Estimating Multiple Tumor Transition Rates Based on Data from Survival/Sacrifice Experiments

In this paper, we focus on the model for two types of tumors. Tumor development can be described by four types of death rates and four tumor transition rates. We present a general semi-parametric model to estimate the tumor transition rates based on data from survival/sacrifice experiments. In the model, we make a proportional assumption of tumor transition rates on a common parametric function but no assumption of the death rates from any states. We derived the likelihood function of the data observed in such an experiment, and an EM algorithm that simplified estimating procedures. This article extends work on semi-parametric models for one type of tumor (see Portier and Dinse and Dinse) to two types of tumors.

Estimation of Transition Probabilities in Animal Carcinogenicity Experiments

This paper discusses estimation of the tumor incidence rate, the death rate given tumor is present and the death rate given tumor is absent using a discrete multistage model. The model was originally proposed by Dewanji and Kalbfleisch (1986) and the maximum likelihood estimate of the tumor incidence rate was obtained using EM algorithm. In this paper, we use a reparametrization to simplify the estimation procedure. The resulting estimates are not always the same as the maximum likelihood estimates but are asymptotically equivalent. In addition, an explicit expression for asymptotic variance and bias of the proposed estimators is also derived. These results can be used to compare efficiency of different sacrifice schemes in carcinogenicity experiments.

On the Synthesis of Microarray Experiments

With many different investigators studying the same disease and with a strong commitment to publish supporting data in the scientific community, there are often many different datasets available for any given disease. Hence there is substantial interest in finding methods for combining these datasets to provide better and more detailed understanding of the underlying biology. We consider the synthesis of different microarray data sets using a random effects paradigm and demonstrate how relatively standard statistical approaches yield good results. We identify a number of important and substantive areas which require further investigation.

Analyzing the effects of vertical acceleration and deceleration in multi-phase, debris-flow sediment-column experiments / by Christine Marie Williams.

Water-saturated debris flows are among some of the most destructive mass movements. Their complex nature presents a challenge for quantitative description and modeling. In order to improve understanding of the dynamics of these flows, it is important to seek a simplified dynamic system underlying their behavior. Models currently in use to describe the motion of debris flows employ depth-averaged equations of motion, typically assuming negligible effects from vertical acceleration. However, in many cases debris flows experience significant vertical acceleration as they move across irregular surfaces, and it has been proposed that friction associated with vertical forces and liquefaction merit inclusion in any comprehensive mechanical model. The intent of this work is to determine the effect of vertical acceleration through a series of laboratory experiments designed to simulate debris flows, testing a recent model for debris flows experimentally. In the experiments, a mass of water-saturated sediment is released suddenly from a holding container, and parameters including rate of collapse, pore-fluid pressure, and bed load are monitored. Experiments are simplified to axial geometry so that variables act solely in the vertical dimension. Steady state equations to infer motion of the moving sediment mass are not sufficient to model accurately the independent solid and fluid constituents in these experiments. The model developed in this work more accurately predicts the bed-normal stress of a saturated sediment mass in motion and illustrates the importance of acceleration and deceleration.

Synthesis of computations and experiments for obtaining pulsatile gas flow rates from dynamic pressure difference measurements across an orifice-plate meter

The use of conventional orifice-plate meter is typically restricted to measurements of steady flows. This study proposes a new and effective computational-experimental approach for measuring the time-varying (but steady-in-the-mean) nature of turbulent pulsatile gas flows. Low Mach number (effectively constant density) steady-in-the-mean gas flows with large amplitude fluctuations (whose highest significant frequency is characterized by the value fF) are termed pulsatile if the fluctuations have a direct correlation with the time-varying signature of the imposed dynamic pressure difference and, furthermore, they have fluctuation amplitudes that are significantly larger than those associated with turbulence or random acoustic wave signatures. The experimental aspect of the proposed calibration approach is based on use of Coriolis-meters (whose oscillating arm frequency fcoriolis >> fF) which are capable of effectively measuring the mean flow rate of the pulsatile flows. Together with the experimental measurements of the mean mass flow rate of these pulsatile flows, the computational approach presented here is shown to be effective in converting the dynamic pressure difference signal into the desired dynamic flow rate signal. The proposed approach is reliable because the time-varying flow rate predictions obtained for two different orifice-plate meters exhibit the approximately same qualitative, dominant features of the pulsatile flow.

Dynamics of settling charged particles in turbulence : theory and experiments

It has been proposed that inertial clustering may lead to an increased collision rate of water droplets in clouds. Atmospheric clouds and electrosprays contain electrically charged particles embedded in turbulent flows, often under the influence of an externally imposed, approximately uniform gravitational or electric force. In this thesis, we present the investigation of charged inertial particles embedded in turbulence. We have developed a theoretical description for the dynamics of such systems of charged, sedimenting particles in turbulence, allowing radial distribution functions to be predicted for both monodisperse and bidisperse particle size distributions. The governing parameters are the particle Stokes number (particle inertial time scale relative to turbulence dissipation time scale), the Coulomb-turbulence parameter (ratio of Coulomb ’terminalar speed to turbulence dissipation velocity scale), and the settling parameter (the ratio of the gravitational terminal speed to turbulence dissipation velocity scale). For the monodispersion particles, The peak in the radial distribution function is well predicted by the balance between the particle terminal velocity under Coulomb repulsion and a time-averaged ’drift’ velocity obtained from the nonuniform sampling of fluid strain and rotation due to finite particle inertia. The theory is compared to measured radial distribution functions for water particles in homogeneous, isotropic air turbulence. The radial distribution functions are obtained from particle positions measured in three dimensions using digital holography. The measurements support the general theoretical expression, consisting of a power law increase in particle clustering due to particle response to dissipative turbulent eddies, modulated by an exponential electrostatic interaction term. Both terms are modified as a result of the gravitational diffusion-like term, and the role of ’gravity’ is explored by imposing a macroscopic uniform electric field to create an enhanced, effective gravity. The relation between the radial distribution functions and inward mean radial relative velocity is established for charged particles.