Fix integers $r \ge 2$ and $1\le s_1\le \cdots \le s_{r-1}\le t$ and set $s=\prod _{i=1}^{r-1}s_i$. Let $K=K(s_1, \ldots , s_{r-1}, t)$ denote the complete $r$-partite $r$-uniform hypergraph with parts of size $s_1, \ldots , s_{r-1}, t$. We prove that the Zarankiewicz number $z(n, K)= n^{r-1/s-o(1)}$ provided $t\gt 3^{s+o(s)}$. Previously this was known only for $t \gt ((r-1)(s-1))!$ due to Pohoata and Zakharov. Our novel approach, which uses Behrend’s construction of sets with no 3-term arithmetic progression, also applies for small values of $s_i$, for example, it gives $z(n, K(2,2,7))=n^{11/4-o(1)}$ where the exponent 11/4 is optimal, whereas previously this was only known with 7 replaced by 721.

The rarity of preserved soft tissues in the fossil record has limited our understanding of the life appearance of extinct vertebrates. However, through examination of various osteological features and comparisons with extant ecomorphological analogues, we can predict some of the external characteristics of ancient taxa. Specifically, for the Cretaceous mosasaurians (a group of seagoing squamates), extant sharks serve as suitable modern analogues because of their comparable caudal vertebral morphologies and ecologies. In this study, we build a novel framework by combining two-block partial least squares (2B-PLS) regression analysis and geometric morphometrics to investigate the relationship between tail fin shape and the underlying musculoskeletal morphology in sharks and mosasaurians. Our analysis reveals a strong correlation between the “tail fin expanded soft tissue” (TFEST) and shape of the associated caudal skeleton/musculature. Moreover, the covariation pattern between these two structures is remarkably similar in sharks and mosasaurians. Based on these findings, we then develop a predictive model that reconstructs the tail fin in mosasaurian taxa without known soft tissues. Our model indicates that all hydropedal forms possessed a bilobed, hypocercal (downturned) fluke, while plesiopedal species lacked a well-developed fleshy dorsal lobe. The variation in fluke morphologies between the four different evolutionary lineages of derived mosasaurians (mosasaurines, halisaurines, plioplatecarpines, and tylosaurines) suggests multiple independent origins of a bilobed tail fin. This study thus highlights the complexity of aquatic adaptations in mosasaurians and demonstrates the utility of predictive models when reconstructing the life appearance of extinct animals.

We study stationary distributions in the context of stochastic reaction networks. In particular, we are interested in complex balanced reaction networks and the reduction of such networks by assuming that a set of species (called non-interacting species) are degraded fast (and therefore essentially absent from the network), implying that some reaction rates are large relative to others. Technically, we assume that these reaction rates are scaled by a common parameter N and let $N\to\infty$. The limiting stationary distribution as $N\to\infty$ is compared with the stationary distribution of the reduced reaction network obtained by elimination of the non-interacting species. In general, the limiting stationary distribution could differ from the stationary distribution of the reduced reaction network. We identify various sufficient conditions under which these two distributions are the same, including when the reaction network is detailed balanced and when the set of non-interacting species consists of intermediate species. In the latter case, the limiting stationary distribution essentially retains the form of the complex balanced distribution. This finding is particularly surprising given that the reduced reaction network could be non-weakly reversible and might exhibit unconventional kinetics.

Gas turbine maintenance strategy relies heavily on accurate estimation of critical component life consumption of gas turbine engines during their operations. The equivalent operating hours (EOH) is a useful concept to measure the engine life consumption and support condition-based maintenance planning for gas turbine engines and their critical components. However, the current EOH calculation methods are mostly empirical and engine-specific, relying on vast operating data and experience. This paper introduces a novel physics-based method to estimate the EOH of the high-pressure turbine rotor blades of a gas turbine engine based on the damages caused by creep and low-cycle fatigue (creep-LCF) interactions. The method has been applied to a typical turbofan engine taking both 440-minute long-haul flight at one flight per day and 60-minute short-haul flight at two flights per day. A comparison of the predicted damages and life consumptions indicates that the creep EOH and also the creep damage of the engine of the short-haul aircraft is about 1.38 times that of the engine of the long-haul aircraft, the LCF equivalent operating cycles (EOC) and also the LCF damage of the engine of the short-haul aircraft is about 2.0 times that of the engine of the long-haul aircraft, and the total damages are more affected by the creep damage than the LCF damage with the creep damage being 6.78 times the LCF damage for the engine of the short-haul aircraft and 9.81 times for the engine of the long-haul aircraft. In addition, the total EOH or the total damage of the engine of the short-haul aircraft is about 1.44 times that of the engine of the long-haul aircraft. The proposed method shows a great potential to provide a quick estimate of the life consumption of gas turbine engines for condition monitoring, and it can be applied to other types of gas turbine engines.

The COVID-19 pandemic profoundly disrupted societies worldwide, creating not only a global health emergency but also a severe test of governance. Governments were required to mobilise resources with unprecedented urgency, under conditions of uncertainty and limited oversight. In this setting, politicians and bureaucrats exercised unusually broad discretion over resource allocation. We argue that these conditions created opportunities for corruption – what we term crisis-induced corruption – the misuse of public resources that emerges in crisis contexts where urgent spending collides with fragile oversight. Drawing on Afrobarometer Round 9 surveys from 39 African countries, we examine how perception of crisis-induced corruption (COVID-19 corruption) shaped citizens’ evaluations of government mismanagement and whether these effects varied with institutional quality (control of corruption). Results from multilevel models show that citizens who perceive higher levels of COVID-19 corruption are more likely to judge their governments as mismanaging the pandemic. However, contrary to expectations, we do not find evidence that stronger corruption control buffers governments from these negative perceptions. Instead, in countries with higher corruption control, corruption perceptions are linked to a sharper increase in perceived government mismanagement of the pandemic. Robustness checks – including disaggregating government mismanagement into pandemic management and relief distribution, and employing alternative outcomes such as trust in vaccine safety and satisfaction with relief provision – confirm the stability of these results. The findings highlight not only the damaging impact of corruption during global emergencies but also the critical importance of effective crisis management for sustaining public trust.

Urban agriculture on extensive green roofs (EGRs), which are lightweight, shallow-profile systems with low maintenance, presents a viable opportunity to enhance food production and ecosystem services in cities. However, the harsh environmental conditions typical of EGRs pose challenges for crop cultivation, especially regarding water availability. This study investigates whether facilitative interactions with a common green roof cover species, Sedum, with bush beans (Phaseolus vulgaris) as our model crop, can improve crop performance under water stress. We tested 48 EGR modules with three planting designs (no Sedum, artificial Sedum, and live Sedum) under two watering regimes (high and low) at a green roof testing facility in Toronto, Canada, and measured above- and belowground functional traits of beans to assess productivity and trait plasticity. Results revealed that water availability had a greater influence on bean performance than planting design, where beans grown with artificial Sedum under high watering showed the highest shoot biomass and yield, while performance declined significantly under low water conditions, particularly with live Sedum. Leaf physiological traits were largely unaffected by treatment, likely due to the variable rooftop conditions, and root traits were significantly influenced by both water availability and planting design. Hypervolume analyses showed that beans exhibited greater root trait plasticity than Sedum, suggesting a stronger capacity to adapt to water stress. Contrary to the hypotheses, live Sedum did not consistently facilitate bean performance, and potential competitive interactions may have outweighed any stress-ameliorating effects. These findings show water management as the main management variable for crops on EGRs. To transition EGRs into viable agricultural spaces, future strategies should explore alternative facilitative species, nutrient amendments, and microbial inoculations to support crop resilience.

Diastasis of rectus abdominis (DRA) is a common pathological condition in postpartum rehabilitation, but with limited treatment strategies. This study aimed to explore the effect of using a trunk-wearable neuromuscular electrical stimulation (NMES) device on postpartum women with moderate and severe DRA. A total of 84 postpartum women with an inter-rectus distance (IRD) of ≥3 cm were randomly assigned to two equal groups. The treatment group received a trunk-wearable NMES device and exercise therapy, whereas the control group received exercise only. We measured IRD and calculated treatment response proportion, improvement of trunk muscle strength, and low-back pain in both groups. Additionally, we evaluated quality of life (QoL) using the SF-36 questionnaire and Hernia-related Quality of Life Survey (HerQLes). Statistical analysis was performed using SAS 9.4. After 8-week treatment, the IRD of the umbilical (M3) sector showed a greater reduction in the treatment group (−10.6 [−17.9 to −3.3]%, p < 0.05). Patients in the treatment group had higher treatment response proportions (p = 0.0031 and p = 0.0010, W2 and W3, respectively). Additionally, the treatment group had higher Janda assessment scores and greater reduction in low-back pain (both p < 0.0001). QoL evaluation indicated greater improvements in the SF-36 questionnaire (pain and role-emotional scales,p < 0.05) and HerQLes (p < 0.0001) in the treatment group. The application of a trunk-wearable NMES device on DRA patients, accompanied by exercise therapy, significantly reduced IRD and increased the treatment response proportion. Moreover, we observed positive improvements in trunk muscle strength, low-back pain, and QoL.

This study uses a basket-based choice experiment with 2,010 U.S. adults to analyze alcohol and cannabis preferences in social settings following cannabis legalization. Through descriptive statistics and multivariate logistic modeling, we highlight the heterogeneous preferences consumers have for alcohol and cannabis products. Specifically, we demonstrate that a substantial portion of the survey respondents prefer to consume these substances together in social settings, while others view them as independent markets. Regression analysis then reveals that males and younger consumers are most likely to bundle these substances, while personality traits also correlate with expected simultaneous substance use. These results offer valuable insights to improve public health policy and messaging on the potential short- and long-term risks associated with cosubstance use.