On the zero set of G-equivariant maps

Let $G$ be a finite group acting on vector spaces $V$ and $W$ and consider a smooth $G$-equivariant mapping $f:V\to W$. This paper addresses the question of the zero set near a zero $x$ of $f$ with isotropy subgroup $G$. It is known from results of Bierstone and Field on $G$-transversality theory that the zero set in a neighborhood of $x$ is a stratified set. The purpose of this paper is to partially determine the structure of the stratified set near $x$ using only information from the representations $V$ and $W$. We define an index $s(\Sigma)$ for isotropy subgroups $\Sigma$ of $G$ which is the difference of the dimension of the fixed point subspace of $\Sigma$ in $V$ and $W$. Our main result states that if $V$ contains a subspace $G$-isomorphic to $W$, then for every maximal isotropy subgroup $\Sigma$ satisfying $s(\Sigma)>s(G)$, the zero set of $f$ near $x$ contains a smooth manifold of zeros with isotropy subgroup $\Sigma$ of dimension $s(\Sigma)$. We also present a systematic method to study the zero sets for group representations $V$ and $W$ which do not satisfy the conditions of our main theorem. The paper contains many examples and raises several questions concerning the computation of zero sets of equivariant maps. These results have application to the bifurcation theory of $G$-reversible equivariant vector fields

Dense, Parsec-Scale Clumps Near the Great Annihilator

We report on Combined Array for Research in Millimeter-Wave Astronomy and James Clerk Maxwell Telescope observations toward the Einstein source 1E 1740.7–2942, a low-mass X-ray binary commonly known as the "Great Annihilator." The Great Annihilator is known to be near a small, bright molecular cloud in a region largely devoid of emission in ^(12)CO surveys of the Galactic center. This region is of interest because it is interior to the dust lanes which may be the shock zones where atomic gas from the HI nuclear disk is converted into molecular gas. We find that the region is populated with a large number of dense (n ~ 10^5 cm^(–3)) regions of excited gas with small filling factors. The gas appears to have turbulent support and may be the result of sprays of material from collisions in the shock zone. We estimate that ~(1-3) × 10^5 M⊙ of shocked gas resides in our r ~ 3', Δv_(LSR) = 100 km s^(–1) field. If this gas has recently shocked and is interior to the inner Lindblad resonance of the dominant bar, it is in transit to the x_2 disk, suggesting that a significant amount of mass may be transported to the disk by a low filling factor population of molecular clouds with low surface brightness in larger surveys

An Integrated Literature Review of Time-on-Task Effects With a Pragmatic Framework for Understanding and Improving Decision-Making in Multidisciplinary Oncology Team Meetings

Multidisciplinary oncology team meetings (MDMs) or tumor boards, like other MDMs in healthcare, facilitate the incorporation of diverse clinical expertise into treatment planning for patients. Decision-making (DM) in relation to treatment planning in MDMs is carried out repeatedly until all patients put forward for discussion have been reviewed. Despite continuing financial pressure and staff shortages, the workload of cancer MDMs, and therefore meeting duration continue to increase (up to 5 h) with patients often receiving less than 2 min of team input. This begs the question as to whether the current set-up is conducive to achieve optimal DM, which these multi-specialty teams were set out to achieve in the first place. Much of what it is known, however, about the effects of prolonged cognitive activity comes from various subfields of science, leaving a gap in applied knowledge relating to complex healthcare environments. The objective of this review was thus to synthesize theory, evidence and clinical practice in order to bring the current understanding of prolonged, repeated DM into the context of cancer MDMs. We explore how and why time spent on a task affects performance in such settings, and what strategies can be employed by cancer teams to counteract negative effects and improve quality and safety. In the process, we propose a pragmatic framework of repeated DM that encompasses the strength, the process and the cost-benefit models of self-control as applied to real-world contexts of cancer MDMs. We also highlight promising research avenues for closing the research-to-practice gap. Theoretical and empirical evidence reviewed in this paper suggests that over prolonged time spent on a task, repeated DM is cognitively taxing, leading to performance detriments. This deterioration is associated with various cognitive-behavioral pitfalls, including decreased attentional capacity and reduced ability to effectively evaluate choices, as well as less analytical DM and increased reliance on heuristics. As a short to medium term improvement for ensuring safety, consistently high quality of care for all patients, and the clinician wellbeing, future research and interventions in cancer MDMs should address time-on-task effects with a combination of evidence-based cognitive strategies. We propose in this review multiple measures that range from food intake, short breaks, rewards, and mental exercises. As a long term imperative, however, capacity within cancer services needs to be reviewed as well as how best to plan workforce development and service delivery models to achieve population coverage whilst maintaining safety and quality of care. Hence the performance detriments that arise in healthcare workers as a result of the intensity (time spent on a task) and complexity of the workload require not only more research, but also wider regulatory focus and recognition

Spontaneous Initiation of Detonations in White Dwarf Environments: Determination of Critical Sizes

Some explosion models for Type Ia supernovae (SN Ia), such as the gravitationally confined detonation (GCD) or the double detonation sub-Chandrasekhar (DDSC) models, rely on the spontaneous initiation of a detonation in the degenerate C/O material of a white dwarf. The length scales pertinent to the initiation of the detonation are notoriously unresolved in multi-dimensional stellar simulations, prompting the use of results of 1D simulations at higher resolution, such as the ones performed for this work, as guidelines for deciding whether or not conditions reached in the higher dimensional full star simulations successfully would lead to the onset of a detonation. Spontaneous initiation relies on the existence of a suitable gradient in self-ignition (induction) times of the fuel, which we set up with a spatially localized non-uniformity of temperature -- a hot spot. We determine the critical (smallest) sizes of such hot spots that still marginally result in a detonation in white dwarf matter by integrating the reactive Euler equations with the hydrodynamics code FLASH. We quantify the dependences of the critical sizes of such hot spots on composition, background temperature, peak temperature, geometry, and functional form of the temperature disturbance, many of which were hitherto largely unexplored in the literature. We discuss the implications of our results in the context of modeling of SNe Ia.Comment: 43 pages, 12 figures, 12 table

A Resolved Ring of Debris Dust around the Solar Analog HD 107146

We present resolved images of the dust continuum emission from the debris disk around the young (80-200 Myr) solar-type star HD 107146 with CARMA at λ = 1.3 mm and the CSO at λ = 350 μ. Both images show that the dust emission extends over an approximately 10" diameter region. The high-resolution (3") CARMA image further reveals that the dust is distributed in a partial ring with significant decrease in a flux inward of 97 AU. Two prominent emission peaks appear within the ring separated by ~140° in the position angle. The morphology of the dust emission is suggestive of dust captured into a mean motion resonance, which would imply the presence of a planet at an orbital radius of ~45-75 AU

Initiation of the detonation in the gravitationally confined detonation model of Type Ia supernovae

We study the initiation of the detonation in the gravitationally confined detonation (GCD) model of Type Ia supernovae (SNe Ia). Initiation of the detonation occurs spontaneously in a region where the length scale of the temperature gradient extending from a flow (in which carbon burning is already occurring) into unburned fuel is commensurate to the range of critical length scales which have been derived from 1D simulations that resolve the initiation of a detonation. By increasing the maximum resolution in a truncated cone that encompasses this region, beginning somewhat before initiation of the detonation occurs, we successfully simulate in situ the first gradient-initiated detonation in a whole-star simulation. The detonation emerges when a compression wave overruns a pocket of fuel situated in a Kelvin-Helmholtz cusp at the leading edge of the inwardly directed jet of burning carbon. The compression wave pre-conditions the temperature in the fuel in such a way that the Zel'dovich gradient mechanism can operate and a detonation ensues. We explore the dependence of the length scale of the temperature gradient on spatial resolution and discuss the implications for the robustness of this detonation mechanism. We find that the time and the location at which initiation of the detonation occurs varies with resolution. In particular, initiation of a detonation had not yet occurred in our highest resolution simulation by the time we ended the simulation because of the computational demand it required. We suggest that the turbulent shear layer surrounding the inwardly directed jet provides the most favorable physical conditions, and therefore the most likely location, for initiation of a detonation in the GCD model.Comment: 28 pages, 12 figures, 1 table, accepted to Ap

Quality improvement for cancer multidisciplinary teams: lessons learned from the Anglian Germ Cell Cancer Collaborative Group

Summary: Shamash and colleagues describe how their supra-regional germ cell tumour multidisciplinary team achieved standardisation of treatment and improved survival. We discuss some of the insights the study provides into prioritising complex patients, streamlining processes, the use of telemedicine, and the centrality of good data collection to continuous quality improvement

The anatomy of clinical decision-making in multidisciplinary cancer meetings:A cross-sectional observational study of teams in a natural context

In the UK, treatment recommendations for patients with cancer are routinely made by multidisciplinary teams in weekly meetings. However, their performance is variable.The aim of this study was to explore the underlying structure of multidisciplinary decision-making process, and examine how it relates to team ability to reach a decision.This is a cross-sectional observational study consisting of 1045 patient reviews across 4 multidisciplinary cancer teams from teaching and community hospitals in London, UK, from 2010 to 2014. Meetings were chaired by surgeons.We used a validated observational instrument (Metric for the Observation of Decision-making in Cancer Multidisciplinary Meetings) consisting of 13 items to assess the decision-making process of each patient discussion. Rated on a 5-point scale, the items measured quality of presented patient information, and contributions to review by individual disciplines. A dichotomous outcome (yes/no) measured team ability to reach a decision. Ratings were submitted to Exploratory Factor Analysis and regression analysis.The exploratory factor analysis produced 4 factors, labeled "Holistic and Clinical inputs" (patient views, psychosocial aspects, patient history, comorbidities, oncologists', nurses', and surgeons' inputs), "Radiology" (radiology results, radiologists' inputs), "Pathology" (pathology results, pathologists' inputs), and "Meeting Management" (meeting chairs' and coordinators' inputs). A negative cross-loading was observed from surgeons' input on the fourth factor with a follow-up analysis showing negative correlation (r = -0.19, P &lt; 0.001). In logistic regression, all 4 factors predicted team ability to reach a decision (P &lt; 0.001).Hawthorne effect is the main limitation of the study.The decision-making process in cancer meetings is driven by 4 underlying factors representing the complete patient profile and contributions to case review by all core disciplines. Evidence of dual-task interference was observed in relation to the meeting chairs' input and their corresponding surgical input into case reviews.</p