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Multi-tissue ivim mri measurement of perfusion in diabetic foot ulceration with semi- supervised bone segmentation
No full textDiabetic foot ulcers (DFUs) are a debilitating complication of type 2 diabetes mellitus (T2DM), driven by a complex interplay of microvascular dysfunction, neuropathy, and impaired wound healing. Traditional clinical tools such as the Ankle Brachial Index (ABI) and Transcutaneous Oxygen Pressure (TcPO₂) offer limited insight into tissue-level perfusion, necessitating more advanced imaging techniques. This thesis explores the use of Intravoxel Incoherent Motion (IVIM) MRI to assess resting-state perfusion across distinct tissue compartments—muscle, fat pad, and bone—in the feet of three subject groups: DFU patients (N=10), diabetic patients without ulcers (DP, N=5), and healthy controls (HC, N=5).
The study demonstrates that DFU patients exhibit significantly elevated perfusion parameters, particularly in muscle and fat pad compartments, suggesting hyperperfusion potentially linked to arteriovenous shunting and impaired vascular regulation. These findings are supported by both bi-exponential and fractional Fickian diffusion (FFD) models, with effect size metrics (Hedge’s g and Cliff’s delta) confirming strong tissue-specific differences.
To enable scalable analysis, a semi-supervised segmentation pipeline was developed using k-means clustering and manual refinement to isolate bone tissue in MRI volumes. The resulting masks achieved Dice Similarity Coefficients (DSC) > 0.7, validating the feasibility of this approach. Comparisons with the Segment Any Bone (SAB) model revealed that k-means clustering provided more anatomically consistent results with reduced false negatives.
This dual investigation—of perfusion imaging and segmentation feasibility—lays the groundwork for future studies aimed at automated tissue compartmentalization and early detection of DFU-related vascular changes. The findings support the use of IVIM MRI as a non-invasive, contrast-free biomarker for microvascular perfusion and highlight the potential of machine learning tools in advancing diabetic foot research.M.S.Biomedical Engineerin
Granular factoring into neuroimaging dynamic across space, time, and modality
No full textThe proliferation of data across scientific, industrial, and biomedical fields has ushered in an era of increasingly complex, high-dimensional, and heterogeneous datasets. These datasets span multiple modalities, temporal dynamics, and spatial hierarchies, rendering conventional analytical methods insufficient. Informative patterns often remain obscured in large-scale datasets due to inherent complexity, including noise, high dimensionality, and confounding variables that mask true underlying signals. Therefore, a central challenge in modern data science is to extract meaningful, interpretable signatures from this layered complexity, particularly when variability across individuals is substantial and multifaceted. Unlocking these hidden structures requires methods that can adapt to heterogeneity, preserve fine-grained information, and operate effectively across multiple levels of abstraction.
In computational neuroscience, the focus is on decoding the human brain through diverse neuroimaging technologies such as magnetic resonance imaging (MRI), positron emission tomography (PET), and electroencephalography (EEG). These technologies generate large-scale data aimed at understanding brain structure, function, and the neural basis of brain disorders. However, individual variability, demographics, and biological underpinnings introduce heterogeneity in the biological population. This heterogeneity is heightened further in neuropsychiatric disorders such as schizophrenia, autism, and Alzheimer's due to diversity in disease effects, progression, and symptom manifestation. Therefore, the explanatory signals, such as features, trends, and biomarkers, are often temporally transient, spatially constrained, and perceptible only within specific subpopulations. Consequently, traditional approaches that rely on population-level averaging often fail to capture the localized or subgroup-specific trends that are critical for understanding complex systems.
This dissertation introduces a comprehensive computational framework for granular factoring into large-scale, heterogeneous data, such as neuroimaging, medical informatics, and genomics. The central idea is to navigate complex data landscapes by stratifying them into smaller, homogeneous substructures, thereby enabling localized exploration and targeted knowledge extraction. Rather than flattening or averaging across differences, the proposed models leverage heterogeneity as a source of insight-preserving local structure, revealing subgroup-specific patterns, and improving generalization across applications.
To operationalize this vision, novel algorithms are developed for spatial, temporal, and modality-aware clustering, biclustering, and subgroup discovery. These methods are complemented by summarization strategies that distill massive datasets into lower-dimensional, information-rich representations while retaining critical trends and associations. Deep neural architectures for multi-modal data fusion further enable the integration of disparate sources, supporting holistic analysis and cross-domain reasoning in environments with high signal complexity and strong domain interdependence. The effectiveness of the proposed methodologies is demonstrated in high-stakes application areas, particularly in neuroimaging and biomedical informatics. Here, the models show promise in characterizing population heterogeneity, identifying subtypes in neuropsychiatric disorders, and uncovering clinically relevant biomarkers in imaging, behavioral, and genomic modalities.
By providing a unified computational toolkit for analyzing large, complex, and heterogeneous datasets, this work contributes to the broader field of data science. Notably, the thesis advances computational neuroscience by introducing scalable modeling techniques that enable fine-grained analysis of brain function and dysfunction across healthy and clinical populations. It bridges algorithmic innovation with domain-driven insight, advancing the design of interpretable and adaptive models capable of addressing real-world challenges across scientific and societal domains. The framework has broader relevance for fields such as bioinformatics, healthcare analytics, environmental monitoring, and beyond, where the ability to decode structure from complexity is essential to translate data into knowledge.Ph.D.Computational Science and Engineerin
Computing transport maps by cumulant matching
No full textIn this thesis, we design algorithms for statistical inference and generative modeling by exploiting interplays between linear algebra, information theory, and combinatorics. In the first part (chapters 1 and 2), we study fast inference in Gaussian processes, or equivalently, fast computation with symmetric positive-definite matrices. Statistical operations like conditioning, evaluation of the (log-)likelihood, and sampling all involve numerical computation with the covariance matrix. Such kernel matrices are often dense and arise naturally from applications in machine learning and statistics, beyond Gaussian processes. Previous work in constructing sparse approximate inverse Cholesky factors of such matrices by minimizing Kullback-Leibler divergence recovers the Vecchia approximation for Gaussian processes. These methods rely only on the geometry of the evaluation points to construct the sparsity pattern. Instead, we propose to use a greedy selection algorithm that maximizes conditional mutual information, improving over k-nearest neighbors selection in a variety of experimental settings. For the ordering, in high-dimensional, low-rank settings, a randomized ordering is often preferred. We propose a deterministic ordering based on mutual information which improves upon these orderings. We apply our approximation framework to earthquake modeling. In the second part of this thesis (chapter 3), we generalize the previous results to non-Gaussian random variables through the formalism of measure transport. The Cholesky factor becomes the Knothe-Rosenblatt rearrangement, a unique transport map whose Jacobian is lower triangular with positive diagonal. In the non-Gaussian case, we cannot hope to match only the mean and covariance, as in Gaussians. Instead, we will use higher-order cumulants to characterize probability distributions, which can be estimated directly from samples. Expansions based on cumulants give simple polynomial expressions for approximate densities, log-densities, and transport maps through Möbius inversion. We can also estimate functionals such as entropy.UndergraduateComputer Scienc
Digitally-Assisted and Artifact-Robust Next-Generation Closed-Loop Neural Interfaces
No full textNext-generation closed-loop neuromodulation systems require miniature, high-density, artifact-tolerant neural sensing, low loop-latency, and spatially selective, programmable neural stimulation.
We introduce a novel digitally-assisted and artifact-robust neural stimulator and recording front-end to meet these needs of future bidirectional neuromodulation.
The proposed stimulator demonstrates spatially targeted neural stimulation with suppression of driver nonideality induced common-mode (CM) artifacts in low-latency closed-loop neuromodulation. The proposed approach utilizes computationally guided concurrent stimulation across multiple electrodes to achieve spatial selectivity. The stimulator architecture supports flexible storage of multiple pre-computed stimulus patterns in integrated memory, allowing rapid recall and delivery of selected patterns in response to decoded neural activity. A combination of the stimulator circuit architecture and mixed-signal current imbalance compensation techniques effectively suppress CM artifacts to below 50 mV. These techniques are demonstrated in a 180 nm HV CMOS test-chip containing 46 stimulation drivers of 26 V compliance and validated through a combination of bench, saline, and in vivo tests.
Our proposed 32-channel recording analog front-end (AFE) architecture exhibits rapid recovery from intrinsic differential-mode large stimulation artifacts while delivering high-resolution digitized data with ultra-low latency. The time-multiplexed AFE architecture ensures low area and power consumption, paving the way for building high-density neural interfaces. We introduce a novel technique for the correction of feedback digital-to-analog converter (DAC) non-linearities, contributing to enhanced Signal-to-Noise-and-Distortion Ratio (SNDR). Additionally, the AFE reduces the input-channel current to prevent signal quality degradation. Fabricated in a 65 nm CMOS process, the direct digitization AFE achieves 85.4 dB SNDR in a 500 Hz bandwidth, resulting in a Schreier figure of merit of 172.1 dB, which is the highest among the existing time-multiplexed neural AFEs.Ph.D.Electrical and Computer Engineerin
Correlation Between the Unsteady Heat Release Rate and Direct Combustion Noise
No full textAs aircraft engines trend towards higher bypass ratios, the relative importance of combustion noise has seen a recent increase. To study and mitigate combustion noise, it is important to understand the different sources and generation mechanisms of sound within a combustor. It was proposed that partial coherence methods using chemiluminescence measurements could provide insight into the contribution of direct combustion noise compared to indirect noise. This requires a priori knowledge of the coherence between the unsteady heat release rate and direct combustion noise. Theory suggests that for a farfield observer and acoustically compact source, the coherence between globally integrated heat release and combustion noise is unity for a direct noise dominant system. However, no such measurements are available in literature. In fact, the very few literature that does report coherence show values well less than unity. The primary goal of this work is to bridge this gap between theory and literature through both analytical and experimental studies on the heat release - direct noise coherence.
An analytical model based on the solution of the wave equation was developed to study nearfield and acoustical noncompactness effects on the heat release - pressure coherence. The governing parameters of coherence were identified: i) the acoustical compactness which is the relative magnitude of the flame dimension to the flame length or width, ii) the observer position relative to the flame, iii) the spatiotemporal statistics of the unsteady heat release, and iv) the flame geometry. Model findings were experimentally verified by measurements taken from a turbulent premixed methane - air Bunsen burner setup. Explicit measurements of unity coherence in the acoustically compact limit were obtained, and noncompactness effects due to the distributed monopole nature of the flame were demonstrated. Results were extended to a ducted configuration, where the effect of reflections on coherence are presented.Ph.D.Aerospace Engineerin
New Accelerated Methods for Optimization and Reinforcement Learning
No full textFirst-order methods are widely used to tackle modern data science and machine learning problems. In this thesis, we focus on the design and analysis of novel accelerated first-order algorithms for large-scale nonlinear and stochastic optimization, addressing key challenges such as stochasticity, nonconvexity, and uncertainty in problem structures and parameters. We also develop new accelerated methods for reinforcement learning, accompanied by improved computational and statistical complexity guarantees.
The main body of this thesis is divided into two parts. Part I studies accelerated methods for different classes of optimization problems. Specifically, Chapter 2 considers stochastic convex optimization under rather general state-dependent noise assumptions. We investigate two accelerated stochastic approximation routines—stochastic accelerated gradient descent (SAGD) and stochastic gradient extrapolation (SGE)—which carry a particular duality relationship. Although both routines can achieve the optimal convergence rate under appropriate conditions, the corresponding assumptions for the SGE algorithm are more general; they allow, for instance, heavy tail noises and discontinuous score functions. We also discuss the application of SGE to problems satisfying quadratic growth conditions, and show how it can be used to recover sparse solutions.
Chapters 3 to 5 focus on designing adaptive accelerated algorithms for optimization problems with ambiguous structures and unknown parameters. In Chapter 3, we begin with convex optimization and propose a new accelerated gradient descent type algorithm, which demonstrates that line search is superfluous in attaining the optimal rate of convergence when problem parameters are not given a priori. In Chapter 4, we consider bilinear saddle point and linearly constrained problems, and introduce new primal-dual hybrid gradient (PDHG) and ADMM-type methods, which can fully adapt to the linear operator while requiring no line search subroutines. In Chapter 5, we present a novel class of projected gradient (PG) methods for stochastic smooth but not necessarily convex problems, establishing new complexity bounds in different oracle settings and developing new parameter-free stepsize policies.
In Part II, we develop acceleration schemes for problems arising from reinforcement learning. Chapter 6 studies the problem of policy evaluation with linear function approximation, proving lower bounds that establish baselines on both the deterministic error and stochastic error. We then develop an accelerated, variance-reduced fast temporal difference algorithm (VRFTD) that simultaneously matches both lower bounds and attains a strong notion of instance-optimality. Chapter 7 investigates the problem of constrained Markov decision process (CMDP) and proposes an accelerated primal-dual approach with a novel integration of entropy regularization and Nesterov’s accelerated gradient method. The proposed approach is shown to converge to the global optimum with an improved complexity in terms of the optimality gap and the constraint violation.Ph.D.Operations Researc
Real-Time Stochastic Terrain Mapping and Processing for Autonomous Safe Landing
No full textOnboard terrain sensing and mapping for safe planetary landings often suffer from missed hazardous features, e.g., small rocks, due to the large observational range and the limited resolution of the obtained terrain data. To this end, this paper develops a novel real-time stochastic terrain mapping algorithm that accounts for topographic uncertainty between the sampled points, or the uncertainty due to the sparse 3D terrain measurements. We introduce a Gaussian digital elevation map that is efficiently constructed using the combination of Delauney triangulation and local Gaussian process regression. The geometric investigation of the lander-terrain interaction is exploited to efficiently evaluate the marginally conservative local slope and roughness while avoiding the costly computation of the local plane. The conservativeness is proved in the paper. The developed real-time uncertainty quantification pipeline enables stochastic landing safety evaluation under challenging operational conditions, such as a large observational range or limited sensor capability, which is a critical stepping stone for the development of predictive guidance algorithms for safe autonomous planetary landing. Detailed reviews on background and related works are also presented
Fluid Flow and Heat Transfer Characteristics of High Prandtl Number Fluids for Fluoride-Salt-Cooled Reactor Applications
No full textFluoride-salt-cooled high-temperature reactors (FHRs) are a new and developing class of reactors that features low-pressure liquid fluoride salt cooling and the graphite-matrix coated-particle fuel developed for high temperature gas reactors (HTGRs) and are designed for a high-temperature power cycle. FHRs have several economic and safety benefits due to higher core power densities compared to HTGRs: near-atmospheric pressure operation, higher safety margins for fuel failure and coolant boiling, and passive decay heat removal using natural circulation. One of the potential fuel designs for FHRs is the plate type configuration in which the molten salt coolant flows in the wide, narrow channels between the array of parallel fuel plates. To aid the further development of FHR designs that employ a plate-type fuel design, this work addresses the need to improve the understanding of the fluid flow dynamics and heat transfer characteristics for a molten salt coolant. The nature of the molten salt requires the flow to be in the transition regime, making predictions based on the literature difficult. In the present study, a test section representing a single coolant channel is designed and fabricated, and a heat transfer test facility is fabricated to measure the heat transfer coefficient and frictional pressure gradient of a surrogate fluid that matches the pertinent dimensionless parameters of molten salt in a plate-type FHR. In addition to the plain coolant channel, a channel with lozenge-shaped dimple features is also developed to study potential heat transfer enhancement. Based on these experimental results, models are developed to predict the heat transfer and pressure drop for such flows experienced in the plate-type FHR. These models are compared with a steady state computational fluid dynamics (CFD) model and a model developed in the thermal-hydraulic program TRACE for a single coolant channel. The experimental study serves as a preliminary verification of the models that use CFD and TRACE. The correlations developed in this study are then used to estimate the temperatures in the core and the overall cooling capacity, demonstrating the benefits of an FHR over conventional reactors. Insights from these experiments and analyses will guide the further development of plate-type FHRs by improving the confidence levels in the predictions of safety analysis codes, thereby assisting the licensing of these reactors.Ph.D.Mechanical Engineerin
Hybrid Lipid Nanocapsules: A Robust Nanoplatform for the Co-delivery of Resiquimod and mRNA
No full textThe ever-progressing field of cancer immunotherapy has sparked interest in development of unique drug platforms. This thesis explores the use of hybrid lipid nanocapsule as a co-delivery platform for mRNA and resiquimod, a toll-like receptor 7/8 agonist. The co-formulation aimed to synergistically combine antigen expression through mRNA transfection with the innate immune stimulation by resiquimod. The formulation of hLNCs with engineered presented optimal characteristics for targeting tumors as well as excellent encapsulation efficiency of resiquimod. This co-delivery of resiquimod with mRNA may enhance immune activation and accurate delivery to target solid-state tumors.M.S.Chemistry and Biochemistr