Accuracy assessment in multivariate Bayesian forecasting linear and nonlinear models

Reduced alertness and high levels of cognitive fatigue due to sleep loss bring forth substantial risks in today\u27s 24/7 society. Biomathematical models can be used to help mitigate such risks by predicting quantitative levels of fatigue under sleep loss. These models help manage risk by providing information on the timing at which high levels of fatigue will occur; countermeasures can then be taken to reduce accident risk at such critical times. Many quantitative models exist to predict cognitive performance based on homeostatic and circadian processes (Mallis et al., 2004). These models have typically been fitted to group average data. Due to large individual variation, group-average predictions are often inaccurate for a given individual. However, since individual differences are trait-like, between subjects variation can be captured by individualizing model parameters using the technique of Bayesian forecasting. In many cases the amount of data collected, and consequently, the prediction accuracy, will be limited by factors such as cost and availability. However; prediction accuracy may still be improved by including information from alternative, correlated performance measures in a multivariate Bayesian forecasting framework. When collecting data from two performance measures, we consider methods of sampling that obtain a desired average level of prediction accuracy for minimal data collection cost. We assess the prediction accuracy using the Bayesian mean squared error (MSE) and derive this measure for a general Bayesian linear model. To understand how the accuracy depends on the number of measurements from primary and secondary tasks in the simplest case, we apply the equation to specify the accuracy for the bivariate Bayesian linear model of subject means. For this simple model, we further assume that observations from each performance measure have a fixed cost per data point, and use this assumption to determine the number of measurements of each variable needed to minimize the cost while still obtaining no less than the desired level of accuracy. To aid the extension of the findings from the linear case to state of the art nonlinear biomathematical fatigue models, we focus on obtaining our extended measure of accuracy for the nonlinear case. Computing this accuracy analytically is often infeasible without reliance on model approximations. Model simulations can be used to compute this accuracy; however, such simulations can be time consuming, especially for models that lack analytic solutions and require that a system of differential equations be solved to produce model dynamics. Much of this computational burden in assessing estimator accuracy, however, is produced by using the Bayesian MMSE estimator, and could be reduced by taking advantage of the quicker to compute Bayesian MAP estimator. We show how for a nonlinear biomathematical model that the accuracy assessment using repeated simulation with the MAP estimator yields a reasonable estimate of the accuracy obtained using the MMSE estimator. Still, however, for any given case, determination of whether the MMSE accuracy can be approximated with the MAP accuracy requires these time consuming simulations. We begin to analytically identify classes of models where the MMSE accuracy can be approximated by the MAP accuracy. We consider a class of quadratic Bayesian models, and show by analytic approximation that for this class, the MMSE has twice the accuracy of the MAP

Planar Supersymmetric Quantum Mechanics of a Charged Particle in an External Electromagnetic Field

The supersymmetric quantum mechanics of a two-dimensional non-relativistic particle subject to external magnetic and electric fields is studied in a superfield formulation and with the typical non-minimal coupling of (2+1) dimensions. Both the N=1 and N=2 cases are contemplated and the introduction of the electric interaction is suitably analysed.Comment: V3-Improved by Referees' sugestions. REVTeX4 6 pages (twocolumn option), no figures. V2-Minor changes. A previous version of this work was presented by JAHN during the II Intern. Conf. on Fundamental Interactions, June 2004, Pedra Azul-ES, Brazil. Submitted to Phys. Rev.

Super-Droplet Method for the Numerical Simulation of Clouds and Precipitation: a Particle-Based Microphysics Model Coupled with Non-hydrostatic Model

A novel simulation model of cloud microphysics is developed, which is named Super-Droplet Method (SDM). SDM enables accurate calculation of cloud microphysics with reasonable cost in computation. A simple SDM for warm rain, which incorporates sedimentation, condensation/evaporation, stochastic coalescence, is developed. The methodology to couple SDM and a non-hydrostatic model is also developed. It is confirmed that the result of our Monte Carlo scheme for the coalescence of super-droplets agrees fairly well with the solution of stochastic coalescence equation. A preliminary simulation of a shallow maritime cumulus formation initiated by a warm bubble is presented to demonstrate the practicality of SDM. Further discussions are devoted for the extension and the computational efficiency of SDM to incorporate various properties of clouds, such as, several types of ice crystals, several sorts of soluble/insoluble CCNs, their chemical reactions, electrification, and the breakup of droplets. It is suggested that the computational cost of SDM becomes lower than spectral (bin) method when the number of attributes $d$ becomes larger than some critical value, which may be $2\sim4$

On Weyl-Titchmarsh Theory for Singular Finite Difference Hamiltonian Systems

We develop the basic theory of matrix-valued Weyl-Titchmarsh M-functions and the associated Green's matrices for whole-line and half-line self-adjoint Hamiltonian finite difference systems with separated boundary conditions.Comment: 30 pages, to appear in J. Comput. Appl. Mat

Close Binary Progenitors of Long Gamma Ray Bursts

The strong dependence of the neutrino annihilation mechanism on the mass accretion rate makes it difficult to explain the LGRBs with duration in excess of 100 seconds as well as the precursors separated from the main gamma-ray pulse by few hundreds of seconds. Even more difficult is to explain the Swift observations of the shallow decay phase and X-ray flares, if they indeed indicate activity of the central engine for as long as 10,000 seconds. These data suggest that some other, most likely magnetic mechanisms have to be considered. The magnetic models do not require the development of accretion disk within the first few seconds of the stellar collapse and hence do not require very rapidly rotating stellar cores at the pre-supernova state. This widens the range of potential LGRB progenitors. In this paper, we re-examine the close binary scenario allowing for the possibility of late development of accretion disks in the collapsar model and investigate the available range of mass accretion rates, black hole masses, and spins. A particularly interesting version of the binary progenitor involves merger of a WR star with an ultra-compact companion, neutron star or black hole. In this case we expect the formation of very long-lived accretion disks, that may explain the phase of shallow decay and X-ray flares observed by Swift. Similarly long-lived magnetic central engines are expected in the current single star models of LGRB progenitors due to their assumed exceptionally fast rotation.Comment: Submitted to MNRA

The role of psychological factors in the career of the independent dancer

Previous research indicates that psychological factors such as motivation and mental skills play an important role in relation to performance and to negotiating talent development stages. However, little is known about these factors in dance, particularly with regard to the independent dancer whose career may involve multiple roles, varied work patterns, and periods of instability. The aim of this study was to explore dancers’ motivation to work in an independent capacity, and the extent to which dancers’ psychological characteristics and skills enabled them to navigate a career in this demanding sector. In-depth semi-structured interviews were conducted with 14 dancers at different stages of their careers. Interviews were transcribed verbatim and content analyzed. Analysis revealed that the dancers were intrinsically motivated and highly committed to the profession. Working in the independent sector offered dancers opportunities for growth and fulfillment; they appreciated the autonomy, flexibility and freedom that the independent career afforded, as well as working with new people across roles and disciplines. In order to overcome the various challenges associated with the independent role, optimism, self-belief, social support, and career management skills were crucial. The mental skills reported by the participants had developed gradually in response to the demands that they faced. Therefore, mental skills training could be invaluable for dancers to help them successfully negotiate the independent sector

Market conditions, trader types and price–volume relation in energy futures markets

We investigate the asymmetric relations between trading volume and price changes, and trading volume and price volatility of energy futures contracts across maturities and under different market conditions. Using a relatively long sample of daily observations, we examine whether the impact of trading volume on returns and volatility of futures contracts can be time-varying and dependent on the market condition. We differentiate the market condition based on the slope of the forward curve into backwardation and contango. The results indicate that trading volume and returns are positively related when the market is in backwardation and negatively related when the market is in contango. In addition, the positive relation between changes in trading volume and volatility of futures contracts seem to be stronger when the market is in backwardation than when it is in contango. Finally, the results indicate that, to a certain extent, trade participation and trading activities of agents in energy futures markets can be explained by the slope of the forward curve which reflects the market condition and sentiment

Instantons at Strong Coupling, Averaging over Vacua, and the Gluino Condensate

We consider instanton contributions to chiral correlators, such as <0| Tr \lambda^2 (x) Tr \lambda^2(x') |0>, in N=1 supersymmetric Yang-Mills theory with either light adjoint or fundamental matter. Within the former model, extraction of the gluino condensate from a connected 1-instanton diagram, evaluated at strong coupling, can be contrasted with expectations from the Seiberg-Witten solution perturbed to an N=1 vacuum. We observe a numerical discrepancy, coinciding with that observed previously in N=1 SQCD. Moreover, since knowledge of the vacuum structure is complete for softly broken N=2 Yang-Mills, this model serves as a counterexample to the hypothesis of Amati et al. that 1-instanton calculations at strong coupling can be interpreted as averaging over vacua. Within N=1 SQCD, we point out that the connected contribution to the relevant correlators actually vanishes in the weakly coupled Higgs phase, despite having a nonzero value through infra-red effects when calculated in the unbroken phase.Comment: 20 pages, LaTeX; minor additions, to appear in Nucl. Phys.

A Remarkable Three Hour Thermonuclear Burst From 4U 1820-30

We present a detailed observational and theoretical study of a ~3 hr long X-ray burst (the ``super burst'') observed by the Rossi X-ray Timing Explorer (RXTE) from the low mass X-ray binary (LMXB) 4U 1820-30. This is the longest X-ray burst ever observed from this source, and perhaps one of the longest ever observed in great detail from any source. We show that the super burst is thermonuclear in origin. The level of the accretion driven flux as well as the total energy release of ~1.5 x 10^{42} ergs indicate that helium could not be the energy source for the super burst. We outline the physics relevant to carbon production and burning on helium accreting neutron stars and present calculations of the thermal evolution and stability of a carbon layer and show that this process is the most likely explanation for the super burst. We show that for large columns of accreted carbon fuel, a substantial fraction of the energy released in the carbon burning layer is radiated away as neutrinos, and the heat that is conducted from the burning layer in large part flows inward, only to be released on timescales longer than the observed burst. Thus the energy released possibly exceeds that observed in X-rays by more than a factor of ten. Spectral analysis during the super burst reveals the presence of a broad emission line between 5.8 - 6.4 keV and an edge at 8 - 9 keV likely due to reflection of the burst flux from the inner accretion disk in 4U 1820-30. We believe this is the first time such a signature has been unambiguously detected in the spectrum of an X-ray burst.Comment: AASTEX, 44 pages, 14 figures. Accepted for publication in the Astrophysical Journa