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Quantitative Aspects of Arakelov Theory in Arithmetic Dynamics
No full textLet be a number field and \vphi: \bb{P}^m \to \bb{P}^m be an endomorphism of degre that is defined over . Let \h_{\vphi}: \bb{P}^m(\ovl{K}) \to \bb{R}_{\geq 0} be the canonical height associated to \vphi. Given a sequence (x_n) \in \bb{P}^m(\ovl{K}), we say that it is generic if no hypersurface contains infinitely many 's. Yuan \cite{Yua08}, using Arakelov theory, proves that given a generic sequence of points with \h_{\vphi}(x_n) \to 0 and a place , the Galois orbits of will equidistribute to the equilibrium measure \mu_{\vphi,v}.
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The aim of this thesis is to prove a quantitative version of Yuan's theorem for archimedean places. Given a smooth function f: \bb{P}^m(\bb{C}) \to \bb{R} and an \eps > 0, we bound the degree of a hypersurface Z(f,\eps) and a constant such that
\left|\frac{1}{|F_x|} \sum_{y \in F_x} f(y) - \int f d \mu_{\vphi,v} \right| \eps
holds for all x \not \in Z(f,\eps) and \h_{\vphi}(x) \delta, where F_x = \Gal(\ovl{K}/K) \cdot x is the Galois orbit of . This upper bound on \deg Z(f,\eps) tells us how generic has to be.
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There are two main new ingredients in the proof which follows Yuan's approach. The first is a quantitative form of the asymptotic expansion of the Bergman kernel, first established by Tian \cite{Tian90}, and the second is a construction of a ``dynamical" basis of polynomials due to Looper \cite{Loo24}. As an application, for \bb{P}^2 or smooth projective surfaces in general, we are able to deduce an exponential rate of convergence of -periodic points \Per_n to the equilibrium measure. A more arithmetic application is that we are able to deduce an exponential growth of the degree [K(\Per_n):K] in terms of , generalizing results due to Baker \cite{Bak06} in dimension one.Mathematic
Kneading the Dough Together: The Application of Strategic Empathy Among American National Security Professionals
No full textThe term “strategic empathy” in national security affairs sounds appealing. Ask practitioners what it means, though, and they will all provide a different answer. Is it Sun Tzu’s “know your enemy?” Is it a tool for Machiavellian manipulation? Is it morally superior to empathize with the adversary? Is it ethically bereft to use that knowledge intentionally to gain advantage? These are questions that national security practitioners wrestle with when attempting to pin down a buzzword in a beltway. Yet, humanity’s history of conflict suggests that there may be a place for strategic empathy to create improved outcomes for national security practitioners when it is employed vis-à-vis a foreign counterpart. This research investigates how national security practitioners can effectively employ strategic empathy to create improved national security outcomes.
Six national security practitioners interviewed for this research shared their lived experiences engaging empathically with foreign counterparts through phenomenological interviews. The qualitative, interdisciplinary data they provided resulted in a process for how to conduct strategic empathy in two phases, analysis and implementation. Woven among the process are themes and best practices related to imagination, dialogue, intersubjectivity, and value salience. The strategic empathy process resulting from this research, along with its best practices, represents a starting hypothesis for national security practitioners to test during their own professional experiences, and a new venture for additional research.Extension Studie
Exploring Interfacial Phenomena During the Electrochemical Oxygen Evolution Reaction
No full textHydrogen plays a critical role in industrial processes such as chemical manufacturing, petroleum refining, and fertilizer synthesis—industries that together contribute approximately 4% of global carbon emissions. These industries currently utilize hydrogen produced via the emissions-intensive steam methane reforming (SMR) process, but production of green hydrogen via electrochemical water-splitting is a promising avenue for wide-scale decarbonization. The production of abundant green hydrogen also has the potential to unlock new use-cases including H2 as a direct iron reductant, H2 as an energy carrier, or H2 as a fuel precursor to decarbonize steel production, shipping, and aviation. However, the emergence of green hydrogen relies upon the development of improved water-splitting catalysts and electrolyzers that exhibit better energy efficiencies (related to the electrochemical overpotential) and lower costs (related to the catalyst materials). Water-splitting involves both the cathodic hydrogen evolution reaction (HER) and the anodic oxygen evolution reaction (OER). Of these, improvement of the OER is particularly challenging as it is a kinetically hindered process requiring four electron transfers and often involves operating conditions which corrode and destabilize earth-abundant catalyst materials.
Improvement of OER catalysts (OEC’s) and overall electrolyzer systems requires a detailed understanding of processes occurring at the electrode-electrolyte interface and further development of catalyst materials, electrolyzer systems, and techniques for studying the electrochemical interface. This thesis explores multiple phenomena occurring at the electrode-electrolyte interface including (1) the formation of local pH gradients, (2) catalyst surface deconstruction, and (3) fundamental catalyst-water interactions, as well as highlights the development of novel techniques for examining catalysts in operando. First, an acid-stable catalyst was used to investigate the formation of locally acidic environments during OER under varied operating conditions. These experiments culminated in the development of a model for quantifying local pH gradients during OER. Secondly, mixed-metal OER catalyst materials with improved OER activity were developed and the origins of activity enhancement were determined. These materials, comprised of rare-earth cations incorporated into transition-metal oxide host materials, revealed increased surface oxide deconstruction, leading to increased active site density. Surface oxide deconstruction, determined here to be the cause of increased activity, is likely a widespread phenomenon, relevant in many OEC systems. Thirdly, a surface-sensitive X-ray technique, ambient-pressure X-ray photoelectron spectroscopy (APXPS), was utilized to explicitly study the solid-water interface of mixed-metal oxide catalyst films. Interfacial catalyst-water studies reveal that lanthanide incorporation results in an increase in partially negative surface oxygen species. The mixed-metal catalysts have multiple protonation states, resulting in a buffering effect which temporarily prolongs mixed-metal catalyst operation in acidic conditions. Finally, this thesis culminates in the development of a proton-exchange-membrane (PEM) electrolyzer assembly incorporating the mixed-metal catalyst materials developed herein. The advanced technique of operando time-resolved APXPS was utilized to examine mixed-metal OEC operation in an industrial-type electrolyzer system for the first time.
This dissertation includes studies ranging from the elucidation of fundamental surface interactions to the engineering of electrolyzer assemblies for advanced characterization. These projects have all furthered our understanding of the OER, enabling future advancements in electrolyzer technologies.Chemistry and Chemical Biolog
Involvement of Transient Receptor Potential Ankyrin 1 (TRPA1) in Inflammatory Dental Pulp Pain
No full textTRPA1 is a cation channel involved in pain detection and inflammatory signaling in
multiple cell types within the dental pulp. However, its role in pulpitis remains unclear. This
study investigates the contribution of TRPA1 to dental pain and pain-like behaviors in a mouse
model. Wild-type (WT) and TRPA1 knockout (KO) mice underwent pulp exposure, followed
by multiple applications of either LPS or saline forming four experimental groups. Then pulp cap
material placed. Pain-like behaviors were assessed on days 1, 3, and 7 post-op using the Nesting
Test, Mouse Grimace Scale (MGS), and Von Frey Filament Test (VFF). Additionally, c-Fos
expression in the trigeminal nucleus of the brainstem was quantified to assess neural activation.
LPS administration in wild-type (WT) mice resulted in a significant increase in pain-
like behaviors compared to TRPA1 knockout (KO) mice (p 0.05), underscoring the role of
TRPA1 in inflammatory pain responses. The most pronounced differences were observed
between WT and KO groups under both LPS and saline treatment. However, differences
between LPS and saline treatments within each genotype were minimal, and the absence of
TRPA1 more substantially attenuated behavioral responses. Consistent with the behavioral data,
c-Fos expression was significantly elevated in WT mice but markedly reduced in KO-LPS mice,
indicating decreased neuronal activation in the trigeminal nucleus in the absence of TRPA1.
These findings demonstrate that TRPA1 plays a critical role in activating the
nociceptive dental pain and triggering pain like behaviors in mice. Further investigations are
needed to explore the therapeutiEndodontic
Hematopoietic stem cell egress and mobilization from the stem cell niche
No full textHematopoietic stem cells (HSCs) produce all mature blood cells throughout the entire life of an organism. HSCs reside in a complex microenvironment, or ‘niche’, where they receive diverse signals that regulate their function. Dysregulation of HSC-intrinsic or extrinsic signals from the niche can lead to hematologic malignancies. To treat hematological disorders, patients undergo conditioning to release or mobilize malignant HSCs from their niche, so that newly transplanted healthy HSCs can colonize the emptied niche. However, traditional myeloablative conditioning strategies for HSCs are often toxic and result in long-term complications. A thorough understanding of HSC egress and mobilization will help develop a safer mobilization-based conditioning regimen for patients. Here, I leveraged the advantages of zebrafish to visualize the release of HSCs, understand mechanisms of HSC egress from the embryonic niche, and target these mechanisms to mobilize HSCs from the adult niche. I created a transgenic line with inducible expression of zebrafish granulocyte colony stimulating factor (G-CSF), the most widely used mobilizing agent, and performed high-resolution confocal microscopy to capture mobilized HSCs in circulation. G-CSF successfully mobilized HSCs from the embryonic niche into circulation, and neutrophils and macrophages were not required for the G-CSF induced mobilization in embryos. Adopting this live-imaging technique, I performed an in vivo live imaging-based chemical screen and identified three putative mobilizing agents in zebrafish embryos, from which one compound, doxepin, successfully mobilized HSCs from the adult hematopoietic niche. Single cell RNA-sequencing of the embryonic niche sinusoidal endothelial cells revealed a downregulation of cathepsin La during development. Morpholino-induced knockdown and chemical inhibition revealed cathepsin La as a potential regulator of HSC maintenance and development of sinusoids in the embryonic niche. Single cell transcriptomics analysis also revealed scavenging receptor-mediated endocytosis as a putative regulator of HSC retention, and disrupting it through administration of dextran sulfate, an inhibitor of scavenger-receptor mediated endocytosis, mobilized HSCs from the adult hematopoietic niche. Lastly, the transcriptomics data also suggested the VCAM1/VLA-4 axis as a regulator of HSC mobilization and chemically or genetically disrupting this interaction mobilized HSCs from the adult hematopoietic niche. Together, this work identifies multiple mechanisms that regulate HSC egress from the hematopoietic niche. These mechanisms can be therapeutically targeted to develop a safe mobilization-based conditioning regimen for HSC transplantation.Medical Science
Insights into ubiquitylation and arginine methylation by HUWE1 and PRMT5
No full textPost-translational modifications allow diversification of proteins beyond the canonical 20 amino acids. These modifications, such as ubiquitylation and methylation, play key roles in mammalian development and disease physiology, and thus constitute a major class of therapeutic targets in human disease. However, developing therapeutics against these enzymes requires a clear understanding of the molecular mechanisms and structural underpinnings of their function.
HUWE1 is a ~3,900 amino acid HECT ligase responsible for regulating a plethora of cellular processes, ranging from protein orphan quality control to apoptosis and DNA damage response. We solved the cryogenic electron microscopy (cryo-EM) structure of full-length HUWE1, revealing a solenoid ring structure with accessory domains located above or below the ring. Reported patient mutations dispersed along the entirety of the HUWE1 ring architecture show hypomorphic effects, providing a molecular understanding of patient mutations outside of the active site. The structure of HUWE1 in complex with its substrate, DDIT4, illuminates how the armadillo repeat regions of HUWE1 can capture both peptide and phosphorylated substrate degrons and provides a basis for HUWE1 substrate recognition.
PRMT5 is a methyltransferase that regulates a large number of cellular pathways through methylation of substrates such as histone tails and spliceosome proteins. PRMT5 functions as a hetero-octamer with its obligate binding partner, WDR77, and uses substate adaptors pICln and RIOK1 to recruit and methylate the C-terminal tails of SmD1 and RPS10, respectively. We show that substrate adaptors compete for binding to PRMT5 and through cryo-EM, we find that substrate adaptor and substrate are bound to PRMT5 through two peptide motifs. Substrate adaptors, while not necessary in vitro, help enhance methylation. These studies illuminate the biochemical nature of PRMT5 interactors and the importance of peptide motifs in regulating PRMT5 activity.
Finally, we utilize proteomics-based approaches and in silico structure prediction to discover novel PRMT5 interactors. We find that ZNRD2 is a novel interactor of PRMT5 that utilizes its N-terminal disordered region to bind to the same interface where the canonical substrate adaptors, pICln and RIOK1, bind. ZNRD2 interacts with incompletely assembled CCT subunits, and methylation of CCT7 by PRMT5 prevents binding with the E3 ligase APPBP2. Collectively, these findings uncover novel PRMT5 interactors and pave the way towards expanding our understanding of PRMT5 biology.
Altogether, we provide unprecedented structural and mechanistic insight into the architecture of the full-length HECT ligase HUWE1, how patient mutations affect multiple aspects of HUWE1 ligase activity, and how HUWE1 utilizes its various auxiliary domains to recruit and ubiquitylate substrates. Next, we determine the biochemical mechanisms of substrate adaptor and substrate recruitment to the PRMT5 methylosome, showing that substrate adaptors, while bound flexibly to PRMT5, nonetheless function to enhance substrate methylation by acting as an additional anchor point. Leveraging the structural insights gained from PRMT5, we discover ZNRD2 as a novel interactor with PRMT5. ZNRD2 interacts with unassembled CCT subunits, implicating a role as a potential substrate adaptor for CCT7 methylation by PRMT5. Methylation of CCT7 by PRMT5 further abrogates binding to the APPBP2 E3 ligase, This body of work sheds light onto how various enzymes responsible for depositing different PTMs in the context of substrate recognition and PTM catalysis, which may pave the framework for developing targeted therapeutics against these enzymes, which are both frequently dysregulated in human disease.Medical Science
Drugs and Deals: Understanding Biopharmaceutical Venture Capital Performance and Behavior
No full textVenture capital plays a critical role in funding the production of life sciences innovation and life-saving therapies in young biopharmaceutical companies. However, many venture capital investors perceive investments in biopharmaceutical companies as risky and unattractive, leading to less capital being allocated towards them. Biopharmaceutical venture capital performance has been sparsely studied in the academic literature, with limited empirical evidence on this underperformance and strategies to mitigate it. I analyze a dataset from Preqin of recent venture capital funds and deals to find that biopharmaceutical funds underperform information technology and diversified healthcare funds. However, their returns are on par with those of diversified funds, suggesting investor concerns around biopharmaceutical investments may be overstated. I also find that the realized returns of biopharmaceutical funds are significantly lower than the interim returns, implying pre-liquidation valuations may be inflated. Additionally, my analysis reveals that biopharmaceutical funds participate in fewer deals, have larger funds, co-invest more, contribute more per deal, and prefer early-stage and mid-stage investments. I design a Monte Carlo simulation for biopharmaceutical investing which reveals that higher returns are correlated with more deals, smaller funds, more co-investing, less deal contributions, and a preference for early-stage and mid-stage investments. This discrepancy between current biopharmaceutical venture capital strategy and optimal strategy may indicate that venture capital investors can improve their returns by modifying their strategy, encouraging further investment in the sector.Applied Mathematic
Macroevolution of Gene Expression in Passerine Birds
No full textA key objective of evolutionary biology is to decipher the molecular mechanisms driving phenotypic diver-
sity. Whereas genomes provide the informational foundation of life, gene expression compromises how that
information is used to define the biology of an organism. As part of the biological cascade from information
to function, gene expression dynamics play a critical role in influencing the evolutionary trajectory of diver-
sity. It is therefore crucial to the understanding of evolutionary processes that we investigate how gene ex-
pression evolves on a macroevolutionary level and what role it plays in life history variation. Advancements in
technologies such as RNA-Seq and evolving computational tools have enabled comparative transcriptomics
research to blossom in recent years with studies steadily gaining in species count and tissue scope. To elucidate
the role of gene expression in macroevolutionary dynamics, my dissertation investigates interspecific differ-
ences in gene expression and their connection to life history trait evolution using passerine birds as a focal
system.
I provide a review of the historical progression of transcriptomic technology, the challenges facing tran-
scriptomic researchers, and the current landscape of comparative transcriptomics. I discuss the vital role of
RNA preservation in museum collections and provide an original analysis of over 300 museum-preserved
tissue samples demonstrating that RNA quality was not significantly affected by preservation method, col-
lection method, or tissue type, underscoring the suitability of these samples for transcriptomic research. I
further discuss recent technological developments, such as single cell sequencing and multi-omic data integra-
tion, which I expect to impact the future directions of comparative transcriptomic research.
Empirically, I investigate the macroevolutionary dynamics of gene expression in the two major clades of passerines: oscines and suboscines. For this analysis, I sequenced 327 transcriptomes from six key tissues
(heart, pectoralis major, liver, brain, eye, and testis) across 22 passerine species and two outgroup species.
Using this dataset, I ask which macroevolutionary models – specifically the Brownian motion and Ornstein–
Uhlenbeck process – best fit the patterns of gene expression observed in these clades and what genes are dif-
ferentially expressed between oscines and suboscines. My findings indicate that most genes’ expression are
best fit by a Brownian motion model of evolution with only a small selection best fit by the Ornstein Uhlen-
beck process indicating the strong role of phylogenetic structure or drift in between-clade gene expression
evolution dynamics. I further find that differential expression between avian clades is enriched for genes with
broad, systemic roles rather than tissue-specific functions.
Expanding on this, I examine the relationship between gene expression evolution and life history traits by
interrogating the correlation of differential expression with the key avian traits of diet and migration. My
results from evolutionary model fit analyses indicate that migratory strategy significantly influences gene
expression in the brain whereas diet had a broader impact across multiple tissues, strongly shaping gene ex-
pression in the brain, heart, liver, and pectoralis major. Similarly, the results from a differential expression
analyses indicated that, of the tissues studied, gonad and muscle were most heavily impacted by migratory
strategy whereas brain and eye were most heavily associated with diet. Similar to the between clade analysis,
GO term enrichment revealed consistent terms across tissue types indicating an important role in differential
expression of broad, systematic roles. The findings from my dissertation enhance our understanding of gene
expression evolution and provide valuable insights into how life history traits correlate with gene expression
across species.Biology, Organismic and Evolutionar
Challenges to Donating Baked Goods to Food Banks
No full textCalifornia is tackling the disparity between landfilled edible food and food
insecurity. The state’s Senate Bill (SB) 1383 requires mandatory donation of edible food
for certain large food companies including grocery stores and distributors. Food donors
have faced barriers to donating while hunger relief organizations have experienced
challenges to accept additional food donations under SB 1383. Food donation barrier
theory has focused on challenges for all types of food categories without going into
specific baked goods barriers. I applied general food donation barrier theory to examine
the most severe barriers to donating and accepting baked goods to inform the
prioritization of interventions and food donation policy. For baked goods donors, the
barriers are in the categories of logistics, company culture, and nonprofit relationships.
For food banks, I analyzed the barriers in the categories of infrastructure, labor, product
desirability, and food donor relations. Baked goods categories were broken down by
sweet and savory as well as whole grain and non-whole grain to evaluate donation
preference based on nutritional quality.
My overarching research question is: What are the challenges and solutions of
forming successful partnerships between baked goods donors and food banks? I used a
mixed methods approach of collecting both quantitative data through surveys and
qualitative data through interviews and survey free response sections. Participants
included staff that oversee donation programs at the food banks and baked goods
companies. The survey questions included impacts of SB 1383, barriers to donating, and
nutritional quality of baked goods. After respondents completed the survey, they were
interviewed to expand on the barriers and share solutions. The semi-structured interviews
were transcribed, coded, and utilized in a thematic analysis with the survey responses in
the barrier categories, impacts of food donation, and SB 1383.
The results indicated that not all baked goods are the same when it comes to
donating as food banks and baked goods donors found it easier to donate and accept
savory over sweet baked goods and whole grain baked goods were also preferable. Baked
goods donors found that sweet baked goods were beneficial for nonprofits that are not
hunger relief organizations to provide desserts at events and fundraisers. Food banks
desired more savory baked goods to be used for meals, while sweets were seen as a
donation in moderation or desired seasonally during holiday times.
The top barriers for baked goods donors were finding a nonprofit to accept their
baked goods donations, and needing to prioritize business needs first before the donation
program. The most predominant barriers for food banks were lack of infrastructure, labor
shortage, and food donor relations. Both food banks and baked goods donors found that
one of the most challenging issues was the high spoilage rate of baked goods.
Baked goods donors can be better partners to food banks by providing funding,
implementing employee volunteer programs, having leadership prioritize donation
efforts, proactively engaging in open communication with food banks, and offering
desirable donations that are not close to spoiling. Recommendations for improved
implementation of SB 1383 include consideration of nutrition, preventive measures for
donation dumping, additional funding to food banks, and increased education to food
donors.Extension Studie
Frontiers in Neuro-Epidemiology: Advancing Methods Across Diverse Modalities of Data
No full textDefined as the study of the distribution and risk factors of neurological disorders, Neuro-epidemiology has been a widely evolving field for the last few decades. The earliest epidemiological studies of neurological disorders attempted to explore often poorly understood neurological manifestation of various conditions. Due to the rather blunt nature of scientific tools in earlier times, most preliminary studies limited themselves to analyzing cross-sectional counts and identifying crude risk factors such as age, sex, and location. Later, there was value seen in the utilizing longitudinal cohorts to better appreciate the temporal occurrences of many diseases including those of neurological origin. While limited in certain aspects, such data provided an additional means of appreciating the development of neurological disease in populations overtime with respect to measured variables.
While the epidemiological study of neurological disease evolved, the scientific community oversaw an exponential growth in medical technology and practice including radiological imaging, genotyping, human biomarker assays, and robust diagnostic criteria. Such technological advancements enhanced the ability to study the etiological pathways of many neurological disorders from granular biochemical pathways to neuroimaging aberrations. These tools also provided epidemiologists greater ability to explore their once blunt risk factor associations in finer detail within large populations. The recent explosion of genetic, proteomic, imaging data in large cohorts in conjunction with developments in predictive modeling, such as machine learning, and causal inference, particularly in the field of statistical genetics, have presented a unique opportunity to interrogate new questions.
Considering such developments, this thesis explores the cutting edge of the various subfields within modern neuro-epidemiology to answer some of the most pertinent questions in the field using most robust and innovative methods.
In Chapter One, we observe the continued relevance of population level data and analyses by determining the trends in acute ischemic stroke presentations and treatments during the 2020 Coronavirus pandemic. In Chapter Two, we leverage geometric machine learning methods in a neuroimaging dataset to explore how we can improve the generalizability of diagnostic computer vision models across various neurological disease. In Chapter Three, we utilize population level genetic and proteomic data in various cohorts to understand possible interaction between protein levels and neuroimaging phenotypes with an eye towards understanding implicated biological pathways and disease phenotypes.Population Health Science