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Full-Text Articles in Physical Sciences and Mathematics
Optimization Framework For Reconstructing Biomedical Images By Efficient Sample-Based Parameterization, Paul Richard Arbic Ii
Optimization Framework For Reconstructing Biomedical Images By Efficient Sample-Based Parameterization, Paul Richard Arbic Ii
Theses and Dissertations
An efficient computational approach for optimal reconstruction of binary-type images suitable for models in various biomedical applications is developed and validated. The methodology includes derivative-free optimization supported by a set of sample solutions with customized geometry generated synthetically. The entire framework has an easy to follow design due to a nominal number of tuning parameters which makes the approach simple for practical implementation in various settings, adjusting it to new models, and enhancing the performance. High efficiency in computational time is achieved through applying the coordinate descent method to work with individual controls in the predefined custom order. This technique …
Optimal Control Of The Second Order Elliptic Equations With Biomedical Applications, Saleheh Seif
Optimal Control Of The Second Order Elliptic Equations With Biomedical Applications, Saleheh Seif
Theses and Dissertations
Dissertation analyzes optimal control of systems with distributed parameters described by the general boundary value problems in a bounded Lipschitz domain for the linear second order uniformly elliptic partial differential equations (PDE) with bounded measurable coefficients. Broad class of elliptic optimal control problems under Dirichlet or Neumann boundary conditions are considered, where the control parameter is the density of sources, and the cost functional is the L2-norm difference of the weak solution of the elliptic problem from measurement along the boundary or subdomain. The optimal control problems are fully discretized using the method of finite differences. Two types of discretization …
Discrete Moment Problems With Logconcave And Logconvex Distributions, Talal Alharbi
Discrete Moment Problems With Logconcave And Logconvex Distributions, Talal Alharbi
Theses and Dissertations
We introduce new shape constraints, logconcavity and logconvexity, to discrete moment problems for bounding the k-out-of-n type probabilities and expectations of higher order convex functions of discrete random variables with non-negative and finite support. The bounds are obtained as the optimum values of non-convex and convex nonlinear optimization problems, where the non-convex problem is reformulated as a bilinear optimization problem. We present numerical experiments to show the improvement in the tightness of the bounds when the shape of underlying unknown probability distribution is prescribed into discrete moment problems. We apply our optimization based bounding methodology in an insurance problem to …