Arni S. R. Srinivasa Rao’s research while affiliated with Augusta University and other places

The Jordan curve theorem states that any simple closed curve in 3D space divides the space into two regions, an interior and an exterior. In this article, we prove the Jordan curve theorem on the boundary of a 3D ball that is inserted in a complex plane bundle. To do so, we make use of the Brownian motion principle, which is a continuous-time and continuous-state stochastic process. We begin by selecting a random point on an arbitrarily chosen complex plane within a bundle G and on the boundary of the 3D ball considered. Using the two-step random process developed on complex planes earlier by Srinivasa Rao (Multilevel contours on bundles of complex planes, 2022), we draw a contour from the initial point to the next point on this plane. We then continue this process until we finish the Jordan curve that connects points on the boundary of a ball within G.

Objective To determine whether initiating saline nasal irrigation after COVID-19 diagnosis reduces hospitalization and death in high-risk outpatients compared with observational controls, and if irrigant composition impacts severity. Methods Participants 55 and older were enrolled within 24 hours of a + PCR COVID-19 test between September 24 and December 21, 2020. Among 826 screened, 79 participants were enrolled and randomly assigned to add 2.5 mL povidone-iodine 10% or 2.5 mL sodium bicarbonate to 240 mL of isotonic nasal irrigation twice daily for 14 days. The primary outcome was hospitalization or death from COVID-19 within 28 days of enrollment by daily self-report confirmed with phone calls and hospital records, compared to the CDC Surveillance Dataset covering the same time. Secondary outcomes compared symptom resolution by irrigant additive. Results Seventy-nine high-risk participants were enrolled (mean [SD] age, 64 [8] years; 36 [46%] women; 71% Non-Hispanic White), with mean BMI 30.3. Analyzed by intention-to-treat, by day 28, COVID-19 symptoms resulted in one ED visit and no hospitalizations in 42 irrigating with alkalinization, one hospitalization of 37 in the povidone-iodine group, (1.27%) and no deaths. Of nearly three million CDC cases, 9.47% were known to be hospitalized, with an additional 1.5% mortality in those without hospitalization data. Age, sex, and percentage with pre-existing conditions did not significantly differ by exact binomial test from the CDC dataset, while reported race and hospitalization rate did. The total risk of hospitalization or death (11%) was 8.57 times that of enrolled nasal irrigation participants (SE = 2.74; P = .006). Sixty-two participants completed daily surveys (78%), averaging 1.8 irrigations/day. Eleven reported irrigation-related complaints and four discontinued use. Symptom resolution was more likely for those reporting twice daily irrigation (X² = 8.728, P = .0031) regardless of additive. Conclusion SARS-CoV-2+ participants initiating nasal irrigation were over 8 times less likely to be hospitalized than the national rate.

From Leonhard Euler to Alfred Lotka and in recent years understanding the stationary process of the human population has been of central interest to scientists. Population reproductive measure NRR (net reproductive rate) has been widely associated with measuring the status of population stationarity and it is also included as one of the measures in the millennium development goals.This article argues how the partition theorem-based approach provides more up-to-date and timely measures to find the status of the population stationarity of a country better than the NRR-based approach. We question the timeliness of the value of NRR in deciding the stationary process of the country. We prove associated theorems on discrete and continuous age distributions and derive measurable functional properties. The partitioning metric captures the underlying age structure dynamic of populations at or near stationarity. As the population growth rates for an ever-increasing number of countries trend towards replacement levels and below, new demographic concepts and metrics are needed to better characterize this emerging global demography.

We have developed a novel Markov Chain modeling system that considers vectors of patients with atrial fibrillation (AF) by their AF status over a period of time. Our model examines the impact of catheter ablation of AF upon the dynamics of a patient's AF status and their potential return to sinus rhythm. We prove several theorems to determine the probabilities of patients achieving sinus rhythm or progressing to permanent AF. Additionally, we observed aggregation of patients within the paroxysmal AF state in simulation. The aggregating property of Markov chains illustrated the potential benefits of catheter ablation on healthcare resource allocation.

Our overarching goal in this paper was to both test and identify applications for a fundamental theorem of replacement-level populations known as the Stationary Population Identity (SPI), a mathematical model that equates the fraction of a population age x and the fraction with x years to live. Since true stationarity is virtually non-existent in human populations as well as in populations of non-human species, we used historical data on the memberships in both chambers of the U.S. Congress as populations. We conceived their fixed numbers (e.g., 100 Senators; 435 Representatives) as stationary populations, and their years served and years remaining as the equivalent of life lived and life remaining. Our main result was the affirmation of the mathematical prediction—i.e., the robust symmetry of years served and years remaining in Congress over the approximately 230 years of its existence (1789–2022). A number of applications emerged from this regularity and the distributional patterns therein including (1) new metrics such as Congressional half-life and other quantiles (e.g., 95% turnover); (2) predictability of the distribution of member’s years remaining; (3) the extraordinary information content of a single number—the mean number of years served [i.e., derive birth ( b ) and death ( d ) rates; use of d as exponential rate parameter for model life tables]; (4) the concept of and metrics associated with period-specific populations (Congress); (5) Congressional life cycle concept with Formation, Growth, Senescence and Extinction Phases; and (6) longitudinal party transition rates for 100% Life Cycle turnover (Democrat/Republican), i.e., each seat from predecessor party-to-incumbent party and from incumbent party-to-successor party. Although our focus is on the use of historical data for Congressional members, we believe that most of the results are general and thus both relevant and applicable to all types of stationary or quasi-stationary populations including to the future world of zero population growth (ZPG).