones. Also, the cohomological properties of the mapping class groups without punctures are closely related to our cases.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-26.abs.htm

Joint Modeling of Content and Discourse Relations in Dialogues

We present a joint modeling approach to identify salient discussion points in spoken meetings as well as to label the discourse relations between speaker turns. A variation of our model is also discussed when discourse relations are treated as latent variables. Experimental results on two popular meeting corpora show that our joint model can outperform state-of-the-art approaches for both phrase-based content selection and discourse relation prediction tasks. We also evaluate our model on predicting the consistency among team members' understanding of their group decisions. Classifiers trained with features constructed from our model achieve significant better predictive performance than the state-of-the-art.Comment: Accepted by ACL 2017. 11 page

A convergent method for linear half-space kinetic equations

We give a unified proof for the well-posedness of a class of linear half-space equations with general incoming data and construct a Galerkin method to numerically resolve this type of equations in a systematic way. Our main strategy in both analysis and numerics includes three steps: adding damping terms to the original half-space equation, using an inf-sup argument and even-odd decomposition to establish the well-posedness of the damped equation, and then recovering solutions to the original half-space equation. The proposed numerical methods for the damped equation is shown to be quasi-optimal and the numerical error of approximations to the original equation is controlled by that of the damped equation. This efficient solution to the half-space problem is useful for kinetic-fluid coupling simulations

Deviation of light curves of gamma-ray burst pulses from standard forms due to the curvature effect of spherical fireballs or uniform jets

As revealed previously, under the assumption that some pulses of gamma-ray bursts are produced by shocks in spherical fireballs or uniform jets of large opening angles, there exists a standard decay form of the profile of pulses arising from very narrow or suddenly dimming local (or intrinsic) pulses due to the relativistic curvature effect (the Doppler effect over the spherical shell surface). Profiles of pulses arising from other local pulses were previously found to possess a reverse S-feature deviation from the standard decay form. We show in this paper that, in addition to the standard decay form shown in Qin et al. (2004), there exists a marginal decay curve associated with a local $\delta$ function pulse with a mono-color radiation. We employ the sample of Kocevski et al. (2003) to check this prediction and find that the phenomenon of the reverse S-feature is common, when compared with both the standard decay form and the marginal decay curve. We accordingly propose to take the marginal decay curve (whose function is simple) as a criteria to check if an observed pulse could be taken as a candidate suffered from the curvature effect. We introduce two quantities $A_1$ and $A_2$ to describe the mentioned deviations within and beyond the $FWHM$ position of the decay phase, respectively. The values of $A_1$ and $A_2$ of pulses of the sample are calculated, and the result suggests that for most of these pulses their corresponding local pulses might contain a long decay time relative to the time scale of the curvature effect.Comment: 24 pages, 7 figures, 1 table accepted for publication in MNRA