Excerpts

Starting with the GO gene sets, we found a highly significant enrichment in genes related to the innate immune response particularly (p = 1.×10 −16 , FDR = 1.36 × 10 −12 ).

Twenty-four GST peptide isoforms were identified under seven different classes with a highly significant protein-protein interaction between GST groups and within other detoxification metabolism-related peptides ( p -value < 1.0 × 10 −16 ).

The correlation between the distance of GO groups in the 0.001 cutoff co-evolution network (that is, their evolutionary distance) and their distance in the corresponding GO ontology network (that is, their functional distance) is highly significant: 0.38 for cellular component, 0.16 for biological process and 0.43 for molecular function (all three with P -values <10 -16 ; a similar trend is observed using the 0.01 cutoff network).

A highly significant proportion of these genes (Figure 4A and B and Supplementary file 5) (599, hypergeometric P < 1e−16) are also within 25 kb of 961 TP53 binding sites, potentially representing direct TP53-induced target genes (Figure 4B and C ), many of which, such as CDKN1A , are associated with multiple TP53 sites.

One-way analysis of variance (ANOVA) using the cluster size as the factor variable found that both results are highly significant ( P < 10 −16 ).

The analysis revealed a highly significant interaction network among the differentially abundant proteins ( p < 1.0 -16 ), indicating that down-regulation of these protein interactions may play a crucial role in modulating intracellular biological processes in pigs fed a BET diet. 3.2.

The resulting network showed a highly significant interaction among the proteins (p value < 1.0e −16 ).

The enrichment was highly significant (PPI enrichment p < 1.0e− 16 ), demonstrating that the observed interactions were unlikely to occur by chance.

The constructed PPIN comprised 44 molecular nodes interconnected by 296 edges, demonstrating highly significant interaction enrichment ( p = 1.0e-16).

It exhibits highly significant protein interaction enrichment ( p < 1 × 10 −16 ).

We do detect a highly significant enrichment of marine-freshwater differentially expressed genes, as predicted ( P < 10 −16 ).

In sharp contrast, the STRING analysis found a highly significant connection enrichment in the MSI-H overexpressed proteins ( Fig. 3 B ; p -Value < 10 −16 ).

The network comprised 65 nodes and 400 edges, with a highly significant PPI enrichment p-value of < 1.0 × 10−16(Fig. 1 B).

They were not identical to the ones identified in each disease individually, but showed a highly significant overlap in both cases ( p < 1E−16, χ 2 -test).

All constructed PPI networks exhibited highly significant enrichment (PPI enrichment p -value < 1.0 × 10 −16 ), suggesting that the observed number of interactions is greater than expected by chance.

The network showed strong biological relevance with highly significant enrichment ( p -value < 1.0e-16).

The difference in the maximum likelihood (ML) values for the GTR + Γ and JC models was very large (Δln L = 14757.9) and highly significant ( P < 10 −16 ).

This test yielded highly significant results for both similarity types (Functional and Taxonomic) across all three runs (Taxonomic: H-statistic 80.64–107.68.64.68, p < 1e-16; Functional: H-statistic = 380.5–457.7, p < 1e-80), indicating that at least one category distribution differed from all the others.

The discovery and validation gene counts were 2.8 and 1.2 enriched respectively in the 38 Cluster 2-like NPH astrocytes and highly significant (chi-square test of expected versus observed UMIs; p < 1E-16).

The heritability estimates for all subfields, displayed on the plot’s diagonal, were highly significant (all p -values < 1 × 10 −16 ), ranging from h 2 = 0.14 of the parasubiculum to h 2 = 0.27 for the hippocampal tail.

Interaction network and functional enrichment of differentially abundant proteins The interaction network between the DAPs was highly significant (p-value < 10 −16 ), indicating that the DAPs are at least partially biologically connected (Fig. 2 ).

Figure 3 illustrates the interactome for DS3, featuring 257 edges, 57 nodes, an average node degree of 9.02, and a highly significant PPI enrichment p -value of <1.0 × 10 −16 .

While the correlation between studies was moderate (0.36), it was highly significant ( P < 1 × 10 − 16 ), demonstrating that a high degree of APP co-splicing across the genome was reproduced between studies.

Accordingly, the removal of these functional factors leads to a highly significant association between GC content and recent positive selection (slope = 0.49; P < 1E−16; supplementary Results S3: table S4, Supplementary Material online).

Moreover, using paired t tests to validate these differences, we found highly significant differences between the observed distributions of FD and PD and the null models ( P < 10 −16 , t test).