Efficient data augmentation for fitting stochastic epidemic models to prevalence data

Stochastic epidemic models describe the dynamics of an epidemic as a disease spreads through a population. Typically, only a fraction of cases are observed at a set of discrete times. The absence of complete information about the time evolution of an epidemic gives rise to a complicated latent variable problem in which the state space size of the epidemic grows large as the population size increases. This makes analytically integrating over the missing data infeasible for populations of even moderate size. We present a data augmentation Markov chain Monte Carlo (MCMC) framework for Bayesian estimation of stochastic epidemic model parameters, in which measurements are augmented with subject-level disease histories. In our MCMC algorithm, we propose each new subject-level path, conditional on the data, using a time-inhomogeneous continuous-time Markov process with rates determined by the infection histories of other individuals. The method is general, and may be applied, with minimal modifications, to a broad class of stochastic epidemic models. We present our algorithm in the context of multiple stochastic epidemic models in which the data are binomially sampled prevalence counts, and apply our method to data from an outbreak of influenza in a British boarding school

High energy scattering in the saturation regime including running coupling and rare fluctuation effects

The analytic result for the $S$-matrix in the saturation regime including the running coupling is obtained. To get this result we solve the Balitsky and Kovchegov-Weigert evolution equations in the saturation regime, which include running coupling corrections. We study also the effect of rare fluctuations on top of the running coupling. We find that the rare fluctuations are less important in the running coupling case as compared to the fixed coupling case.Comment: 10 page

Gear optimization

The use of formal numerical optimization methods for the design of gears is investigated. To achieve this, computer codes were developed for the analysis of spur gears and spiral bevel gears. These codes calculate the life, dynamic load, bending strength, surface durability, gear weight and size, and various geometric parameters. It is necessary to calculate all such important responses because they all represent competing requirements in the design process. The codes developed here were written in subroutine form and coupled to the COPES/ADS general purpose optimization program. This code allows the user to define the optimization problem at the time of program execution. Typical design variables include face width, number of teeth and diametral pitch. The user is free to choose any calculated response as the design objective to minimize or maximize and may impose lower and upper bounds on any calculated responses. Typical examples include life maximization with limits on dynamic load, stress, weight, etc. or minimization of weight subject to limits on life, dynamic load, etc. The research codes were written in modular form for easy expansion and so that they could be combined to create a multiple reduction optimization capability in future

Ballistic electronic transport in Quantum Cables

We studied theoretically ballistic electronic transport in a proposed mesoscopic structure - Quantum Cable. Our results demonstrated that Qauntum Cable is a unique structure for the study of mesoscopic transport. As a function of Fermi energy, Ballistic conductance exhibits interesting stepwise features. Besides the steps of one or two quantum conductance units ($2e^2/h$), conductance plateaus of more than two quantum conductance units can also be expected due to the accidental degeneracies (crossings) of subbands. As structure parameters is varied, conductance width displays oscillatory properties arising from the inhomogeneous variation of energy difference betweeen adjoining transverse subbands. In the weak coupling limits, conductance steps of height $2e^2/h$ becomes the first and second plateaus for the Quantum Cable of two cylinder wires with the same width.Comment: 11 pages, 5 figure

Eulerian and modified Lagrangian approaches to multi-dimensional condensation and collection

Turbulence is argued to play a crucial role in cloud droplet growth. The combined problem of turbulence and cloud droplet growth is numerically challenging. Here, an Eulerian scheme based on the Smoluchowski equation is compared with two Lagrangian superparticle (or su- perdroplet) schemes in the presence of condensation and collection. The growth processes are studied either separately or in combination using either two-dimensional turbulence, a steady flow, or just gravitational acceleration without gas flow. Good agreement between the differ- ent schemes for the time evolution of the size spectra is observed in the presence of gravity or turbulence. Higher moments of the size spectra are found to be a useful tool to characterize the growth of the largest drops through collection. Remarkably, the tails of the size spectra are reasonably well described by a gamma distribution in cases with gravity or turbulence. The Lagrangian schemes are generally found to be superior over the Eulerian one in terms of computational performance. However, it is shown that the use of interpolation schemes such as the cloud-in-cell algorithm is detrimental in connection with superparticle or superdroplet approaches. Furthermore, the use of symmetric over asymmetric collection schemes is shown to reduce the amount of scatter in the results.Comment: 36 pages, 17 figure

Internal magnetic fields in thin ZnSe epilayers

Strain induced spin-splitting is observed and characterized using pump-probe Kerr rotation spectroscopy in n-ZnSe epilayers grown on GaAs substrates. The spin-splitting energies are mapped out as a function of pump-probe separation, applied voltage, and temperature in a series of samples of varying epilayer thicknesses and compressive strain arising from epilayer-substrate lattice mismatch. The strain is independently quantified using photoluminescence and x-ray diffraction measurements. We observe that the magnitude of the spin splitting increases with applied voltage and temperature, and is highly crystal direction dependent, vanishing along [1 1-bar 0].Comment: 9 pages, 3 figure

Diffractive lens fabricated with binary features less than 60 nm

We designed, fabricated, and characterized a binary diffractive lens with features less than 60nm. The lens was designed for operation in the red portion of the spectrum. Experimental measurements of lens performance agree with predictions generated by rigorous models of diffraction