Counting Cards: Combinatorics, Group Theory, and Probability in War

My project involved taking a look at the card game War, searching for patterns which develop in the game, and then looking for Mathematical explanations for those patterns. The project began when my advisor, Professor Marc Brodie, was playing War with his children and began to notice patterns and ask questions about them. The questions I set out to answer were: What is the probability of playing a game of war in which a loop develops? If we know the size of the deck we are using, can we determine what loop lengths are possible? How are cards cycling between players within a loop? What patterns of winning occur within a loop? What effect does changing the number of suits in the deck or the number of players have on the cycling of cards within a loop and the loop length? We found at least partial answers to all of these questions and more using Mathematica programs of simulated games along with basic theory from Combinatorics, Group Theory, and Probability

Defining the Environmental Niche of the Two Main Clades of \u3ci\u3eTrichodesmium\u3c/i\u3e: A Study on the West Florida Shelf

Dinitrogen (N2) fixation is the process of taking widely abundant but mostly biologically inaccessible N2 gas and converting it into more biologically accessible forms of the essential macronutrient nitrogen. Only a small fraction of organisms known as diazotrophs can perform biological N2 fixation. Trichodesmium is one such genus of N2-fixing marine cyanobacteria that is commonly observed in waters along the West Florida Shelf (WFS). We hypothesize that the two main Trichodesmium clades (T. erythraeum and T. thiebautii) occupy distinct environmental niches, one being more coastal and one being more oceanic. To test this hypothesis, we quantified gene abundance of both clades and compared the results with hydrographic data to distinguish any trends in niche distribution in samples collected on the WFS from three separate cruises. T. thiebautii abundance was higher further from the coast (at stations with greater bottom depths) and the T. erythraeum abundance was higher closer to the coast (at stations with lower bottom depths). A lack of nearshore sampling in 2015 initially made it difficult to conclusively identify trends in niche distribution, however with the addition of 2018 and 2019 samples, we observed a consistent coastal vs. open ocean niche separation for the two clades. In addition, T.thiebautii abundance was also significantly positively correlated with salinity. While previous work has found T. thiebautii is more abundant than T. erythraeum in open ocean surface waters, this is the first study to examine Trichodesmium clade abundance in a near-shore environment.https://digitalcommons.odu.edu/gradposters2021_sciences/1010/thumbnail.jp

Longitudinal changes of white matter hyperintensities in sporadic small vessel disease: a systematic review and meta-analysis

BACKGROUND AND OBJECTIVES: White matter hyperintensities (WMHs) are frequent imaging features of small vessel disease (SVD) and related to poor clinical outcomes. WMH progression over time is well described, but regression was also noted recently, although the frequency and associated factors are unknown. This systematic review and meta-analysis aims to assess longitudinal intraindividual WMH volume changes in sporadic SVD. METHODS: We searched EMBASE and MEDLINE for articles up to 28 January 2022 on WMH volume changes using MRI on ≥2 time points in adults with sporadic SVD. We classified populations (healthy/community-dwelling, stroke, cognitive, other vascular risk factors, and depression) based on study characteristics. We performed random-effects meta-analyses with Knapp-Hartung adjustment to determine mean WMH volume change (change in milliliters, percentage of intracranial volume [%ICV], or milliliters per year), 95% CI, and prediction intervals (PIs, limits of increase and decrease) using unadjusted data. Risk of bias assessment tool for nonrandomized studies was used to assess risk of bias. We followed Preferred Reporting in Systematic Review and Meta-Analysis guidelines. RESULTS: Forty-one articles, 12,284 participants, met the inclusion criteria. Thirteen articles had low risk of bias across all domains. Mean WMH volume increased over time by 1.74 mL (95% CI 1.23–2.26; PI −1.24 to 4.73 mL; 27 articles, N = 7,411, mean time interval 2.7 years, SD = 1.65); 0.25 %ICV (95% CI 0.14–0.36; PI −0.06 to 0.56; 6 articles, N = 1,071, mean time interval 3.5 years, SD = 1.54); or 0.58 mL/y (95% CI 0.35–0.81; PI −0.26 to 1.41; 8 articles, N = 3,802). In addition, 13 articles specifically mentioned and/or provided data on WMH regression, which occurred in asymptomatic, stroke, and cognitive disorders related to SVD. DISCUSSION: Net mean WMH volume increases over time mask wide-ranging change (e.g., mean increase of 1.75 mL ranging from 1.25 mL decrease to 4.75 mL increase), with regression documented explicitly in up to one-third of participants. More knowledge on underlying mechanisms, associated factors, and clinical correlates is needed, as WMH regression could be an important intervention target

Defining the Realized Niche of the Two Major Clades of \u3ci\u3eTrichodesmium\u3c/i\u3e: A Study on the West Florida Shelf

The cyanobacterium Trichodesmium plays an essential role supporting ocean productivity by relieving nitrogen limitation via dinitrogen (N-2) fixation. The two common Trichodesmium clades, T. erythraeum and T. thiebautii, are both observed in waters along the West Florida Shelf (WFS). We hypothesized that these taxa occupy distinct realized niches, where T. thiebautii is the more oceanic clade. Samples for DNA and water chemistry analyses were collected on three separate WFS expeditions (2015, 2018, and 2019) spanning multiple seasons; abundances of the single copy housekeeping gene rnpB from both clades were enumerated via quantitative PCR. We conducted a suite of statistical analyses to assess Trichodesmium clade abundances in the context of the physicochemical data. We observed a consistent coastal vs. open ocean separation of the two clades: T. erythraeum was found in shallow waters where the concentrations of dissolved iron (dFe) and the groundwater tracer Ba were significantly higher, while T. thiebautii abundance was positively correlated with water column depth. The Loop Current intrusion in 2015 with entrained Missisippi River water brought higher dFe and elevated abundance of both clades offshore of the 50 m isobath, suggesting that both clades are subject to Fe limitation on the outer shelf. Whereas, previous work has observed that T. thiebautii is more abundant than T. erythraeum in open ocean surface waters, this is the first study to examine Trichodesmium niche differentiation in a coastal environment. Understanding the environmental niches of these two key taxa bears important implications for their contributions to global nitrogen and carbon cycling and their response to global climate change

Temporal trends in pregnancy-associated stroke and its outcomes among women with hypertensive disorders of pregnancy

Funding PW is funded by a NIHR Transitional Research Fellowship. CCG is part-funded by West Midlands ARC. LCC is funded by a NIHR Professorship (RP-2014-05-019). This paper presents independent research funded by the NIHR. The views expressed are those of the authors and not necessarily those of the NHS, the NIHR or the Department of Health and Social Care. The funders had no involvement in the conduct of this research.Peer reviewedPublisher PD

Risk assessments and structured care interventions for prevention of foot ulceration in diabetes:development and validation of a prognostic model

Background: Diabetes-related foot ulcers give rise to considerable morbidity, generate a high monetary cost for health and social care services and precede the majority of diabetes-related lower extremity amputations. There are many clinical prediction rules in existence to assess risk of foot ulceration but few have been subject to validation. Objectives: Our objectives were to produce an evidence-based clinical pathway for risk assessment and management of the foot in people with diabetes mellitus to estimate cost-effective monitoring intervals and to perform cost-effectiveness analyses and a value-of-information analysis. Design: We developed and validated a prognostic model using predictive modelling, calibration and discrimination techniques. An overview of systematic reviews already completed was followed by a review of randomised controlled trials of interventions to prevent foot ulceration in diabetes mellitus. A review of the health economic literature was followed by the construction of an economic model, an analysis of the transitional probability of moving from one foot risk state to another, an assessment of cost-effectiveness and a value-of-information analysis. Interventions: The effects of simple and complex interventions and different monitoring intervals for the clinical prediction rules were evaluated. Main outcome measure: The main outcome was the incidence of foot ulceration. We compared the new clinical prediction rules in conjunction with the most effective preventative interventions at different monitoring intervals with a ‘treat-all’ strategy. Data sources: Data from an electronic health record for 26,154 people with diabetes mellitus in one Scottish health board were used to estimate the monitoring interval. The Prediction Of Diabetic foot UlcerationS (PODUS) data set was used to develop and validate the clinical prediction rule. Review methods: We searched for eligible randomised controlled trials of interventions using search strategies created for Ovid® (Wolters Kluwer, Alphen aan den Rijn, the Netherlands), MEDLINE, EMBASE and the Cochrane Central Register of Controlled Trials. Randomised controlled trials in progress were identified via the International Standard Randomised Controlled Trial Number Registry and systematic reviews were identified via PROSPERO. Databases were searched from inception to February 2019. Results: The clinical prediction rule was found to accurately assess the risk of foot ulceration. Digital infrared thermometry, complex interventions and therapeutic footwear with offloading devices were found to be effective in preventing foot ulcers. The risk of developing a foot ulcer did not change over time for most people. We found that interventions to prevent foot ulceration may be cost-effective but there is uncertainty about this. Digital infrared thermometry and therapeutic footwear with offloading devices may be cost-effective when used to treat all people with diabetes mellitus regardless of their ulcer risk. Limitations: The threats to the validity of the results in some randomised controlled trials in the review and the large number of missing data in the electronic health record mean that there is uncertainty in our estimates. Conclusions: There is evidence that interventions to prevent foot ulceration are effective but it is not clear who would benefit most from receiving the interventions. The ulceration risk does not change over an 8-year period for most people with diabetes mellitus. A change in the monitoring interval from annually to every 2 years for those at low risk would be acceptable. Future work recommendations: Improving the completeness of electronic health records and sharing data would help improve our knowledge about the most clinically effective and cost-effective approaches to prevent foot ulceration in diabetes mellitus. Study registration: This study is registered as PROSPERO CRD42016052324. Funding: This project was funded by the National Institute for Health Research (NIHR) Health Technology Assessment programme and will be published in full in Health Technology Assessment; Vol. 24, No. 62. See the NIHR Journals Library website for further project information

Impact of the COVID-19 pandemic on the provision and uptake of services for the prevention of mother-to-child transmission of HIV in Zimbabwe

Zimbabwe is targeting elimination of mother-to-child transmission of HIV by December 2025, however the COVID-19 pandemic challenged health service delivery globally. Monthly aggregated data were extracted from DHIS-2 for all facilities delivering antenatal care (ANC). ZIMSTAT and Spectrum demographic estimates were used for population-level denominators. Programme indicators are among those in HIV care and population indicators reflect the total population. The mean estimated proportion of pregnant women booking for ANC per month did not change (91% pre-pandemic vs 91% during pandemic, p = 0.95), despite dropping to 47% in April 2020. At a programme-level, the estimated proportion of women who received at least one HIV test fell in April 2020 (3.6% relative reduction vs March (95% CI 2.2–5.1), p<0.001) with gradual recovery towards pre-pandemic levels. The estimated proportion of women who were retested among those initially negative in pregnancy fell markedly in April 2020 (39% reduction (32–45%), p<0.001) and the subsequent increase was much slower, only reaching 39% by September 2021 compared to average 53% pre-pandemic. The mean estimated proportion of pregnant women with HIV on ART was unchanged at programme-level (98% vs 98%, p = 0.26), but decreased at population-level (86% vs 80%, p = 0.049). Antiretroviral prophylaxis coverage decreased among HIV-exposed infants, at programme- (94% vs 87%, p = 0.001) and population-levels (76% vs 68%, p<0.001). There was no significant change in HIV-exposed infants receiving EID (programme: 107% vs 103%, p = 0.52; population: 87% vs 79%, p = 0.081). The estimated proportion of infants with HIV diagnosed fell from 27% to 18%, (p<0.001), while the estimated proportion on ART was stable at a programme (88% vs 90%, p = 0.82) but not population (22% vs 16%, p = 0.004) level. Despite a drop at the start of the pandemic most programme indicators rapidly recovered. At a population-level indicators were slower to return, suggesting less women with HIV identified in care

Tihomil Beritić (1919.-1999.)

No abstract available

Biallelic CPAMD8 Variants Are a Frequent Cause of Childhood and Juvenile Open-Angle Glaucoma

© 2020 by the American Academy of Ophthalmology. This is an open access article under the CC BY-NC-ND licensePurpose Developmental abnormalities of the ocular anterior segment in some cases can lead to ocular hypertension and glaucoma. CPAMD8 is a gene of unknown function recently associated with ocular anterior segment dysgenesis, myopia, and ectopia lentis. We sought to assess the contribution of biallelic CPAMD8 variants to childhood and juvenile open-angle glaucoma. Design Retrospective, multicenter case series. Participants A total of 268 probands and their relatives with a diagnosis of childhood or juvenile open-angle glaucoma. Purpose Developmental abnormalities of the ocular anterior segment in some cases can lead to ocular hypertension and glaucoma. CPAMD8 is a gene of unknown function recently associated with ocular anterior segment dysgenesis, myopia, and ectopia lentis. We sought to assess the contribution of biallelic CPAMD8 variants to childhood and juvenile open-angle glaucoma. Methods Patients underwent a comprehensive ophthalmic assessment, with DNA from patients and their relatives subjected to genome, exome, or capillary sequencing. CPAMD8 RNA expression analysis was performed on tissues dissected from cadaveric human eyes. Main Outcome Measures Diagnostic yield within a cohort of childhood and juvenile open-angle glaucoma, prevalence and risk of ophthalmic phenotypes, and relative expression of CPAMD8 in the human eye. Results We identified rare (allele frequency < 4×10−5) biallelic CPAMD8 variants in 5.7% (5/88) of probands with childhood glaucoma and 2.1% (2/96) of probands with juvenile open-angle glaucoma. When including family members, we identified 11 individuals with biallelic variants in CPAMD8 from 7 unrelated families. Nine of these individuals were diagnosed with glaucoma (9/11, 81.8%), with a mean age at diagnosis of 9.22±14.89 years, and all individuals with glaucoma required 1 or more incisional procedures to control high intraocular pressure. Iris abnormalities were observed in 9 of 11 individuals, cataract was observed in 8 of 11 individuals (72.7%), and retinal detachment was observed in 3 of 11 individuals (27.3%). CPAMD8 expression was highest in neural crest–derived tissues of the adult anterior segment, suggesting that CPAMD8 variation may cause malformation or obstruction of key drainage structures. Conclusions Biallelic CPAMD8 variation was associated with a highly heterogeneous phenotype and in our cohorts was the second most common inherited cause of childhood glaucoma after CYP1B1 and juvenile open-angle glaucoma after MYOC. CPAMD8 sequencing should be considered in the investigation of both childhood and juvenile open-angle glaucoma, particularly when associated with iris abnormalities, cataract, or retinal detachment

Relationship Between Venules and Perivascular Spaces in Sporadic Small Vessel Diseases

Background and Purpose— Perivascular spaces (PVS) around venules may help drain interstitial fluid from the brain. We examined relationships between suspected venules and PVS visible on brain magnetic resonance imaging. Methods— We developed a visual venular quantification method to examine the spatial relationship between venules and PVS. We recruited patients with lacunar stroke or minor nondisabling ischemic stroke and performed brain magnetic resonance imaging and retinal imaging. We quantified venules on gradient echo or susceptibility-weighted imaging and PVS on T2-weighted magnetic resonance imaging in the centrum semiovale and then determined overlap between venules and PVS. We assessed associations between venular count and patient demographic characteristics, vascular risk factors, small vessel disease features, retinal vessels, and venous sinus pulsatility. Results— Among 67 patients (69% men, 69.0±9.8 years), only 4.6% (range, 0%–18%) of venules overlapped with PVS. Total venular count increased with total centrum semiovale PVS count in 55 patients after accounting for venule-PVS overlap (β=0.468 [95% CI, 0.187–0.750]) and transverse sinus pulsatility (β=0.547 [95% CI, 0.309–0.786]) and adjusting for age, sex, and systolic blood pressure. Conclusions— Despite increases in both visible PVS and suspected venules, we found minimal spatial overlap between them in patients with sporadic small vessel disease, suggesting that most magnetic resonance imaging-visible centrum semiovale PVS are periarteriolar rather than perivenular