Estimating the Survival Distribution for Right-Censored Data with Delayed Ascertainment

In many clinical trials, patients are not followed continuously. This means their vital status may not be immediately recorded. In such cases, the results from the Kaplan-Meier estimator or the log rank test, popular methods used for survival analysis, may be biased or inconsistent. Hu and Tsiatis first produced a new estimator to estimate survival distribution for right-censored data with delayed ascertainment, Van der Laan and Hubbard modified their estimator. We investigate each of these proposed estimators and their properties. Using simulations, we compare these new estimators to each other and to the Kaplan-Meier estimator using different sample sizes, different failure rates, and different maximum delay times. The public health importance of this thesis is that we can partially alleviate the problem caused by delayed ascertainment in the analysis of right-censored time to event data by choosing the most accurate and consistent estimator that accounts for the delayed ascertainment. The reduction of bias in analyses of public health data ensures that such studies are reliable so that proper inference can be made and hence, potential public health policy can be based on an accurate decision making process

Concrete Static Stress Estimation Using Computer Vision-Based Digital Image Processing

Department of Urban and Environmental Engineering (Urban Infrastructure Engineering)As increasing interests about structural safety due to occasionally occurring collapse of structures and social infrastructures, efforts to identify and monitor the current state of structure are also increasing. Recently, most structures have been built of concrete, so identification of safety level of concrete structures becomes a critical issue. One of such techniques is to evaluate the current stress state in concrete. This technique is essential in various fields involved in an investigation of tensile stress of tendons in pre- and post-tensioned structures, building remodeling which needs to remove bearing walls and adds other foundations, and identification of load distribution in enlarged concrete structures. In other words, current stress level in concrete is an important factor to check the safety level of the structures in service. Although it is obvious that a technique for estimating the static stress level of concrete is essential, the method to identify the stress state of the currently used concrete structure is definitely limited. Several efforts for estimating the current stress state have been developed in previous research, including a stress-strain relationship based on elastic theory and a stress relaxation method (SRM) for concrete. These methods in the previous researches have made a certain contribution in this field but practical use in real structures is still inadequate. Therefore, an objective of this study is to develop a static stress estimation technique which can be applied to real concrete structures. This study proposes a method that can measure the static stress level of concrete by incorporating SRM and computer vision-based image processing. Applying a small damage to concrete specimen can release the current stress state and induce stress field change inside concrete around the damage. Computer vision-based measurement can measure the deformation due to this stress field change. This deformation measurement is used in the static stress estimation algorithm developed in this study. The proposed method is validated using several concrete specimens and consequently demonstrates the performance.clos

Information length as a new diagnostic of stochastic resonance

Stochastic resonance is a subtle, yet powerful phenomenon in which noise plays an interesting role of amplifying a signal instead of attenuating it. It has attracted great attention with a vast number of applications in physics, chemistry, biology, etc. Popular measures to study stochastic resonance include signal-to-noise ratios, residence time distributions, and different information theoretic measures. Here, we show that the information length provides a novel method to capture stochastic resonance. The information length measures the total number of statistically different states along the path of a system. Specifically, we consider the classical double-well model of stochastic resonance in which a particle in a potential V ( x , t ) = [ - x 2 / 2 + x 4 / 4 - A sin ( ω t ) x ] is subject to an additional stochastic forcing that causes it to occasionally jump between the two wells at x ≈ ± 1 . We present direct numerical solutions of the Fokker–Planck equation for the probability density function p ( x , t ) for ω = 10 - 2 to 10 - 6 , and A ∈ [ 0 , 0 . 2 ] and show that the information length shows a very clear signal of the resonance. That is, stochastic resonance is reflected in the total number of different statistical states that a system passes through

On a long-term dynamics of the magnetised solar tachocline

We investigate the confinement and long-term dynamics of the magnetised solar tachocline. Starting from first principles, we derive the values of turbulent transport coefficients and then explore the implications for the confinement and long-term dynamics of the tachocline. For reasonable parameter values, the turbulent eddy viscosity is found to be negative, with turbulence enhancing the radial shear in the tachocline. Both magnetic diffusivity and thermal diffusivity are severely quenched, with the values much smaller than the magnitude of the eddy viscosity. The effect of the meridional circulation on momentum transport via the hyperviscosity becomes important when the radial shear becomes large (larger than the presently inferred value) due to the negative viscosity

Predicting PDF tails of flux in plasma sheath region

This letter provides the first prediction of the probability density function (PDF) of flux $R$ in plasma sheath sheath region in magnetic fusion devices which is characterized by dynamical equations with exponential non-linearities. By using a non-perturbative statistical theory (instantons), the PDF tails of first moment are shown to be modified Gumbel distribution which represents a frequency distribution of the extreme values of the ensemble. The non-Gaussian PDF tails that are enhanced over Gaussian predictions are the result of intermittency caused by short lived coherent structures (instantons).Comment: 13 pages, 1 figur

Self-consistent Mean Field theory in weakly ionized media

We present a self-consistent mean field theory of the dynamo in 3D and turbulent diffusion in 2D in weakly ionized gas. We find that in 3D, the backreaction does not alter the beta effect while it suppresses the alpha effect when the strength of a mean magnetic field exceeds a critical value. These results suggest that a mean field dynamo operates much more efficiently in weakly ionized gas compared to the fully ionized gas. Furthermore, we show that in 2D, the turbulent diffusion is suppressed by back reaction when a mean magnetic field reaches the same critical strength, with the upper bound on turbulent diffusion given by its kinematic value. Astrophysical implications are discussed

Self-consistent theory of turbulent transport in the solar tachocline. II. Tachocline confinement

We provide a consistent theory of the tachocline confinement (or anisotropic momentum transport) within an hydrodynamical turbulence model. The goal is to explain helioseismological data, which show that the solar tachocline thickness is at most 5% of the solar radius, despite the fact that, due to radiative spreading, this transition layer should have thickened to a much more significant value during the sun's evolution. Starting from the first principle with the physically plausible assumption that turbulence is driven externally (e.g. by plumes penetrating from the convection zone), we derive turbulent (eddy) viscosity in the radial (vertical) and azimuthal (horizontal) directions by incorporating the crucial effects of shearing due to radial and latitudinal differential rotations in the tachocline. We show that the simultaneous presence of both shears induces effectively a much more efficient momentum transport in the horizontal plane than in the radial direction. In particular, in the case of strong radial turbulence (driven by overshooting plumes from the convection zone), the ratio of the radial to horizontal eddy viscosity is proportional to ${\cal A}^{-1/3}$, where ${\cal A}$ is the strength of the shear due to radial differential rotation. In comparison, in the case of horizontally driven turbulence, this ratio becomes of order $-\epsilon^2$, with negative radial eddy viscosity. Here, $\epsilon$ ($\ll 1$) is the ratio of the radial to latitudinal shear. The resulting anisotropy in momentum transport could thus be sufficiently strong to operate as a mechanism for the tachocline confinement against spreading

Information Length as a Useful Index to Understand Variability in the Global Circulation

With improved measurement and modelling technology, variability has emerged as an essential feature in non-equilibrium processes. While traditionally, mean values and variance have been heavily used, they are not appropriate in describing extreme events where a significant deviation from mean values often occurs. Furthermore, stationary Probability Density Functions (PDFs) miss crucial information about the dynamics associated with variability. It is thus critical to go beyond a traditional approach and deal with time-dependent PDFs. Here, we consider atmospheric data from the Whole Atmosphere Community Climate Model (WACCM) model and calculate time-dependent PDFs and the information length from these PDFs, which is the total number of statistically different states that a system passes through in time. Time-dependent PDFs are shown to be non-Gaussian in general, and the information length calculated from these PDFs shed us a new perspective of understanding variabilities, correlation among different variables and regions. Specifically, we calculate time-dependent PDFs and information length and show that the information length tends to increase with the altitude albeit in a complex form. This tendency is more robust for flows/shears than temperature. Also, much similarity among flows and shears in the information length is found in comparison with the temperature. These results also suggest the importance of high latitude/altitude in the information budge in the Earth's atmosphere, the spatial gradient of the information as a useful proxy for the transport of physical quantities.Comment: 15 pages, 5 figure