Exploring Diagonals in the Calkin-Wilf Tree

For centuries, people have been interested in patterns. Even in that which appears random, humans have been trying to understand the underlying order of things. Mathematicians throughout time have studied many phenomena, including infinite sequences of numbers and have been able, at times, to see structure. Many have found the satisfaction, even joy, of discovering patterns in sequences. A typical way to describe this is by a recursive formula. A recursive definition defines a term in the sequence using the previous terms in the sequence. Even more satisfying than a recursive formula is a closed formula. With this, one can find the number at any position in the sequence. A closed formula is like a locksmith cutting a master key for every lock in a building

Hilbert Space Theory and Applications in Basic Quantum Mechanics

We explore the basic mathematical physics of quantum mechanics. Our primary focus will be on Hilbert space theory and applications as well as the theory of linear operators on Hilbert space. We show how Hermitian operators are used to represent quantum observables and investigate the spectrum of various linear operators. We discuss deviation and uncertainty and briefly suggest how symmetry and representations are involved in quantum theory

The design and implementation of a CT and MRI compatible multipurpose phantom: testing the effectiveness of multiple contrast material concentrations for CTA

Thesis (M.A.)--Boston UniversityThe purpose of our study was to determine if it is possible to acquire CTA images of small vessels using lower concentrations of iodinated contrast material without substantially diminishing image quality. A custom designed multi-purpose phantom was used to test multiple concentrations of iodinated contrast material using low x-ray tube voltage experimental CTA protocols. A single scan using 120 kVp and Noise Index at a setting of 23 was compared to scans using 100 kVp and 80 kVp tube voltages and Noise Index settings of 23, 21, and 19. Lower tube voltages did produce increased attenuation in contrast material regions of interest, however, increased image noise caused the CNR and FOM for the currently established imaging protocol to be superior to the experimental protocols tested. Despite minor decreases in image quality, the experimental imaging protocols were able to produce images utilizing significantly decrease levels of radiation dose. Given minor changes in imaging quality, the ability to substantially reduce dose while maintaining a satisfactory level of image quality was positive. Further experimentation with low kVp CTA imaging utilizing additional NI settings is warranted to measure possible further improvements in image quality while still maintaining low radiation dose

Cellular mechanisms that establish HIV-1 latency in CD4+ T cells and the potential for their manipulation as a therapeutic strategy

Human Immunodeficiency Virus 1 (HIV-1) remains a significant public health concern due to the lack of a cure. In spite of anti-retroviral therapies, HIV-1 persists within infected cells as integrated transcriptionally silent proviruses. Re-activation after therapy interruption results in new HIV-1 replication. Attempts to clear this reservoir through the use of latency reversing agents by targeting cellular mechanisms that maintain HIV-1 in a latent state have been unsuccessful. In addition, subsets of latently infected cells exist within the reservoir that display differential capacities for provirus induction. In order to understand the nature of the reservoir and manipulate it therapeutically, more knowledge is needed regarding factors that bias a virus towards latency or replication at the time of infection. Because multiple mechanisms that regulate HIV-1 transcription, including chromatin remodeling, transcription factor activation and polymerase pausing, are regulated by the T cell receptor (TCR), I hypothesized that signaling at the time of infection determines proviral fate. I transduced Jurkat cell lines and primary CD4+ T cells with chimeric antigen receptors (CARs) that mimicked signaling from the TCR. These CARs spanned a 3-log range of binding affinities for their ligand, providing a tunable model. High levels of TCR stimulation during infection biased cells towards productive replication and the formation of an inducible latent reservoir. Examination of the mechanisms downstream from TCR signaling revealed that robust cellular activation led to a release of the repressor Negative Elongation Factor from the paused RNA Polymerase II, facilitating transcriptional elongation. Because signaling determined the presence of repressive factors, I sought to manipulate the balance between latency and expression through recruitment of repressors to the HIV-1 provirus using a nuclease-deficient CRISPR Associated Protein 9 fused to a Krüppel Associated Box Domain. I screened a pool of guide RNAs that mediated transcriptional repression of HIV-1. Our lab discovered that guides bound to the HIV-1 Long Terminal Repeat prevented viral re-activation in an integrated cell model of HIV-1 latency. The research presented here confirms my hypothesis that signals during infection have prolonged effects on latency reversal. I provide evidence that manipulation of these mechanisms represent therapeutic targets for cure efforts

Mimicking non-ideal instrument behavior for hologram processing using neural style translation

Holographic cloud probes provide unprecedented information on cloud particle density, size and position. Each laser shot captures particles within a large volume, where images can be computationally refocused to determine particle size and shape. However, processing these holograms, either with standard methods or with machine learning (ML) models, requires considerable computational resources, time and occasional human intervention. ML models are trained on simulated holograms obtained from the physical model of the probe since real holograms have no absolute truth labels. Using another processing method to produce labels would be subject to errors that the ML model would subsequently inherit. Models perform well on real holograms only when image corruption is performed on the simulated images during training, thereby mimicking non-ideal conditions in the actual probe (Schreck et. al, 2022). Optimizing image corruption requires a cumbersome manual labeling effort. Here we demonstrate the application of the neural style translation approach (Gatys et. al, 2016) to the simulated holograms. With a pre-trained convolutional neural network (VGG-19), the simulated holograms are ``stylized'' to resemble the real ones obtained from the probe, while at the same time preserving the simulated image ``content'' (e.g. the particle locations and sizes). Two image similarity metrics concur that the stylized images are more like real holograms than the synthetic ones. With an ML model trained to predict particle locations and shapes on the stylized data sets, we observed comparable performance on both simulated and real holograms, obviating the need to perform manual labeling. The described approach is not specific to hologram images and could be applied in other domains for capturing noise and imperfections in observational instruments to make simulated data more like real world observations.Comment: 23 pages, 9 figure

Final Technical Report Power through Policy: "Best Practices" for Cost-Effective Distributed Wind

Power through Policy: 'Best Practices' for Cost-Effective Distributed Wind is a U.S. Department of Energy (DOE)-funded project to identify distributed wind technology policy best practices and to help policymakers, utilities, advocates, and consumers examine their effectiveness using a pro forma model. Incorporating a customized feed from the Database of State Incentives for Renewables and Efficiency (DSIRE), the Web-based Distributed Wind Policy Comparison Tool (Policy Tool) is designed to assist state, local, and utility officials in understanding the financial impacts of different policy options to help reduce the cost of distributed wind technologies. The project's final products include the Distributed Wind Policy Comparison Tool, found at www.windpolicytool.org, and its accompanying documentation: Distributed Wind Policy Comparison Tool Guidebook: User Instructions, Assumptions, and Case Studies. With only two initial user inputs required, the Policy Tool allows users to adjust and test a wide range of policy-related variables through a user-friendly dashboard interface with slider bars. The Policy Tool is populated with a variety of financial variables, including turbine costs, electricity rates, policies, and financial incentives; economic variables including discount and escalation rates; as well as technical variables that impact electricity production, such as turbine power curves and wind speed. The Policy Tool allows users to change many of the variables, including the policies, to gauge the expected impacts that various policy combinations could have on the cost of energy (COE), net present value (NPV), internal rate of return (IRR), and the simple payback of distributed wind projects ranging in size from 2.4 kilowatts (kW) to 100 kW. The project conducted case studies to demonstrate how the Policy Tool can provide insights into 'what if' scenarios and also allow the current status of incentives to be examined or defended when necessary. The ranking of distributed wind state policy and economic environments summarized in the attached report, based on the Policy Tool's default COE results, highlights favorable market opportunities for distributed wind growth as well as market conditions ripe for improvement. Best practices for distributed wind state policies are identified through an evaluation of their effect on improving the bottom line of project investments. The case studies and state rankings were based on incentives, power curves, and turbine pricing as of 2010, and may not match the current results from the Policy Tool. The Policy Tool can be used to evaluate the ways that a variety of federal and state policies and incentives impact the economics of distributed wind (and subsequently its expected market growth). It also allows policymakers to determine the impact of policy options, addressing market challenges identified in the U.S. DOE's '20% Wind Energy by 2030' report and helping to meet COE targets. In providing a simple and easy-to-use policy comparison tool that estimates financial performance, the Policy Tool and guidebook are expected to enhance market expansion by the small wind industry by increasing and refining the understanding of distributed wind costs, policy best practices, and key market opportunities in all 50 states. This comprehensive overview and customized software to quickly calculate and compare policy scenarios represent a fundamental step in allowing policymakers to see how their decisions impact the bottom line for distributed wind consumers, while estimating the relative advantages of different options available in their policy toolboxes. Interested stakeholders have suggested numerous ways to enhance and expand the initial effort to develop an even more user-friendly Policy Tool and guidebook, including the enhancement and expansion of the current tool, and conducting further analysis. The report and the project's Guidebook include further details on possible next steps. NREL Report No. BK-5500-53127; DOE/GO-102011-3453

Evidence of potential bias in a comparison of beta blockers and calcium channel blockers in patients with chronic obstructive pulmonary disease and acute coronary syndrome: results of a multinational study

OBJECTIVES: A number of observational studies have reported that, in patients with chronic obstructive pulmonary disease (COPD), beta blockers (BBs) decrease risk of mortality and COPD exacerbations. To address important methodological concerns of these studies, we compared the effectiveness and safety of cardioselective BBs versus non-dihydropyridine calcium channel blockers (non-DHP CCBs) in patients with COPD and acute coronary syndromes (ACS) using a propensity score (PS)-matched, active comparator, new user design. We also assessed for potential unmeasured confounding by examining a short-term COPD hospitalisation outcome. SETTING AND PARTICIPANTS: We identified 22 985 patients with COPD and ACS starting cardioselective BBs or non-DHP CCBs across 5 claims databases from the USA, Italy and Taiwan. PRIMARY AND SECONDARY OUTCOME MEASURES: Stratified Cox regression models were used to estimate HRs for mortality, cardiovascular (CV) hospitalisations and COPD hospitalisations in each database after variable-ratio PS matching. Results were combined with random-effects meta-analyses. RESULTS: Cardioselective BBs were not associated with reduced risk of mortality (HR, 0.90; 95% CI 0.78 to 1.02) or CV hospitalisations (HR, 1.06; 95% CI 0.91 to 1.23), although statistical heterogeneity was observed across databases. In contrast, a consistent, inverse association for COPD hospitalisations was identified across databases (HR, 0.54; 95% CI 0.47 to 0.61), which persisted even within the first 30 days of follow-up (HR, 0.55; 95% CI 0.37 to 0.82). Results were similar across a variety of sensitivity analyses, including PS trimming, high dimensional-PS matching and restricting to high-risk patients. CONCLUSIONS: This multinational study found a large inverse association between cardioselective BBs and short-term COPD hospitalisations. The persistence of this bias despite state-of-the-art pharmacoepidemiologic methods calls into question the ability of claims data to address confounding in studies of BBs in patients with COPD

In Utero Exposures, Infant Growth, and DNA Methylation of Repetitive Elements and Developmentally Related Genes in Human Placenta

BACKGROUND: Fetal programming describes the theory linking environmental conditions during embryonic and fetal development with risk of diseases later in life. Environmental insults in utero may lead to changes in epigenetic mechanisms potentially affecting fetal development. OBJECTIVES: We examined associations between in utero exposures, infant growth, and methylation of repetitive elements and gene-associated DNA in human term placenta tissue samples. METHODS: Placental tissues and associated demographic and clinical data were obtained from subjects delivering at Women and Infants Hospital in Providence, Rhode Island (USA). Methylation levels of long interspersed nuclear element-1 (LINE-1) and the Alu element AluYb8 were determined in 380 placental samples from term deliveries using bisulfite pyrosequencing. Genomewide DNA methylation profiles were obtained in a subset of 184 samples using the Illumina Infinium HumanMethylation27 BeadArray. Multiple linear regression, model-based clustering methods, and gene set enrichment analysis examined the association between birth weight percentile, demographic variables, and repetitive element methylation and gene-associated CpG locus methylation. RESULTS: LINE-1 and AluYb8 methylation levels were found to be significantly positively associated with birth weight percentile (p = 0.01 and p \u3c 0.0001, respectively) and were found to differ significantly among infants exposed to tobacco smoke and alcohol. Increased placental AluYb8 methylation was positively associated with average methylation among CpG loci found in polycomb group target genes; developmentally related transcription factor binding sites were overrepresented for differentially methylated loci associated with both elements. CONCLUSIONS: Our results suggest that repetitive element methylation markers, most notably AluYb8 methylation, may be susceptible to epigenetic alterations resulting from the intrauterine environment and play a critical role in mediating placenta function, and may ultimately inform on the developmental basis of health and disease

Carina OB Stars: X-ray Signatures of Wind Shocks and Magnetic Fields

The Chandra Carina Complex contains 200 known O- and B type stars. The Chandra survey detected 68 of the 70 O stars and 61 of 127 known B0-B3 stars. We have assembled a publicly available optical/X-ray database to identify OB stars that depart from the canonical Lx/Lbol relation, or whose average X-ray temperatures exceed 1 keV. Among the single O stars with high kT we identify two candidate magnetically confined wind shock sources: Tr16-22, O8.5 V, and LS 1865, O8.5 V((f)). The O4 III(fc) star HD 93250 exhibits strong, hard, variable X-rays, suggesting it may be a massive binary with a period of >30 days. The visual O2 If* binary HD 93129A shows soft 0.6 keV and hard 1.9 keV emission components, suggesting embedded wind shocks close to the O2 If* Aa primary, and colliding wind shocks between Aa and Ab. Of the 11 known O-type spectroscopic binaries, the long orbital-period systems HD 93343, HD 93403 and QZ Car have higher shock temperatures than short-period systems such as HD 93205 and FO 15. Although the X-rays from most B stars may be produced in the coronae of unseen, low-mass pre-main-sequence companions, a dozen B stars with high Lx cannot be explained by a distribution of unseen companions. One of these, SS73 24 in the Treasure Chest cluster, is a new candidate Herbig Be star.Comment: To be published in a special issue of the Astrophysical Journal Supplement on the Chandra Carina Complex Projec

Activation of Latent HIV Using Drug-Loaded Nanoparticles

Antiretroviral therapy is currently only capable of controlling HIV replication rather than completely eradicating virus from patients. This is due in part to the establishment of a latent virus reservoir in resting CD4+ T cells, which persists even in the presence of HAART. It is thought that forced activation of latently infected cells could induce virus production, allowing targeting of the cell by the immune response. A variety of molecules are able to stimulate HIV from latency. However no tested purging strategy has proven capable of eliminating the infection completely or preventing viral rebound if therapy is stopped. Hence novel latency activation approaches are required. Nanoparticles can offer several advantages over more traditional drug delivery methods, including improved drug solubility, stability, and the ability to simultaneously target multiple different molecules to particular cell or tissue types. Here we describe the development of a novel lipid nanoparticle with the protein kinase C activator bryostatin-2 incorporated (LNP-Bry). These particles can target and activate primary human CD4+ T-cells and stimulate latent virus production from human T-cell lines in vitro and from latently infected cells in a humanized mouse model ex vivo. This activation was synergistically enhanced by the HDAC inhibitor sodium butyrate. Furthermore, LNP-Bry can also be loaded with the protease inhibitor nelfinavir (LNP-Bry-Nel), producing a particle capable of both activating latent virus and inhibiting viral spread. Taken together these data demonstrate the ability of nanotechnological approaches to provide improved methods for activating latent HIV and provide key proof-of-principle experiments showing how novel delivery systems may enhance future HIV therapy