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Full-Text Articles in Mathematics
Inverse Boundary Value Problems For Polyharmonic Operators With Non-Smooth Coefficients, Landon Gauthier
Inverse Boundary Value Problems For Polyharmonic Operators With Non-Smooth Coefficients, Landon Gauthier
Theses and Dissertations--Mathematics
We consider inverse boundary problems for polyharmonic operators and in particular, the problem of recovering the coefficients of terms up to order one. The main interest of our result is that it further relaxes the regularity required to establish uniqueness. The proof relies on an averaging technique introduced by Haberman and Tataru for the study of an inverse boundary value problem for a second order operator.
An Integrated Computational Pipeline To Construct Patient-Specific Cancer Models, Daniel Plaugher
An Integrated Computational Pipeline To Construct Patient-Specific Cancer Models, Daniel Plaugher
Theses and Dissertations--Mathematics
Precision oncology largely involves tumor genomics to guide therapy protocols. Yet, it is well known that many commonly mutated genes cannot be easily targeted. Even when genes can be targeted, resistance to therapy is quite common. A rising field with promising results is that of mathematical biology, where in silico models are often used for the discovery of general principles and novel hypotheses that can guide the development of new treatments. A major goal is that eventually in silico models will accurately predict clinically relevant endpoints and find optimal control interventions to stop (or reverse) disease progression. Thus, it is …