Innovative Applications of Robust Optimization for Long-Term Decision-Making

This dissertation presents innovative applications of robust optimization for long-term decision-making. The first chapter focuses on Value Based Insurance Design (VBID) in the context of heart disease treatment. The high-level aim of VBID is to provide incentives for patients to better align their behavior with the system-level optimum of medication adherence and early (as opposed to late and more expensive) treatment. Our goal is to investigate a VBID approach with different cost-sharing parameters for low risk and high risk patients, in order to achieve a trade off for current and future costs for patients while improving patients’ life quality. The second chapter analyzes via simulation two mathematical modeling frameworks that reflect different managerial attitudes toward upside risk in the context of R&D portfolio selection. The manager seeks to allocate a development budget between low-risk, low-reward projects, called incremental projects, and high-risk, high-reward projects, called innovational projects. We study the differences in strategy and portfolio’s risk profile that arise between a risk-aware manager, who takes upside risk because he has to for the long-term competitive advantage of his company, and a risk-seeking manager, who will take as big a bet as allowed by the model. The third chapter studies hospitals’ optimal strategies of building community health program portfolio in order to achieve the maximum potential benefits under a worst case benefit tolerance level. Our model incorporates the fact that hospitals might have tolerances for upside and downside deviation and thus different uncertainty budgets for upside risk and downside risk and analyzes how key parameters influence the optimal portfolio and implement our approach in a numerical example with promising and insightful results

Uncertainties in the Assessment of Individual and Compound Flooding from River Discharge and Coastal Water Levels under Climate Change

It is widely recognized that climate change can impact the risks of flooding in many regions around the world especially the low-lying coastal areas. The concurrent occurrence of multiple flood drivers such as high river flows and coastal water levels can aggravate such impacts causing catastrophic damages. In this study, the individual and compounding effects of riverine and coastal flooding are investigated over Stephenville Crossing, a town located in the coastal-estuarine region of Newfoundland and Labrador (NL), Canada. The impacts of climate change on flood characteristics and the corresponding uncertainties associated with model inputs and structure, and emission scenarios are assessed. A hydrologic model (HEC-HMS) and a 2D hydrodynamic model (HEC-RAS 2D) are setup and calibrated to simulate the flood inundation for the historical period (1976-2005) as well as near future (2041-2070) and far future (2071-2100) periods under Representative Concentration Pathways (RCPs) 4.5 and 8.5. Results of the HEC-RAS 2D model, including the water surface elevations, are then compared with the 1D model simulations. Future storm events are generated based on projected Intensity-Duration-Frequency (IDF) curves from the convection-permitting Weather Research and Forecasting (WRF) climate model simulations, using SCS, Huff, and alternative block design storm methods. The results are compared with simulations based on projected IDF curves that are derived from statistically downscaled General Circulation Models (GCMs) and the uncertainties from different sources are quantified. Overall, the compounding effects of river overflows, sea-level rise, storm surge and wave can result in extensive inundation of the study area under climate change. The uncertainties associated with climate change impact analyses are propagated from GCMs to flood inundation estimations through design storms, projected IDF curves and modeling processes. Simulations based on projected WRF-IDF curves show higher risks of flooding compared to the ones associated with GCM-IDFs. This research provides a new approach to apply projected IDF curve for compound flood analysis under changing climate conditions

Design of a vector multi-foci metalens for full stokes imaging polarimetry

Imaging polarimetry based on dielectric metasurface is well-known for its ultra-compactness and high integration. However, previous works suffer from low energy efficiency, limited restrictions on choice of target polarization states, or inability to focus light. Here, by inverse design, we numerically demonstrate a multi-foci metalens-based polarimetry that can simultaneously separate and focus the four free-chosen elliptical polarization states at the wavelength of 10.6 \mu m. Such a full-stokes polarimetry features an average absolute efficiency up to 54.63%, and an average relative error as low as 0.00137%. This spatial-multiplexing-free full stokes polarimetry exceeds the theoretical maximum efficiency of traditional polarization-filtering counterparts, and resolves the restriction faced by the orthogonal polarization-multiplexed method

Local connectivity of Julia sets for rational maps with Siegel disks

We prove that a long iteration of rational maps is expansive near boundaries of bounded type Siegel disks. This leads us to extend Petersen's local connectivity result on the Julia sets of quadratic Siegel polynomials to a general case. A new key feature in the proof is that the puzzles are not used.Comment: 42 pages, 12 figures; The introduction was rewritten and some references were update