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Time-dependent Time Fractional Equations and Probabilistic Representation
No full textThesis (Ph.D.)--University of Washington, 2025We study the nonlocal initial-value problem of the form \begin{align*}
\sL u(x, t) &= h(x, t) \quad \text{for}\ (x,t)\in \R^d\times (0,\infty), \\
u(x,t) &= f(x) \quad \text{on}\ \R^d\times (-\infty, 0]
\end{align*}
where \sL is an integro-differential operator given by
\begin{eqnarray*}
&& \hskip -0.2truein \mathcal L \varphi(x,t) \nonumber \\
& =& \frac{1}{2}\sum_{i,j=1}^{d} a_{ij}(x,t)\:\partial_{x_ix_j}^{2} \varphi(x,t) +
\sum_{i=1}^{d} b_i(x,t)\:\partial_{x_i} \varphi (x,t) % + \gamma (x, t) \partial_t u(x, t)
\\
& &+ \int_{\R^d\times \R\setminus\{(0,0)\}} \bigg[ \varphi (x+y,t-s)-\varphi (x,t) -\nabla_x \varphi(x,t) \cdot y
\: \mathbf 1_{\{|y|\le1\}} \bigg] J(x,t;dy,ds). \nonumber
\end{eqnarray*}
For the case where the jump measure takes form for some L\'evy measure on , if and satisfies for each for some , then the above parabolic equation has a unique classical solution. See Theorem \ref{TimeFracEqn} for precise statement. When the joint process generated by \sL is a L\'{e}vy process, i.e. , are constants and is a L\'{e}vy measure on , and if and , then the above parabolic equation also has a unique classical solution. In this case, the solution is a bounded and continuous function on and for each . See Theorem \ref{MainTheorem4LevyCase} for precise statement. Our method is probabilistic and direct. Probabilistic representation of solutions to the time-fractional equations is given
Predicting the impact of climate change-induced resource loss on the endangered Golden-cheeked Warbler (Setophaga chrysoparia)
No full textThesis (Master's)--University of Washington, 2025Although human land use has been the leading driver of endangerment, climate change continues to compound global biodiversity loss and poses a major risk to threatened and endangered species (Thomas et al. 2004, Chapin et al. Wilkening et al. 2019). For habitat specialists, such as the Golden-cheeked Warbler (Setophaga chrysoparia), climate change will have lasting consequences on habitat configuration, resource availability, phenology, and population densities (Wilkening et al. 2019, Maxwell et al. 2019). The Golden-cheeked Warbler, an endangered migratory songbird, breeds exclusively in the Ashe juniper (Juniperus ashei)-oak (Quercus sp.) woodlands of central Texas and depends on the shedding bark of mature juniper for nesting (Kroll 1980, Ladd and Gass 1999, Pulich 1976). Understanding how climate change will alter Golden-cheeked Warbler habitat is essential to the conservation of this at-risk species. In this study, I explore how modeling approaches can be used to project the potential impacts of climate change on at-risk species, with the focus of informing landscape-level management decisions for the conservation of both the Golden-cheeked Warbler and Ashe juniper. In Chapter 1, I describe how I developed an ensembled species distribution model for Ashe juniper using edaphic, topographic and climatic predictor variables. I then used the best-performing model to project the potential future distributions of juniper through 2100 using the outputs from two generalized circulation models (GCMs) run for two shared socio-economic pathways (SSPs). Across all models, I observed a contraction of the distribution of juniper within Texas. The juniper projections were then overlayed with a model of warbler densities to determine the potential loss of optimal and marginal warbler habitat through 2100 due to resource loss (Mueller et al. 2022). Under the most extreme climate scenario, the models predicted an almost complete loss of optimal and marginal warbler habitat, nearly 1,027 km2 and 9,485 km2, respectively. This approach detected areas where warbler habitat would persist even in the most extreme scenarios of climate-driven resource loss, allowing us to inform managers of areas of highest conservation priority. In Chapter 2, with the support of my collaborators, I built a population model to simulate the effects of climate change-driven resource loss on the population responses of Golden-cheeked Warblers within Texas. Using the modeling platform HexSim, we leveraged literature and expert knowledge on the life history of the endangered warbler to parameterize a spatially explicit, individual-based model. I created a time series of habitat maps based on the work from Chapter 1. I then simulated warbler responses to a changing habitat under the same four climate scenarios. The model outcomes allowed me to determine the importance of selected protected areas to the persistence of warbler populations and confirm which of the areas could strategically be prioritized in conservation management. Results indicate that climate-induced resource loss has the potential to reduce warbler abundance by up to 94% in the most extreme climate scenarios (UKESM1-0-LL), with 10% and 51% reduction in the MPI-ESM1-2-HR SSP2-4.5 and SSP3-7.0 scenarios, respectively. At 4 out of 14 protected sites, our simulation forecasted complete loss of occupancy with the MPI-ESM1-2-HR SSP3-7.0 scenario but forecasted complete loss at 11 out of the 14 sites with the UKESM1-0-LL SSP2-4.5 scenario. Through this analysis, our model identified the Balcones Canyonlands Preserve, Balcones Canyonlands National Wildlife Refuge, and Fort Cavazos as containing important climate refugia. Our study presents the immense impact climate change will potentially have on the persistence of the endangered Golden-cheeked Warbler and its habitat. This work contributes to the scientific understanding of how complex modeling can be leveraged to inform landscape-level conservation efforts of at-risk species threatened by climate change
Constraining Antarctic polynya formation and sea ice and snow evolution using autonomous observations and modeling
No full textThesis (Ph.D.)--University of Washington, 2025This dissertation focuses on resolving key uncertainties in Southern Ocean sea ice and snow processes using under-ice autonomous ocean observations and modeling techniques in a Lagrangian, or flow-following, framework. After an introduction to the region and relevant processes (Chapter 1), the first portion of this work (Chapter 2) investigates the periodic appearance of large sea ice openings offshore of Antarctica, known as open-ocean polynyas. The rarity of these intermittent events in the 50-year satellite record has prevented oceanographers from pinpointing the factors that initiate polynyas and fully characterizing the vigorous cycle of ocean mixing and heat exchange believed to sustain them. Fortuitously, two Argo profiling floats, which are free-drifting robotic instruments that can collect ocean measurements beneath sea ice, were present during unexpected polynya events that occurred over Maud Rise in the Weddell Sea in 2016 and 2017. By placing their ocean measurements in context of meteorological data and past hydrographic and satellite records, we conclude that these sea ice openings were preconditioned by reduced upper-ocean salinity stratification and triggered by storms. Identifying links between these conditions and fluctuations in the primary mode of Southern Hemisphere climate variability, the Southern Annular Mode, yields a robust explanation for why polynyas have appeared at this location in some years but not others. These first in situ ocean observations also confirm that the anomalous openings were maintained by deep convective mixing, as long suspected. Antarctic sea ice thickness and overlying snow depth are important climate variables due to their strong influence on freshwater fluxes, ocean-atmosphere heat exchange, and momentum transfer. Yet monitoring their evolution from satellites has proven challenging, partly due to a sparsity of in situ measurements for validation purposes. The next portion of this work (Chapter 3) presents a newly developed numerical model that reconstructs the daily evolution of snow deposited on Antarctic sea ice along satellite-observed Lagrangian ice drift trajectories. Atmospheric reanalysis input data and parameterizations of key snow accumulation, erosion, and transformation processes are calibrated using autonomous snow buoy measurements. The resulting model reconstruction from 2003 to 2024 offers constraints on the annual mass budget of snow intercepted by sea ice in the Southern Ocean, including the magnitude and timing of freshwater release to the ocean. This represents a substantially larger flux than previously diagnosed, with implications for water mass transformation and vertical mixing. Snow-ice formation is inferred by comparing the simulated snow accumulation with satellite-observed snow depths, and trends in the reconstruction estimates are assessed. In the third portion of this work (Chapter 4), Antarctic sea ice formation and melt rates are directly estimated by calculating mixed layer salinity budgets along the wintertime drift trajectories of over 300 under-ice Argo profiling floats in the Southern Ocean. All except one budget term can be constrained using the float measurements and auxiliary data sources, leaving sea ice-induced fluxes from brine rejection during ice formation and freshwater release during ice melt to be inferred as the large budget residual. The seasonal cycle of sea ice exhibits a pronounced asymmetry with a prolonged net growth phase that slows in mid-winter before the initiation of rapid melt in fall. A circumpolar climatology of sea ice growth and melt rates within the Antarctic seasonal ice zone show net annual sea ice production near the Antarctic continent that switches to net annual melt at around 65°S. However, sea ice freezing and melt rates estimated from the float observations are found to be highly sensitive to uncertainties in the magnitude and timing of freshwater fluxes from snow. This float-based methodology highlights the potential to reconstruct climatological Antarctic sea ice thickness using autonomous ocean measurements. The final portion of this dissertation (Chapter 5) highlights a retrospective study on an undergraduate Python programming and ocean data analysis course that was co-developed and taught remotely in 2020 with another graduate student. Our teaching integrated evidence-based teaching practices—a flipped structure, activities infused with active learning, an individualized final research project, and efforts to center accessibility. A mixed-methods approach is used to evaluate the efficacy of the instructional design using data from surveys, online teaching platforms, student work, assessments, and a focus group. We find that the course elements bolstered student engagement and learning, allowing students with less or no prior coding experience to achieve similar success as peers with more experience
Seattle SMART: Digitizing the Last Mile of Urban Goods to Improve Curb Access and Utilization
Get PDFIn Spring 2023, the Seattle Department of Transportation (SDOT) was awarded a Stage-1 grant under the Strengthening Mobility and Revolutionizing Transportation (SMART) Grants Program by the US DOT. The University of Washington’s Urban Freight Lab (UFL) partnered with SDOT to develop the methodological approach and analysis for the SMART project, titled “Last-mile freight curb access: digitizing the last-mile of urban goods to improve curb access and utilization,” and determine key research discoveries that contribute to the existing body of work and support development for a SMART Stage-2 grant. This technical report describes the research study, data collected, and findings from analysis of those data.
This project tested a Vehicle-to-Curb (V2C) technology that investigated the digitization of the existing CVLZ permit and to potentially enable pricing strategies. While parking pricing policies have been successful to manage passenger vehicle demand and their parking behaviors, the response of commercial vehicles to parking pricing is not sufficiently understood, and little information is available to predict their behavioral response.
The overarching goals of this project were to:
pilot test the effectiveness of a V2C technology to enable the digitization of the existing Seattle CVLZ permit system and
to qualitatively understand the role parking pricing and permitting programs play in affecting drivers’ ability to find and utilize authorized parking within the context of north downtown Seattle.
Key insights were gained through multiple research strategies: on-the-ground parking behavior data collection, carrier interviews, and a carrier survey. These insights allowed SDOT to develop a successful Stage-2 grant submission and will inform future parking and permit policy decisions
Laura Netzel's Works for the Flute: New Editions with Historical Context
Get PDFThesis (D.M.A.)--University of Washington, 2025Romantic-era composer Laura Netzel ranked among the most-performed Swedish female composers during her lifetime but is now all but forgotten by scholars and performers. This dissertation examines how Netzel’s social class, gender, choice of instrumentation, and choice of compositional genres situated her life’s work outside of the repertorial and pedagogical musical canons. It also presents newly-edited versions of Netzel’s works for the flute: Suite op. 33 for Flute and Piano, Colibri op. 72 for Flute and Piano, and a new adaptation of Berceuse op. 69 for Violin (or flute) and Piano. The new editions expand the flute repertoire of the Romantic period, which is the era with arguably the least number of solo flute pieces in the standard literature. Current canonical Romantic flute repertoire consists mainly of variations on popular themes, but adding these three pieces from different genres can broaden understanding of Romantic flute repertoire and provide a more complete picture of flute works written during the period
Towards High-redshift Cosmology with Lyman-break Galaxies Detected by LSST
Get PDFThesis (Ph.D.)--University of Washington, 2025The Vera C. Rubin Observatory is set to begin the Legacy Survey of Space and Time (LSST), a generation-defining astronomical survey that will image the entire southern sky in 6 photometric bands to unprecedented depth.LSST promises to discover hundreds-of-millions of high-redshift galaxies, opening a huge, previously unprobed volume of the universe to precision cosmology.
These high-redshift constraints will provide new ways to test the standard cosmological model and have the potential to shed new light on the many tensions present in modern cosmology, including the evolution of dark energy, the sum of neutrino masses, and the mass density of the cosmos.
Extracting information about the evolution of the high-redshift universe from LSST data will require careful modeling and new analysis tools to control systematic errors. This dissertation develops new methods for estimating the distance to galaxies using photometric data (photometric redshifts, or photo-z's) and studying the systematic errors that plague them.Using machine learning tools, we show that galaxy spectral templates can be learned directly from broadband photometry, increasing the accuracy and precision of template-based photo-z estimation, which will figure prominently in the analysis of high-redshift galaxies.
Using normalizing flows, we develop a statistical forward model of photometric galaxy catalogs, enabling new and more reliable studies of photo-z calibration, including consistent evaluation of photo-z posterior distributions. We then discuss optimizing the LSST survey strategy for the detection and photo-z estimation of high-redshift galaxies, before forecasting number densities by combining simulations of LSST with calibration data from precursor surveys.Using this model, we forecast the power of LSST for constraining the growth of large scale structure and the evolution of dark energy, finding that a joint analysis of high- and low-redshift data increases the constraining power of LSST by a factor of three compared to constraints from low-redshift data alone.
We also study various sources of systematic error, quantifying their impact on cosmological constraints, and considering how data from LSST and CMB lensing surveys can be combined to reduce the impact of these errors. A series of appendices present research on wave-front estimation for the Rubin Observatory's active optics system (AOS), which maintains the telescope's optical alignment and mirror figure to correct for optical aberrations and deliver high image quality across Rubin's wide field of view.First we describe the physical components of the AOS, before deriving an algorithm for wave-front estimation in Rubin's fast, wide-field optical system.
We then introduce and validate a deep learning algorithm for wave-front estimation, showing it to be faster and more robust than traditional methods.
We conclude by studying the information content carried by the shape and intensity of stars in the defocused images used for wave-front estimation
Characterizing the Structural and Physiological Effects of IMPDH2 Mutations Associated with Neurodevelopmental Disorders
Get PDFThesis (Ph.D.)--University of Washington, 2025Inosine-5'-monophosphate dehydrogenase (IMPDH) catalyzes the first committed step of de novo guanine nucleotide biosynthesis, converting IMP to XMP. To control this important metabolic branch point between adenine and guanine nucleotide synthesis, IMPDH is highly regulated, including through assembly into filaments. There are two isoforms of IMPDH in humans, but IMPDH2 is specifically essential for development and is upregulated during proliferation. Mutations in IMPDH2 have been identified in patients with neurodevelopmental disorders exhibiting a range of neurological symptoms, including dystonia. Here, we show with in vitro enzyme assays, negative stain electron microscopy, and high-resolution structures determined by cryo-EM, how each mutation affects the structure, activity, and allosteric regulation of IMPDH2 filaments and octamers. We also develop Xenopus tropicalis as a model to study the effects of one variant, the in-frame deletion of serine 160, on metabolism, neuromuscular development, and IMPDH filament formation in a vertebrate system. This work establishes a model for studying the mechanisms of disease that arise from IMPDH2 dysregulation
Systematics, diversity dynamics, and paleobiogeography of early Paleocene mammals from northeastern Montana and the Western Interior of North America
No full textThesis (Ph.D.)--University of Washington, 2025The early Paleocene was a critical interval in the evolution of mammals during which the group underwent a remarkable evolutionary radiation following the Cretaceous/Paleogene (K/Pg) mass extinction ca. 66 Ma. Although the broad patterns of this mammalian radiation are well established, the precise details remain more poorly understood and ongoing work continues to refine our understanding of this important episode in mammal evolution. The Hell Creek Formation and overlying Tullock Member of the Fort Union Formation in northeastern Montana are well known as an excellent study system for examining the evolution of mammals leading up to and across the K/Pg extinction event. Substantial work in this region has focused on the record of mammals immediately before and after the K/Pg boundary, whereas the younger mammal-bearing horizons have received less attention and until recently have produced fewer fossils. Consequently, this has hindered a more complete understanding of the recovery and subsequent diversification of mammals in this area. This dissertation seeks to add to our knowledge of early Paleocene mammal systematics and diversity dynamics by way of three studies that vary in spatiotemporal scale. In Chapter 2, a coauthor and I describe a new assemblage of mammalian dental fossils from the stratigraphically highest mammal-bearing localities from the upper part of the Tullock Member in Garfield County, Montana—the Farrand Channel and Horsethief Canyon local faunas. Both local faunas have been correlated to the early Torrejonian (To1) North American Land Mammal ‘age’ and currently represent the oldest and most northerly occurrences of To1 mammals. These new fossils substantially increase the previously known sample size from the Farrand Channel and Horsethief Canyon local faunas and document as many as 40 distinct taxa, several new occurrences, and likely more than one new species. Further, these fossils help better characterize the age and composition of both local faunas, which are temporally intermediate between the youngest Puercan and oldest Torrejonian faunas known elsewhere. More broadly, we contribute to the limited record of To1 mammals and demonstrate that within less than 1 Ma after the K/Pg boundary mammals were considerably more taxonomically diverse in the Hell Creek region than previously appreciated.
In Chapter 3, coauthors and I report new plesiadapiform (putative stem primates) dental fossils from the Farrand Channel and Horsethief Canyon local faunas that record several poorly known taxa and represent the largest and most diverse assemblage of To1 plesiadapiforms known. We describe a new species of purgatoriid plesiadapiform (Ursolestes blissorum, sp. nov.) that represents the largest plesiadapiform known from the early Paleocene. We also document intraspecific variability and one undescribed tooth locus of the oldest known member of the Paromomyidae, Paromomys farrandi. Further, we evaluate plesiadapiform species richness, mean body mass, and body-mass disparity through the Paleocene and reveal unrecognized levels of richness in To1 and a general trend of stable body mass and body-mass disparity, thereby providing new insights into the early evolutionary history of Primates.
In Chapter 4, I provide a quantitative assessment of the taxonomic composition of the Farrand Channel and Horsethief Canyon local faunas and the biogeography of early Paleocene mammals from the Western Interior using a newly assembled dataset of North American mammalian occurrences. Further, I compare geographic patterns of mammalian diet and body mass distributions to test for regional differences in community structure that may be indicative of differences in habitat and a driver of compositional differentiation. I find that the Farrand Channel and Horsethief Canyon local faunas are compositionally most similar to other To1 faunas, supporting their previous correlation. I also find evidence of temporal and latitudinal differentiation among early Paleocene faunas. My ecological analyses reveal some geographic patterning but ultimately cannot detect meaningful differences in community structure, likely due to the lack of certain ecological data currently available and sampling gaps in the fossil record. Collectively, these studies add to our knowledge of early Paleocene mammal systematics and help emphasize the importance of continued collecting efforts and specimen-based work
Advancing Time Series Forecasting: Insights from Deep Learning and Dynamic Mode Decomposition
Get PDFThesis (Ph.D.)--University of Washington, 2025Time series forecasting presents significant challenges across engineering and scientific disciplines, particularly in handling non-stationary real-world data and providing real-time predictions from streaming sources. Deep learning approaches, including Recurrent Neural Networks (RNNs), Convolutional Neural Networks (CNNs), and Transformer-based models, have advanced the field but often fall short in interpretability, computational efficiency, and real-time adaptability. Despite their capacity for modeling complex non-linear dynamics, these models require extensive hyperparameter tuning and lack robust mechanisms for incremental updates. They also suffer from catastrophic forgetting in streaming scenarios, limiting their deployment in dynamic and resource-constrained environments. This dissertation addresses these limitations through two complementary research directions: enhancing deep learning interpretability through distance correlation analysis and developing efficient Dynamic Mode Decomposition (DMD) methods for batch and streaming forecasting. First, this work introduces a distance correlation-based framework to examine the internal mechanics of RNNs in time series forecasting. This versatile metric enables systematic analysis of information flow through RNN activation layers, revealing how these networks process temporal dependencies. Empirical analysis demonstrates that RNN activation layers effectively learn lag structures in early layers but progressively lose this temporal information in deeper layers, degrading forecast quality for series with large lag dependencies. The study further reveals fundamental limitations in RNN capabilities for modeling moving average and heteroskedastic processes. Distance correlation heatmaps provide visual comparisons across architectures and hyperparameters, demonstrating that input window size influences model behavior far more than conventional hyperparameters such as hidden units or activation functions. These findings enable practitioners to assess RNN suitability for specific time series characteristics without extensive trial-and-error experimentation. The second direction introduces novel DMD-based forecasting methods that address deep learning limitations. For batch scenarios, Incremental Kernel Dynamic Mode Decomposition (IKDMD) enhances adaptability and efficiency by integrating incremental kernel singular value decomposition and randomized linear algebra into the kernel DMD framework. Comparative analysis across real-world datasets demonstrates that IKDMD outperforms state-of-the-art deep learning methods, particularly for highly non-stationary and volatile data, while providing interpretable eigenvalue diagnostics unavailable in black-box neural networks. For streaming applications, this dissertation presents Windowed Online Random Kernel Dynamic Mode Decomposition (WORK-DMD), which integrates Random Fourier Features with online DMD to enable real-time forecasting from continuously arriving data. By employing explicit feature mappings rather than implicit kernel methods, WORK-DMD achieves fixed computational complexity per update while capturing nonlinear dynamics. Its adaptive windowing mechanism naturally handles non-stationary dynamics without catastrophic forgetting. Experimental evaluation across benchmark datasets demonstrates remarkable sample efficiency, requiring only single-pass learning while achieving competitive or superior accuracy compared to deep learning methods that demand multiple training epochs and extensive sample exposures. This efficiency translates to reduced computational costs, faster deployment, and viability for resource-constrained edge devices. Together, these contributions advance time series forecasting by providing both diagnostic tools for understanding deep learning limitations and computationally efficient alternatives that balance accuracy, interpretability, and real-time adaptability. The methods presented enable practical deployment in scenarios where traditional deep learning approaches struggle with sample efficiency, computational constraints, and evolving data dynamics
Essays in Contract Theory
No full textThesis (Ph.D.)--University of Washington, 2025This dissertation comprises three essays in contract theory on the regulation of risky projects and the optimal organizational form of sequential projects. The first chapter analyzes how a legislature delegates authority to a regulator with expert information and a pro-firm bias to oversee firms that undertake socially risky activities, and shows that the legislature optimally grants more discretion when the regulator is less motivated and has a weaker bias. The second chapter studies the organization of a sequential project with design and construction, in which an owner chooses between unbundling and bundling the tasks; with moral hazard in design effort and private information about construction cost, bundling links the stages by allowing design incentives to depend on the reported cost type. This linkage is valuable when it is optimal to induce effort only from the efficient type, because construction-stage information rents can then be used to motivate design effort, so that bundling can dominate unbundling. The third chapter reviews the theoretical literature on public–private partnerships, summarizing how contractual and political factors influence their efficiency