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.

Alweiss, Lovett, Wu, and Zhang introduced $q$-spread hypergraphs in their breakthrough work regarding the sunflower conjecture, and since then $q$-spread hypergraphs have been used to give short proofs of several outstanding problems in probabilistic combinatorics. A variant of $q$-spread hypergraphs was implicitly used by Kahn, Narayanan, and Park to determine the threshold for when a square of a Hamiltonian cycle appears in the random graph $G_{n,p}$. In this paper, we give a common generalization of the original notion of $q$-spread hypergraphs and the variant used by Kahn, Narayanan, and Park.

Carl Knight argues that lexical sufficientarianism, which holds that sufficientarian concerns should have lexical priority over other distributive goals, is ‘excessive’ in many distinct ways and that sufficientarians should either defend weighted sufficientarianism or become prioritarians. In this article, I distinguish three types of weighted sufficientarianism and propose a weighted sufficientarian view that meets the excessiveness objection and is preferable to both Knight’s proposal and prioritarianism. More specifically, I defend a multi-threshold view which gives weighted priority to benefits directly above and below its thresholds, but gives benefits below the lowest threshold lexical priority over benefits above the highest threshold.

The influence of weeds on cranberry yield and quality is not well known and cannot be extrapolated from other cropping systems given the unique nature of both cranberry production and the weed species spectrum. The work presented here addresses this need with four common weed species across multiple production seasons and systems in Wisconsin, Massachusetts, and New Jersey: Carolina redroot, earth loosestrife, bristly dewberry, and polytrichum moss. The objectives were to use these representative species to quantify the impact of weed density, groundcover, and biomass on several cranberry yield components and related interactions with other cranberry pests, and to determine whether these relationships were consistent enough across seasons to be reliably used in weed management decision-making. The relationships between Carolina redroot and bristly dewberry growth measures and marketable cranberry yield were highly significant (P ≤ 0.001 in 12 of 13 regressions) and consistent across growing seasons, but not significant for similar regressions with earth loosestrife. In particular, the strong relationship between Carolina redroot and bristly dewberry visual groundcover observations and cranberry yield suggests a simple way for growers and crop scouts to reliably estimate yield loss. The relationship between polytrichum moss biomass and cranberry yield was also significant in both years, but not consistent between years. Weed competition also affected cranberry quality, in that Carolina redroot density was strongly related to the percentage of insect-damaged fruit and bristly dewberry growth reduced cranberry color development. On a practical level, this information can be used to educate growers, consultants, agrichemical registrants, and regulators about the impacts of weeds on cranberry yield and quality, and to economically prioritize management efforts based on the weed species and extent of infestation.

Existing studies on legal approaches to ethnic minority representation often highlight different systems’ strengths and weaknesses. While this scholarship provides important insights into the growing body of literature on minority representation, the topic remains largely under-theorized. Because systems of ethnic minority representation clarify the organizations and philosophies of diverse states, more theoretical analyses can enrich the descriptive literature. Building on the existing scholarship, this article assesses Romania’s particular version of proportional representation regarding designated national minorities. It applies two theoretical models: (1) institutional activism and (2) ethnic intermediation. The former clarifies the establishment of Romania’s post-communist constitutional provisions regarding minority organizations, and the latter explains how small yet influential minority populations make claims to and reallocate resources from the Romanian state. Through a unique, understudied case study – the Armenian community of Romania – this article attempts to broaden ethnic minority representation scholarship by refining the theoretical frameworks of institutional activism and ethnic intermediation.

Influenza and respiratory syncytial virus (RSV) are common causes of respiratory tract infections and place a burden on health services each winter. Systems to describe the timing and intensity of such activity will improve the public health response and deployment of interventions to these pressures. Here we develop early warning and activity intensity thresholds for monitoring influenza and RSV using two novel data sources: general practitioner out-of-hours consultations (GP OOH) and telehealth calls (NHS 111). Moving Epidemic Method (MEM) thresholds were developed for winter 2017–2018. The NHS 111 cold/flu threshold was breached several weeks in advance of other systems. The NHS 111 RSV epidemic threshold was breached in week 41, in advance of RSV laboratory reporting. Combining the use of MEM thresholds with daily monitoring of NHS 111 and GP OOH syndromic surveillance systems provides the potential to alert to threshold breaches in real-time. An advantage of using thresholds across different health systems is the ability to capture a range of healthcare-seeking behaviour, which may reflect differences in disease severity. This study also provides a quantifiable measure of seasonal RSV activity, which contributes to our understanding of RSV activity in advance of the potential introduction of new RSV vaccines.

Creontiades dilutus (green mirid) and C. pacificus (brown mirid) are major hemipteran pests of transgenic (Bt) cotton in Australia. Current integrated pest management (IPM) guidelines for mirids in Australian cotton, based on economic thresholds and sampling recommendations, were developed and disseminated to industry at the start of the 2005–06 growing season and have remained largely unchanged since then. However, adoption of mirid IPM guidelines by industry has been highly variable and generally well below expectation. Annual surveys of crop protection practices across the Australian cotton industry, from 2010 to 2017, indicate that a third of all mirid sprays are applied below the recommended thresholds each year. More than half of all survey respondents in the 2017 survey indicated lack of confidence in the mirid thresholds due to highly variable and disproportionate damage, a phenomenon best described as the ‘mirid enigma’. A critical review of RD&E outputs since 1998 shows that potential contributors to the mirid enigma include but are not limited to biological, ecological and methodological factors. Mirid feeding damage is likely to vary with developmental stage, gender and reproductive status. Ecological factors including trophic effects and multiple host plant usage are potential modifiers of mirid feeding damage. Methodological and technological constraints and shortcomings are evident in the threshold research done to date. Inadequate commercial sampling that results in unreliable estimates of pest density in the crop is a major contributor to the mirid enigma. Failure to account for the complexity of factors that can influence the nature and severity of mirid damage to cotton often results in fruit loss due to non-mirid related factors being incorrectly attributed to mirids. An alternative approach to mirid management based on modelling the dynamics of net fruit load (production–loss) proposed over 15 years ago is discussed.