Optimizing the design and performance of photonic systems has been an active and growing area of research over the past decade with many practical applications such as image sensors, augmented reality and virtual reality, on-chip photonic systems, and more. Moreover, gradient-based methods, such as the adjoint variable method (AVM), have led to very distinctive and complex designs for on-chip multiplexers, tapers, dielectric laser accelerators, and more, while yielding much higher performance metrics which classical design approaches using first principles physics cannot match. However, less research has been dedicated in the photonics community to understanding and improving the underlying numerical methods which are critical for the success of these applications. In this thesis, we will demonstrate four key numerical advancements in the use of gradient-based design methods using frequency domain numerical solvers of Maxwell's equations, particularly finite difference frequency domain (FDFD) solvers. The first is the application of domain decomposition techniques to gradient-based optimization, allowing us to reduce the effective system size for a gain in efficiency. The second exploits the physics of perturbative series expansions to efficiently determine the optimal learning rate essential to gradient-based optimization. The third leverages the fundamental similarities of the previous two methods, allowing us to combine the two to achieve a further multiplicative acceleration. The fourth is exploiting the choice of boundary condition in the context of perfectly matched layers to minimize overhead and optimize the efficiency of the simulations required during the optimization procedure. Furthermore, we will demonstrate one novel practical application in designing a next generation replacement for traditional filter-based image sensors that we term a 'color router'. By using a gradient-based approach, we demonstrate not only can we overcome the traditional limitations of filter-based approaches, but we can approach the absolute physical limit of color separation efficiency. In the context of this problem as well, we also demonstrate one further novel method to accelerate optimization, using an L1-like penalty method inspired by L1-regularization popularized in machine learning to improve the robustness to manufacturing errors and other perturbations to the device design. Finally, as a contrast to the gradient-based technique of optimization, we also showcase two examples of more traditional device optimization using the theoretical principles of Maxwell's equations. The first is to exploit analytic continuation and the band-structure of insulator-metal-insulator waveguides to design a reflector with superior reflection properties to that of a uniform metal but with lower loss (essentially a nearly metal-less metallic metamaterial). The second is to engineer interesting radiative properties and extraordinarily high reflection in atomically-thin monolayer graphene nano-ribbon system

Unprecedented volumes of data from upcoming sky surveys will yield precise constraints on parameters governing the evolution history of the Universe. One that has received particular attention over the past decade is the Hubble constant (H0) describing the expansion rate of the Universe. This thesis focuses on measuring H0 from an astrophysical phenomenon called strong gravitational lensing. The Vera Rubin Observatory's Legacy Survey of Space and Time (LSST) will increase the sample size of strong lenses from ~100 to ~100,000. This creates an opportunity to obtain the most precise measurement of H0 to date. Fully realizing the potential of LSST data entails rapidly extracting cosmological information from the images, tables, and time series associated with these lenses. My research has focused on developing analysis techniques using Bayesian deep learning, which combines the efficiency of deep learning with principled uncertainty quantification. The techniques promise to automate the analysis of tens of thousands of strong lensing systems in a robust manner. They constitute core methodology that can combine information from all the LSST lenses -- with varying types and signal-to-noise ratios -- into a large-scale hierarchical inference of H0

At That Time (2021) is a twenty-minute audiovisual chamber opera composed for the Decoder Ensemble, directed by Heinrich Horwitz, and premiered at the Music Biennale Zagreb in July 2021. I will discuss my artistic priorities and working process as they appear in this piece and connect to my recent research and composition

Objective assessment of cancer imaging studies remains a gap in patient care. Although lesion assessment is a critical part of assessing cancer treatment response, in current clinical practice it is mostly done qualitatively through free-text reports. Quantitative lesion assessment is usually only done in clinical trials, representing a small fraction of all cancer cases. To address this need, this thesis presents an automated pipeline for longitudinal assessment of cancer lesions. Given an annotated baseline exam, the system automatically detects, segments and measures the corresponding target lesions in one or more follow-up exams. It also learns from prior time points by training on partial lesion annotations made by physicians. The core components of this system are neural networks for organ and lesion segmentation, image registration from 3D SIFT-like keypoints, and a method for combining all of these into an end-to-end system that learns from prior time points. This thesis presents several contributions to each of these technical areas. For organ segmentation, we present a new dataset labeling six organs in a variety of CT scans. Despite the relative ease of locating organs in the human body, automated organ segmentation has been hindered by the scarcity of labeled training data. Due to the tedium of labeling organ boundaries, most datasets are limited to either a small number of cases or a single organ. Furthermore, many are restricted to specific imaging conditions unrepresentative of clinical practice. To address this need, we developed a diverse dataset of 140 CT scans containing six organ classes: liver, lungs, bladder, kidney, bones and brain. For the lungs and bones, we expedited annotation using unsupervised morphological segmentation algorithms, which were accelerated by 3D Fourier transforms. We trained a deep neural network which requires only 4.3 s to simultaneously segment all the organs in a CT exam. We also show how to efficiently augment the data to improve model generalization, providing a GPU library for doing so. The dataset and code are available through The Cancer Imaging Archive. For lesion segmentation, we show how the same neural network architecture can be generalized to segment lesions using public datasets with CT scans of two different organs: the liver and the lungs. For our ultimate goal of longitudinal segmentation, we also show how to train these models on partially labeled CT scans from prior timepoints in the clinical record. For image registration, we present a method based on 3D scale- and rotation-invariant keypoints. The method extends the Scale Invariant Feature Transform (SIFT) to arbitrary dimensions by making key modifications to orientation assignment and gradient histograms. Rotation invariance is proven mathematically. Additional modifications are made to extrema detection and keypoint matching based on the demands of image registration. Our experiments suggest that the choice of neighborhood in discrete extrema detection has a strong impact on image registration accuracy. In head MR images, the brain is registered to a labeled atlas with an average Dice coefficient of 92%, outperforming registration from mutual information as well as an existing 3D SIFT implementation. In abdominal CT images, the spine is registered with an average error of 4.82 mm. Furthermore, keypoints are matched with high precision in simulated head MR images exhibiting lesions from multiple sclerosis. These results were achieved using only affine transforms, and with no change in parameters across a wide variety of medical images. This work is freely available as a cross-platform software library. Finally, we combine all these technologies into and end-to-end system for tracking cancer lesions over time in CT images. We tested this system on a retrospective cohort of clinical trial lesion annotations which was automatically curated from our institutional record. Our retrospective study involved 407 patients (51% male and 49% female) with exam dates ranging from 05/02/2006 -- 09/30/2020. Given an annotated baseline exam, we used an automatic pipeline to detect, segment and measure lesions in subsequent exams. We compared our lesion measurements to those made in clinical trials, reporting statistics on lesion detection and measurement errors, as well as the improvement from training on prior exams. When tracking a labeled a baseline lesion in a follow-up exam, our system detected the correct follow-up lesion for 55.5% of liver and 49.6% of lung annotations. In other cases, the system either identified a different lesion (37.9% liver, 49.6% lung), or found no corresponding lesions in the follow-up (6.6% liver, 0.8% lung). The median measurement error for correctly-detected lesions was 3.47 mm (95% CI: [2.22, 5.67]) for liver and 1.36 mm (95% CI: [0.97, 2.03]) for lung. This resulted in 83.9% of exams receiving a correct tumor response grade for liver and 90.4% for lung, using the Response Evaluation Criteria in Solid Tumors (RECIST) guidelines. Training on prior exams improved both detection (p = .000024) and segmentation (p = .018) in the liver, while degrading both detection (p = .00019) and segmentation (p = .018) in the lung. Overall, our system automates detection and measurement of roughly half of all target lesions across multiple organs. As the main contribution is heavily dependent on deep learning, this thesis also contains a pair of appendices presenting original results on neural network theory. The first discusses convexity properties of the training loss function, and the second discusses the effect of model architecture on neuron death, studied through random initialization of model parameters. The appendix proves some local convexity properties of the training loss and inference functions, as well as upper and lower bounds on the probability that a ReLU network is initialized to a trainable point, as a function of model hyperparameters. It also contains some proposals for initialization and local optimization strategies based on these results

The focusing of a seismic image is directly linked to the accuracy of the migration velocity model. Therefore, a critical step in a seismic imaging workflow is to perform a focusing analysis on a seismic image to determine errors within the migration velocity model. While the residual curvature information provided within the offset/angle axis is commonly used to assess velocity errors, the focusing within the physical (i.e., midpoint) axes of a seismic image is often neglected. This is due to the highly interpretative nature of the focusing of geological features within seismic images, therefore making focusing analysis within the physical space difficult to automate. In this dissertation, I present an automatic data-driven approach that makes use of a convolutional neural network (CNN) equipped with high-dimensional convolutional operators to automate seismic image-focusing analysis. Training the CNN on focused and unfocused geological faults within synthetic and real prestack seismic images, I demonstrate this approach can make use of both spatial and offset/angle focusing information to robustly estimate velocity errors within seismic images. To test effectiveness of the approach, I apply it to an unfocused 2D limited-aperture image from the Gulf of Mexico and an unfocused 3D image from the Dutch Sector of the North Sea and show that it can robustly estimate velocity errors in the presence of limited illumination and coherent noise. For both applications, I show that performing a refocusing correction using the estimated velocity errors leads to an improved focusing in the unfocused images and consequently, improves the automatic detection of the faults within the images

In epithelial cancers, cells must invade through basement membranes (BMs) to metastasize. The BM, a thin layer of extracellular matrix (ECM) underlying epithelial and endothelial tissues, is primarily composed of laminin and collagen IV and serves as a structural barrier to cancer cell invasion, intravasation, and extravasation. Bm invasion has been thought to require protease degradation since cells, which are typically on the order of 10um in size, are too large to squeeze through the nanometer-scale pores of the BM. However, recent studies point toward a more complex picture, with physical forces generated by cancer cells facilitating protease-independent BM invasion. In this dissertation, I present work studying the impact of ECM mechanics on cancer cell invasion of the BM during breast cancer progression. Specifically, I will present work investigating the impact of ECM stiffness on the ability of cancer cells to form invadopodia protrusions in three-dimensional (3D) BM-like matrices. We show that increased stiffness of BM-like matrices diminishes invadopodia protrusion formation and cancer cell migration, contrasting the results from traditional 2D culture studies. Additionally, I will discuss my work on the development of a 3D in vitro model of collective invasion through endogenously produced BM. We find that cells utilize both proteases and forces to invade through the BM collectively. We also show that cells rely on volume expansion and contractility to exert pulling forces on the BM during invasion. These results reveal new mechanisms underlying breast cancer invasion and may lead to new strategies to inhibiting BM invasion. Ultimately, a comprehensive understanding of the diverse modes of BM invasion may yield new strategies for blocking cancer progression and metastasis

The act of prediction is ubiquitous in health care--be it via clinician gestalt, or through algorithms. Increasingly, predictive algorithms are beginning to displace clinician decision-making and to drive interventions of all types. Underscoring their importance, just one category of clinical predictive algorithms alone--those used for case management--is used to drive care for over 200 million individuals in the U.S. each year. However, evidence remains scant that algorithm deployments for this and other use cases actually improve clinical outcomes. This evidence gap is further compounded by the particular impracticality of conducting randomized controlled trials to study these algorithms' impacts, and by the lack of alternative design approaches. Moreover, there also exists a currently-unmet need for approaches to iteration on preexisting algorithmic deployments, so that an intervention can be re-prioritized to the patients most likely to benefit. This thesis attempts to fill this methodological vacuum using established tools from causal inference, with the problem of hospital readmission prediction and prevention as a test case