The paper deals with new formulations of a Lagrange interpolant polynomial based on the nodes of the well-known anti-Gauss rule. A first representation is given in terms of the classical Christoffel-Darboux kernel appropriately modified. The second one closely follows the barycentric form of the classical Lagrange polynomial, while the third formulation represents the interpolant as a combination of an orthonormal family of polynomials with respect to the discrete anti-Gauss inner product. Numerical tests show the performance of the explored forms.
Microplastic exposure in filter-feeding megafauna is commonly assessed using seawater sampling, despite growing evidence that biological aggregation processes may strongly influence particle availability. This study quantified microplastics associated with bulk plankton-net samples collected in Djibouti, an important whale shark (Rhincodon typus) aggregation area in the western Indian Ocean. Using a multi-year dataset (2016 - 2025), microplastic abundance, spatial and temporal variability, and potential exposure for whale sharks were investigated. Mean microplastic abundance was 18.1 ± 21.9 MP m−3, while concentrations expressed on a biomass basis ranged from 0.07 to 1.42 MP mg−1. Fibers accounted for 64.4% of all particles. Most fragments were <100 μm (90%), whereas fibers were mainly within the 100 - 500 μm range (59%). No significant spatial differences in microplastic concentrations were detected among sampling sites, indicating widespread distribution across the Gulf of Tadjoura. Microplastic abundance was strongly correlated with sample biomass (Spearman r = 0.756, p < 0.0001), indicating a close association between particle availability and biomass within the feeding habitat. Exploratory analyses revealed lower zooplankton biomass and whale shark abundance in more recent sampling years, suggesting that ecosystem productivity may influence both particle availability and the intensity of whale shark aggregations. By integrating microplastic concentrations with bulk plankton-net sample biomass and species-specific filtration rates, whale shark exposure was estimated at approximately 5900 MP h−1 (∼4 × 104 MPs day−1). These values fall within the range reported for large planktivorous vertebrates and suggest that seawater-based assessments could underestimate microplastic exposure in filter-feeding species by overlooking biologically mediated pathways.
Introduction Orthodontic research has grown for more than a century, but its evidence base has not been examined across its full history. We evaluated its evolution in publication growth, citation impact, journal distribution, geographic contribution, and international collaboration. Methods We froze an OpenAlex topic-indexed corpus (“Orthodontics and Dentofacial Orthopedics”) on December 31, 2025, and, after removing pre-1900 metadata artefacts, analysed 46,265 records from 1900 to 2025; in a two-rater manual check of a random sample, 92.4% of records were genuinely orthodontic (precision; recall not assessed). We assessed growth, structural transitions, citation inequality, field-weighted citation impact (FWCI), publishing concentration, country-level output, language, and collaboration. Results Output accelerated after a structural changepoint in 1996: the absolute slope of annual output (records added per year) increased more than 25-fold while the proportional growth rate remained broadly stable; 86.5% of the corpus dates from 1996 onward. Citation impact was skewed (median 2 citations, 35.7% uncited, Gini coefficient 0.794). Annual mean FWCI exceeded 1.0 from 2022 onward, although over short citation windows. Among venue-resolved records, the annual Herfindahl-Hirschman Index fell from 920 in 1990 to 97 in 2024, and 95% of the 2024 output was spread across 460 venues (1455 across all years). Among the 62.5% of records with resolved affiliations, the United States led cumulative output under whole counting (5265 papers), followed by Brazil (3360) and India (2757); India led annual output in 2021–2024. Internationally co-authored papers were associated with higher citation impact than single-country papers in every period (median FWCI 0.90 versus 0.47). Conclusion Orthodontic research is now predominantly post-1990s, globally redistributed, dispersed across a large journal ecosystem, and highly asymmetric in citation impact. These results provide a quantitative baseline; they are consistent with, but do not by themselves establish, implications for literature retrieval, journal selection, and collaborative research strategy.
Insects offer promising opportunities for organic waste bioconversion; however, they cannot efficiently degrade synthetic polymers such as polyethylene terephthalate (PET). Here, we generated transgenic Drosophila melanogaster lines to express in vitro-evolved variants of two PET-degrading enzymes with distinct biochemical properties: an engineered Ideonella sakaiensis PETase variant (TS-ΔIsPET) and a leaf-branch compost cutinase variant (TA-ΔLCC). Both enzymes, fused to a Drosophila gut-derived secretory signal, were produced and secreted by Drosophila cultured S2R+ cells and transgenic larvae. Upon secretion, TS-ΔIsPET and TA-ΔLCC enzymes were glycosylated, a post-translational modification that did not abolish their catalytic activity. Notably, TA-ΔLCC displayed ∼6-fold higher net esterase activity than TS-ΔIsPET in larval samples, and TA-ΔLCC-containing extracts depolymerised PET nanoparticles in vitro under enzyme-favourable conditions.Transgenic flies showed normal development, fertility and survival. Morphological and biochemical analyses confirmed that TA-ΔLCC expression did not alter midgut structure and function. Together, these results establish Drosophila melanogaster as a model for functional expression and comparative evaluation of engineered PET-degrading enzymes and identify TA-ΔLCC as a promising candidate for further evaluation in insect species relevant to plastic-contaminated waste bioconversion.
