We prove a surprising symmetry between the law of the size $G_n$ of the greedy independent set on a uniform Cayley tree $ \mathcal{T}_n$ of size n and that of its complement. We show that $G_n$ has the same law as the number of vertices at even height in $ \mathcal{T}_n$ rooted at a uniform vertex. This enables us to compute the exact law of $G_n$. We also give a Markovian construction of the greedy independent set, which highlights the symmetry of $G_n$ and whose proof uses a new Markovian exploration of rooted Cayley trees that is of independent interest.

Dual-purpose sorghum response to anthracnose disease, growth, and yield was undertaken in Derashe and Arba Minch trial sites during March–June 2018 and 2019. Five sorghum varieties and Rara (local check) were arranged in a randomized complete block design with four replications. Variety Chelenko exhibited the tallest main crop plant height (430 cm) while Dishkara was the tallest (196.65 cm) at ratoon crop harvesting. Rara had a higher tiller number (main = 6.73, ratoon = 9.73) among the varieties. Dishkara and Chelenko varieties produced 50 and 10% more dry biomass yield (DBY) than the overall mean DBY, while Konoda produced 40% less. Although the anthracnose infestation was highest on the varieties Konoda (percentage severity index [PSI] = 20.37%) and NTJ_2 (PSI = 32.19%), they produced significantly (p < .001) higher grain yield (3.89 t/ha) than others. Under anthracnose pressure, Chelenko and Dishkara varieties are suggested for dry matter yield while NTJ_2 for grain yield production in the study area and similar agroecology.

During military operations, soldiers are required to successfully complete numerous physical and cognitive tasks concurrently. Understanding the typical variance in research tools that may be used to provide insight into the interrelationship between physical and cognitive performance is therefore highly important. This study assessed the inter-day variability of two military-specific cognitive assessments: a Military-Specific Auditory N-Back Task (MSANT) and a Shoot-/Don’t-Shoot Task (SDST) in 28 participants. Limits of agreement ±95% confidence intervals, standard error of the mean, and smallest detectable change were calculated to quantify the typical variance in task performance. All parameters within the MSANT and SDST demonstrated no mean difference for trial visit in either the seated or walking condition, with equivalency demonstrated for the majority of comparisons. Collectively, these data provided an indication of the typical variance in MSANT and SDST performance, while demonstrating that both assessments can be used during seated and walking conditions.

The response to the COVID-19 pandemic has, from the outset, been characterized by a strong focus on real-time data intelligence and the use of data-driven technologies. Against this backdrop, this article investigates the impacts of the pandemic on Scottish local government’s data practices and, in turn, whether the crisis acted as a driver for digital transformation. Mobilizing the literatures on digital government transformation, and on the impacts of crises on public administrations, the article provides insights into the dynamics of digital transformation during a heightened period of acute demands on the public sector. The research evidences an intensification of public sector data use and sharing in Scottish local authorities, with focus on health-related data and the integration of existing datasets to gather local intelligence. The research reveals significant changes related to the technical and social systems of local government organizations. These include the repurposing and adoption of information systems, the acceleration of inter and intraorganizational data sharing processes, as well as changes in ways of working and in attitudes toward data sharing and collaborations. Drawing on these findings, the article highlights the importance of identifying and articulating specific data needs in relation to concrete policy questions in order to render digital transformation relevant and effective. The article also points to the need of addressing the persistent systemic challenges underlying public sector data engagement through, on one hand, sustained investment in data capabilities and infrastructures and, on the other, support for cross-organizational collaborative spaces and networks.

We investigate expansions for connectedness functions in the random connection model of continuum percolation in powers of the intensity. Precisely, we study the pair-connectedness and the direct-connectedness functions, related to each other via the Ornstein–Zernike equation. We exhibit the fact that the coefficients of the expansions consist of sums over connected and 2-connected graphs. In the physics literature, this is known to be the case more generally for percolation models based on Gibbs point processes and stands in analogy to the formalism developed for correlation functions in liquid-state statistical mechanics.

We find a representation of the direct-connectedness function and bounds on the intensity which allow us to pass to the thermodynamic limit. In some cases (e.g., in high dimensions), the results are valid in almost the entire subcritical regime. Moreover, we relate these expansions to the physics literature and we show how they coincide with the expression provided by the lace expansion.

This article illustrates the use of unsupervised probabilistic learning techniques for the analysis of planetary reentry trajectories. A three-degree-of-freedom model was employed to generate optimal trajectories that comprise the training datasets. The algorithm first extracts the intrinsic structure in the data via a diffusion map approach. We find that data resides on manifolds of much lower dimensionality compared to the high-dimensional state space that describes each trajectory. Using the diffusion coordinates on the graph of training samples, the probabilistic framework subsequently augments the original data with samples that are statistically consistent with the original set. The augmented samples are then used to construct conditional statistics that are ultimately assembled in a path planning algorithm. In this framework, the controls are determined stage by stage during the flight to adapt to changing mission objectives in real-time.

This study assesses governments' long-term non-pharmaceutical interventions upon the coronavirus disease 2019 (COVID-19) pandemic in East Asia. It advances the literature towards a better understanding of when and which control measures are effective. We (1) provide time-varying case fatality ratios and focus on the elderly's mortality and case fatality ratios, (2) measure the correlations between daily new cases (daily new deaths) and each index based on multiple domestic pandemic waves and (3) examine the lead–lag relationship between daily new cases (daily new deaths) and each index via the cross-correlation functions on the pre-whitened series. Our results show that the interventions reduce COVID-19 infections for some periods before the period of the Omicron variant. Moreover, there is no COVID-19 policy lag in Taiwan between daily new confirmed cases and each index. As of March 2022, the case fatality ratios of the elderly group in Japan, Hong Kong and South Korea are 4.69%, 4.72% and 1.48%, respectively, while the case fatality ratio of the elderly group in Taiwan is 25.01%. A government's COVID-19 vaccination distribution and prioritisation policies are pivotal for the elderly group to reduce the number of deaths. Immunising this specific group as best as possible should undoubtedly be a top priority.

This study aimed to assess the impact of the introduction of pneumococcal conjugate vaccine 13 (PCV13) on the molecular epidemiology of invasive pneumococcal disease (IPD) in children from Andalusia. A population-based prospective surveillance study was conducted on IPD in children aged <14 years from Andalusia (2018–2020). Pneumococcal invasive isolates collected between 2006 and 2009 in the two largest tertiary hospitals in Andalusia were used as pre-PCV13 controls for comparison of serotype/genotype distribution. Overall IPD incidence rate was 3.55 cases per 100 000 in 2018; increased non-significantly to 4.20 cases per 100 000 in 2019 and declined in 2020 to 1.69 cases per 100 000 (incidence rate ratio 2020 vs. 2019: 0.40, 95% confidence interval (CI) 0.20–0.89, P = 0.01). Proportion of IPD cases due to PCV13 serotypes in 2018–2020 was 28% (P = 0.0001 for comparison with 2006–2009). Serotypes 24F (15%) and 11A (8.3%) were the most frequently identified non-PCV13 serotypes (NVT) in 2018–2020. Penicillin- and/or ampicillin-resistant clones mostly belonged to clonal complex 156 (serotype 14-ST156 and ST2944 and serotype 11A-ST6521). The proportion of IPD cases caused by PCV13 serotypes declined significantly after the initiation of the PCV13 vaccination programme in 2016. Certain NVT, such as serotypes 24F and 11A, warrant future monitoring in IPD owing to invasive potential and/or antibiotic resistance rates.

This paper studies a mixed singular/switching stochastic control problem for a multidimensional diffusion with multiple regimes on a bounded domain. Using probabilistic partial differential equation and penalization techniques, we show that the value function associated with this problem agrees with the solution to a Hamilton–Jacobi–Bellman equation. In this way, we see that the regularity of the value function is $ \textrm{C}^{0,1}\cap \textrm{W}^{2,\infty}_{\textrm{loc}}$.

This paper explores data and modelling considerations in the risk assessment and underwriting of mental health conditions in life insurance products. Alongside this, it considers the possibilities that improved data availability could open up in terms of additional underwriting designs that could further improve the accessibility and affordability of life insurance products for those with mental health conditions. Rather than being a prescriptive recommendation, our aim is for the considerations set out in this paper to form a basis of discussion for Members of the Profession and other insurance professionals.

Controlling the bias is central to estimating semiparametric models. Many methods have been developed to control bias in estimating conditional expectations while maintaining a desirable variance order. However, these methods typically do not perform well at moderate sample sizes. Moreover, and perhaps related to their performance, nonoptimal windows are selected with undersmoothing needed to ensure the appropriate bias order. In this paper, we propose a recursive differencing estimator for conditional expectations. When this method is combined with a bias control targeting the derivative of the semiparametric expectation, we are able to obtain asymptotic normality under optimal windows. As suggested by the structure of the recursion, in a wide variety of triple index designs, the proposed bias control performs much better at moderate sample sizes than regular or higher-order kernels and local polynomials.