Toric partial density functions and stability of toric varieties

Let $(L, h)\to (X, \omega)$ denote a polarized toric K\"ahler manifold. Fix a toric submanifold $Y$ and denote by $\hat{\rho}_{tk}:X\to \mathbb{R}$ the partial density function corresponding to the partial Bergman kernel projecting smooth sections of $L^k$ onto holomorphic sections of $L^k$ that vanish to order at least $tk$ along $Y$, for fixed $t>0$ such that $tk\in \mathbb{N}$. We prove the existence of a distributional expansion of $\hat{\rho}_{tk}$ as $k\to \infty$, including the identification of the coefficient of $k^{n-1}$ as a distribution on $X$. This expansion is used to give a direct proof that if $\omega$ has constant scalar curvature, then $(X, L)$ must be slope semi-stable with respect to $Y$. Similar results are also obtained for more general partial density functions. These results have analogous applications to the study of toric K-stability of toric varieties.Comment: Accepted by Mathematische Annalen on 13 September 201

Managing uncertainty in creative industries: film sequels and Hollywood's profitability, 1988-2015

The film industry is characterised by high levels of uncertainty, yet the firms that dominate global film distribution have remained remarkably stable over the last century. The ability to transform uncertainty into risk, and to manage these risks effectively, has arguably been the outstanding achievement of major American film studios since the 1920s. This article examines how the risk management strategies of these firms have evolved over time, with a particular focus on the growing prevalence of sequels during the last 30 years. We analyse data on the box-office earnings and budgets of over 4000 films released between 1988 and 2015, and find that sequels have become an increasingly important source of industry profits since c.2000. We place this trend in historical context, and argue that while sequels themselves are not new, their role within film portfolios has changed, and that this represents a distinctive approach to risk management within the industry

Spatiotemporal brain dynamics of emotional face processing modulations induced by the serotonin 1A/2A receptor agonist psilocybin

Emotional face processing is critically modulated by the serotonergic system. For instance, emotional face processing is impaired by acute psilocybin administration, a serotonin (5-HT) 1A and 2A receptor agonist. However, the spatiotemporal brain mechanisms underlying these modulations are poorly understood. Here, we investigated the spatiotemporal brain dynamics underlying psilocybin-induced modulations during emotional face processing. Electrical neuroimaging analyses were applied to visual evoked potentials in response to emotional faces, following psilocybin and placebo administration. Our results indicate a first time period of strength (i.e., Global Field Power) modulation over the 168-189 ms poststimulus interval, induced by psilocybin. A second time period of strength modulation was identified over the 211-242 ms poststimulus interval. Source estimations over these 2 time periods further revealed decreased activity in response to both neutral and fearful faces within limbic areas, including amygdala and parahippocampal gyrus, and the right temporal cortex over the 168-189 ms interval, and reduced activity in response to happy faces within limbic and right temporo-occipital brain areas over the 211-242 ms interval. Our results indicate a selective and temporally dissociable effect of psilocybin on the neuronal correlates of emotional face processing, consistent with a modulation of the top-down contro

Modeling and Analysis of Interactions in Virtual Enterprises

Advances in computer networking technology and open system standards are making the creation and management of virtual enterprises feasible. A virtual enterprise is a temporary consortium of autonomous, diverse, and possibly geographically dispersed organizations that pool their resources to meet short-term objectives and exploit fastchanging market trends. For a virtual enterprise to succeed, its business processes must be automated, and its startup costs must be minimized. In this paper we describe a formal framework for modeling and reasoning about interactions in a virtual enterprise. Such a framework will form the basis for tools that provide automated support for creation and operation of virtual enterprises. 1

Precision measurements of radar transverse scattering speeds from meteor phase characteristics

We describe an improved technique for using the backscattered phase from meteor radar echo measurements just prior to the specular point ($t_{0}$) to calculate meteor speeds and their uncertainty. Our method, which builds on earlier work of Cervera et al (1997), scans possible speeds in the Fresnel distance - time domain with a dynamic, sliding window and derives a best-speed estimate from the resultant speed distribution. We test the performance of our method, called pre-$t_{0}$ speeds by sliding-slopes technique (PSSST), on transverse scattered meteor echoes observed by the Middle Atmosphere Alomar Radar System (MAARSY) and the Canadian Meteor Orbit Radar (CMOR), and compare the results to time-of-flight and Fresnel transform speed estimates. Our novel technique is shown to produce good results when compared to both model and speed measurements using other techniques. We show that our speed precision is $\pm$5$\%$ at speeds less than 40 km/s and we find that more than 90$\%$ of all CMOR multi-station echoes have PSSST solutions. For CMOR data, PSSST is robust against the selection of critical phase value and poor phase unwrapping. Pick errors of up to $\pm$6 pulses for meteor speeds less than about 50 km/s produce errors of less than $\pm$5$\%$ of the meteoroid speed. In addition, the width of the PSSST speed Kernel density estimate (KDE) is used as a natural measure of uncertainty that captures both noise and $t_0$ pick uncertainties.Comment: Accepted for publication to Radio Science on 2020-06-2

The RRAT Trap: Interferometric Localization of Radio Pulses from J0628+0909

We present the first blind interferometric detection and imaging of a millisecond radio transient with an observation of transient pulsar J0628+0909. We developed a special observing mode of the Karl G. Jansky Very Large Array (VLA) to produce correlated data products (i.e., visibilities and images) on a time scale of 10 ms. Correlated data effectively produce thousands of beams on the sky that can localize sources anywhere over a wide field of view. We used this new observing mode to find and image pulses from the rotating radio transient (RRAT) J0628+0909, improving its localization by two orders of magnitude. Since the location of the RRAT was only approximately known when first observed, we searched for transients using a wide-field detection algorithm based on the bispectrum, an interferometric closure quantity. Over 16 minutes of observing, this algorithm detected one transient offset roughly 1' from its nominal location; this allowed us to image the RRAT to localize it with an accuracy of 1.6". With a priori knowledge of the RRAT location, a traditional beamforming search of the same data found two, lower significance pulses. The refined RRAT position excludes all potential multiwavelength counterparts, limiting its optical luminosity to L_i'<1.1x10^31 erg/s and excluding its association with a young, luminous neutron star.Comment: Submitted to ApJ, 7 pages, 5 figure

Widening participation in higher education: student quantitative skills and independent learning as impediments to progression

The UK government's widening participation strategy, and the concomitant development of a mass higher education system, has imposed a variety of pressures on higher education institutions. Not least of these is the changing nature of the student population, and the assumptions that can be made about its skills and knowledge base. It should not be surprising that this rapid expansion of the higher education system has resulted in declining student progression and retention rates. This paper takes a case study approach and attempts to identify the range of factors that might explain the variability of student performance on a first year undergraduate introductory statistics module. The paper concludes that there are no simple predictors of success or failure. However, there is evidence to suggest that any innovations in delivery need to take account of individual student development and that the presumption that students can rapidly become independent learners upon initial entry to higher education is an unrealistic one

Changing the perspective on early development of Rett syndrome

We delineated the achievement of early speech-language milestones in 15 young children with Rett syndrome (MECP2 positive) in the first two years of life using retrospective video analysis. By contrast to the commonly accepted concept that these children are normal in the pre-regression period, we found markedly atypical development of speech-language capacities, suggesting a paradigm shift in the pathogenesis of Rett syndrome and a possible approach to its early detection

Multi-armed bandit models for 2D grasp planning with uncertainty

Abstract — For applications such as warehouse order fulfill-ment, robot grasps must be robust to uncertainty arising from sensing, mechanics, and control. One way to achieve robustness is to evaluate the performance of candidate grasps by sampling perturbations in shape, pose, and gripper approach and to com-pute the probability of force closure for each candidate to iden-tify a grasp with the highest expected quality. Since evaluating the quality of each grasp is computationally demanding, prior work has turned to cloud computing. To improve computational efficiency and to extend this work, we consider how Multi-Armed Bandit (MAB) models for optimizing decisions can be applied in this context. We formulate robust grasp planning as a MAB problem and evaluate convergence times towards an optimal grasp candidate using 100 object shapes from the Brown Vision 2D Lab Dataset with 1000 grasp candidates per object. We consider the case where shape uncertainty is represented as a Gaussian process implicit surface (GPIS) with Gaussian uncertainty in pose, gripper approach angle, and coefficient of friction. We find that Thompson Sampling and the Gittins index MAB methods converged to within 3 % of the optimal grasp up to 10x faster than uniform allocation and 5x faster than iterative pruning. I