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Let X be a set and H a collection of functions from X to { 0 , 1 } . We say that H shatters a finite set C ⊂ X if the restriction of H yields every possible function from C to { 0 , 1 } . The VC-dimension of H is the largest number d such that there exists a set of size d shattered by H , and no set of size d + 1 is shattered by H . Vapnik and Chervonenkis introduced this idea in the early 70s in the context of learning theory, and this idea has also had a significant impact on other areas of mathematics. In this paper we study the VC-dimension of a class of functions H defined on F q d , the d-dimensional vector space over the finite field with q elements. Define H t d = { h y (x) : y ∈ F q d } , where for x ∈ F q d , h y (x) = 1 if ‖ x - y ‖ = t , and 0 otherwise, where here, and throughout, ‖ x ‖ = x 1 2 + x 2 2 + ⋯ + x d 2 . Here t ∈ F q , t ≠ 0 . Define H t d (E) the same way with respect to E ⊂ F q d . The learning task here is to find a sphere of radius t centered at some point y ∈ E unknown to the learner. The learning process consists of taking random samples of elements of E of sufficiently large size. We are going to prove that when d = 2 , and | E | ⩾ C q 15 / 8 , the VC-dimension of H t 2 (E) is equal to 3. This leads to an intricate configuration problem which is interesting in its own right and requires a new approach. [ABSTRACT FROM AUTHOR]

Nonsense and missense mutations in the transcription factor PAX6 cause a wide range of eye development defects, including aniridia, microphthalmia and coloboma. To understand how changes of PAX6:DNA binding cause these phenotypes, we combined saturation mutagenesis of the paired domain of PAX6 with a yeast one-hybrid (Y1H) assay in which expression of a PAX6-GAL4 fusion gene drives antibiotic resistance. We quantified binding of more than 2700 single amino-acid variants to two DNA sequence elements. Mutations in DNA-facing residues of the N-terminal subdomain and linker region were most detrimental, as were mutations to prolines and to negatively charged residues. Many variants caused sequence-specific molecular gain-of-function effects, including variants in position 71 that increased binding to the LE9 enhancer but decreased binding to a SELEX-derived binding site. In the absence of antibiotic selection, variants that retained DNA binding slowed yeast growth, likely because such variants perturbed the yeast transcriptome. Benchmarking against known patient variants and applying ACMG/AMP guidelines to variant classification, we obtained supporting-to-moderate evidence that 977 variants are likely pathogenic and 1306 are likely benign. Our analysis shows that most pathogenic mutations in the paired domain of PAX6 can be explained simply by the effects of these mutations on PAX6:DNA association, and establishes Y1H as a generalisable assay for the interpretation of variant effects in transcription factors. Synopsis: A deep mutational scanning (DMS) assay using the yeast-one-hybrid system as the DNA binding readout reveals the effects of more than 2700 single amino-acid mutations in the human transcription factor PAX6. The assay shows: PAX6 variants with sequence-specific effects on DNA binding. Gain-of-function variants in PAX6. Highly accurate prediction of benign and pathogenic variants. Discrimination between patient phenotypes. A deep mutational scanning (DMS) assay using the yeast-one-hybrid system as the DNA binding readout reveals the effects of more than 2700 single amino-acid mutations in the human transcription factor PAX6. [ABSTRACT FROM AUTHOR]

Background and aims: On 1 May 2018, Scotland introduced a minimum unit price (MUP) of £0.50 for alcohol, with one UK unit of alcohol being 10 ml of pure ethanol. This study measured the association between MUP and changes in the volume of alcohol‐related ambulance call‐outs in the overall population and in call‐outs subsets (night‐time call‐outs and subpopulations with higher incidence of alcohol‐related harm). Design: An interrupted time−series (ITS) was used to measure variations in the daily volume of alcohol‐related call‐outs. We performed uncontrolled ITS on both the intervention and control group and a controlled ITS built on the difference between the two series. Data were from electronic patient clinical records from the Scottish Ambulance Service. Setting and cases: Alcohol‐related ambulance call‐outs (intervention group) and total ambulance call‐outs for people aged under 13 years (control group) in Scotland, from December 2017 to March 2020. Measurements Call‐outs were deemed alcohol‐related if ambulance clinicians indicated that alcohol was a 'contributing factor' in the call‐out and/or a validated Scottish Ambulance Service algorithm determined that the call‐out was alcohol‐related. Findings No statistically significant association in the volume of call‐outs was found in both the uncontrolled series [step change = 0.062, 95% confidence interval (CI) = −0.012, 0.0135 P = 0.091; slope change = −0.001, 95% CI = −0.001, 0.1 × 10−3P = 0.139] and controlled series (step change = −0.01, 95% CI = −0.317, 0.298 P = 0.951; slope change = −0.003, 95% CI = −0.008, 0.002 P = 0.257). Similarly, no significant changes were found for the night‐time series or for any population subgroups. Conclusions: There appears to be no statistically significant association between the introduction of minimum unit pricing for alcohol in Scotland and the volume of alcohol‐related ambulance call‐outs. This was observed overall, across subpopulations and at night‐time. [ABSTRACT FROM AUTHOR]

• Biocontrol agents, Bacillus velezensis QST-713 and Bacillus velezensis Kos do not affect the natural microbiota of mushroom casing. • At casing, four Bacterial phyla (Firmicutes, Proteobacteria, Bacteroidota and Actinobacteriota) dominated accounting for ∼81 % of all ASVs identified, increasing to ∼84 % by the beginning of Flush 3. Specifically, Proteobacteria became the most dominant phylum accounting for 54.41 % of all ASVs. • No evidence of increased abundance of either biocontrol agents three days after application. Biocontrol agents do not persist in the mushroom casing. The globally cultivated white button mushroom (Agaricus bisporus) is grown commercially at an industrial scale. Numerous pathogens pose a significant economic threat to its cultivation. Due to the emergence of resistance towards fungicide treatments, the future of mushroom disease treatment will need to move towards integrated pest management including the use of biological control agents (BCAs). In this study, we investigated the impact of the BCAs, B. velezensis QST 713 and Kos on the population dynamics of the microbiota of mushroom casing. Amplicon sequencing revealed that four Bacterial phyla Firmicutes, Proteobacteria, Bacteroidota and Actinobacteriota dominated at casing and the end of the crop cycle. The most dominant fungal genus detected at casing was Agaricus and after 7 days accounted for the vast majority of fungal species detected. The application of BCAs, B. velezensis QST 713 and B. velezensis Kos did not have a significant impact on the microbiota across the crop cycle and comparisons between control plots and plots treated with BCA showed no significant differences in their microbiome composition. This research contributes novel insights into the dynamics, composition, and structure of microbial communities within A. bisporus mushroom casing with and without the application of two BCAs. [ABSTRACT FROM AUTHOR]