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Succinct Verification Through Reed-Solomon and Folded Reed-Solomon Codes
The overarching problem for our thesis talks is succinct verification: how can one check that a computation (e.g. ) has been performed correctly? A natural way to verify is to repeat the claimed computation from scratch and check that the results agree. However, repeating computations from scratch can be very expensive, especially when the computation is not as simple as the given example. Given a computation that takes time naively, can we instead produce a proof that can be checked reasonably accurately in time sublinear in , such as ? In the 1990s, researchers studied probabilistically checkable proofs (PCPs) that solved the above problem. Informally, the PCP theorem (ALMSS, 1992) stated that there exists a proof format that allows a grader to read 3 words in a proof and still successfully grade the proof as correct or incorrect with high probability. The tradeoff in accuracy in exchange for succinct verifiability is called soundness. Such initial proof formats produced implausibly long proofs (despite being quick to verify), so some recent research has focused on making proof systems that are not only succinctly verifiable but also concretely efficient. Their primary real-world application today is making cryptocurrencies more scalable – networks like Ethereum are currently limited in their throughput due to it being time and energy intensive to verify transactions. However, such proof systems involve many beautiful mathematical tools as well. They reduce the verification step to a math problem called Reed-Solomon proximity testing (RPT): discerning whether a polynomial is low degree or far from a low-degree polynomial for some notion of ``farness".
One algorithm used to solve RPT in succinct verification systems is the Fast Reed-Solomon IOPP (FRI). The first few chapters of this thesis are expository sections introducing succinct verification and how succinct verification is connected to mathematical objects called error-correcting codes (ECCs). These sections build up to an explanation of FRI and its soundness.
We then explain a related ECC called Folded Reed-Solomon codes have a property called list decodable up to capacity. Informally, this means that such codes can tolerate a large number of errors while still being able to output a small list of candidate code words. FRI can solve RPT, but its soundness depends on the list-decoding size of Reed-Solomon codes, which is not known to achieve list-decoding capacity. Folded Reed-Solomon codes do achieve capacity when instantiated with the right parameters.
In the final part of this thesis, we propose modifications to FRI that can solve proximity testing for Folded Reed-Solomon codes.Computer Scienc
PTH signaling in Ctsk+ cells is critical for skeletal homeostasis and tooth formation and eruption
PTH signaling is of primordial clinical importance in the regulation of skeletal development and homeostasis, as well as in tooth formation and eruption. Both skeletal and dental mesenchymal cells express PTH1r and are target of PTH signaling. Our lab has been investigating the function of a recently identified periosteal stem cell (PSC) population labeled by Cathepsin K (Ctsk) in the regulation of cortical bone homeostasis. Ctsk+ lineage PSCs, which fulfil stemness criteria, express high levels of the PTH1r and respond to iPTH treatment. Ctsk is also expressed in dental pulp cells, dental follicle cells, and the periodontal ligament which are known to play a key role in tooth development and eruption. Whether PTH signaling in Ctsk+ lineage cells is required for proper periosteal bone formation and tooth development and eruption is not known. We, therefore, undertook a study to investigate whether PTH signaling in the Ctsk expressing PSCs and dental mesenchymal cells regulates these processes. To this end, we generated mice lacking PTH1r, specifically in Ctsk+ cells, using the CtskCre mice and analysed their cortical bone and teeth.
Eight-week-old CtskCre;PTH1rfl/fl (CtskPTH1r) male and female mice are significantly smaller than their control littermates (PTH1rfl/fl). microCT and bone histomorphometry analyses revealed a significant decrease in cortical bone volume (%), cortical thickness, and periosteal MAR in CtskPTH1r mice compared to PTH1rfl/fl littermates. Notably, CtskPTH1r male and female mice present with failure of molar eruption and impaired incisor eruption. microCT analyses and histological examination revealed several abnormalities in 8-week-old CtskPTH1r mice, including truncated molar roots, loss of the periodontal ligament, root ankylosis, reduced cementoblasts, and markedly decreased alveolar bone. Severe dental anomalies werealso seen in CtskPTH1rmice at P12 and P19. Confirming that both the skeletal and the tooth phenotype are a consequence of deletion of the PTH1r in the mesenchymal cell lineage, Lys2Cre mice, widely used to deleted genes of interest in osteoclasts, do not present with any skeletal and dental phenotype.
While our findings confirm the significance of PTH signaling in both periosteal bone formation and tooth development and eruption, they reveal for the first time a crucial role for Ctsk+ lineage cell- dependent PTH signaling within the periosteum and dental mesenchyme. The periosteum is a significant source of stem cells and progenitors contributing to bone growth and homeostasis, regeneration and response to anabolic drugs. Investigating the signaling molecules and pathways regulating periosteal stem cells offers an opportunity to advance our understanding of the mechanisms involved in these processes and may open novel and targeted therapeutic approaches for human diseases associated with bone fragility and impaired bone regeneration. Similarly, a comprehensive understanding of distinct subsets of dental mesenchymal cell populations and unravelling their regulation is of significance for the effective pursuit of novel dental regenerative strategies.Oral Biolog
Linking regulatory variants to target genes by integrating single-cell multiome methods and genomic distance
Methods that analyze single-cell paired RNA-seq and ATAC-seq multiome data have shown great promise in linking regulatory elements to genes. However, existing methods differ in their modeling assumptions and approaches to account for biological and technical noise—leading to low concordance in their linking scores—and do not capture the effects of genomic distance. We propose pgBoost, an integrative modeling framework that trains a non-linear combination of existing linking strategies (including genomic distance) on fine-mapped eQTL data to assign a probabilistic score to each candidate SNP-gene link. We applied pgBoost to single-cell multiome data from 85k cells representing 6 major immune/blood cell types. pgBoost attained higher enrichment for fine-mapped eSNP-eGene pairs (e.g. 21x at distance >10kb) than existing methods (1.2-10x; p-value for difference = 5e-13 vs. distance-based method and < 4e-35 for each other method), with larger improvements at larger distances (e.g. 35x vs. 0.89-6.6x at distance >100kb; p-value for difference < 0.002 vs. each other method). pgBoost also outperformed existing methods in enrichment for CRISPR-validated links (e.g. 4.8x vs. 1.6-4.1x at distance >10kb; p-value for difference = 0.25 vs. distance-based method and < 2e-5 for each other method), with larger improvements at larger distances (e.g. 15x vs. 1.6-2.5x at distance >100kb; p-value for difference < 0.009 for each other method). Similar improvements in enrichment were observed for links derived from Activity-By-Contact (ABC) scores and GWAS data. We further determined that restricting pgBoost to features from a focal cell type improved the identification of SNP-gene links relevant to that cell type. We highlight several examples where pgBoost linked fine-mapped GWAS variants to experimentally validated or biologically plausible target genes that were not implicated by other methods. In conclusion, a non-linear combination of linking strategies, including genomic distance, improves power to identify target genes underlying GWAS associations.Accepted Manuscrip
Tracing the Origins: Cosmological Information in the Large-Scale Structure of the Universe
One of the central observables in cosmology is the correlation function of the matter density field. Yet, the large-scale structure of the universe cannot be directly observed, as it is dominated by dark matter. To probe it, we rely on indirect tracers such as galaxy surveys, 21-cm observations, gravitational lensing, and the cosmic microwave background. Recent advances in cosmological observations have produced a wealth of data across these tracers, offering unprecedented opportunities to investigate the physical processes and cosmic history that shaped the universe—from its initial conditions to its present state. This data abundance, however, raises two major challenges: (1) How can we efficiently and accurately extract information from the large-scale structure? (2) How can we combine different observational datasets in a consistent joint analysis? Addressing these questions is central to modern cosmological data analysis pipelines.
This thesis tackles these challenges through four directions:
(1) We apply a novel statistic—the skew-spectrum—to galaxy survey data, enabling efficient compression of the three-point correlation function and improved constraints on primordial non-Gaussianity, a potential signature of inflation.
(2) We study the combined information content of galaxy clustering and CMB lensing using both two- and three-point correlation functions. To support this analysis, we develop a new method based on the FFTLog algorithm that significantly accelerates the theoretical computation of projected angular statistics for galaxy surveys and weak lensing.
(3) We generalize the skew-spectrum formalism from redshift space to harmonic space, facilitating consistent and efficient cross-correlation studies across different cosmological probes. As a proof of concept, we implement this approach on N-body simulations.
(4) We perform field-level inference—applied for the first time to 21-cm signals from the epoch of reionization—within the framework of the effective field theory of large-scale structure. Despite foreground contamination, our high-dimensional Bayesian analysis enables reconstruction of the obscured signal and constraints on key physical parameters. We further explore cutting-edge diffusion-based generative models as an alternative inference method and find that their performance is comparable to traditional approaches.Physic
Lifting As We Climb: Community wealth-building as collaborative solutioning, a journey of transformation for systemic impact in a social change organization
In an era where policymaking has become increasingly gridlocked, social change organizations, like nonprofits and school systems, must take on a more dynamic role—not just as advocates, but as architects of tangible solutions. The mid-20th-century policies that once undergirded widespread economic mobility and social progress emerged from a political climate willing to confront systemic challenges head-on. Today, however, the tools of large-scale governmental intervention have weakened, leaving many of society’s most persistent and perplexing problems—wealth inequality, educational disparities, housing instability—unresolved or even worsening. In this vacuum, collaborative solutioning becomes an imperative: the process of actively designing and implementing bold, innovative strategies to reshape societal possibilities from the ground up through public-private partnerships that are community-driven, unlocking the resources necessary to fix problems quickly. Rather than waiting for legislation that may never materialize, organizations committed to social change must reimagine what is possible, mobilize strategic partnerships, unlock resources, and activate community-driven change that demonstrate alternative futures in real time.
This capstone illustrates the journey of my 10-month residency at the Chicago Urban League (CUL), examining how a prestigious, social change organization can transform its strategic direction and operating model to drive systemic impact. Through collaborating with a core team to conduct a strategic planning process and leading an internal CUL center to demonstrate a case study for reimagining what is possible, I explore how leading organizational change and transformation efforts require adaptive leadership, innovative approaches, and change management. By adapting CUL’s mission from solely economic empowerment to include an aspirational vision for building generational wealth, my strategic project developed a framework for wealth-building as a form of collaborative solutioning, designing and implementing a bold vision of economic prosperity for all through public-private partnerships.
My strategic project and learning experiences at CUL have significant implications for my own practice of exercising leadership, CUL as an organization, and the nonprofit and education sectors as components of the broader social change ecosystem, stressing the need for collaborative solutioning as a liberatory framework to co-create and implement our bold visions of futures where everyone can thrive. This capstone offers those interested in a more just world, where everyone has access to the financial security they need to live fully and be well, a possible pathway towards that transformation.Educatio
Regulation of intercellular communication by Alzheimer's disease genetic risk factors
Intercellular communication between glial cells, neurons, and the vasculature drives the progression of neurodegenerative diseases like Alzheimer’s disease (AD). The accumulation of misfolded proteins initiates neuroinflammation, activating microglia to release proinflammatory signals that, in turn, drive astrocyte reactivity. This feedback loop sustains and amplifies inflammation, disrupts vascular function, and accelerates the progression of synapse loss and neurodegeneration. Although hallmark features of AD—tau tangles, Aβ deposits, and synapse loss—emphasize neuronal dysfunction, genetic studies underscore the pivotal role of glial-specific genes, including TREM2, APOE, and CLU, in late-onset AD (LOAD). In contrast, familial AD (fAD) is driven by mutations in APP and PSEN1/2, which are known to induce altered Aβ production within neurons. Understanding how glial-driven LOAD risk factors contribute to neuronal dysfunction and how fAD-linked mutations disrupt glial communication is crucial for unraveling the interconnected mechanisms of AD pathogenesis.
Advancements in single-nucleus RNA sequencing (snRNAseq) have uncovered diverse cellular states implicated in neurodegenerative diseases, including disease-associated microglia (DAM), which are closely tied to neuronal function. However, testing hypotheses regarding glial-neuronal intercellular communication derived from these datasets requires a reproducible human model system capable of capturing the complexity of these interactions. To address this, we developed a robust human iPSC-derived triple-culture platform incorporating astrocytes, neurons, and microglia. Analyses of each cell type in mono- and co-culture uncovered distinct transcriptional signatures uniquely shaped by co-culture interactions. For example, astrocyte co-culture strongly induced the upregulation of DAM-associated proteins, including TREM2, SPP1, APOE, and GPNMB. Strikingly, exposure to fAD neurons initially suppressed astrocyte-mediated DAM induction while activating NfB-dependent inflammatory responses. These findings validate our platform's ability to model glial-neuronal interactions and provide insights into how fAD mutations disrupt intercellular signaling.
We then leveraged this platform to investigate the intercellular mechanisms underlying the AD risk gene Clusterin (CLU). Genetic studies implicate CLU in AD pathogenesis, and CLU levels are elevated in the brains of individuals with AD. Despite nearly three decades of research, the role of CLU remains enigmatic: it is unclear whether CLU upregulation is neuroprotective, contributes to pathology, or serves merely as a biomarker. Based on multi-omic analyses of postmortem human brain tissue, we hypothesized that sufficient astrocytic CLU upregulation in response to neuropathology preserves cognitive function, while reduced CLU expression, as seen in individuals carrying CLU risk alleles, increases disease susceptibility. Using human iPSC-based models, we explored the molecular and functional consequences of CLU deficiency. Unbiased proteomic profiling and functional validation revealed that CLU deficiency activates NFκB-dependent signaling, leading to elevated secretion of complement component C3 and proinflammatory cytokines. By establishing co-cultures of astrocytes with neurons, microglia, or both, we demonstrate an intricate network of intercellular signaling, leading to microglia-dependent tau phosphorylation, increased microglia phagocytosis, and reduced synapse density in CLU deficient conditions. Remarkedly, longitudinal analysis of human plasma samples revealed that individuals with CLU protective alleles showed an increase in CLU levels over time without changes in inflammatory markers, while those with risk alleles exhibited stable CLU levels alongside an upregulation in inflammatory markers. By integrating mouse and human cellular models, we demonstrate that CLU risk alleles recapitulate CLU-loss-of-function phenotypes under neuropathological burden. In vivo, mice carrying a humanized CLU risk allele showed reduced CLU protein levels and increased expression of phagocytosis- and complement-related genes. In vitro, we used genetically diverse iPSC-derived astrocytes to demonstrate that CLU risk alleles led to reduced CLU and APOE levels and increased complement protein and phosphorylated tau levels in co-cultures with microglia and neurons. Taken together, our findings establish a mechanistic link between AD genetic risk factors, astrocyte reactivity, and microglia-mediated effects on synaptic integrity, underscoring CLU as a pivotal neuroprotective factor in AD pathogenesis and brain health.
Our triple-culture model effectively captures critical signaling dynamics among microglia, neurons, and astrocytes but lacks vascular components, such as brain endothelial cells and pericytes, which are integral to the blood-brain barrier (BBB). The BBB, a cornerstone of the neurovascular unit (NVU), preserves brain homeostasis, and its dysfunction contributes to neurodegenerative processes. To extend our platform, we developed an all-human BBB model that incorporates endothelial cells, pericytes, astrocytes, neurons, and microglia. We demonstrate the utility of this model by profiling the molecular responses of BBB cells exposed to fAD neurons, revealing dysregulated pathways across multiple cell types, including extracellular matrix (ECM) degradation, complement activation, and TNF signaling via NFκB. Furthermore, endothelial cells exhibited upregulation of matrisome proteins (e.g., SMOC1, SPOCK3, MDK) and increased matrix metalloproteinase activity, recapitulating vascular changes observed in the AD brain. Our findings provide a powerful resource for investigating cell-type-specific responses to pathogenic Aβ and provide a platform for exploring therapeutic interventions targeting the NVU.
Collectively, these studies illuminate the critical role of glial-neuronal and vasculature interactions in AD pathogenesis, revealing how glial-driven risk factors affect neuronal homeostasis and how fAD-associated mutations disrupt intercellular communication. Using our co-culture systems, we found that acute exposure to fAD neurons suppresses astrocyte-induced DAM states, triggers inflammatory responses, and upregulates matrisome proteins in BBB cell types, reflecting AD-related vascular changes. Moreover, we demonstrate that CLU protects neuronal synapses by mitigating complement and inflammatory signaling between microglia and astrocytes. These findings underscore the utility of co-culture models in uncovering mechanisms by which glial-neuronal and vasculature interactions preserve brain homeostasis and how their disruption by genetic risk factors contributes to neurodegeneration.Biological and Biomedical Science
Rewriting the Dinosaur Tail: Evidence for Dvl2 Deletion and Changes to Tailbud Development in Birds
The evolutionary reduction of the tail is one of the most striking anatomical transformations in the lineage leading from non-avian dinosaurs to modern birds. This dissertation investigates the developmental and genomic mechanisms underlying premature tail termination in birds using comparative embryology, genomics and transcriptomics in the context of the fossil record. I identify a bird-specific deletion of Disheveled-2 (Dvl2), a key conductor of Wnt signaling, that results in axial truncations when it is deleted across vertebrates. This is combined with temporally dynamic shifts in the organization and elongation dynamics of tailbud tissues in chicken relative to alligator, the closest extant relative of birds that possesses a tail. Tailbud transcriptomic analyses conserved, species-specific temporal expression dynamics of both Hox genes and Wnt ligands in both alligator and chicken. Alligator tail initiation exhibited steep bursts of expression, while chickens showed a more graded process, and alligator tailbuds showed an overall coupling of Hox and Wnt dynamics that was absent in chicken. Overall, the findings suggest a more robust onset and maintenance of elongation in alligator tail tissues, while a loss of Dvl2 and disruption of Wnt signaling in birds may have resulted in a gradual tail developmental progression that cannot sufficiently maintain progenitors of the axis.Biological and Biomedical Science
Trustworthy Machine Learning Through Interpretability and Fairness
The deployment of machine learning (ML) systems across diverse domains has led to groundbreaking advancements in vision and language tasks. However, ensuring that these systems are trustworthy—encompassing attributes such as interpretability, fairness, reliability, and alignment with human values—remains a significant challenge. This dissertation develops novel methodologies to enhance trustworthiness throughout the ML pipeline, addressing critical issues in data preparation, model training, model evaluation, and model deployment. To improve data preparation, this dissertation introduces concept-based auditing frameworks that systematically identify harmful biases and misaligned associations in large-scale and synthetic datasets. In the model training stage, two architectural innovations are proposed: channel embed- dings that improve interpretability in multiplexed biological data and architectural enhancements for super-resolution tasks that ensure semantic consistency by preserving high-frequency details. In the evaluation stage, traditional performance metrics are expanded with a texture-based evaluation framework that provides more human-understandable, context-sensitive insights. Lastly, in the deployment stage, synthetic counterfactual generation and fine-tuning techniques are introduced to mitigate biases in deployed models, enhancing fairness while preserving performance. These contributions address the trustworthiness of ML systems holistically, bridging the gap between low-level computational processes and high-level human understanding. This dissertation advances ML research by providing a comprehensive framework that improves transparency, reliability, and alignment with societal values across the entire machine learning pipeline.Engineering and Applied Sciences - Computer Scienc
Convergent processing of auditory and tactile vibration in the inferior colliculus
Vibrations are ubiquitous in nature, shaping behavior across the animal kingdom. For mammals, mechanical vibrations acting on the body are detected by mechanoreceptors of the skin and deep tissue and processed by the somatosensory system, while sound waves traveling through air are captured by the cochlea and encoded in the auditory system. Here, we report that mechanical vibrations detected by the body’s Pacinian corpuscle neurons, which are unique in their ability to entrain to high-frequency (40-1000 Hz) environmental vibrations, are prominently encoded by neurons in the lateral cortex of the inferior colliculus (LCIC) of the midbrain. Remarkably, most LCIC neurons receive convergent Pacinian and auditory input and respond more strongly to coincident tactile-auditory stimulation than to either modality alone. Moreover, the LCIC is required for behavioral responses to high frequency mechanical vibrations. Thus, environmental vibrations captured by Pacinian corpuscles of the body are encoded in the auditory midbrain to mediate behavior.Medical Science