Physical Sciences and Mathematics Commons^™

Radical Impact Of Change In Actions And Confidence Index On Reverse Decision Making An Application Based Study, Swatee Trimbak Paithankar

Engineering Management & Systems Engineering Theses & Dissertations

While making decisions under uncertainty, people are often unaware of the logical approach to form the decision process. It is assumed that collecting details, analyzing and evaluating data is enough to make 'proper' decisions. However, past research in the decision making arena has significantly validated that there exists a class of decision problems which is complex, ill-structured and not defined to the level where decision makers can draw logical conclusions based on existing traditional decision approaches. RDM (reverse decision making), one of the novel approaches of decision making under conditions of uncertainty, has shown potential towards addressing some of these …

Mathematical Models Of Tumors And Their Remote Metastases, Carryn Bellomo

Mathematics & Statistics Theses & Dissertations

Clinical observations and indications in the literature have led us to investigate several models of tumors. For example, it has been shown that a tumor has the ability to send out anti-growth factors, or inhibitors, to keep its remote metastases from growing. Thus, we model the depleting effect of such a growth inhibitor after the removal of the primary tumor (thus removing the source) as a function of time t and distance from the original tumor r.

It has also been shown clinically that oxygen and glucose are nutrients critical to the survival and growth of tumors. Thus, we model …

Visibility-Related Problems On Parallel Computational Models, Himabindu Gurla

Computer Science Theses & Dissertations

Visibility-related problems find applications in seemingly unrelated and diverse fields such as computer graphics, scene analysis, robotics and VLSI design. While there are common threads running through these problems, most existing solutions do not exploit these commonalities. With this in mind, this thesis identifies these common threads and provides a unified approach to solve these problems and develops solutions that can be viewed as template algorithms for an abstract computational model. A template algorithm provides an architecture independent solution for a problem, from which solutions can be generated for diverse computational models. In particular, the template algorithms presented in this …

Multiple Learner Systems Using Resampling Methods, Binyun Xie

Computer Science Theses & Dissertations

The N-Learners Problem deals with combining a number of learners such that the resultant system is "better", under some criterion, than the best of the individual learners. We consider a system of probably approximately correct concept learners. Depending on the available information, there are several methods to make the composite system better than the best of the individual learners. If a sample and an oracle that generates data points (but, not their classification) is available, then we show that we can achieve arbitrary levels of the normalized confidence of the composite system if (a) a robust learning algorithm is available, …

Mathematical Models Of Prevascular Tumor Growth By Diffusion, Sophia A. Maggelakis

Mathematics & Statistics Theses & Dissertations

A study of several complementary mathematical models that describe the early, prevascular stages of solid tumor growth by diffusion under various simplifying assumptions is presented. The advantage of these models is that their degree of complexity is relatively low, which ensures fairly straightforward comparisons with experimental or clinical data (as it becomes available), yet they are mathematically sophisticated enough to capture the main biological phenomena of interest.

The tumor growth and cell proliferation rate are assumed to depend on the local concentrations of nutrients and inhibitory factors. The effects of geometry and spatially non-uniform inhibitor production and non-uniform nutrient consumption …

Numerical Experiments With The Quasigeostrophic Potential-Vorticity Equation, Peter L. Spence

OES Theses and Dissertations

A method is developed to model the circulation of a barotropic, 8-plane ocean under an imposed steady wind stress. The model includes the effect of both horizontal and vertical friction along with nonlinear advection of vorticity. Implementing the method involves solving the unsteady quasigeostrophic potential-vorticity equation using a compact finite difference scheme (Gatski, Grosch, and Rose, 1982).

Once developed, this model is used in four separate numerical experiments. In each experiment, a model ocean with an initial flow field is driven to a steady state solution. Vertical viscosity is held constant in the first three experiments while lateral viscosity is …

A Theoretical Model For Calculation Of Molecular Stopping Power, Yuan-Jian Xu

Physics Theses & Dissertations

A modified local plasma model based on the work of Linhard-Winther, Bethe, Brown, and Walske is established. The Gordon-Kim's molecular charged density model is employed to obtain a formula to evaluate the stopping power of many useful molecular systems. The stopping power of H₂ and He gas was calculated for incident proton energy ranging from 100 KeV to 2.5 MeV. The stopping power of O₂, N₂ and water vapor was also calculated for incident proton energy ranging from 40 keV to 2.5 MeV. Good agreement with experimental data was obtained.

A discussion of molecular effects leading …