A 'Darboux Theorem' for shifted symplectic structures on derived Artin stacks, with applications

This is the fifth in a series arXiv:1304.4508, arXiv:1305,6302, arXiv:1211.3259, arXiv:1305.6428 on the '$k$-shifted symplectic derived algebraic geometry' of Pantev, Toen, Vaquie and Vezzosi, arXiv:1111.3209. This paper extends the previous three from (derived) schemes to (derived) Artin stacks. We prove four main results: (a) If $(X,\omega)$ is a $k$-shifted symplectic derived Artin stack for $k<0$ in the sense of arXiv:1111.3209, then near each $x\in X$ we can find a 'minimal' smooth atlas $\varphi:U\to X$ with $U$ an affine derived scheme, such that $(U,\varphi^*(\omega))$ may be written explicitly in coordinates in a standard 'Darboux form'. (b) If $(X,\omega)$ is a $-1$-shifted symplectic derived Artin stack and $X'$ the underlying classical Artin stack, then $X'$ extends naturally to a 'd-critical stack' $(X',s)$ in the sense of arXiv:1304.4508. (c) If $(X,s)$ is an oriented d-critical stack, we can define a natural perverse sheaf $P^\bullet_{X,s}$ on $X$, such that whenever $T$ is a scheme and $t:T\to X$ is smooth of relative dimension $n$, then $T$ is locally modelled on a critical locus Crit$(f:U\to{\mathbb A}^1)$ for $U$ smooth, and $t^*(P^\bullet_{X,s})[n]$ is locally modelled on the perverse sheaf of vanishing cycles $PV_{U,f}^\bullet$ of $f$. (d) If $(X,s)$ is a finite type oriented d-critical stack, we can define a natural motive $MF_{X,s}$ in a ring of motives $\bar{\mathcal M}^{st,\hat\mu}_X$ on $X$, such that whenever $T$ is a finite type scheme and $t:T\to X$ is smooth of dimension $n$, then $T$ is locally modelled on a critical locus Crit$(f:U\to{\mathbb A}^1)$ for $U$ smooth, and ${\mathbb L}^{-n/2}\odot t^*(MF_{X,s})$ is locally modelled on the motivic vanishing cycle $MF^{mot,\phi}_{U,f}$ of $f$ in $\bar{\mathcal M}^{st,\hat\mu}_T$. Our results have applications to categorified and motivic extensions of Donaldson-Thomas theory of Calabi-Yau 3-foldsComment: (v2) 61 pages. Minor corrections, foundational material on perverse sheaves shortene

Focus on quality in healthcare in Ireland.

PURPOSE: The purpose of this paper is to summarise the recent debates and issues on the healthcare system in Ireland, which have come to the fore through media exposure. The implications for these debates on quality are suggested and questions are raised to stimulate further debate. DESIGN/METHODOLOGY/APPROACH: Recent reports and media opinion articles are reviewed in the light of the health reform programme and the increased prosperity due to the Celtic Tiger era in Ireland. FINDINGS: The Health Service in Ireland is not what it should be. Progress has been made but resistance at all levels is significant due to the mistrust and miscommunication between the managerial and clinical personnel which have built up during the past number of years. The trust of the public is at an all-time low. However, once patients are within the system they are satisfied with their care. ORIGINALITY/VALUE: This is a discussion paper which raises more questions than answers and is timely with the focus on quality in healthcare, particularly now as Ireland prepares for a general election for a new government with healthcare a priority issue

A Note on Fluxes and Superpotentials in M-theory Compactifications on Manifolds of G_2 Holonomy

We consider the breaking of N=1 supersymmetry by non-zero G-flux when M-theory is compactified on a smooth manifold X of G_2 holonomy. Gukov has proposed a superpotential W to describe this breaking in the low-energy effective theory. We check this proposal by comparing the bosonic potential implied by W with the corresponding potential deduced from the eleven-dimensional supergravity action. One interesting aspect of this check is that, though W depends explicitly only on G-flux supported on X, W also describes the breaking of supersymmetry by G-flux transverse to X.Comment: 15 pages, harvmac, v2: reference adde

Investigating the lexico-grammatical resources of a non-native user of English:The case of can and could in email requests

Individual users of English as a first or second language are assumed to possess or aspire to a monolithic grammar, an internally consistent set of rules which represents the idealized norms or conventions of native speakers. This position reflects a deficit view of L2 learning and usage, and is at odds with usage-based approaches to language development and research findings on idiolectal variation. This study problematizes the assumption of monolithic ontologies of grammar for TESOL by exploring a fragment of genre-specific lexico-grammatical knowledge (the can you/could you V construction alternation in requests) in a single non-native user of English, post-instruction. A corpus sample of the individual’s output was compared with the input he was exposed to and broader norms for the genre. The analysis confirms findings in usage-based linguistics which demonstrate that an individual’s lexico-grammatical knowledge constitutes an inventory of constructions shaped in large part by distributional patterns in the input. But it also provides evidence for idiosyncratic preferences resulting from exemplar-based inertia in production, suggesting that input is not the sole factor. Results are discussed in the context of a “plurilithic” ontology of grammar and the challenges this represents for pedagogy and teacher development

Opacity Effects on Pulsations of Main-Sequence A-Type Stars

Opacity enhancements for stellar interior conditions have been explored to explain observed pulsation frequencies and to extend the pulsation instability region for B-type main-sequence variable stars. For these stars, the pulsations are driven in the region of the opacity bump of Fe-group elements at $\sim$200,000 K in the stellar envelope. Here we explore effects of opacity enhancements for the somewhat cooler main-sequence A-type stars, in which $p$-mode pulsations are driven instead in the second helium ionization region at $\sim$50,000 K. We compare models using the new LANL OPLIB vs. LLNL OPAL opacities for the AGSS09 solar mixture. For models of 2 solar masses and effective temperature 7600 K, opacity enhancements have only a mild effect on pulsations, shifting mode frequencies and/or slightly changing kinetic-energy growth rates. Increased opacity near the bump at 200,000 K can induce convection that may alter composition gradients created by diffusive settling and radiative levitation. Opacity increases around the hydrogen and 1st He ionization region (13,000 K) can cause additional higher-frequency $p$ modes to be excited, raising the possibility that improved treatment of these layers may result in prediction of new modes that could be tested by observations. New or wider convective zones and higher convective velocities produced by opacity increases could also affect angular momentum transport during evolution. More work needs to be done to quantify the effects of opacity on the boundaries of the pulsation instability regions for A-type stars.Comment: 14 pages, 12 figures. Accepted version for MDPI Atoms Special Issue "Atomic and Molecular Opacity Data for Astrophysics", Published 4 June 2018, Atoms 2018, 6(2), 31, https://doi.org/10.3390/atoms602003