Multi-point distribution of discrete time periodic TASEP

We study the one-dimensional discrete time totally asymmetric simple exclusion process with parallel update rules on a spatially periodic domain. A multi-point space-time joint distribution formula is obtained for general initial conditions. The formula involves contour integrals of Fredholm determinants with kernels acting on certain discrete spaces. For a class of initial conditions satisfying certain technical assumptions, we are able to derive large-time, large-period limit of the joint distribution, under the relaxation time scale $$t=O(L^{3/2})$$ t = O ( L 3 / 2 ) when the height fluctuations are critically affected by the finite geometry. The assumptions are verified for the step and flat initial conditions. As a corollary we obtain the multi-point distribution of discrete time TASEP on the whole integer lattice $${\mathbb {Z}}$$ Z by taking the period L large enough so that the finite-time distribution is not affected by the boundary. The large time limit for the multi-time distribution of discrete time TASEP on $${\mathbb {Z}}$$ Z is then obtained for the step initial condition.

Caveats on COVID-19 herd immunity threshold: the Spain case

After a year of living with the COVID-19 pandemic and its associated consequences, hope looms on the horizon thanks to vaccines. The question is what percentage of the population needs to be immune to reach herd immunity, that is to avoid future outbreaks. The answer depends on the basic reproductive number, R0, a key epidemiological parameter measuring the transmission capacity of a disease. In addition to the virus itself, R0 also depends on the characteristics of the population and their environment. Additionally, the estimate of R0 depends on the methodology used, the accuracy of data and the generation time distribution. This study aims to reflect on the difficulties surrounding R0 estimation, and provides Spain with a threshold for herd immunity, for which we considered the different combinations of all the factors that affect the R0 of the Spanish population. Estimates of R0 range from 1.39 to 3.10 for the ancestral SARS-CoV-2 variant, with the largest differences produced by the method chosen to estimate R0. With these values, the herd immunity threshold (HIT) ranges from 28.1 to 67.7%, which would have made 70% a realistic upper bound for Spain. However, the imposition of the delta variant (B.1.617.2 lineage) in late summer 2021 may have expanded the range of R0 to 4.02–8.96 and pushed the upper bound of the HIT to 90%.

Estimation of the test to test distribution as a proxy for generation interval distribution for the Omicron variant in England

Background Early estimates from South Africa indicated that the Omicron COVID-19 variant may be both more transmissible and have greater immune escape than the previously dominant Delta variant. The rapid turnover of the latest epidemic wave in South Africa as well as initial evidence from contact tracing and household infection studies has prompted speculation that the generation time of the Omicron variant may be shorter in comparable settings than the generation time of the Delta variant. Methods We estimated daily growth rates for the Omicron and Delta variants in each UKHSA region from the 23rd of November to the 23rd of December 2021 using surveillance case counts by date of specimen and S-gene target failure status with an autoregressive model that allowed for time-varying differences in the transmission advantage of the Delta variant where the evidence supported this. By assuming a gamma distributed generation distribution we then estimated the generation time distribution and transmission advantage of the Omicron variant that would be required to explain this time varying advantage. We repeated this estimation process using two different prior estimates for the generation time of the Delta variant first based on household transmission and then based on its intrinsic generation time. Results Visualising our growth rate estimates provided initial evidence for a difference in generation time distributions. Assuming a generation time distribution for Delta with a mean of 2.5-4 days (90% credible interval) and a standard deviation of 1.9-3 days we estimated a shorter generation time distribution for Omicron with a mean of 1.5-3.2 days and a standard deviation of 1.3-4.6 days. This implied a transmission advantage for Omicron in this setting of 160%-210% compared to Delta. We found similar relative results using an estimate of the intrinsic generation time for Delta though all estimates increased in magnitude due to the longer assumed generation time. Conclusions We found that a reduction in the generation time of Omicron compared to Delta was able to explain the observed variation over time in the transmission advantage of the Omicron variant. However, this analysis cannot rule out the role of other factors such as differences in the populations the variants were mixing in, differences in immune escape between variants or bias due to using the test to test distribution as a proxy for the generation time distribution.

Population attributes of Littoraria angulifera (Gastropoda: Littorinidae) in mangroves in Bahia State, northeastern Brazil

Littoraria angulifera (Lamarck, 1822) is an estuarine gastropod of tropical occurrence, which lives mainly on trunks of mangrove tree species. This study aimed to evaluate the population attributes of this species, such as abundance, space-time distribution, sex ratio and recruitment in mangroves in Bahia State, northeastern Brazil. The specimens were collected monthly throughout 2018, on trunks of the red mangrove Rhizophora mangle L. at two heights and on two horizontal levels. Specimens that were on the marine grass Spartina alterniflora Loisel were also collected. After counting, biometrics and sexing, the specimens were returned alive to the environment. The average size and weight of L. angulifera was higher (p<0.05) in places with taller and less sparse trees and the vertical distribution on the trunks showed a preference for strata close to the soil. Both results are related to shading and protection against desiccation. Females were more abundant than males, at an approximate sex ratio F: M of 1.4: 1. Recruits were observed throughout the period, showing continuous reproduction of the species with a recruitment peak in spring (September to November). The study revealed the importance of keep the mangroves intact to allow the maintenance of the natural stocks of the species.

Investigation of Oxy-Fuel Combustion through Reactor Network and Residence Time Data

Oxy-fuel combustion is a promising strategy to minimize the environmental impact of combustion-based energy conversion. Simple and flexible tools are required to facilitate the successful integration of such strategies at the industrial level. This study couples measured residence time distribution with chemical reactor network analysis in a close-to-reality combustor. This provides detailed knowledge about the various mixing and reactive characteristics arising from the use of the two different oxidizing streams.

SUCCESSION PLANNING AS A CRITICAL MANAGEMENT IMPERATIVE: A SYSTEMATIC REVIEW

This paper conducted a systematic review of succession planning (SP) articles published over the last decade. The Systematic Quantitative Assessment Technique was used to identify 174 SP articles. The review covered five key issues: 1) Time distribution, 2) Geographic distribution, 3) Article type, 4) Data collection methods, and 5) Themes explored. The findings revealed that interest in SP fluctuated over the last decade, and that South America and Oceania were the least represented by SP scholarship. The spread between conceptual and empirical SP articles were skewed towards the former, and survey was the most popular data collection method. Five themes were identified, with the most striking finding being that that if the ‘going concern’ principle of organizations is to be achieved, management must make deliberate efforts to formalize the SP process with the clear understanding that it is a continuous, transparent and participatory process, and thus a crucial management imperative.