A Spatio-Temporal Point Process Model for Ambulance Demand

Ambulance demand estimation at fine time and location scales is critical for fleet management and dynamic deployment. We are motivated by the problem of estimating the spatial distribution of ambulance demand in Toronto, Canada, as it changes over discrete 2-hour intervals. This large-scale dataset is sparse at the desired temporal resolutions and exhibits location-specific serial dependence, daily and weekly seasonality. We address these challenges by introducing a novel characterization of time-varying Gaussian mixture models. We fix the mixture component distributions across all time periods to overcome data sparsity and accurately describe Toronto's spatial structure, while representing the complex spatio-temporal dynamics through time-varying mixture weights. We constrain the mixture weights to capture weekly seasonality, and apply a conditionally autoregressive prior on the mixture weights of each component to represent location-specific short-term serial dependence and daily seasonality. While estimation may be performed using a fixed number of mixture components, we also extend to estimate the number of components using birth-and-death Markov chain Monte Carlo. The proposed model is shown to give higher statistical predictive accuracy and to reduce the error in predicting EMS operational performance by as much as two-thirds compared to a typical industry practice

Two Loop Scalar Bilinears for Inflationary SQED

We evaluate the one and two loop contributions to the expectation values of two coincident and gauge invariant scalar bilinears in the theory of massless, minimally coupled scalar quantum electrodynamics on a locally de Sitter background. One of these bilinears is the product of two covariantly differentiated scalars, the other is the product of two undifferentiated scalars. The computations are done using dimensional regularization and the Schwinger-Keldysh formalism. Our results are in perfect agreement with the stochastic predictions at this order.Comment: 43 pages, LaTeX 2epsilon, 5 figures (using axodraw.sty) Version 2 has updated references and important corrections to Tables 3-5 and to eqns (139-141), (145-146), (153-155), (158) and (160

The Fermion Self-Energy during Inflation

We compute the one loop fermion self-energy for massless Dirac + Einstein in the presence of a locally de Sitter background. We employ dimensional regularization and obtain a fully renormalized result by absorbing all divergences with BPHZ counterterms. An interesting technical aspect of this computation is the need for a noninvariant counterterm owing to the breaking of de Sitter invariance by our gauge condition. Our result can be used in the quantum-corrected Dirac equation to search for inflation-enhanced quantum effects from gravitons, analogous to those which have been found for massless, minimally coupled scalars.Comment: 63 pages, 3 figures (uses axodraw.sty), LaTeX 2epsilon. Revised version (to appear in Classical and Quantum Gravity) corrects some typoes and contains some new reference

Forecasting emergency medical service call arrival rates

We introduce a new method for forecasting emergency call arrival rates that combines integer-valued time series models with a dynamic latent factor structure. Covariate information is captured via simple constraints on the factor loadings. We directly model the count-valued arrivals per hour, rather than using an artificial assumption of normality. This is crucial for the emergency medical service context, in which the volume of calls may be very low. Smoothing splines are used in estimating the factor levels and loadings to improve long-term forecasts. We impose time series structure at the hourly level, rather than at the daily level, capturing the fine-scale dependence in addition to the long-term structure. Our analysis considers all emergency priority calls received by Toronto EMS between January 2007 and December 2008 for which an ambulance was dispatched. Empirical results demonstrate significantly reduced error in forecasting call arrival volume. To quantify the impact of reduced forecast errors, we design a queueing model simulation that approximates the dynamics of an ambulance system. The results show better performance as the forecasting method improves. This notion of quantifying the operational impact of improved statistical procedures may be of independent interest.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS442 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Solving the Effective Field Equations for the Newtonian Potential

Loop corrections to the gravitational potential are usually inferred from scattering amplitudes, which seems quite different from how the linearized Einstein equations are solved with a static, point mass to give the classical potential. In this study we show how the Schwinger-Keldysh effective field equations can be used to compute loop corrections to the potential in a way which parallels the classical treatment. We derive explicit results for the one loop correction from the graviton self-energy induced by a massless, minimally coupled scalar.Comment: 15 pages, uses LaTeX2

Motor vehicle accidents in patients with an implantable cardioverter-defibrillator

Objectives.This study was designed to examine driving safety in patients at risk for sudden death after implantation of a cardioverter-defibrillator.Background.Cardioverter-defibrillators are frequently implanted in patients at high risk for sudden death. Despite concern about the safety of driving in these patients, little is known about their actual motor vehicle accident rates.Methods.Surveys were sent to all 742 physicians in the United States involved in cardioverter-defibrillator implantation and follow-up. Physicians were questioned about numbers of patients followed up, numbers of fatal and nonfatal accidents, physician recommendations to patients about driving and knowledge of state driving laws.Results.Surveys were returned by 452 physicians (61%). A total of 30 motor vehicle accidents related to shocks from implantable defibrillators were reported by 25 physicians over a 12-year period from 1980 to 1992. Of these, nine were fatal accidents involving eight patients with a defibrillator and one passenger in a car driven by a patient. No bystanders were fatally injured. There were 21 nonfatal accidents involving 15 patients, 3 passengers and 3 bystanders. The estimated fatality rate for patients with a defibrillator, 7.5/100,000 patient-years, is significantly lower than that for the general population (18.4/100,000 patient-years, p < 0.05). The estimated injury rate, 17.6/100,000 patient-years, is also significantly lower than that for the general public (2,224/100,000 patient-years, p < 0.05). Only 10.5% (30 of 286) of all defibrillator discharges during driving resulted in accidents. Regarding physician recommendations, most physicians (58.1%) ask their patients to wait a mean (± SD) of 7.3 ± 3.4 months after implantation or a shock before driving again.Conclusions.The motor vehicle accident rate caused by discharge from an implantable cardioverter-defibrillator is low. Although restricting driving for a short period of time after implantation may be appropriate, excessive restrictions or a total ban on driving appears to be unwarranted

Summary of Ice Shape Geometric Fidelity Studies on an Iced Swept Wing

Understanding the aerodynamic impact of swept-wing ice accretions is a crucial component of the design of modern aircraft. Computer-simulation tools are commonly used to approximate ice shapes, so the necessary level of detail or fidelity of those simulated ice shapes must be understood relative to high-fidelity representations of the ice. Previous tests were performed in the NASA Icing Research Tunnel to acquire high-fidelity ice shapes. Some of those ice shapes are based on aircraft certification requirements. From this database, full-span artificial ice shapes were designed and manufactured for both an 8.9%-scale and 13.3%-scale semispan wing model of the CRM65 which has been established as the full-scale baseline for this swept-wing project. These models were tested in the Walter H. Beech wind tunnel at Wichita State University and at the ONERA (Office national d'etudes et de recherches aerospatiales) F1 facility, respectively. The data collected in the Wichita State University wind tunnel provided a low-Reynolds number baseline study while the pressurized F1 facility produced data over a wide range of Reynolds and Mach numbers with the highest Reynolds number studied being approximately Re = 11.9 by 10 (sup 6). Three different fidelity representations were created based on three different icing conditions. Lower-fidelity ice shapes were created by lofting a smooth ice shape between cross-section cuts of the high-fidelity ice shape. Grit roughness was attached to this smooth ice shape as another fidelity variant. The data indicates that the geometric fidelity of the ice shapes resulted in significant differences in lift and drag. These results were similar at both facilities over the wide range of test conditions utilized

Quantum Stress Tensor Fluctuations of a Conformal Field and Inflationary Cosmology

We discuss the additional perturbation introduced during inflation by quantum stress tensor fluctuations of a conformally invariant field such as the photon. We consider both a kinematical model, which deals only with the expansion fluctuations of geodesics, and a dynamical model which treats the coupling of the stress tensor fluctuations to a scalar inflaton. In neither model do we find any growth at late times, in accordance with a theorem due to Weinberg. What we find instead is a correction which becomes larger the earlier one starts inflation. This correction is non-Gaussian and highly scale dependent, so the absence of such effects from the observed power spectra may imply a constraint on the total duration of inflation. We discuss different views about the validity of perturbation theory at very early times during which currently observable modes are transplanckian.Comment: 31 pages, 1 figure, uses LaTeX2epsilo