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

CONFIRM: a double-blind, placebo controlled phase III clinical trial investigating the effect of nivolumab in patients with relapsed mesothelioma: study protocol for a randomised controlled trial

Background: Mesothelioma is an incurable, apoptosis-resistant cancer caused in most cases by previous exposure to asbestos and is increasing in incidence. It represents a growing health burden but remains under-researched, with limited treatment options. Early promising signals of activity relating to both PD-L1- and PD-1-targeted treatment in mesothelioma implicate a dependency of mesothelioma on this immune checkpoint. There is a need to evaluate checkpoint inhibitors in patients with relapsed mesothelioma where treatment options are limited. Methods: The addition of 12 months of nivolumab (anti-PD1 antibody) to standard practice will be conducted in the UK using a randomised, placebo-controlled phase III trial (the Cancer Research UK CONFIRM trial). A total of 336 patients with pleural or peritoneal mesothelioma who have received at least two prior lines of therapy will be recruited from UK secondary care sites. Patients will be randomised 2:1 (nivolumab:placebo), stratified according to epithelioid/non-epithelioid, to receive either 240 mg nivolumab monotherapy or saline placebo as a 30-min intravenous infusion. Treatment will be for up to 12 months. We will determine whether the use of nivolumab increases overall survival (the primary efficacy endpoint). Secondary endpoints will include progression-free survival, objective response rate, toxicity, quality of life and cost-effectiveness. Analysis will be performed according to the intention-to-treat principle using a Cox regression analysis for the primary endpoint (and for other time-to-event endpoints). Discussion: The outcome of this trial will provide evidence of the potential benefit of the use of nivolumab in the treatment of relapsed mesothelioma. If found to be clinically effective, safe and cost-effective it is likely to become the new standard of care in the UK