In this paper, we prove pure point spectrum for a large class of Schrödinger operators over circle maps with conditions on the rotation number going beyond the Diophantine. More specifically, we develop the scheme to obtain pure point spectrum for Schrödinger operators with monotone bi-Lipschitz potentials over orientation-preserving circle homeomorphisms with Diophantine or weakly Liouville rotation number. The localization is uniform when the coupling constant is large enough.

Influenza viruses continually evolve new antigenic variants, through mutations in epitopes of their major surface proteins, hemagglutinin (HA) and neuraminidase (NA). Antigenic drift potentiates the reinfection of previously infected individuals, but the contribution of this process to variability in annual epidemics is not well understood. Here, we link influenza A(H3N2) virus evolution to regional epidemic dynamics in the United States during 1997-2019. We integrate phenotypic measures of HA antigenic drift and sequence-based measures of HA and NA fitness to infer antigenic and genetic distances between viruses circulating in successive seasons. We estimate the magnitude, severity, timing, transmission rate, age-specific patterns, and subtype dominance of each regional outbreak and find that genetic distance based on broad sets of epitope sites is the strongest evolutionary predictor of A(H3N2) virus epidemiology. Increased HA and NA epitope distance between seasons correlates with larger, more intense epidemics, higher transmission, greater A(H3N2) subtype dominance, and a greater proportion of cases in adults relative to children, consistent with increased population susceptibility. Based on random forest models, A(H1N1) incidence impacts A(H3N2) epidemics to a greater extent than viral evolution, suggesting that subtype interference is a major driver of influenza A virus infection ynamics, presumably via heterosubtypic cross-immunity.

Influenza viruses continually evolve new antigenic variants, through mutations in epitopes of their major surface proteins, hemagglutinin (HA) and neuraminidase (NA). Antigenic drift potentiates the reinfection of previously infected individuals, but the contribution of this process to variability in annual epidemics is not well understood. Here, we link influenza A(H3N2) virus evolution to regional epidemic dynamics in the United States during 1997—2019. We integrate phenotypic measures of HA antigenic drift and sequence-based measures of HA and NA fitness to infer antigenic and genetic distances between viruses circulating in successive seasons. We estimate the magnitude, severity, timing, transmission rate, age-specific patterns, and subtype dominance of each regional outbreak and find that genetic distance based on broad sets of epitope sites is the strongest evolutionary predictor of A(H3N2) virus epidemiology. Increased HA and NA epitope distance between seasons correlates with larger, more intense epidemics, higher transmission, greater A(H3N2) subtype dominance, and a greater proportion of cases in adults relative to children, consistent with increased population susceptibility. Based on random forest models, A(H1N1) incidence impacts A(H3N2) epidemics to a greater extent than viral evolution, suggesting that subtype interference is a major driver of influenza A virus infection ynamics, presumably via heterosubtypic cross-immunity.

We are now in the era of millimeter-scale electron microscopy (EM) volumes collected at nanometer resolution. Dense reconstruction of cellular compartments in these EM volumes has been enabled by recent advances in Machine Learning (ML). Automated segmentation methods produce exceptionally accurate reconstructions of cells, but post-hoc proofreading is still required to generate large connectomes free of merge and split errors. The elaborate 3-D meshes of neurons in these volumes contain detailed morphological information at multiple scales, from the diameter, shape, and branching patterns of axons and dendrites, down to the fine-scale structure of dendritic spines. However, extracting these features can require substantial effort to piece together existing tools into custom workflows. Building on existing open-source software for mesh manipulation, here we present "NEURD", a software package that decomposes meshed neurons into compact and extensively-annotated graph representations. With these feature-rich graphs, we automate a variety of tasks such as state of the art automated proofreading of merge errors, cell classification, spine detection, axon-dendritic proximities, and other annotations. These features enable many downstream analyses of neural morphology and connectivity, making these massive and complex datasets more accessible to neuroscience researchers focused on a variety of scientific questions.

Genome-wide association studies (GWAS) have identified hundreds of genetic signals associated with autoimmune disease. The majority of these signals are located in non-coding regions and likely impact cis-regulatory elements (cRE). Because cRE function is dynamic across cell types and states, profiling the epigenetic status of cRE across physiological processes is necessary to characterize the molecular mechanisms by which autoimmune variants contribute to disease risk. We localized risk variants from 15 autoimmune GWAS to cRE active during TCR-CD28 co-stimulation of naïve human CD4+ T cells. To characterize how dynamic changes in gene expression correlate with cRE activity, we measured transcript levels, chromatin accessibility, and promoter-cRE contacts across three phases of naive CD4+ T cell activation using RNA-seq, ATAC-seq, and HiC. We identified ~1200 protein-coding genes physically connected to accessible disease-associated variants at 423 GWAS signals, at least one-third of which are dynamically regulated by activation. From these maps, we functionally validated a novel stretch of evolutionarily conserved intergenic enhancers whose activity is required for activation-induced IL2 gene expression in human and mouse, and is influenced by autoimmune-associated genetic variation. The set of genes implicated by this approach are enriched for genes controlling CD4+ T cell function and genes involved in human inborn errors of immunity, and we pharmacologically validated eight implicated genes as novel regulators of T cell activation. These studies directly show how autoimmune variants and the genes they regulate influence processes involved in CD4+ T cell proliferation and activation.

Early host immunity to acute respiratory infections (ARIs) is heterogenous, dynamic, and critical to an individual's infection outcome. Due to limitations in sampling frequency/timepoints, kinetics of early immune dynamics in natural human infections remain poorly understood. In this nationwide prospective cohort study, we leveraged a Tasso-SST based self-blood collection and stabilization tool (homeRNA) to profile detailed kinetics of the presymptomatic to convalescence host immunity to contemporaneous respiratory pathogens. We enrolled non-symptomatic adults with recent exposure to ARIs who subsequently tested negative (exposed-uninfected) or positive for respiratory pathogens. Participants self-collected blood and nasal swabs daily for seven consecutive days followed by weekly blood collection for up to seven additional weeks. Symptom burden was assessed during each collection. Nasal swabs were tested for SARS-CoV-2 and common respiratory pathogens. 92 longitudinal blood samples spanning the presymptomatic to convalescence phase of eight SARS-CoV-2-infected participants and 40 interval-matched samples from four exposed-uninfected participants were subjected to high-frequency longitudinal profiling of 785 immune genes. Generalized additive mixed models (GAMM) were used to identify temporally dynamic genes from the longitudinal samples and linear mixed models (LMM) were used to identify baseline differences between exposed-infected (n = 8), exposed-uninfected (n = 4), and uninfected (n = 13) participant groups. Between June 2021 - April 2022, 68 participants across 26 U.S. states completed the study and self-collected a total of 691 and 466 longitudinal blood and nasal swab samples along with 688 symptom surveys. SARS-CoV-2 was detected in 17 out of 22 individuals with study-confirmed respiratory infection, of which five were still presymptomatic or pre-shedding, enabling us to profile detailed expression kinetics of the earliest blood transcriptional response to contemporaneous variants of concern. 51% of the genes assessed were found to be temporally dynamic during COVID-19 infection. During the pre-shedding phase, a robust but transient response consisting of genes involved in cell migration, stress response, and T cell activation were observed. This is followed by a rapid induction of many interferon-stimulated genes (ISGs), concurrent to onset of viral shedding and increase in nasal viral load and symptom burden. Finally, elevated baseline expression of antimicrobial peptides were observed in exposed-uninfected individuals. We demonstrated that unsupervised self-collection and stabilization of capillary blood can be applied to natural infection studies to characterize detailed early host immune kinetics at a temporal resolution comparable to that of human challenge studies. The remote (decentralized) study framework enables conduct of large-scale population-wide longitudinal mechanistic studies. This study was funded by R35GM128648 to ABT for in-lab developments of homeRNA and data analysis, a Packard Fellowship for Science and Engineering from the David and Lucile Packard Foundation to ABT, and R01AI153087 to AW.

Robust sampling methods are foundational to inferences using phylogenies. Yet the impact of using contact tracing, a type of non-uniform sampling used in public health applications such as infectious disease outbreak investigations, has not been investigated in the molecular epidemiology field. To understand how contact tracing influences a recovered phylogeny, we developed a new simulation tool called SEEPS (Sequence Evolution and Epidemiological Process Simulator) that allows for the simulation of contact tracing and the resulting transmission tree, pathogen phylogeny, and corresponding virus genetic sequences. Importantly, SEEPS takes within-host evolution into account when generating pathogen phylogenies and sequences from transmission histories. Using SEEPS, we demonstrate that contact tracing can significantly impact the structure of the resulting tree, as described by popular tree statistics. Contact tracing generates phylogenies that are less balanced than the underlying transmission process, less representative of the larger epidemiological process, and affects the internal/external branch length ratios that characterize specific epidemiological scenarios. We also examined real data from a 2007-2008 Swedish HIV-1 outbreak and the broader 1998-2010 European HIV-1 epidemic to highlight the differences in contact tracing and expected phylogenies. Aided by SEEPS, we show that the data collection of the Swedish outbreak was strongly influenced by contact tracing even after downsampling, while the broader European Union epidemic showed little evidence of universal contact tracing, agreeing with the known epidemiological information about sampling and spread. Overall, our results highlight the importance of including possible non-uniform sampling schemes when examining phylogenetic trees. For that, SEEPS serves as a useful tool to evaluate such impacts, thereby facilitating better phylogenetic inferences of the characteristics of a disease outbreak. SEEPS is available at github.com/MolEvolEpid/SEEPS.

Determining the presence and frequency of neural oscillations is essential to understanding dynamic brain function. Traditional methods that detect peaks over 1/f noise within the power spectrum fail to distinguish between the fundamental frequency and harmonics of often highly non-sinusoidal neural oscillations. To overcome this limitation, we define fundamental criteria that characterize neural oscillations and introduce the cyclic homogeneous oscillation (CHO) detection method. We implemented these criteria based on an autocorrelation approach to determine an oscillation's fundamental frequency. We evaluated CHO by verifying its performance on simulated non-sinusoidal oscillatory bursts and validated its ability to determine the fundamental frequency of neural oscillations in electrocorticographic (ECoG), electroencephalographic (EEG), and stereoelectroencephalographic (SEEG) signals recorded from 27 human subjects. Our results demonstrate that CHO outperforms conventional techniques in accurately detecting oscillations. In summary, CHO demonstrates high precision and specificity in detecting neural oscillations in time and frequency domains. The method's specificity enables the detailed study of non-sinusoidal characteristics of oscillations, such as the degree of asymmetry and waveform of an oscillation. Furthermore, CHO can be applied to identify how neural oscillations govern interactions throughout the brain and to determine oscillatory biomarkers that index abnormal brain function.

Researchers have derived many theoretical models for specifying users' insights as they interact with a visualization system. These representations are essential for understanding the insight discovery process, such as when inferring user interaction patterns that lead to insight or assessing the rigor of reported insights. However, theoretical models can be difficult to apply to existing tools and user studies, often due to discrepancies in how insight and its constituent parts are defined. This article calls attention to the consistent structures that recur across the visualization literature and describes how they connect multiple theoretical representations of insight. We synthesize a unified formalism for insights using these structures, enabling a wider audience of researchers and developers to adopt the corresponding models. Through a series of theoretical case studies, we use our formalism to compare and contrast existing theories, revealing interesting research challenges in reasoning about a user's domain knowledge and leveraging synergistic approaches in data mining and data management research.