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•Outbreak potential is greater than expected if non-vaccination is clustered.•Vaccination targets are insufficient to achieve herd immunity in many settings.•Impact of susceptibility clustering highest in countries near disease elimination.•Countries with high vaccination should shift focus to local vaccination targets. Measles elimination efforts are primarily focused on achieving and maintaining national vaccination coverage goals, based on estimates of the critical vaccination threshold (Vc): the proportion of the population that must be immune to prevent sustained epidemics. Traditionally, Vc estimates assume evenly mixing populations, an invalid assumption. If susceptible individuals preferentially contact one another, communities may remain vulnerable to epidemics even when vaccination coverage targets are met at the national level. Here we present a simple method to estimate Vc and the effective reproductive number, R, while accounting for spatial clustering of susceptibility. For measles, assuming R0 = 15 and 95% population immunity, adjustment for high clustering of susceptibility increases R from 0.75 to 1.29, Vc from 93% to 96%, and outbreak probability after a single introduction from <1% to 23%. The impact of clustering remains minimal until vaccination coverage nears elimination levels. We illustrate our approach using Demographic and Health Survey data from Tanzania and show how non-vaccination clustering potentially contributed to continued endemic transmission of measles virus during the last two decades. Our approach demonstrates why high national vaccination coverage sometimes fails to achieve measles elimination, and that a shift from national to subnational focus is needed as countries approach elimination.

We study the large-time behaviour of Eulerian systems augmented with non-local alignment. Such systems arise as hydrodynamic descriptions of agent-based models for self-organized dynamics, e.g. Cucker & Smale (2007 IEEE Trans. Autom. Control 52, 852-862. (doi:10.1109/TAC.2007.895842)) and Motsch & Tadmor (2011 J. Stat. Phys. 144, 923-947. (doi:10.1007/s10955-011-0285-9)) models. We prove that, in analogy with the agent-based models, the presence of non-local alignment enforces strong solutions to self-organize into a macroscopic flock. This then raises the question of existence of such strong solutions. We address this question in one- and two-dimensional set-ups, proving global regularity for subcritical initial data. Indeed, we show that there exist critical thresholds in the phase space of the initial configuration which dictate the global regularity versus a finite-time blow-up. In particular, we explore the regularity of non-local alignment in the presence of vacuum.

High temperature may lead to the development of new microcracks or growth of pre-existing microcracks within granite, varying its physical and mechanical properties. Experiments were conducted to study the evolution of the physical and mechanical properties of granite specimens from room temperature to 800 °C. The specimens were heated in heating furnace and uniaxial compression tests were done using MTS servo-controlled testing machine. The results indicate five phases in the variation of physical and mechanical properties with temperature: from room temperature to 100, 100–300, 300–400, 400–600, and 600–800 °C. The first phase corresponds to the vaporization-escaping interval of adhered water, bound water, and structural water. Larger changes of physical and mechanical parameters in the temperature range of 300–600 °C, mostly 400–600 °C, are probably caused by the transition from the brittle state to plasticity (or ductility) of granite, and 400 °C may be a critical threshold of its thermal damage. These results confirm the important link among physical and mechanical properties in response to thermal treatment.

Droughts have increased globally in the twenty-first century and are expected to become more extreme and widespread in the future. Assessments of how drought affects plants and ecosystems lack consistency in scope and methodology, confounding efforts to mechanistically interpret structural and functional impacts and predict future transformations under climate change. To promote integration among studies, we identify water deficit conditions that are ecologically meaningful, clarify the stages in which ecological drought progresses, and consider approaches to synthesize drought effects across multiple species and ecosystems. This improved ecological drought framework reveals advantages of using different ecological drought metrics and strengthens approaches to distinguish ecosystem stress from crossing an irreversible threshold. We employ several well-studied examples from water-limited ecosystems, which contain plants that are often at their physiological limits and highly responsive to climate variability. We suggest that emerging research on early warning signs, drought recovery, and the effects of land management interventions be incorporated into the ecological drought framework. An integrative approach to understand ecological drought can accelerate scientific advancement and create opportunity to adapt and prepare for crossing irreversible ecosystem thresholds.

Interdependent networks in areas ranging from infrastructure to economics are ubiquitous in our society, and the study of their cascading behaviors using percolation theory has attracted much attention in recent years. To analyze the percolation phenomena of these systems, different mathematical frameworks have been proposed, including generating functions and eigenvalues, and others. These different frameworks approach phase transition behaviors from different angles and have been very successful in shaping the different quantities of interest, including critical threshold, size of the giant component, order of phase transition, and the dynamics of cascading. These methods also vary in their mathematical complexity in dealing with interdependent networks that have additional complexity in terms of the correlation among different layers of networks or links. In this work, we review a particular approach of simple, self-consistent probability equations, and we illustrate that this approach can greatly simplify the mathematical analysis for systems ranging from single-layer network to various different interdependent networks. We give an overview of the detailed framework to study the nature of the critical phase transition, the value of the critical threshold, and the size of the giant component for these different systems.

While most cases of pancreatitis in dogs are thought to be idiopathic, potential risk factors are identified. In this article we provide a state‐of‐the‐art overview of suspected risk factors for pancreatitis in dogs, allowing for improved awareness and detection of potential dog‐specific risk factors, which might guide the development of disease prevention strategies. Additionally, we review important advances in our understanding of the pathophysiology of pancreatitis and potential areas for therapeutic manipulation based thereof. The outcome of pathophysiologic mechanisms and the development of clinical disease is dependent on the balance between stressors and protective mechanisms, which can be evaluated using the critical threshold theory.

Although absolute jump heights should be considered an important factor in judging the performance requirements of volleyball players, limited data is available on age-appropriate categories. The purpose of this study is to determine the differences in specific anthropometric characteristics and jumping performance variables in under−19 female volleyball players in relation to playing position and performance level. The sample of subjects consisted of 354 players who prepared for the U19 Women’s Volleyball European Championship 2020 (17.4 ± 0.8 years, 1.81 ± 0.07 m, 67.5 ± 7.1 kg). Playing positions analyzed were setters (n = 55), opposites (n = 37), middle blockers (n = 82), outside hitters (n = 137), and liberos (n = 43). The results showed player position differences in every performance level group in variables of body height, spike, and block jump. Observed differences are a consequence of highly specific tasks of different positions in the composition of the team. Players of different performance levels are significantly different, with athletes of higher-ranked teams achieving better results. The acquired data could be useful for the selection and profiling of young volleyball players.

The onset of xylogenesis plays an important role in tree growth and carbon sequestration, and it is thus a key variable in modelling the responses of forest ecosystems to climate change. Temperature regulates the resumption of cambial activity, but little is known about the effect of water availability on the onset of xylogenesis in cold but semi-arid regions. The onset of xylogenesis during 2009-2014 was monitored by weekly microcoring Juniperus przewalskii trees at upper and lower treelines on the north-eastern Tibetan Plateau. A logistic regression was used to calculate the probability of xylogenic activity at a given temperature and a two-dimensional reverse Gaussian model to fit the differences between the observed and estimated days of xylogenesis onset at given temperatures and precipitation within a certain time window. The thermal thresholds at the beginning of the growing season were highly variable, suggesting that temperature was not the only factor initiating xylem growth under cold and dry climatic conditions. The onset of xylogenesis was well predicted for climatic thresholds characterized by a cumulative precipitation of 17.0 ± 5.6 mm and an average minimum temperature of 1.5 ± 1.4 °C for a period of 12 d. Xylogenesis in semi-arid regions with dry winters and springs can start when both critical temperature and precipitation thresholds are reached. Such findings contribute to our knowledge of the environmental drivers of growth resumption that previously had been investigated largely in cold regions without water shortages during early growing seasons. Models of the onset of xylogenesis should include water availability to improve predictions of xylem phenology in dry areas. A mismatch between the thresholds of temperature and moisture for the onset of xylogenesis may increase forest vulnerability in semi-arid areas under forecasted warmer and drier conditions.

We expand the critical point for site percolation on the d -dimensional hypercubic lattice in terms of inverse powers of 2 d , and we obtain the first three terms rigorously. This is achieved using the lace expansion.