Browsing by Author "Cao, Yan"
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Item A General Framework of Non-convex Models for Sparse Recovery With Applications(December 2021) Hu, Mengqi; Gassensmith, Jeremiah; Lou, Yifei; Cao, Yan; Rachinskiy, Dmitry; Pereira, Felipe; Ramakrishna, ViswanathThanks to latest developments of science and technology, large data sets are becoming increasingly popular that lead to an emerging field, called compressive sensing (CS), which is about acquiring and processing sparse signals. In this thesis, we first propose a general framework to estimate sparse coefficients of generalized polynomial chaos (gPC) used in uncertainty quantification (UQ). In particular, we aim to identify a rotation matrix such that the gPC expansion of a set of random variables after the rotation has a sparser representation. However, this rotational approach alters the underlying linear system to be solved, which makes finding the sparse coefficients more difficult than the case without rotation. To resolve this issue, we examine several popular non-convex regularizations in CS that empirically perform better than the classic `1 approach. All these regularizations can be minimized by the alternating direction method of multipliers (ADMM). Numerical examples show superior performance of the proposed combination of rotation and non-convex sparsity promoting regularizations over the ones without rotation and with rotation but using the `1 norm. We observe through the UQ study that the `1 − `2 regularization often performs satisfactorily among the others. We then apply it to synthetic aperture radar (SAR) imaging based on a mathematical model of how electromagnetic waves are scattered in the space using Maxwell’s equations. Specifically we deduce an efficient sensing matrix for SAR and examine the efficiency of the `1 − `2 regularization to promote sparsity of scattered signals. Experimental results demonstrate that `1 − `2 can enhance the resolution of reconstructed image over the classic `1 approach. Motivated by conjugate gradient and adaptive momentum in the optimization literature, we propose a novel algorithmic improvement. The proposed algorithm works for general minimization problems, though numerical experiments are limited to `1 and `1 − `2 with a least-squares data fidelity term, showcasing faster convergence of the proposed algorithm over the traditional methods. We also establish the convergence of our algorithm for a quadratic problem.Item Automatic and Reproducible Positioning of Phase-Contrast MRI for the Quantification of Global Cerebral Blood Flow(Public Library of Science) Liu, Peiying; Lu, Hanzhang; Filbey, Francesca M.; Pinkham, Amy E.; McAdams, Carrie J.; Adinoff, Bryon; Daliparthi, Vamsi; Cao, Yan; 0000 0001 3618 6298 (Filbey, FM); 0000 0001 2904 8428 (Cao, Y); 11522796 (Cao, Y); Filbey, Francesca M.; Cao, YanPhase-Contrast MRI (PC-MRI) is a noninvasive technique to measure blood flow. In particular, global but highly quantitative cerebral blood flow (CBF) measurement using PC-MRI complements several other CBF mapping methods such as arterial spin labeling and dynamic susceptibility contrast MRI by providing a calibration factor. The ability to estimate blood supply in physiological units also lays a foundation for assessment of brain metabolic rate. However, a major obstacle before wider applications of this method is that the slice positioning of the scan, ideally placed perpendicular to the feeding arteries, requires considerable expertise and can present a burden to the operator. In the present work, we proposed that the majority of PC-MRI scans can be positioned using an automatic algorithm, leaving only a small fraction of arteries requiring manual positioning. We implemented and evaluated an algorithm for this purpose based on feature extraction of a survey angiogram, which is of minimal operator dependence. In a comparative test-retest study with 7 subjects, the blood flow measurement using this algorithm showed an inter-session coefficient of variation (CoV) of 4.07 ± 3.03%. The Bland-Altman method showed that the automatic method differs from the manual method by between -8% and 11%, for 95% of the CBF measurements. This is comparable to the variance in CBF measurement using manually-positioned PC MRI alone. In a further application of this algorithm to 157 consecutive subjects from typical clinical cohorts, the algorithm provided successful positioning in 89.7% of the arteries. In 79.6% of the subjects, all four arteries could be planned using the algorithm. Chi-square tests of independence showed that the success rate was not dependent on the age or gender, but the patients showed a trend of lower success rate (p = 0.14) compared to healthy controls. In conclusion, this automatic positioning algorithm could improve the application of PC-MRI in CBF quantification.Item Bi-tensor Free Water Model With Positive Definite Diffusion Tensor and Fast Optimization(2021-08-01T05:00:00.000Z) Wang, Siyuan; Cao, Yan; Stefan, Mihaela C.; Lou, Yifei; Dabkowski, Mieczyslaw K.; Minkoff, Susan E.Diffusion tensor imaging is a widely used imaging methodology to infer the microstructure of brain tissues. When an image voxel contains partial volume of brain tissue with free water, the traditional one tensor model is not appropriate. A bi-tensor free water elimination model has been proposed to correct for the mixing effects. Moreover, recent studies have shown that the free water volume derived from this model could be a biomarker for brain aging and numerous brain disorders such as Parkinson’s and Alzheimer’s disease. However, the problem of fitting this model is ill-posed without additional assumptions. Models by adding spatial constraints or using data from multi-shell acquisition are proposed to stabilize the fitting, but none of them restricts the diffusion tensor D to be positive definite, which is a necessary condition. In this work, we formulate the bi-tensor model fitting as an optimization problem over the space of symmetric positive definite matrices and show that the objective function is a ratio of two geodesically convex functions. We also demonstrate by simulation that the estimation may be highly biased with single-shell data in the presence of noise, so multi-shell data are needed for the fitting of the bi-tensor free water elimination model. Inspired by the Cholesky decomposition, we treat the diffusion tensor D as the product LLT where L is a lower triangular matrix. The optimization is performed on L which guarantees the positive definiteness of D. Our model are evaluated with both simulations and real human brain data. Simulation results show that the model is computationally efficient and the two-shell acquisition gives the best estimation.Item Cell Nuclei Segmentation Using Deep Learning Techniques(2021-08-01T05:00:00.000Z) K. C. Khatri, Rajendra; Cao, Yan; Lv, Bing; Dabkowski, Mieczyslaw K.; Ramakrishna, Viswanath; Lou, YifeiPathological examination usually involves manual inspection of hematoxylin and eosin (H&E)- stained images, which is labor-intensive, prone to significant variations, and lacking reproducibility. One of the fundamental tasks to automate this process is to find all the cell nuclei in the H&E-stained images for further analysis. We attempt this problem using deep learning techniques. First, we introduce a semantic pixel-wise segmentation technique using dilated convolutions. We show that dilated convolutions are superior in extracting information from textured images. H&E-stained images are highly textured, which makes dilated convolutions an ideal technique to apply. Our dilated convolutional network (DCN) is constructed based on SegNet, a deep convolutional encoder-decoder architecture. Dilated convolution layers with increased dilation factors are used in the encoder to preserve image resolution. Dilated convolution layers with decreased dilation factors are used in the decoder to reduce gridding artifacts. Our DCN network was tested on synthetic data sets and a publicly available data set of H&E-stained images. We achieve better segmentation results than state-of-the-art. To further separate the instance of each cell nuclei, we adapt our DCN with a single shot multibox detector (SSD) and achieve promising results. Our methods are computationally efficient and can be run on a personal laptop computer. This work is the first step to wards using mathematical models to generate diagnostic inferences and providing clinically actionable knowledge to physicians and patients.Item Coupling of Ionic and Electronic Processes in Lead Halide Perovskite Devices and Nanostructures(2021-12-01T06:00:00.000Z) Haroldson, Ross Everett; Zakhidov, Anvar; Cao, Yan; Gartstein, Yuri; Lee, Mark; Slinker, Jason; Stefan, MihaelaLead Halide Perovskites (LHPs) such as Methylammonium Lead Iodide (MAPbI3) or Cesium Lead Bromide (CsPbBr3) have garnered massive attention from researchers in photovoltaic, light emitting, and other optoelectronic fields as an interesting class of materials with attractive semiconducting and optical properties. Fabrication processes of LHPs are relatively simple compared to conventional inorganic semiconductors and don’t require powerful or expensive equipment which is promising for commercial development. However, they have shown dynamic performance behaviors and instabilities that have yet to be fully understood. These dynamic behaviors on the time scale of seconds have been attributed to their mobile charged point defects redistributing themselves during device operation. The ions (or charged defects) act as mobile intrinsic donors and acceptors that can be utilized in device operations. This thesis discusses the physical origin that strongly couples the electronic and ionic transport of LHPs and demonstrates devices that exploit and utilize this coupling. This coupling enables the dual functionality of mixed halide solar cells to also act as effective light emitting devices. We also demonstrate that utilizing extrinsic ionic salts such as lithium hexafluorophosphate (LiPF6) can serve as sacrificial ions that help protect the bulk of the perovskite from fast degradation. We studied the dynamic performance of LHP optoelectronic devices configured as perovskite lightemitting electrochemical cells (PeLECs) under various temperatures and conditions. We develop novel equivalent circuit models to extract the diffusion coefficients and concentrations of dominant ionic species at play in PeLEC devices in vacuum and dry air, in the dark or under illumination, and at different temperatures. Activation energies of ionic species in PeLECs were calculated by the temperature dependence of fitted parameters from diffusion elements in the equivalent circuits used to model impedance spectroscopy measurements. This thesis advances the knowledge and understanding of ion migration (or charged point defect transport) in LHP devices and how it affects their performance.Item Forecasting Stock Price Movements and Stock Trading Automation Using Deep Learning and Reinforcement Learning(August 2022) Annan, Augustine; Turi, Janos; Sibert, John; Ramakrishna, Viswanath; Cao, Yan; Arreche, CarlosArtificial intelligence algorithms and big data analysis approaches are becoming more signif- icant in a variety of application fields, including stock market trading and automation. Few research, on the other hand, have concentrated on predicting the future directional change in stock prices, particularly when utilizing strong machine learning methods like deep recurrent neural networks (DRNNs) to conduct the analysis. For algorithmic trading and investment management, developing a forecasting system that accurately anticipates future changes in a stock price is critical. To address that, we propose a hybrid deep learning model with self attention mechanism, dense layers, and a stacked bidirectional long-short term memory neural network. Many scholars have used technical analysis for financial forecasting with great success. When computing the technical indicators, a time horizon parameter needs to be specified as an input window size. In this work, the input size is set same as the prediction horizon or time step. This is due to the fact that the stock price’s behavior over a prediction horizon may, to some extent, mirror its previous behavior over the same time period. For extracting temporal features from stock sequential data, a stacked bidirectional long- short term memory neural network is proposed. The self-attention mechanism which directs the neural network to place more weight on important temporal information is also proposed. Following the model evaluation methods, experiments demonstrated that the proposed model’s trading strategy is better than the buy-and hold trading strategy and the model also out- performs other state-of-the art learning algorithms based on the evaluation metrics. Majority of trades are now entirely automated, and algorithmic stock trading has become a standard in today’s financial market. In many difficult games, like Go and Chess, Reinforce- ment Learning (RL) agents have shown to be a formidable opponent. The historical prices and movements of the stock market may be seen as a complicated, chaotic and imperfect environment in which we aim to optimize return while minimizing risk. Three deep rein- forcement learning agents are trained and an ensemble trading strategy is obtained using policy gradient based algorithms: Deep Deterministic Policy Gradient (DDPG), Proximal Policy Optimization (PPO) and Soft Actor Critic (SAC). To improve the robustness and accuracy for representing stock market conditions, the Long Short Term Memory (LSTM) is proposed to extract important and informative features from raw financial data and technical indicators. The ensemble approach takes the best elements of the three techniques and combines them, allowing it to adapt to changing market conditions with ease. We use a load-on-demand strategy for processing extremely big data to prevent significant memory usage in training networks with continuous action space. The algorithms are tested on the 30 Dow Jones equities. The trading agent’s performance is assessed and compared to the Dow Jones Industrial Average index and the classic min-variance portfolio allocation approach. In terms of risk-adjusted return as evaluated by the Sortino ratio, the proposed deep ensemble method outperforms the two baselines and a state-of-the-art deep reinforcement algorithm.Item Investigation Into Higher Dimensional Rotations(2022-12-01T06:00:00.000Z) Bal, Sabindra Singh 1981-; Zakhidov, Anvar A.; Ramakrishna, Viswanath; Cao, Yan; Dabkowski, Mieczyslaw K.; Choudhary, Pankaj K.Axis-angle representations provides efficient methods to study three dimensional rotations. The representation imparts visualization and thus aids the analysis of a three-dimensional proper rotation by reducing its study to that of a two dimensional one. In this dissertation, we accomplish a similar result for five dimensional proper rotation by reducing its study to that of either two or four dimensional proper rotations. For a matrix in SO(5, R), we complete a closed from formula for the axis which is the fixed point set of the matrix as well as the formula for the angle which is the complementary proper rotation that the matrix performs in the orthogonal complement to the axis. In fact, two such derivations are provided. The first is based on the properties of a matrix in SO(5, R) such as the special structure of its characteristic polynomial being skew palindromic while the second utilizes the structure of the Lie algebra of the covering group. Closed form formula for the logarithm in the covering group of SO(5, R) is also derived as it is essential for the second method. Further, we study indefinite rotations with signature (1,9) and come close to establish that the group of such rotations is isomorphic to 2x2 octonion matrices with determinant 1.Item Modeling and Sensitivity Analysis for Trace Gas Sensors(2022-12-01T06:00:00.000Z) Mozumder, Ali Ahammed; Minkoff, Susan E.; Zweck, John; King, Lindsay J.; Cao, Yan; Pereira, L. FelipeTrace gas sensors can detect very low concentrations of gases such as methane and sulfur dioxide. An important class of trace gas sensors are quartz-enhanced photoacoustic spectroscopy (QEPAS) sensors, which employ a quartz tuning fork (QTF) and modulated laser to detect trace gases. Existing models of QEPAS sensors employ one-way coupling from the fluid to the structure that requires prior experimental measurements of the damping of the QTF due to its motion in the viscous fluid. We study an improved two-way coupled model that is based on a Helmholtz system of thermo- visco-acoustic equations in the fluid, together with a system of equations for the temperature and the displacement of the structure. These two subsystems are coupled across the fluid-structure interface via several conditions. With this model, the user specifies the geometry of the structure and the viscous and thermal parameters of the fluid, and the model outputs an effective damping parameter and a signal strength that is proportional to the concentration of the trace gas. We derive analytic solutions of the two-way coupled model in the special case that the QTF is replaced by an annular structure. This simplification of the geometry allows the pressure, temperature of the fluid, and the displacement of the structure to be expressed in terms of Bessel functions. These solutions show reasonable agreement between the one-way and two-way coupled models at higher ambient pressures. However, at low ambient pressure the one-way coupled model does not adequately capture thermo-viscous effects. For the two-way coupled model, excellent agreement is obtained between the analytical results and simulations performed using a finite element formulation of the model. Computational models for trace gas sensors involve a large number of parameters. If one wants to quantify uncertainty of the output quantities of interest (for example, pressure, temperature or displacement of the tuning fork tines) then one must estimate statistical distributions that describe these quantities. However, statistical studies require that one runs the physical simulator for hundreds or thousands of different input parameter values. This process is computationally prohibitive unless one can first identify which parameters influence the model output. We use the active sub- space method to identify a subset of parameters that is influential for the output. The application of the active subspace method to the pressure-temperature subsystem in the special case of cylindrical symmetry identifies one influential parameter for the fluid temperature and three for the pressure from the five dimensional parameter space. Similarly, for the two-way coupled model with annular geometry the active subspace method reduces the 13 dimensional parameter space to a 5 dimensional subspace by identifying 4 influential parameters for the fluid temperature and 5 influential parameters for the remaining quantities of interest. Finally, for the one-way coupled model with tuning fork geometry, the active subspace method identifies 5 influential parameters for the fluid pressure, temperature, and displacement of the QTF reducing a 10 dimensional parameter space to a 5 dimensional subspace. These results also show an excellent agreement with the results obtained using kernel density estimation and a simple sensitivity study.Item Molecular Basis for Chaperone Control of Rtt109 Acetylation of Histone H3-H4(2021-08-01T05:00:00.000Z) Akhavantabib, Noushin; D'Arcy, Sheena; Cao, Yan; Meloni, Gabriele; Zheng, Jie; Pantano, PaulAcetylation is one of many protein post-translational modifications (PTMs) that frequently occurs in the cell. One type of acetylation is when the acetyl group from acetyl-coenzyme A (Ac-CoA) is transferred onto the ε-amino group of lysine sidechains. Histones are highly basic proteins that associate with genomic DNA and compact it into chromatin in the nucleus of the cell. They are often accompanied by a group of histone-binding proteins called histone chaperones in events such as nucleosome assembly/disassembly, histone transport and nuclear import. Being rich in lysine content, histones are frequently acetylated and therefore influence chromatin structure. Enzymes that carry out histone acetylation are termed histone acetyltransferases (HATs). Rtt109 is one such HAT that is found in fungal species, and requires association with histone chaperones to efficiently acetylate histones. Vps75 and Asf1 are the two known histone chaperones that when bound to Rtt109, enhance its enzymatic activity significantly. They also play a role determining Rtt109 selectivity and specificity towards different lysine residues in histones H3-H4. Cells deleted for Rtt109, Asf1 or both, are highly sensitive to genotoxic exposure; and it has been shown that Rtt109 acetylation of K56 is required for a cell to maintain its genomic integrity. This has made Rtt109 and its chaperone-containing complexes attractive anti-fungal therapeutic targets. The structure, dynamics and function of Rtt109 complexes are the focus of this dissertation. Utilizing comprehensive biophysical and biochemical analysis, we first investigate molecular interactions between Vps75 and H3-H4. We report the stoichiometry of binding in multiple ionic conditions and compare their interactions to a homologous complex containing Nap1. We identify the interface between Vps75 and H3-H4, and reveal how specific structural elements are tailored for Vps75 chaperoning activity with Rtt109. Next, we add Rtt109 to the Vps75-(H3-H4) complex and extensively characterize complex homogeneity and absolute stoichiometry. We define a detailed step-by-step Rtt109-Vps75 co-expression and purification protocol that maximizes yield and purity. We show the stoichiometry of binding is 1:2, with a second Rtt109 binding only at high concentration and readily replaced with H3-H4. We show that Rtt109-Vps75-(H3-H4) has a 1:2:1 unit that can self-associate to become a 2:4:2 complex through the H3-H3 contacts in a H3-H4 tetramer. Our large-scale reconstitution methods for various Rtt109 complexes paved the way for acquiring high-resolution structures via crystallography or cryo-electron microscopy. It also facilitated solution characterization via hydrogen-deuterium exchange mass spectrometry (HDXMS). Finally, we added Asf1, the last binding partner to reconstitute the double-chaperone complex − Rtt109-Vps75-(H3-H4)-Asf1. This allows for a comprehensive comparative HDX-MS experiment to uncover the mechanism behind chaperone activation of Rtt109. We purified and reconstituted eleven relevant protein complexes for analysis. We identify direct binding sites between each member of the complex and compare them to existing structures, and show different conformations upon addition of each chaperone. These results elucidate the acetylation mechanisms facilitated by cross-talk between two histone chaperones Vps75 and Asf1.Item Optimal Control of Human Balance Models With Reflex Delay(August 2023) Rajapaksha, Lashika Nishamani 1990-; Anderson, Phillip C.; Turi, Janos; Lou, Yifei; Cao, Yan; Pereira, FelipeFalls are the leading cause of injury-related deaths among the elderly, and scientists are increasingly interested in understanding the mechanism of human balance control. A single inverted pendulum is used to model the musculoskeletal dynamics of the human body with an ankle torque. There is a brief period of time between detecting a problem in proper positioning and applying torque to correct it. We present a mathematical optimal control model with delay for identifying human balance postural dynamics considering humans as a single inverted pendulum with an ankle torque. The equation of motion is a second-order delay differential equation, and it is solved numerically. Optimal feedback gains obtained from the optimal control problem with linear quadratic regulator function vary in time for a short period of time before becoming constant. These optimal feed- back gains are time and delay-dependent to compensate for the effect of the delay. We provide numerical simulations for different parameter values and scenarios to investigate human postural dynamics’ stability and demonstrate the model’s capabilities. Finally, we extend our study by investigating the dynamics of ankle and hip movement in response to perturbations using a double-inverted pendulum.Item Preparation of Functionalized Graphenes and Their Performance for Corrosion Resistance and Synthesis of Vanadium Nitridecarbon Nanofiber Mats and Their Application for Asymmetric Supercapacitor Electrodes(2020-12-01T06:00:00.000Z) Wunch, Melissa Ann; Yang, Duck Joo; Cao, Yan; Balkus, Jr., Kenneth J.; Ferraris, John P.; Smaldone, RonaldCarbon materials have been researched in a wide range of applications, including energy storage, corrosion protection, catalyst support, etc. Though many people have studied properties of carbon with/without modification, research in the synthesis of functionalized carbon and carbon composites therefrom will be important. This dissertation outlines the synthesis of functionalized graphene, development of graphene composites, and metal nitride-carbon nanofiber composites and their application for electrode for super-capacitor. Graphene is single layer carbon-based material known for its multifunctional properties (e.g. hydrophobicity, mechanical strength, etc.). This work studies application of graphene through functionalization of mechanically exfoliated graphene and functionalized graphene use for corrosion resistance. Functionalization of graphene is first discussed in the eco-friendly synthesis of aminated mechanically exfoliated graphene (MEG). Here we are able to directly functionalize MEG with amine groups using glycerol as the reaction medium and urea as the amine source. The aminated MEG (AG) also showed enhanced dispersion stability in organic solvents and aquous-solvent mixtures for >60 days. In the second area, we discussed how functionalized graphenes affected surface properties and corrosion resistance when composited with a polymer coating. Graphene, aminated graphene (AG), and fluorinated graphene (FG) were studied for corrosion resistance. Both AG and FG exhibited enhanced corrosion resistance when composited with a 2K urethane coating. Composite coating with FG showed a 94% increase in corrosion resistance versus graphene at a concentration of 4% by weight of solids. These materials also enhanced the surface properties of the coating. Electrochemical analysis of composite coatings showed that through inclusion of functionalized graphenes (AG or FG), barrier and adhesion properties were strengthened. Both FG and AG composite coatings showed an increase in contact angle versus graphene, with FG resulting in a hydrophobic surface (>90o ) at 4wt%. This project shows a step towards the potential removal of sacrificial zinc as a barrier for corrosion resistance of steel substrate. The increase in energy consumption over the last decade has led to research in the development of alternative energy storage devices which can meet the demand. Supercapacitors have garnered increased attention in this field due to their ability to provide high power and high energy. Electrodes within these devices can consist of two different materials, carbon or pseudocapacitive material. While carbon-based supercapacitors, or EDLCs, can provide high power density, they suffer from low energy densities. This has led researchers to study composite, or hybrid electrodes which combine the high power EDLC material with a high energy pseudocapacitive material (e.g. metal oxide or metal nitride). In the third area, we assembled and tested hybrid-asymmetric devices using activated vanadium nitride-carbon nanofiber (VN-CNF) electrodes. The VN was made using vanadium oxide (V2O5) nanoflowers by a new synthesis method. Composite electrodes were made by electrospinning of a poly(acrylonitrile-co-itaconic acid) (PANIA) solution with the vanadium oxide (V2O5) nanoflowers dispersed within it to produce freestanding mats. VN-CNF freestanding mats were used as anode material and CNF as the cathode when assembling the device. Ionic liquid electrolyte 1-butyl-1-methylpyrrolidinium bis(trifluoromethanesulfonyl)imide (Pyr14TFSI) with 0.5M lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) was used, which widens the operating voltage window (>3.5V) compared with aqueous (e.g. KOH or Na2SO4) or organic electrolytes (e.g. TEA-BF4 in ACN). Chapter 1 introduces the material graphene, its properties, and methods of synthesis. In this section we also review methods of functionalization and application in the field of corrosion protection. Chapter 2 describes the eco-friendly method of functionalization of mechanically exfoliated graphene (MEG) with amine groups and the effect of these groups on dispersion stability in organic solvents and aqueous-solvent mixtures are studied. Chapter 3 studies the effect of graphene, aminated graphene (AG), and fluorinated graphene (FG) on surface properties and corrosion resistance when composited with a urethane coating. Contact angle measurements and electrochemical analysis were performed to determine which graphene and concentration provides best corrosion resistance. Chapter 4 introduces supercapacitors and the concepts behind the different types. This section describes charge storage mechanisms of the pseudocapacitors and discusses different aspects of metal oxides and nitrides. Chapter 5 describes the preparation of vanadium nitride-carbon nanofiber (VN-CNF) composite electrodes and analysis of their electrochemical properties. Charge contributions and storage mechanisms for each sample was studied to understand the mechanism in which their charge is stored (e.g. intercalative or pseudocapacitive/capacitive).Item Topological Machine Learning in Medical Image Analysis(December 2023) Ahmed, Faisal 1988-; Coskunuzer, Baris; Balkus Jr., Kenneth J.; Gel, Yulia; Li, Qiwei; Cao, Yan; Wu, NanMedical image analysis is a critical component of modern healthcare, aiding in the detection, diagnosis, and treatment of various diseases. In recent years, the fusion of topological data analysis (TDA) and machine learning has brought about a transformative approach to understanding and leveraging the complex patterns inherent in medical images. This thesis explores the application of TDA, with a focus on persistent and cubical homology, as a powerful tool for extracting topological features from 2D and 3D medical images. By capturing the birth and death of these features through a filtration process and representing them as feature vectors, we enhance the interpretability and performance of machine learning models. Our journey begins with the transformation of color images into grayscale, RGB, and HSV channels, laying the foundation for versatility in our approach. The three-step process of persistent homology unfolds through filtration, persistence diagram generation, and vectorization, leading to feature vectors that outperform traditional image inputs in machine learning models. In our investigations, we utilized this methodology across various medical imaging contexts such as cancer histopathology, chest X-rays, retinal images, and MEDMNIST a collection of various medical image datasets. Our findings highlight the effectiveness of topological features in analyzing images, particularly in classifying and identifying abnormalities in these settings. Additionally, when we merged these topological aspects with deep learning characteristics, we observed an improved model efficiency. This presents a novel, comprehensive approach to medical image analysis. This research further demonstrates the potential of TDA in image analysis and classification, providing valuable insights into complex structural information not readily apparent through conventional techniques. In the realm of histopathological cancer detection, we introduce a groundbreaking Topo-ML model that adapts to multiple cancer types, offering remarkable computational efficiency. In the evaluation of chest X-ray images, our Topo-CXR model excels in terms of reliability and interpretability, outperforming deep learning models on benchmark datasets to detect Pneumonia and Tuberculosis. Additionally, our analysis of fundus images for retinal diseases presents a dual contribution, introducing effective feature extraction methods and topological deep learning models that surpass existing models. Beyond these specific applications, we conducted a comprehensive evaluation of TDA methods across various medical image datasets, demonstrating competitive performance with deep learning models in certain cases. These findings underscore the potential of topological features in boosting the capabilities of future machine learning models in diverse medical domains, ultimately advancing our understanding and utilization of digital images in healthcare.