Reverse Mathematics and Algebraic Field Extensions

This paper analyzes theorems about algebraic field extensions using the techniques of reverse mathematics. In section 2, we show that $\mathsf{WKL}_0$ is equivalent to the ability to extend $F$-automorphisms of field extensions to automorphisms of $\bar{F}$, the algebraic closure of $F$. Section 3 explores finitary conditions for embeddability. Normal and Galois extensions are discussed in section 4, and the Galois correspondence theorems for infinite field extensions are treated in section 5.Comment: 25 page

Effect of the Affordable Care Act on utilization of emergency and primary care

The Affordable Care Act (ACA) has considerably reduced the uninsured rate nationally through availability of guaranteed issue private plans (Marketplace) and Medicaid expansion. However, expanding access to health insurance coverage may not be a sufficient incentive for consumers to change their usual setting for care, reduce avoidable use of emergency departments (ED), or increase use of preventive care. One of the core arguments for expansion has been that individuals without coverage may forego preventive care, delay treatment, and subsequently overutilize the ED––leading to worse health outcomes and higher long-run health expenditures. The objective of this dissertation is to investigate the effect of the ACA on substitution between ED and primary care among the newly insured (aim 1), potential delayed effects of coverage gains on avoidable use of the ED (aim 2), and whether high deductibles serve as a barrier to the use of no-cost preventive services (aim 3). Aim 1 uses the linkage between the 2012 National Health Interview Survey and 2013 and 2014 Medical Expenditure Panel Survey to quantify substitution between the ED and primary care settings using linear and multinomial logistic regression models. Aim 2 uses the Healthcare Cost and Utilization Project State Inpatient and Emergency Department Databases for 2008 to 2016 to identify the effect trajectory of coverage gains on avoidable ED use using county-level fixed effects and spatial regression models. Aim 3 uses insurance claims from IBM Health® MarketScan® for 2008 through 2016 to estimate the effect of high deductible health plan enrollment on use of high-value preventive services using difference-in-differences models. This project will provide new understanding of how consumers respond to coverage gains at both the individual and population level with a focus on emergency and primary care services—two ends of the health care spectrum that can often be substitutable, particularly for the newly insured. It will address if and when consumers substitute towards a more appropriate setting for care and also how eliminating cost sharing affects use of preventive services. These insights can be used to refine benefit design, consumer education, and expectations about the costs and health benefits of future reforms.Doctor of Philosoph

Nuclear magnetic resonance spectroscopy: Abnormal splitting of ethyl groups due to molecular asymmetry

Nuclear magnetic resonance (n.m.r.) spectroscopy provides an excellent means for qualitative identification of ethyl groups by use of the familiar three-four pattern of spin-spin splitting (1). It has been observed previously (2) that the methylene protons of systems of the type R-CH2-CR1R2R3 (where R1 can be the same as R or different) may be magnetically nonequivalent and display AB rather than A2-type spectra (3). We now wish to report several examples of this type of behavior with ethyl groups, particularly ethoxy groups, knowledge of which could be important to anyone using n.m.r. for organic qualitative analysis

Hubs of knowledge: using the functional link structure in Biozon to mine for biologically significant entities

BACKGROUND: Existing biological databases support a variety of queries such as keyword or definition search. However, they do not provide any measure of relevance for the instances reported, and result sets are usually sorted arbitrarily. RESULTS: We describe a system that builds upon the complex infrastructure of the Biozon database and applies methods similar to those of Google to rank documents that match queries. We explore different prominence models and study the spectral properties of the corresponding data graphs. We evaluate the information content of principal and non-principal eigenspaces, and test various scoring functions which combine contributions from multiple eigenspaces. We also test the effect of similarity data and other variations which are unique to the biological knowledge domain on the quality of the results. Query result sets are assessed using a probabilistic approach that measures the significance of coherence between directly connected nodes in the data graph. This model allows us, for the first time, to compare different prominence models quantitatively and effectively and to observe unique trends. CONCLUSION: Our tests show that the ranked query results outperform unsorted results with respect to our significance measure and the top ranked entities are typically linked to many other biological entities. Our study resulted in a working ranking system of biological entities that was integrated into Biozon at

EST2Prot: Mapping EST sequences to proteins

BACKGROUND: EST libraries are used in various biological studies, from microarray experiments to proteomic and genetic screens. These libraries usually contain many uncharacterized ESTs that are typically ignored since they cannot be mapped to known genes. Consequently, new discoveries are possibly overlooked. RESULTS: We describe a system (EST2Prot) that uses multiple elements to map EST sequences to their corresponding protein products. EST2Prot uses UniGene clusters, substring analysis, information about protein coding regions in existing DNA sequences and protein database searches to detect protein products related to a query EST sequence. Gene Ontology terms, Swiss-Prot keywords, and protein similarity data are used to map the ESTs to functional descriptors. CONCLUSION: EST2Prot extends and significantly enriches the popular UniGene mapping by utilizing multiple relations between known biological entities. It produces a mapping between ESTs and proteins in real-time through a simple web-interface. The system is part of the Biozon database and is accessible at

Is the length of time uninsured prior to gaining coverage associated with changes in relative utilization of ED and primary care?

Introduction: Utilization of hospital emergency departments (ED) as a safety net provider for routine and non-emergent care by the uninsured is an oft cited problem. Expansion of health insurance coverage under the Affordable Care Act (ACA) to those previously uninsured allows for a potential reallocation of care away from more expensive settings (e.g., ED to office-based primary care). If familiarity with the health care system and connection with a primary care provider is important, those with longer spells of being uninsured prior to gaining coverage may be less likely to shift their utilization of services towards primary care. This study seeks to assess whether length of time uninsured is associated with changes in relative utilization of ED and primary care. Methods: This study uses the Medical Expenditure Panel Survey (MEPS), a comprehensive survey of health insurance, healthcare utilization, and medical expenditures in the United States Population – Adults (18 years or older) who were fully insured (covered for all 12 months) in 2014 [from longitudinal data file (HC 172) for those participating in both 2013 and 2014 (Panel 18)] Policy variable – Insurance status in 2013 – Fully insured - covered for all 12 months – Transiently uninsured – covered for 1-11 months – Persistently uninsured -uninsured for all 12 months Outcomes – Change in relative utilization of primary care to ED visits from 2013 to 2014 (primary) – Relative utilization is defined as the proportion of the total number of office-based physician, office-based physician assistant, office based nurse or nurse practitioner visits, and ED visits in a year that were not ED visits – If utilization was zero for both visit types in a given year, relative utilization was set to zero (i.e., no primary care used) – Change in utilization of primary care and ED visits (separately) from 2013 to 2014 (secondary) Model – Ordinary least squares controlling for insurance status, age, gender, race/ethnicity, education, employment, and family income (all in 2013) – Weighted using AHRQ-provided longitudinal survey weights. Results: Being transiently uninsured in 2013 is associated with a 6.3 percentage point increase (p<0.01) in relative utilization of primary care in 2014 (compared with those who were fully insured). Being persistently uninsured in 2013 was associated with a 9.0 percentage point increase (p<0.01) in relative utilization of primary care in 2014 (compared with those who were fully insured). The restricted model, which excludes education and employment due to missing values, yields similar findings. Conclusions: Longer spells of being uninsured were associated with larger shifts in relative utilization of primary versus ED care after gaining coverage. Implications: The potential for substitution away from ED utilization towards primary care by the persistently uninsured could help ease ED overcrowding and encourage earlier detection and treatment of disease. Further research is needed to determine whether selection bias may play a role in these findings (e.g., are persistently uninsured more likely to have a pre-existing condition that would encourage utilization of primary care when insured?

Comparing the strength of diagonally non-recursive functions in the absence of Σ02 induction

We prove that the statement there is a k such that for every f there is a k-bounded diagonally non-recursive function relative to f does not imply weak K\ onig\u27s lemma over RCA0+BΣ02. This answers a question posed by Simpson. A recursion-theoretic consequence is that the classic fact that every k-bounded diagonally non-recursive function computes a 2-bounded diagonally non-recursive function may fail in the absence of IΣ02

Identifying access barriers to outpatient rehabilitative care after stroke

Introduction: Those who survive a stroke are often left with physical, cognitive, and/or communicative disabilities, requiring varying degrees of rehabilitative therapy and assistance with activities of daily living; Stroke-related disabilities can negatively impact both survivor and caregiver quality of life and mental health, and many stroke survivors report having unmet needs; Using focus groups, we aimed to identify access barriers to outpatient rehabilitative care among stroke survivors and moderating factors associated with encountering these barriers Methods: Five (5) one-hour focus groups (n=36); Four (4) with stroke survivors with communication disorders (n=22) and/or caregivers (n=7); One (1) with hospital administrators and rehab providers (n=7); Recruited from 1) a non-profit organization providing group therapy services for persons with aphasia (Triangle Aphasia Project Unlimited) and 2) a rehab services patient and family advisory board at an academic medical center (UNC Hospitals); Stroke survivor and caregiver groups; Stroke characteristics (e.g., type of stroke, impairment – immediately following stroke and long-term); Rehab service utilization (e.g., types of inpatient therapy received, time to entry into outpatient rehab after discharge); Barriers (e.g., financial and non financial barriers experienced, how they changed setting and utilization of care, how to address to improve access); Hospital administrator and rehab provider group – Barriers (e.g., financial and non financial barriers observed, how they change utilization of care, administrative challenges, potential solutions to improve access); This study was approved by the UNC Non-Biomedical IRB (#16 2295) Participants: Stroke survivors (n=22); Average age: 58.1 years; Average time since stroke: 36.3 months; 14 male, 8 female; 13 White, 6 African American, 2 Asian, 1 Other Results: Financial barriers: Therapy caps and high costs were the most frequently mentioned barriers to accessing timely and appropriate outpatient rehabilitative care; Therapy caps specifically appeared to be a source of a frustration given the seemingly arbitrary nature with which they are set (e.g., 30 visits per calendar year for physical, occupational, and speech therapy combined); These often changed the way people opted to get care – For example, a participant and his caregiver sought additional help from friends who were speech pathologists; In addition to cost, loss of income—either by the stroke survivor, the caregiver or both—can have a major impact on a person’s ability to access outpatient care ; Non-financial barriers: Non-financial barriers consisted largely of issues within the client therapist relationship, issues with transportation and scheduling, and patient and/or caregiver characteristics; Many stroke survivors and their caregivers did not feel as though the therapist had adequately included the patient in the goal setting process, which resulted in participants stated that they often went to therapy and completed activities without understanding why they were doing certain tasks; Stroke survivors with physical and/or cognitive impairment often depend on a caregiver to attend therapy appointments; When caregivers are not able to take time away from work or other responsibilities, stroke survivors miss therapy appointments and that creates scheduling issues for the facility; Stroke survivors and caregivers sometimes struggled with the new reality of post-stroke life and spoke of loss of identity, which was often not addressed by families and/or providers Conclusions: Financial and bureaucratic barriers were common as were issues with the client-therapist relationship; Consideration of alternative benefit designs for outpatient rehabilitative care may be warranted, focusing on continued progression in functional status rather than arbitrary caps; Such an approach could allow for greater independence and lower social burden of stroke survivors in the long-term