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Inverse problems governed by partial differential equations (PDEs) is a means to learn, from data, unknown or uncertain aspects of PDE-based mathematical models. PDE-based models often are constructed from scientific principles and are pervasive in science and engineering. The improvement of such a model can be accomplished by determining a ``best'' set of model parameters, or by reducing the uncertainty of the parameters that characterize the model. Ultimately, the goal is to improve the predictive capacity of such models and quantitatively understand the limitations of model-based predictions.In this dissertation, we describe algorithmic approaches for the Newton-based solution of large-scale computational inverse problems governed by PDEs. We present and motivate hierarchical matrix approximations of the Hessian, a key-component of Newton's method, as a means to exploit localized sensitivities of underlying elliptic PDE operators and which perform well for inverse problems with highly-informative data. To circumvent the computational challenges associated with generating hierarchical matrix approximations of matrix-free operators, such as the Hessian, we describe a local point spread function methodology, whose computational cost is independent of the problem discretization. It is numerically demonstrated that hierarchical matrix approximations of the Hessian can be effective for large-scale ice sheet inverse problems with highly informative data and thin ice sheets. Lastly, we present a scalable means to solve PDE- and bound-constrained optimization problems by an interior-point filter line-search strategy that leverages performant algebraic multigrid linear solvers. Bound constraints arise naturally in many inverse problems as a means to enforce sign-definiteness as dictated by e.g., physical principles. The inclusion of bound constraints does add particular computational challenges such as non-smooth complementarity conditions as part of the conditions for optimality. The Newton linear system solve strategy described in Chapter 4 is accelerated due to the inclusion of bound-constraints, wherein the performance of many other strategies is negatively impacted by such bound-constraints. A theoretical analysis is provided which demonstrates the algorithmic scaling of the approach. In addition, we demonstrate algorithmic and parallel scaling of the described approach by applying the framework to an example elliptic PDE- and bound-constrained problem.

Obtaining lightweight and accurate approximations of Hessian applies in inverse problems governed by partial differential equations (PDEs) is an essential task to make both deterministic and Bayesian statistical large-scale inverse problems computationally tractable. The $\mathcal{O}(N^{3})$ computational complexity of dense linear algebraic routines such as that needed for sampling from Gaussian proposal distributions and Newton solves by direct linear methods, can be reduced to log-linear complexity by utilizing hierarchical off-diagonal low-rank (HODLR) matrix approximations. In this work, we show that a class of Hessians that arise from inverse problems governed by PDEs are well approximated by the HODLR matrix format. In particular, we study inverse problems governed by PDEs that model the instantaneous viscous flow of ice sheets. In these problems, we seek a spatially distributed basal sliding parameter field such that the flow predicted by the ice sheet model is consistent with ice sheet surface velocity observations. We demonstrate the use of HODLR approximation by efficiently generating Hessian approximations that allow fast generation of samples from a Gaussianized posterior proposal distribution. Computational studies are performed which illustrate ice sheet problem regimes for which the Gauss-Newton data-misfit Hessian is more efficiently approximated by the HODLR matrix format than the low-rank (LR) format. We then demonstrate that HODLR approximations can be favorable, when compared to global low-rank approximations, for large-scale problems by studying the data-misfit Hessian associated to inverse problems governed by the Stokes flow model on the Humboldt glacier and Greenland ice sheets., 28 pages, 12 figures, submitted to Inverse Problems

The restrictive measures implemented in response to the COVID-19 pandemic have triggered sudden massive changes to travel behaviors of people all around the world. This study examines the individual mobility patterns for all transport modes (walk, bicycle, motorcycle, car driven alone, car driven in company, bus, subway, tram, train, airplane) before and during the restrictions adopted in ten countries on six continents: Australia, Brazil, China, Ghana, India, Iran, Italy, Norway, South Africa and the United States. This cross-country study also aims at understanding the predictors of protective behaviors related to the transport sector and COVID-19. Findings hinge upon an online survey conducted in May 2020 (N = 9,394). The empirical results quantify tremendous disruptions for both commuting and non-commuting travels, highlighting substantial reductions in the frequency of all types of trips and use of all modes. In terms of potential virus spread, airplanes and buses are perceived to be the riskiest transport modes, while avoidance of public transport is consistently found across the countries. According to the Protection Motivation Theory, the study sheds new light on the fact that two indicators, namely income inequality, expressed as Gini index, and the reported number of deaths due to COVID-19 per 100,000 inhabitants, aggravate respondents' perceptions. This research indicates that socio-economic inequality and morbidity are not only related to actual health risks, as well documented in the relevant literature, but also to the perceived risks. These findings document the global impact of the COVID-19 crisis as well as provide guidance for transportation practitioners in developing future strategies.

Primary bone tumor, also known as osteosarcoma (OS), is the most common primary malignancy of bone in children and young adults. Current treatment protocols yield a 5-year survival rate of near 70% although approximately 80% of patients have metastatic disease at the time of diagnosis. However, long-term survival rates have remained virtually unchanged for nearly four decades, largely due to our limited understanding of the disease process. One major signaling pathway that has been implicated in human OS tumorigenesis is the insulin-like growth factor (IGF)/insulin-like growth factor-1 receptor (IGF1R) signaling axis. IGF1R is a heterotetrameric α2β2 receptor, in which the α subunits comprise the ligand binding site, whereas the β subunits are transmembrane proteins containing intracellular tyrosine kinase domains. Although numerous strategies have been devised to target IGF/IGF1R axis, most of them have failed in clinical trials due to the lack of specificity and/or limited efficacy. Here, we investigated whether a more effective and specific blockade of IGF1R activity in human OS cells can be accomplished by employing dominant-negative IGF1R (dnIGF1R) mutants. We engineered the recombinant adenoviruses expressing two IGF1R mutants derived from the α (aa 1-524) and β (aa 741-936) subunits, and found that either dnIGF1Rα and/or dnIGF1Rβ effectively inhibited cell migration, colony formation, and cell cycle progression of human OS cells, which could be reversed by exogenous IGF1. Furthermore, dnIGF1Rα and/or dnIGF1Rβ inhibited OS xenograft tumor growth in vivo, with the greatest inhibition of tumor growth shown by dnIGF1Rα. Mechanistically, the dnIGF1R mutants down-regulated the expression of PI3K/AKT and RAS/RAF/MAPK, BCL2, Cyclin D1 and most EMT regulators, while up-regulating pro-apoptotic genes in human OS cells. Collectively, these findings strongly suggest that the dnIGF1R mutants, especially dnIGF1Rα, may be further developed as novel anticancer agents that target IGF signaling axis with high specificity and efficacy.

The dataset deals with the air quality perceived by citizens before and during the enforcement of COVID-19 restrictions in ten countries around the world: Australia, Brazil, China, Ghana, India, Iran, Italy, Norway, South Africa and the United States. An online survey conveniently translated into Chinese, English, Italian, Norwegian, Persian, Portuguese collected information regarding the perceived quality of air pollution according to a Likert scale. The questionnaire was distributed between 11-05-2020 and 31-05-2020 and 9 394 respondents took part. Both the survey and the dataset (stored in a Microsoft Excel Worksheet) are available in a public repository. The collected data offer the people's subjective perspectives related to the objective improvement in air quality occurred during the COVID-19 restrictions. Furthermore, the dataset can be used for research studies involving the reduction in air pollution as experienced, to a different extent, by populations of all the ten countries. Published version