This paper is concerned with the optimal number of redundant allocation to n-component coherent systems consisting of heterogeneous dependent components. We assume that the system is built up of L groups of different components, $L\geq 1$, where there are $n_i$ components in group i, and $\sum_{i=1}^{L}n_i=n$. The problem of interest is to allocate $v_i$ active redundant components to each component of type i, $i=1,\dots, L$. To get the optimal values of $v_i$ we propose two cost-based criteria. One of them is introduced based on the costs of renewing the failed components and the costs of refreshing the alive ones at the system failure time. The other criterion is proposed based on the costs of replacing the system at its failure time or at a predetermined time $\tau$, whichever occurs first. The expressions for the proposed functions are derived using the mixture representation of the system reliability function based on the notion of survival signature. We assume that a given copula function models the dependency structure between the components. In the particular case that the system is a series-parallel structure, we provide the formulas for the proposed cost-based functions. The results are discussed numerically for some specific coherent systems.

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.