Given a family of graphs $\mathcal{F}$ and an integer $r$, we say that a graph is $r$-Ramsey for $\mathcal{F}$ if any $r$-colouring of its edges admits a monochromatic copy of a graph from $\mathcal{F}$. The threshold for the classic Ramsey property, where $\mathcal{F}$ consists of one graph, in the binomial random graph was located in the celebrated work of Rödl and Ruciński.

In this paper, we offer a twofold generalisation to the Rödl–Ruciński theorem. First, we show that the list-colouring version of the property has the same threshold. Second, we extend this result to finite families $\mathcal{F}$, where the threshold statements might also diverge. This also confirms further special cases of the Kohayakawa–Kreuter conjecture. Along the way, we supply a short(-ish), self-contained proof of the $0$-statement of the Rödl–Ruciński theorem.

Limited Aggregation is the view that when there are competing moral claims that demand our attention, we should sometimes satisfy the largest aggregate of claims, depending on the strength of the claims in question. In recent years, philosophers such as Patrick Tomlin and Alastair Norcross have argued that Limited Aggregation violates a number of rational choice principles such as Transitivity, Separability, and Contraction Consistency. Current versions of Limited Aggregation are what may be called Comparative Approaches because they involve assessing the relative strengths of various claims. In this paper, we offer a non-comparative version of Limited Aggregation, what we call the Threshold Approach. It states that there is a non-relative threshold that separates various claims. We demonstrate that the Threshold Approach does not violate rational choice principles such as Transitivity, Separability, and Contraction Consistency, and we show that potential concerns regarding such a view are surmountable.

The proposal of improving reproducibility by lowering the significance threshold to 0.005 has been discussed, but the impact on conducting clinical trials has yet to be examined from a study design perspective. The impact on sample size and study duration was investigated using design setups from 125 phase II studies published between 2015 and 2022. The impact was assessed using percent increase in sample size and additional years of accrual with the medians being 110.97% higher and 2.65 years longer respectively. The results indicated that this proposal causes additional financial burdens that reduce the efficiency of conducting clinical trials.

We extend a recent argument of Kahn, Narayanan and Park ((2021) Proceedings of the AMS 149 3201–3208) about the threshold for the appearance of the square of a Hamilton cycle to other spanning structures. In particular, for any spanning graph, we give a sufficient condition under which we may determine its threshold. As an application, we find the threshold for a set of cyclically ordered copies of $C_4$ that span the entire vertex set, so that any two consecutive copies overlap in exactly one edge and all overlapping edges are disjoint. This answers a question of Frieze. We also determine the threshold for edge-overlapping spanning $K_r$-cycles.

Arising of disasters by climate change had affected crop growth and yield, and then threaten local to global food security, particularly heat stress. Therefore, hazard assessment is essential to develop effective disaster risk management and adaptation interventions to ensure food security. In this study, the accumulated heat stress days (DAY), heat stress intensity (HSI) and heat degree-days (HDD) during the post-silking period of summer maize in The Huang-Huai-Hai Plain were investigated. Based on the optimal probability distribution function of HDD and information diffusion theory, we compute heat stress classification index and the possibility of heat stress, respectively. During 1981–2019, DAY, HSI and HDD were 11.8 d, 31.9°C and 23.6°Cd and increased by 0.67 d/decade, 0.10°C/decade and 3.14°Cd/decade, respectively. The threshold and hazard probability of mild, moderate and severe heat stress were 9.4, 19.4 and 34.2°Cd and 16.6, 9.3 and 4.5%, respectively. The heat stress hazard index (M) was 0.48, ranged from 0 to 0.77 during 1981 to 2019. M will increase in the future at all regions, particularly after 2060. Under SSP5-8.5 climate scenario, M ranged from 0.95 to 1.20 in 2080s, about two times than historical period. This could be used in optimizing agricultural management in summer maize production in order to combat heat stress under projected climate change.

In people and animals, low birth weight (LBW) is recognized as highly predictive of health trajectory from the neonatal period to elderly ages. Regarding the neonatal period, although LBW is recognized as a major risk factor for neonatal mortality, there does not appear to be a clear definition of ‘when a birth weight should be considered low’ in all species. The aim of this work was to use the scientific literature available to map the various thresholds proposed to define LBW in domestic mammals. Using a standardized methodology, a scoping review was conducted through a literature search in three different bibliographic databases. After a two-step screening of 1729 abstracts and full-text publications by two independent reviewers, eleven studies met the inclusion criteria. Selected publications represented six mammalian species (rat, mouse, dog, pig, cow, and rabbit). Birth weight thresholds were identified through six different methods. In addition to the scarcity of scientific literature about the definition of LBW, this scoping review revealed the lack of standardization for the description, evaluation or the pertinence these definitions. Because the health consequences of LBW could be preventable, providing early identification of at-risk neonates, a consensus for the standardized definition of LBW is required.

The study of threshold functions has a long history in random graph theory. It is known that the thresholds for minimum degree k, k-connectivity, as well as k-robustness coincide for a binomial random graph. In this paper we consider an inhomogeneous random graph model, which is obtained by including each possible edge independently with an individual probability. Based on an intuitive concept of neighborhood density, we show two sufficient conditions guaranteeing k-connectivity and k-robustness, respectively, which are asymptotically equivalent. Our framework sheds some light on extending uniform threshold values in homogeneous random graphs to threshold landscapes in inhomogeneous random graphs.

Strapdown inertial navigation systems are widely used in surface ships and warships. Although high-precision optical fibre inertial navigation systems are available, they have high cost and limited practicality. Therefore, they cannot replace the traditional platform inertial navigation systems in all ships. Hence, microelectromechanical system (MEMS)-based inertial sensors are widely used for robust navigation. Accurate and timely identification of sensor faults while ensuring stable navigation is a challenging task. This paper proposes a robust fault detection (FD) approach for a low-cost system that loosely integrates a strapdown inertial navigation system and the global navigation satellite system, where the integrated navigation state estimation provides high-accuracy output. A cubature Hi/H∞-optimised FD filter was designed for a nonlinear discrete time-varying system considering sensitivity to faults and robustness to disturbances. Furthermore, a threshold for FD was derived considering a compromise between the false alarm rate and fault diagnosis accuracy. Finally, the proposed method was validated through simulations using multiple noise distribution sensor data generated by a ship-manoeuvring simulator.

Rapid and comprehensive social change is required to mitigate pressing environmental issues such as climate change. Social tipping interventions have been proposed as a policy tool for creating this kind of change. Social tipping means that a small minority committed to a target behaviour can create a self-reinforcing dynamic, which establishes the target behaviour as a social norm. The possibility of achieving the large-scale diffusion of pro-environmental norms and related behaviours with an intervention delimited in size and time is tempting. Yet, the canonical model of tipping, the coordination game, may evoke overly optimistic expectations regarding the potential of tipping, due to the underlying assumption of homogenous preferences. Relaxing this assumption, we devise a threshold model of tipping pro-environmental norm diffusion. The model suggests that depending on the distribution of social preferences in a population, and the individual cost of adopting a given pro-environmental behaviour, the same intervention can activate tipping, have little effect, or produce a backlash. Favourable to tip pro-environmental norms are widespread advantageous inequity aversion and low adoption costs. Adverse are widespread self-regarding preferences or disadvantageous inequity aversion, and high costs. We discuss the policy implications of these findings and suggest suitable intervention strategies for different contexts.

This article looks at the complexity of the thought processes that lead Seneca's Oedipus to choose the mors longa of blindness as punishment for his crime (in his blindness, he is to live in a kind of ostracism, separately from both the living and the dead). It offers an analysis of the consolation of this existence on the threshold between life and death, notably with reference to the end of the Oedipus, but also of the sorrow of this liminal existence. The latter is described in Seneca's Phoenissae, which suggests an escape, by death stricto sensu, from the threshold represented by blindness, by which Oedipus now feels trapped.

By examining these three topics, the article shows how the threshold between life and death which Oedipus chooses at the end of Seneca's Oedipus and experiences in the Phoenissae mirrors the ambivalence and the errors of his life before he blinded himself. Ultimately, it also illustrates Oedipus’ continuing failure to achieve self-knowledge.

The critical period for weed control (CPWC) adds value to integrated weed management by identifying the period during which weeds need to be controlled to avoid yield losses exceeding a defined threshold. However, the traditional application of the CPWC does not identify the timing of control needed for weeds that emerge late in the critical period. In this study, CPWC models were developed from field data in high-yielding cotton crops during three summer seasons from 2005 to 2008, using the mimic weed, common sunflower, at densities of two to 20 plants per square meter. Common sunflower plants were introduced at up to 450 growing degree days (GDD) after crop planting and removed at successive 200 GDD intervals after introduction. The CPWC models were described using extended Gompertz and logistic functions that included weed density, time of weed introduction, and time of weed removal (logistic function only) in the relationships. The resulting models defined the CPWC for late-emerging weeds, identifying a period after weed emergence before weed control was required to prevent yield loss exceeding the yield-loss threshold. When weeds emerged in sufficient numbers toward the end of the critical period, the model predicted that crop yield loss resulting from competition by these weeds would not exceed the yield-loss threshold until well after the end of the CPWC. These findings support the traditional practice of ensuring weeds are controlled before crop canopy closure, with later weed control inputs used as required.

Glyphosate-tolerant and glyphosate-resistant weeds are becoming increasingly problematic in cotton fields in Australia, necessitating a return from a glyphosate dominated system to a more integrated approach to weed management. The development of an integrated weed management system can be facilitated by identifying the critical period for weed control (CPWC), a model that enables cotton growers to optimize the timing of their weed control inputs. Using data from field studies conducted from 2003 to 2015, CPWC models using extended functions, including weed biomass in the relationships, were developed for the mimic weeds, common sunflower and Japanese millet, in high-yielding, fully irrigated cotton. A multispecies CPWC model was developed after combining these data sets with data for mungbean in irrigated cotton, using weed height and weed biomass as descriptors in the models. Comparison of observed and predicted relative cotton-lint yields from the multispecies CPWC model demonstrated that the model reasonably described the competition from these three very different mimic weeds, opening the possibility for cotton growers to use a multispecies CPWC model in their production systems.