Modularity of logarithmic parafermion vertex algebras

The parafermionic cosets $C_k = \mathrm{Com} (H, L_k(\mathfrak{sl}_2) )$ are studied for negative admissible levels $k$, as are certain infinite-order simple current extensions $B_k$ of $C_k$. Under the assumption that the tensor theory considerations of Huang, Lepowsky and Zhang apply to $C_k$, all irreducible $C_k$- and $B_k$-modules are obtained from those of $L_k(\mathfrak{sl}_2)$, as are the Grothendieck fusion rules of these irreducible modules. Notably, there are only finitely many irreducible $B_k$-modules. The irreducible $C_k$- and $B_k$-characters are computed and the latter are shown, when supplemented by pseudotraces, to carry a finite-dimensional representation of the modular group. The natural conjecture then is that the $B_k$ are $C_2$-cofinite vertex operator algebras.Comment: 28 pages; v2 31 pages: many clarifications and improvements, especially to the example in Sec. 4.

Minimal identifying codes in trees and planar graphs with large girth

AbstractLet G be a finite undirected graph with vertex set V(G). If v∈V(G), let N[v] denote the closed neighbourhood of v, i.e. v itself and all its adjacent vertices in G. An identifying code in G is a subset C of V(G) such that the sets N[v]∩C are nonempty and pairwise distinct for each vertex v∈V(G). We consider the problem of finding the minimum size of an identifying code in a given graph, which is known to be NP-hard. We give a linear algorithm that solves it in the class of trees, but show that the problem remains NP-hard in the class of planar graphs with arbitrarily large girth

Multiple Tree for Partially Observable Monte-Carlo Tree Search

We propose an algorithm for computing approximate Nash equilibria of partially observable games using Monte-Carlo tree search based on recent bandit methods. We obtain experimental results for the game of phantom tic-tac-toe, showing that strong strategies can be efficiently computed by our algorithm

A Difference-in-Differences Approach to Assess the Effect of a Heat Action Plan on Heat-Related Mortality, and Differences in Effectiveness According to Sex, Age, and Socioeconomic Status (Montreal, Quebec).

BackgroundThe impact of heat waves on mortality and health inequalities is well documented. Very few studies have assessed the effectiveness of heat action plans (HAPs) on health, and none has used quasi-experimental methods to estimate causal effects of such programs.ObjectivesWe developed a quasi-experimental method to estimate the causal effects associated with HAPs that allows the identification of heterogeneity across subpopulations, and to apply this method specifically to the case of the Montreal (Quebec, Canada) HAP.MethodsA difference-in-differences approach was undertaken using Montreal death registry data for the summers of 2000-2007 to assess the effectiveness of the Montreal HAP, implemented in 2004, on mortality. To study equity in the effect of HAP implementation, we assessed whether the program effects were heterogeneous across sex (male vs. female), age (≥ 65 years vs. < 65 years), and neighborhood education levels (first vs. third tertile). We conducted sensitivity analyses to assess the validity of the estimated causal effect of the HAP program.ResultsWe found evidence that the HAP contributed to reducing mortality on hot days, and that the mortality reduction attributable to the program was greater for elderly people and people living in low-education neighborhoods.ConclusionThese findings show promise for programs aimed at reducing the impact of extreme temperatures and health inequities. We propose a new quasi-experimental approach that can be easily applied to evaluate the impact of any program or intervention triggered when daily thresholds are reached. Citation: Benmarhnia T, Bailey Z, Kaiser D, Auger N, King N, Kaufman J. 2016. A difference-in-differences approach to assess the effect of a heat action plan on heat-related mortality, and differences in effectiveness according to sex, age, and socioeconomic status (Montreal, Quebec). Environ Health Perspect 124:1694-1699; http://dx.doi.org/10.1289/EHP203

Fast Removal of Synaptic Glutamate by Postsynaptic Transporters

AbstractGlutamate transporters are believed to remove glutamate from the synaptic cleft only slowly because they cycle slowly. However, we show that when glutamate binds to postsynaptic transporters at the cerebellar climbing fiber synapse, it evokes a conformation change and inward current that reflect glutamate removal from the synaptic cleft within a few milliseconds, a time scale much faster than the overall cycle time. Contrary to present models, glutamate removal does not require binding of an extracellular proton, and the time course of transporter anion conductance activation differs from that of glutamate removal. The charge movement associated with glutamate removal is consistent with the majority of synaptically released glutamate being removed from the synaptic cleft by postsynaptic transporters

Finding Optimal Strategies of Almost Acyclic Simple Stochatic Games

The optimal value computation for turned-based stochastic games with reachability objectives, also known as simple stochastic games, is one of the few problems in $NP \cap coNP$ which are not known to be in $P$. However, there are some cases where these games can be easily solved, as for instance when the underlying graph is acyclic. In this work, we try to extend this tractability to several classes of games that can be thought as "almost" acyclic. We give some fixed-parameter tractable or polynomial algorithms in terms of different parameters such as the number of cycles or the size of the minimal feedback vertex set

Solving Simple Stochastic Games with Few Random Nodes Faster Using Bland\u27s Rule

The best algorithm so far for solving Simple Stochastic Games is Ludwig\u27s randomized algorithm [Ludwig, 1995] which works in expected 2^{O(sqrt{n})} time. We first give a simpler iterative variant of this algorithm, using Bland\u27s rule from the simplex algorithm, which uses exponentially less random bits than Ludwig\u27s version. Then, we show how to adapt this method to the algorithm of Gimbert and Horn [Gimbert and Horn, 2008] whose worst case complexity is O(k!), where k is the number of random nodes. Our algorithm has an expected running time of 2^{O(k)}, and works for general random nodes with arbitrary outdegree and probability distribution on outgoing arcs

The fundamental plane of evolving red nuggets

We present an exploration of the mass structure of a sample of 12 strongly lensed massive, compact early-type galaxies at redshifts $z\sim0.6$ to provide further possible evidence for their inside-out growth. We obtain new ESI/Keck spectroscopy and infer the kinematics of both lens and source galaxies, and combine these with existing photometry to construct (a) the fundamental plane (FP) of the source galaxies and (b) physical models for their dark and luminous mass structure. We find their FP to be tilted towards the virial plane relative to the local FP, and attribute this to their unusual compactness, which causes their kinematics to be totally dominated by the stellar mass as opposed to their dark matter; that their FP is nevertheless still inconsistent with the virial plane implies that both the stellar and dark structure of early-type galaxies is non-homologous. We also find the intrinsic scatter of their FP to be comparable to the local value, indicating that variations in the stellar mass structure outweight variations in the dark halo in the central regions of early-type galaxies. Finally, we show that inference on the dark halo structure -- and, in turn, the underlying physics -- is sensitive to assumptions about the stellar initial mass function (IMF), but that physically-motivated assumptions about the IMF imply haloes with sub-NFW inner density slopes, and may present further evidence for the inside-out growth of compact early-type galaxies via minor mergers and accretion.Comment: 10 pages, 3 figures, 3 tables; submitted to MNRA

The SWELLS Survey. I. A large spectroscopically selected sample of edge-on late-type lens galaxies

The relative contribution of baryons and dark matter to the inner regions of spiral galaxies provides critical clues to their formation and evolution, but it is generally difficult to determine. For spiral galaxies that are strong gravitational lenses, however, the combination of lensing and kinematic observations can be used to break the disk-halo degeneracy. In turn, such data constrain fundamental parameters such as i) the mass density profile slope and axis ratio of the dark matter halo, and by comparison with dark matter-only numerical simulations the modifications imposed by baryons; ii) the mass in stars and therefore the overall star formation efficiency, and the amount of feedback; iii) by comparison with stellar population synthesis models, the normalization of the stellar initial mass function. In this first paper of a series, we present a sample of 16 secure, 1 probable, and 6 possible strong lensing spiral galaxies, for which multi-band high-resolution images and rotation curves were obtained using the Hubble Space Telescope and Keck-II Telescope as part of the Sloan WFC Edge-on Late-type Lens Survey (SWELLS). The sample includes 8 newly discovered secure systems. [abridged] We find that the SWELLS sample of secure lenses spans a broad range of morphologies (from lenticular to late-type spiral), spectral types (quantified by Halpha emission), and bulge to total stellar mass ratio (0.22-0.85), while being limited to M_*>10^{10.5} M_sun. The SWELLS sample is thus well-suited for exploring the relationship between dark and luminous matter in a broad range of galaxies. We find that the deflector galaxies obey the same size-mass relation as that of a comparison sample of elongated non-lens galaxies selected from the SDSS survey. We conclude that the SWELLS sample is consistent with being representative of the overall population of high-mass high-inclination disky galaxies.Comment: 21 pages, 6 figures, MNRAS, in pres