Error bounds for the asymptotic expansion of the Hurwitz zeta function

In this paper, we reconsider the large-$a$ asymptotic expansion of the Hurwitz zeta function $\zeta(s,a)$. New representations for the remainder term of the asymptotic expansion are found and used to obtain sharp and realistic error bounds. Applications to the asymptotic expansions of the polygamma functions, the gamma function, the Barnes $G$-function and the $s$-derivative of the Hurwitz zeta function $\zeta(s,a)$ are provided. A detailed discussion on the sharpness of our error bounds is also given.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1606.07961, accepted for publication in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science

Higher Equations of Motion in Boundary Liouville Field Theory

In addition to the ordinary bulk higher equations of motion in the boundary version of the Liouville conformal field theory, an infinite set of relations containing the boundary operators is found. These equations are in one-to-one correspondence with the singular representations of the Virasoro algebra. We comment on the possible applications in the context of minimal boundary Liouville gravity.Comment: 18 page

Riemann-Hilbert problems from Donaldson-Thomas theory

We study a class of Riemann-Hilbert problems arising naturally in Donaldson-Thomas theory. In certain special cases we show that these problems have unique solutions which can be written explicitly as products of gamma functions. We briefly explain connections with Gromov-Witten theory and exact WKB analysis

Improving delirium care in the intensive care unit: The design of a pragmatic study

<p>Abstract</p> <p>Background</p> <p>Delirium prevalence in the intensive care unit (ICU) is high. Numerous psychotropic agents are used to manage delirium in the ICU with limited data regarding their efficacy or harms.</p> <p>Methods/Design</p> <p>This is a randomized controlled trial of 428 patients aged 18 and older suffering from delirium and admitted to the ICU of Wishard Memorial Hospital in Indianapolis. Subjects assigned to the intervention group will receive a multicomponent pharmacological management protocol for delirium (PMD) and those assigned to the control group will receive no change in their usual ICU care. The primary outcomes of the trial are (1) delirium severity as measured by the Delirium Rating Scale revised-98 (DRS-R-98) and (2) delirium duration as determined by the Confusion Assessment Method for the ICU (CAM-ICU). The PMD protocol targets the three neurotransmitter systems thought to be compromised in delirious patients: dopamine, acetylcholine, and gamma-aminobutyric acid. The PMD protocol will target the reduction of anticholinergic medications and benzodiazepines, and introduce a low-dose of haloperidol at 0.5-1 mg for 7 days. The protocol will be delivered by a combination of computer (artificial intelligence) and pharmacist (human intelligence) decision support system to increase adherence to the PMD protocol.</p> <p>Discussion</p> <p>The proposed study will evaluate the content and the delivery process of a multicomponent pharmacological management program for delirium in the ICU.</p> <p>Trial Registration</p> <p>ClinicalTrials.gov: <a href="http://www.clinicaltrials.gov/ct2/show/NCT00842608">NCT00842608</a></p

Environment Orientation : a structured simulation approach for agent-based complex systems

Complex systems are collections of independent agents interacting with each other and with their environment to produce emergent behaviour. Agent-based computer simulation is one of the main ways of studying complex systems. A naive approach to such simulation can fare poorly, due to large communication overhead, and due to the scope for deadlock between the interacting agents sharing a computational platform. Agent interaction can instead be considered entirely from the point of view of the environment(s) within which the agents interact. Structuring a simulation using such Environment Orientation leads to a simulation that reduces communication overhead, that is effectively deadlock-free, and yet still behaves in the manner required. Additionally the Environment Orientation architecture eases the development of more sophisticated large-scale simulations, with multiple kinds of complex agents, situated in and interacting with multiple kinds of environments. We describe the Environment Orientation simulation architecture. We report on a number of experiments that demonstrate the effectiveness of the Environment Orientation approach: a simple flocking system, a flocking system with multiple sensory environments, and a flocking system in an external environment

The Distances of the Magellanic Clouds

The present status of our knowledge of the distances to the Magellanic Clouds is evaluated from a post-Hipparcos perspective. After a brief summary of the effects of structure, reddening, age and metallicity, the primary distance indicators for the Large Magellanic Cloud are reviewed: The SN 1987A ring, Cepheids, RR Lyraes, Mira variables, and Eclipsing Binaries. Distances derived via these methods are weighted and combined to produce final "best" estimates for the Magellanic Clouds distance moduli.Comment: Invited review article to appear in ``Post Hipparcos Cosmic Candles'', F. Caputo & A. Heck (Eds.), Kluwer Academic Publ., Dordrecht, in pres

Large scale analytic calculations in quantum field theories

We present a survey on the mathematical structure of zero- and single scale quantities and the associated calculation methods and function spaces in higher order perturbative calculations in relativistic renormalizable quantum field theories.Comment: 25 pages Latex, 1 style fil

S-duality as a beta-deformed Fourier transform

An attempt is made to formulate Gaiotto's S-duality relations in an explicit quantitative form. Formally the problem is that of evaluation of the Racah coefficients for the Virasoro algebra, and we approach it with the help of the matrix model representation of the AGT-related conformal blocks and Nekrasov functions. In the Seiberg-Witten limit, this S-duality reduces to the Legendre transformation. In the simplest case, its lifting to the level of Nekrasov functions is just the Fourier transform, while corrections are related to the beta-deformation. We calculate them with the help of the matrix model approach and observe that they vanish for beta=1. Explicit evaluation of the same corrections from the U_q(sl(2)) infinite-dimensional representation formulas due to B.Ponsot and J.Teshner remains an open problem.Comment: 21 page

Nucleoside diphosphate kinase A as a controller of AMP-kinase in airway epithelia

This review integrates recent understanding of a novel role for NDPK-A in two related directions: Firstly, its role in an airway epithelial cell when bound to the luminal (apical) membrane and secondly in the cytosol of many different cells (epithelial and non-epithelial) where an isoform-specific interaction occurs with a regulatory partner, AMPKα1. Thus NDPK-A is present in both a membrane and cytosolic environment but in the apical membrane, its roles are not understood in detail; preliminary data suggest that it co-localises with the cystic fibrosis protein (CFTR). In cytosol, we find that NDPK-A is coupled to the catalytic alpha1 isoform of the AMP-activated protein kinase (AMPKα subunit), which is part of a heterotrimeric protein complex that responds to cellular energy status by switching off ATP-consuming pathways and switching on ATP-generating pathways when ATP is limiting. We find that ATP is located within this complex and ‘fed’ from NDPK to AMPK without ever ‘seeing’ bulk solution. Importantly, the reverse can also happen such that AMPK activity can be made to decline when NDPK-A ‘steals’ ATP from AMPK. Thus we propose a novel paradigm in NDPK-A function by suggesting that AMP-kinase can be regulated by NDPK-A, independently of AMP