Rewrite the prose.
Keep every claim.

After a median follow-up of 31 months, patients randomised to early anticoagulation had a lower incidence of the composite primary endpoint than those assigned to delayed treatment (hazard ratio 0.78, 95% CI 0.64 to 0.95; p = 0.013). The reduction was smaller among participants aged 75 years or older, which may partly reflect the higher rate of major bleeding in that subgroup (Table 3).

After a median of 31 months of follow-up, the composite primary endpoint occurred less often among participants randomised to early anticoagulation than among those allocated to delayed treatment (p = 0.013); the hazard ratio was 0.78 (95% CI 0.64 to 0.95). In patients aged 75 years and over, the reduction was less marked, which may in part reflect the greater frequency of major bleeding in this subgroup (Table 3).

Between 2019 and 2023, childhood obesity prevalence fell by 4.2 percentage points in districts that adopted the sugar-sweetened beverage levy, against 1.6 points in districts that did not (Fig. 2). This difference is consistent with a protective effect of the levy but does not establish one: adoption was voluntary rather than randomised, and only 14 of the 61 districts supplied complete follow-up data.

In districts adopting the sugar-sweetened beverage levy, childhood obesity prevalence dropped by 4.2 percentage points from 2019 to 2023, compared with 1.6 points in non-adopting districts (Fig. 2). Although consistent with the levy having a protective effect, the difference does not establish that such an effect exists, because adoption was left to each district instead of being randomised, and only 14 districts out of 61 returned complete follow-up data.

After 28 days of curing at 5 °C, the fly ash specimens reached a mean compressive strength of 31.2 MPa, 14% lower than the companion set cured at 20 °C. Chloride diffusivity, by contrast, did not differ significantly between the two regimes. The strength deficit may stem from a slower pozzolanic reaction at low temperature rather than from any change in porosity.

For the fly ash specimens cured at 5 °C, mean compressive strength after 28 days was 31.2 MPa, a value 14% lower than that of the companion specimens cured at 20 °C. In contrast, chloride diffusivity showed no significant difference between the two regimes. This shortfall in strength may be due to the pozzolanic reaction proceeding more slowly under low-temperature curing, rather than to any change in porosity.

As shown in Table 4, the pruned model retained 97.8% of the baseline accuracy while cutting inference latency from 41 ms to 26 ms per batch. These gains held for all three datasets but did not carry over to the quantised variant described in Algorithm 2. We therefore follow the calibration procedure of [12] rather than the per-layer scheme proposed in [7].

Table 4 shows that the pruned model preserved 97.8% of baseline accuracy while reducing per-batch inference latency to 26 ms, down from 41 ms. The gains held across all three datasets, yet they did not extend to the quantised variant outlined in Algorithm 2. For this reason, we calibrate using the procedure of [12] instead of the per-layer scheme put forward in [7].

Consistent with earlier work on attentional bias (Okafor et al., 2021), most participants in the high-anxiety group fixated on threat-related faces within the first 500 ms of each trial. However, this pattern emerged only when stimuli were presented peripherally; with central presentation, fixation latencies did not differ between groups, suggesting that spatial uncertainty may be a necessary condition for the bias.

In the high-anxiety group, most participants fixated threat-related faces during the initial 500 ms of every trial, a finding in line with earlier attentional bias research (Okafor et al., 2021). The pattern was observed, however, only when the stimuli appeared in the periphery; with centrally presented stimuli, the groups showed no difference in fixation latency, which suggests that the bias may require spatial uncertainty.

Following the 2019 childcare reform, the share of mothers with children under five working full time rose by 2.4 percentage points (Table 3). The rise appears to stem mainly from part-time employees extending their hours, rather than from inactive mothers entering work: transitions out of inactivity did not increase relative to the pre-reform trend in any of the 12 quarters examined.

Among mothers of under-fives, the proportion in full-time work increased by 2.4 percentage points after the 2019 childcare reform (Table 3). This increase appears to be driven chiefly by part-time employees lengthening their hours rather than by inactive mothers taking up employment: in none of the 12 quarters studied did transitions out of inactivity rise above the pre-reform trend.

The crude ester was first dissolved in anhydrous toluene and stirred at 65 °C for 2 h under nitrogen. The mixture was then cooled to 0 °C, after which triethylamine (1.2 equiv.) was added dropwise over 15 min. Finally, the solids were removed by filtration and the filtrate was concentrated under reduced pressure, giving the product in 81% yield (Table 2).

First, the crude ester was taken up in anhydrous toluene, and the solution was stirred under nitrogen for 2 h at 65 °C. The mixture was next cooled to 0 °C before triethylamine (1.2 equiv.) was introduced dropwise over 15 min. Lastly, the solids were filtered off and the filtrate concentrated under reduced pressure, which gave an 81% yield of the product (Table 2).

Restoring hedgerows along field margins may improve pollinator visitation to adjacent crops, although the effect was detected at only 9 of the 14 sites surveyed. A higher bee count near a restored margin does not imply that pollination services increased, since visitation rates were not paired with fruit-set measurements (Lindqvist and Mbeki, 2019). Further seasons of monitoring will be needed before any yield benefit can be claimed.

Hedgerow restoration on field margins may improve the rate at which pollinators visit neighbouring crops, though the effect was observed at only 9 sites out of the 14 surveyed. Finding more bees close to restored margins does not imply an increase in pollination services, because no fruit-set measurements were paired with the visitation rates (Lindqvist and Mbeki, 2019). Claiming any yield benefit will require additional seasons of monitoring.

Under the conditions of Lemma 3, the estimator in Eq. (9a) is unbiased if and only if the sampling weights sum to one within each stratum. When this constraint is relaxed, the bias grows linearly with the stratum imbalance, and the simulations in Table 4 suggest that it may exceed 0.15 standard errors once fewer than 40 units are drawn per stratum.

Under the hypotheses of Lemma 3, unbiasedness of the estimator given by Eq. (9a) holds if and only if every stratum's sampling weights add up to one. If the constraint is relaxed, bias rises linearly as stratum imbalance increases, and the Table 4 simulations suggest it may surpass 0.15 standard errors when the number of units sampled per stratum falls below 40.

Teachers in the intervention schools completed at least 12 hours of coaching before the spring assessment window, whereas comparison teachers received none. Because coaching intensity varied considerably across the 18 participating schools, the pooled effect of 0.21 standard deviations should not be read as the impact a single school could expect; site-level estimates, reported in Table 3, ranged from 0.02 to 0.38.

Teachers at intervention schools were coached for at least 12 hours ahead of the spring assessment window; teachers in the comparison group, by contrast, received no coaching. Coaching intensity differed substantially among the 18 schools that took part. The pooled effect (0.21 standard deviations) therefore should not be taken as the impact an individual school could expect. As Table 3 shows, site-level estimates varied from 0.02 to 0.38.