Physical Sciences and Mathematics Commons^™

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 …

On Vector Sequence Transforms And Acceleration Techniques, Steven L. Hodge

Mathematics & Statistics Theses & Dissertations

This dissertation is devoted to the acceleration of convergence of vector sequences. This means to produce a replacement sequence from the original sequence with higher rate of convergence.

It is assumed that the sequence is generated from a linear matrix iteration x_i+ i = Gx_i + k where G is an n x n square matrix and x_I+1 , x_i,and k are n x 1 vectors. Acceleration of convergence is obtained when we are able to resolve approximations to low dimension invariant subspaces of G which contain large components of the error. When …

Weak Bipolarizable Graphs, Stephan Olariu

Computer Science Faculty Publications

We characterize a new class of perfectly orderable graphs and give a polynomial-time recognition algorithm, together with linear-time optimization algorithms for this class of graphs.