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School of Biological Sciences

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School of Chemistry and Biochemistry

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School of Earth and Atmospheric Sciences

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School of Mathematics

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Random subsequences problems : asymptotics, variance, and quantum statistics.

(Georgia Institute of Technology, 2024-05-07) Deslandes, Clement

This work considers some random words combinatorial problems and their applications. The starting point of this endeavor is the following question : given two random words, ”how much do they have in common” ? Even if this question has emerged independently in various fields, including computer science, biology, linguistics, it remains mostly unsolved. Firstly, we study the asymptotic distribution of the length of the longest common and increasing subsequences. There we consider a totally ordered alphabet with an order, say 1,...,m, and the subsequences are simply made of a block of 1’s, followed by a block of 2’s, ... and so on (such a subsequence is increasing, but not strictly). Secondly, we deal with the problem of the variance of the LCS. By introducing a general framework going beyond this problem, partial results in this direction are presented, and various upper and lower variance bounds are revisited in diverse settings. Lastly, we consider the Longest Increasing Subsequences (LIS) of one random word, and the surprising connection with quantum statistics.
Topology, Geometry, and Combinatorics of Fine Curve Graphs

(Georgia Institute of Technology, 2024-05-02) Shapiro, Roberta

The goal of this thesis is to explore curve graphs, which are combinatorial tools that encode topological information about surfaces. We focus on variants of the fine curve graph of a surface, which has its vertices essential simple closed curves on the surface and whose edges connect pairs of curves that are disjoint. We will prove various geometric, topological, and combinatorial results about these curve graph variants, including hyperbolicity (or lack thereof), contractibility of induced flag complexes, automorphism groups, and admissible induced subgraphs.
Integrating Machine Learning Solutions into Untargeted Metabolomics and Xenobiotics Workflows

(Georgia Institute of Technology, 2024-05-01) Rainey, Markace Alan

Untargeted metabolomics explores the entirety of small molecules within biological samples, providing insights into metabolic alterations associated with various conditions. Standard methodologies like NMR and LC-MS are pivotal in identifying molecular markers but often fall short in fully deciphering the metabolic landscape due to limitations in accurately annotating a vast number of metabolites. This gap in annotation hampers the diagnostic application and biological interpretation of metabolomic data. Ion mobility spectrometry (IMS) offers a solution by providing semi-orthogonal data that enhances metabolite annotation. IMS separates ions based on their collision cross-section (CCS), a property influenced by an ion's mass, shape, charge, and external factors like temperature and pressure. When integrated with mass spectrometry (MS), IMS aids in resolving ions’ of similar or identical mass-to-charge ratio (m/z), offering a refined approach to metabolite characterization. This thesis focuses on employing computational strategies within LC-IM-MS workflows to facilitate rapid metabolite characterization. Chapter 1 outlines the challenges in metabolomics, specifically the limitations of current LC-MS workflows and the concept of the "dark metabolome." This introductory chapter provides the theoretical framework to better understand ion mobility and the use of quantitative-structural activity relationships to predict molecular properties. The chapter also discusses xenobiotics—external compounds impacting health—and their characterization challenges. Chapter 2 introduces Collision Cross Section Predictor 2.0 (CCSP 2.0), a machine learning-based tool for predicting ion mobility-derived CCS values. CCSP 2.0, developed to improve the accuracy and ease of CCS prediction, is evaluated for its efficacy in enhancing annotation accuracy in LC-MS workflows. It utilizes a support-vector regression model and incorporates a comprehensive library of molecular descriptors, demonstrating superior prediction accuracy and utility in reducing false positive annotations. Chapter 3 presents a workflow for automated detection of polyhalogenated xenobiotics in biological samples using LC-IM-MS. This approach combines CCS to m/z ratios, Kendrick mass defect analysis, and CCS prediction to filter isomeric candidates. A case study on the detection of per- and polyfluorinated alkyl substances in human serum exemplifies the workflow's effectiveness. Chapter 4 describes an analytical chemistry experiment for undergraduate students, focusing on laser-induced breakdown spectroscopy (LIBS) and its application in data science education. This chapter emphasizes enhancing students' programming literacy and analytical skills through hands-on experiments and analysis using Jupyter Notebooks. The experiment, adaptable to various curricula, showcases real-world applications of LIBS, including its use in space exploration. Chapter 5 summarizes key findings from the research, discussing the implications of integrating computational methods in metabolomics and the potential advancements in ion-mobility mass spectrometry. Future research directions are proposed to further explore and refine these methodologies. Appendix A explores an on-going project aimed at predicting analyte concentrations without standard calibration curves using machine learning. This approach predicts relative ionization efficiencies of lipids from their structural properties, demonstrating the potential of machine learning in streamlining quantitative analyses in metabolomics. In conclusion, this thesis underscores the importance of computational approaches in enhancing metabolite annotation and characterizing xenobiotics, contributing valuable tools and methodologies to the field of metabolomics.
Investigating The Mechanisms Underlying Metamorphosis in The Chordate Ciona Robusta

(Georgia Institute of Technology, 2024-04-29) Johnson, Christopher

In our study, we investigate the multifaceted roles of papillae in tunicate larvae, pivotal for sensory perception, adhesion, and metamorphosis regulation, particularly in the model organism Ciona. Through molecular marker identification and CRISPR/Cas9-mediated mutagenesis, we delineate the intricate cellular diversity within papillae, elucidating the regulatory networks orchestrated by key transcription factors and signaling pathways. Concurrently, we explore the evolutionary divergence in the expression patterns of Myomaker (Mymk), a fusogenic factor crucial for myoblast fusion and muscle multinucleation, between vertebrates and tunicates. By analyzing cisregulatory sequences of Mymk, we unveil the underlying mechanisms driving the differential spatiotemporal expression patterns in these organisms. Our findings not only deepen our understanding of tunicate development but also provide insights into the evolutionary history of myoblast fusion regulation across chordates.
Toric and Tropical Geometry: Positivity and Completion

(Georgia Institute of Technology, 2024-04-28) Cai, May

This thesis is divided into the introductory chapter and then three main chapters. The the introductory first chapter is devoted to providing some preliminary background on polytopes, tropical geometry, and tropical linear algebra. The second chapter consists of a result on the probability completion of log-linear models. In particular, given partial entry-wise information about a point in some toric variety intersected with the set of probability vectors, we describe the number of completions of that partial point into an actual point in the semi-algebraic set, as well as necessary conditions to be a valid partial point. A preprint of the content of this chapter can be found online at https://arxiv.org/abs/2312.15154, and was joint work with Cecilie Olesen Recke and Thomas Yahl. The third chapter is concerned with the tropical variety of symmetric tropical rank at most 2. We discuss a refinement of the fan of the variety that gives a tree characterization of the variety, as in Markwig and Yu, and from this we deduce the shellability for the tropical variety as well as a condition to verify independence in the algebraic matroid of this variety. This chapter was joint work with Kisun Lee and Josephine Yu, and a preprint of the content can be found online at https://arxiv.org/abs/2404.08121. The fourth chapter focuses on applying notions of tropical positivity developed by Brandenburg, Loho, and Sinn to tropical symmetric determinantal varieties. It describes the ``positive'' and ``really positive'' parts of the tropical varieties of rank 2 symmetric matrices, using the tree characterization established in the third chapter, as well as of the symmetric tropical determinantal hypersurface. We also re-prove certain results about the really positive part of the tropical varieties of rank 2 usual tropical matrix and of the usual tropical determinantal hypersurface. This chapter was joint work with Abeer al Ahmadieh and Josephine Yu.
Density-Induced Spin-Nematic Squeezing in a Spin-1 Bose-Einstein Condensate

(Georgia Institute of Technology, 2024-04-28) Barrios, Maryrose

Density or pressure modulation of materials is an important method for tuning and engineering interactions within materials studied in condensed matter systems. This tuning is often used to alter or modify the underlying properties of the material, leading to the crossing of a phase transition or enhanced chemical or mechanical properties. This thesis investigates the possibility of whether a similar approach might be employed in the study of ultracold atoms present within a spinor condensate. In our system we use the confining trap potential to modulate and increase the density of the system in such a way as to push the cloud of atoms from non-interacting to interacting, and across a quantum critical point. By crossing over into this new phase, we are able to perform a constant magnetic field quench to observe both spin mixing and spin-nematic squeezing. This allows us to achieve -8.4 ± 0.8 dB of squeezing and shows promise for future density-driven interactions.
Unraveling the Knot-so-Simple Behavior of Knitted Fabrics

(Georgia Institute of Technology, 2024-04-27) Singal, Krishma

Knitted fabrics are a ubiquitous part of our day-to-day lives. Although we primarily interact with it through clothing, the programmable nature of knitted fabrics lends to its potential in a myriad of fields. Knitting is made by manipulating yarn, which is often inelastic, into a lattice of slipknots with emergent elastic properties. How the yarn is manipulated throughout the fabric, what stitches it forms and how they’re patterned, impacts the resultant fabric behavior under mechanical deformation. Traditionally, this elastic response of knitted fabrics is qualitatively determined, but this study works to systematically understand and quantify the programmable nature of knitted materials. We find that small scale changes in the topology of the yarn between stitches, the boundaries between stitches, have large scale impacts on the bulk fabric response. Not only on the stitch level, but the lengthscale of these boundaries further influences the fabric behavior. We probe the multi-scale behavior and application of knitting through several experimental studies: varying constituent yarn type composing the fabrics, comparing behaviors of classic periodic knitting patterns, exploring the impact of aperiodic patterned fabrics, and testing applications of knitting in biomimicry and biomechanics via known pattern composites.
Exciton and Charge Carrier Nonlinear Dynamics in Hybrid Organic-Inorganic Metal Halides

(Georgia Institute of Technology, 2024-04-27) Rojas Gatjens, Jorge Esteban

Hybrid-organic inorganic metal-halide semiconductors pose an interesting photophysical scenario. Due to the ionic and dynamic nature of the structure, their excited-state properties are highly correlated with the structure's vibrations, distortions, and solvation dynamics. This thesis studies the interactions between excited states (nonlinear dynamics), their manifestation in physical observables, and their relation to the material's structure and fabrication. We explore the exciton and charge carrier nonlinear dynamics, via incoherent and coherent spectroscopy, in hybrid organic-inorganic mixed-halide lead perovskites, Ruddlesden-Popper metal halides, and perovskite nanocrystals. The many-body interactions manifest in incoherent spectroscopy as nonlinearities in the photoluminescence and/or photocurrent and, in two-dimensional coherent spectroscopy lineshapes, in the spectral linewidth, phase, and many-particle state feature (e.g. biexcitons, trions). For bulk hybrid organic-inorganic mixed-halide lead perovskites, we resolve incoherent nonlinear dynamics with sub-picosecond resolution in the photoluminescence and photocurrent. We were able to characterize the competition between defect-assisted recombination, Auger recombination, and amplified spontaneous emission. For the Ruddlesden-Popper metal halide perovskites and perovskite nanocrystals, we used two-dimensional coherent spectroscopy to explore ultrafast exciton scattering events and exciton-carrier coupling dictating the exciton-quantum dynamics. The work of this thesis sheds light on the many-body interactions in hybrid-organic inorganic metal-halide semiconductors and provides the tools to transition from the description to the control of nonlinear dynamics.
The Second Rational Homology of the Torelli Group

(Georgia Institute of Technology, 2024-04-27) Minahan, Daniel Sulla

We show that the second rational homology of the Torelli group of a closed, orientable, connected surface is finite dimensional for all surfaces of sufficiently high genus.
Evolution Before Origin: A Conceptual and Experimental Framework

(Georgia Institute of Technology, 2024-04-27) Matange, Kavita

The search for chemical processes preceding the emergence of life presents a significant challenge in scientific inquiry. The development of biochemistry on early Earth presents some of the most creative chemistry in the known universe. In this work, we present a novel approach to advance our understanding of chemistry on early Earth based on wet-dry cycling. We outline a conceptual and experimental model of chemical evolution. As context, we outline currently accepted models of the origins of life and emphasize the utility of chemical evolution. With water at the center of the model, we demonstrate or infer that chemical systems are capable of selection, coupling, and creativity. We outline the framework of our wet-dry cycling-based model of chemical evolution and hold that during early chemical evolution, molecules were selected based on solubility in water, condensation-dehydration chemistry and resistance to hydrolysis upon assembly assemblies. Our model maps evolutionary concepts onto chemical processes. (a) a generation is a single wet-dry cycle; (b) heredity is information passed from one generation to the next; (c) information is associated with non-random chemical composition; (d) selection results in inheritance of certain molecular species over generations; (e) fitness confers persistence (i.e., survival) of molecules and specific molecular assemblies; (f) variation is spatiotemporal differences in information; and (g) water is an “energy currency” that links reactions and, upon changing activity, alters reaction free energies. In this work, we have employed wet-dry cycling and observed unexpected experimental outcomes like combinatorial compression, synchronicity, and continuous chemical change. We have suggested that biologically relevant concepts like adaptation and exaptation are universal, synergistic, and recursive, and along with biopolymers, apply to small molecules such as metabolites, cofactors, and building blocks of extant polymers. Altogether, this research establishes a platform for the analysis of complex mixtures at the Origin of Life and offers new horizons for the mapping of evolutionary phenomena onto prebiotic systems.