Coordinate rings and birational charts

Let G G be a semisimple simply connected complex algebraic group. Let U U be the unipotent radical of a Borel subgroup in G G . We describe the coordinate rings of U U (resp., G / U G/U , G G ) in terms of two (resp., four, eight) birational charts introduced by Lusztig [Total positivity in reductive groups, Birkhäuser Boston, Boston, MA, 1994; Bull. Inst. Math. Sin. (N.S.) 14 (2019), pp. 403–459] in connection with the study of total positivity.

Trees, Forests, and Total Positivity: I. $q$-Trees and $q$-Forests Matrices

We consider matrices with entries that are polynomials in $q$ arising from natural $q$-generalisations of two well-known formulas that count: forests on $n$ vertices with $k$ components; and rooted labelled trees on $n+1$ vertices where $k$ children of the root are lower-numbered than the root. We give a combinatorial interpretation of the corresponding statistic on forests and trees and show, via the construction of various planar networks and the Lindström-Gessel-Viennot lemma, that these matrices are coefficientwise totally positive. We also exhibit generalisations of the entries of these matrices to polynomials in eight indeterminates, and present some conjectures concerning the coefficientwise Hankel-total positivity of their row-generating polynomials.

Increased vulnerability to SARS-CoV-2 infection among indigenous people living in the urban area of Manaus

The COVID-19 pandemic threatens indigenous peoples living in suburban areas of large Brazilian cities and has thus far intensified their pre-existing socio-economic inequalities. We evaluated the epidemiological situation of SARS-CoV-2 infection among residents of the biggest urban multiethnic indigenous community of the Amazonas state, Brazil. Blood samples of 280 indigenous people living in the surrounding area of Manaus were tested for the presence of anti-SARS-CoV-2 IgA or IgG antibodies. The risk factors and sociodemographic information were assessed through an epidemiological questionnaire. We found a total positivity rate of 64.64% (95% CI 59.01–70.28) for SARS-CoV-2 infection. IgA and IgG were detected in 55.71% (95% CI 49.89–61.54) and 60.71% (95% CI 54.98–66.45) of the individuals, respectively. Over 80% of positive individuals were positive for both IgA and IgG.No significant difference in positivity rates between genders or age groups was observed. Moreover, the age group ≥ 60 years old showed the highest antibody ratios (IgA mean ratio = 3.080 ± 1.623; IgG mean ratio = 4.221 ± 1.832), while the age groups 13–19 and 20–29 showed the lowest IgA (mean ratio = 2.268 ± 0.919) and IgG ratios (mean ratio = 2.207 ± 1.246), respectively. Individuals leaving the home more frequently were at higher risk of infection (Odds ratio (OD) 2.61; 95% CI 1.00–1.49; p = 0.048). Five or more individuals per household increased fivefold the risk of virus transmission (OR 2.56; 95% CI 1.09–6.01; p = 0.019). The disproportionate dissemination of SARS-CoV-2 infection observed among the study population might be driven by typical cultural behavior and socioeconomic inequalities. Despite the pandemic threat, this population is not being targeted by public policies and appears to be chronically invisible to the Brazilian authorities.

The impact of the Beirut blast on the COVID-19 situation in Lebanon

Aim On August 4, 2020, a massive explosion hit Lebanon’s capital city, Beirut. The aim of this study was to explore the effect of the Beirut blast on the COVID-19 situation in the country. Subject and Methods Data on COVID-19 were retrieved from the Lebanese Ministry of Public Health (LMOPH), where all the COVID-19 positive cases were reported. The study was divided into two periods, considering the incubation period of the COVID-19 virus: (July 27–August 9, 2020) and (August 10–23, 2020). Information obtained included daily number of cases, tests, deaths, hospitalized patients, intensive care unit (ICU) patients, and mode of acquisition (local vs. expat). Daily positivity rates were reported per 100 tests. An independent sample t-test and a Joinpoint regression analysis were used to determine significance. A p value less than 0.05 was considered significant. Results A total of 201,010 tests were conducted during our studied period, with 8993 positive cases, constituting a total positivity rate of 4.5 per 100 tests. Case fatality rate over the studied period was 0.8%. The positivity rate of the period prior to August 10, 2020, was 2.7 per 100 tests, significantly less than that of the period following the explosion, which was 6.4 per 100 tests (p < 0.001). During our studied period, daily positivity rates were significantly increasing at a slope of 0.29 (p < 0.001). A significant increase in slope was noted on August 13, 2020 (p < 0.001). The number of hospitalized patients increased from 139 patients on July 27 to 266 on August 23, 2020, and that of ICU patients increased from 36 to 75. Conclusion The port of Beirut explosion resulted in a significant increase in the daily number of positive COVID-19 cases. The aftermath of the explosion, the damage to healthcare facilities, and the overcrowding due to emergency efforts were contributing factors to that increase.

A Generalized Quasi Cubic Trigonometric Bernstein Basis Functions and Its B-Spline Form

In this paper, under the framework of Extended Chebyshev space, four new generalized quasi cubic trigonometric Bernstein basis functions with two shape functions α(t) and β(t) are constructed in a generalized quasi cubic trigonometric space span{1,sin2t,(1−sint)2α(t),(1−cost)2β(t)}, which includes lots of previous work as special cases. Sufficient conditions concerning the two shape functions to guarantee the new construction of Bernstein basis functions are given, and three specific examples of the shape functions and the related applications are shown. The corresponding generalized quasi cubic trigonometric Bézier curves and the corner cutting algorithm are also given. Based on the new constructed generalized quasi cubic trigonometric Bernstein basis functions, a kind of new generalized quasi cubic trigonometric B-spline basis functions with two local shape functions αi(t) and βi(t) is also constructed in detail. Some important properties of the new generalized quasi cubic trigonometric B-spline basis functions are proven, including partition of unity, nonnegativity, linear independence, total positivity and C2 continuity. The shape of the parametric curves generated by the new proposed B-spline basis functions can be adjusted flexibly.

Properly collected plasma metanephrines excludes PPGL after false positive screening tests

Context False positive results are common for pheochromocytoma/paraganglioma(PPGL) real-world screening. Objective Determine the correlation between screening urine and seated plasma metanephrines in outpatients where PPGL was absent, compared to meticulously prepared and supine-collected plasma metanephrines with age-adjusted references. Design Retrospective cohort study Setting Databases from a single-provider provincial laboratory(2012-2018), a validated PPGL registry and a manual chart review from a specialized endocrine testing unit. Patients PPGL registry data excluded known PPGL cases from the laboratory database. Outpatients having both urine and plasma metanephrines &lt;90 days apart. Methods The correlation between urine and seated plasma measures along with the total positivity rate. All cases of plasma metanephrines drawn in the endocrine unit were reviewed for test indication and test positivity rate. Results There were 810 non-PPGL pairs of urine and plasma metanephrines in the laboratory database; 46.1% of urine metanephrines were reported high. Of seated outpatient plasma metanephrines drawn a median of 5.9 days later, 19.2% were also high (r=0.33 and 0.50 for normetanephrine and metanephrine, respectively). In contrast, the meticulously prepared and supine collected patients(n=139, 51% prior high urine metanephrines) had &lt;3% rate of abnormal high results in patients without known PPGL/adrenal mass. Conclusions There was a poor-to-moderate correlation between urine and seated plasma metanephrines. Up to 20% of those with high urine measures also had high seated plasma metanephrines in the absence of PPGL. Properly prepared and collected supine plasma metanephrines had a false positive rate of &lt;3% in the absence of known PPGL/adrenal mass.

Increased vulnerability to SARS-CoV-2 infection among indigenous people living in the urban area of Manaus

Background: The COVID-19 pandemic threatens indigenous peoples living in suburban areas of large Brazilian cities and has thus far intensified their pre-existing socio-economic inequalities. This study evaluated the epidemiological situation of SARS-CoV-2 infection among residents of the biggest urban multiethnic indigenous community of the Amazonas state, Brazil. Methods: Blood samples of 280 indigenous people who live in the urban community known as Parque das Tribos, which is located in the surrounding area of Manaus, were tested for the presence of anti-SARS-CoV-2 IgA or IgG antibodies using an enzyme-linked immunosorbent assay. An epidemiological standardized interviewer-administered questionnaire was applied to assess the risk factors and sociodemographic information of the study population. Results: We found a total positivity rate of 64.64% (95% CI 59.01-70.28) for SARS-CoV-2 infection. IgA and IgG were detected in 55.71% (95% CI 49.89-61.54) and 60.71% (95% CI 54.98-66.45) of the individuals tested, respectively. From the total number (n=280), 80.11% of positive individuals (95%; CI 74.24-85.98) were positive for both IgA and IgG Abs. All individuals with COVID-19-related symptoms on the day of blood collection (n=11) were positive for IgG, while IgA was detected in 84.61% (n=55) of individuals who had presented symptoms several weeks before the blood collection. Individuals aged 30-39 were more susceptible to SARS-CoV-2 infection (prevalence ratio [PR] 0.77; 95% CI 0.58-1.03; p=0.033). People whose main source of information on COVID-19 was religious leaders or friends showed higher susceptibility to infection (PR 1.22; 95% CI 1.00-1.49; p=0.040). In addition, individuals who left home more frequently were at higher risk of infection (PR 1.22; 95% CI 1.00-1.49; p=0.048). Five or more individuals per household increased almost 5-fold the risk of virus transmission (Odds ratio [OR] 2.56; 95% CI; 1.09-6.01; p=0.019). Over 95% of the study population had no access to clean water and/or sanitation. Conclusions: The disproportionate dissemination of SARS-CoV-2 infection observed in the Parque das Tribos urban indigenous community might be driven by typical cultural behavior and socioeconomic inequalities. Despite the pandemic threat, this population is not being targeted by public policies and appears to be chronically invisible to the Brazilian authorities.