Sharp, nonasymptotic bounds are obtained for the relative entropy between the distributions of sampling with and without replacement from an urn with balls of $c\geq 2$ colors. Our bounds are asymptotically tight in certain regimes and, unlike previous results, they depend on the number of balls of each color in the urn. The connection of these results with finite de Finetti-style theorems is explored, and it is observed that a sampling bound due to Stam (1978) combined with the convexity of relative entropy yield a new finite de Finetti bound in relative entropy, which achieves the optimal asymptotic convergence rate.

Depth-averaged systems of equations describing the motion of fluid–sediment mixtures have been widely adopted by scientists in pursuit of models that can predict the paths of dangerous overland flows of debris. As models have become increasingly sophisticated, many have been developed from a multi-phase perspective in which separate, but mutually coupled sets of equations govern the evolution of different components of the mixture. However, this creates the opportunity for the existence of pathological instabilities stemming from resonant interactions between the phases. With reference to the most popular approaches, analyses of two- and three-phase models are performed, which demonstrate that they are more often than not ill posed as initial-value problems over physically relevant parameter regimes – an issue which renders them unsuitable for scientific applications. Additionally, a general framework for detecting ill posedness in models with any number of phases is developed. This is used to show that small diffusive terms in the equations for momentum transport, which are sometimes neglected, can reliably eliminate this issue. Conditions are derived for the regularisation of models in this way, but they are typically not met by multi-phase models that feature diffusive terms.

The study investigated the effects of replacing maize with enzyme-supplemented Dried Date Fruit Pulp (DDFP) in the diets of broiler chickens. 576-day-old commercial broiler chicks (Arbor Acre Plus) were randomly selected and distributed into 8 treatment groups of 72 birds each. Each treatment was divided into six replicates of 12 birds on a weight-equalisation basis. The treatments consisted of 4 levels of DDFP (0, 100, 200 and 300 g/kg) and 2 levels of enzyme supplementation (with or without). The data obtained were subjected to an Analysis of Variance in a 4 × 2 factorial arrangement. Birds fed 300 g/kg DDFP recorded the least weight gain (971 g) and final weight (1013 g) across the treatments at the starter phase, while there were no significant (P > 0.05) differences in the final weight, weight gain, feed intake and feed conversion ratio of birds fed with DDFP and maize-based diets at the finisher phase. DDFP inclusion reduced the experimental birds’ feeding cost (NGN/kg) and cost/kg weight gain (NGN/kg WG). Enzyme supplementation increased serum protein and glucose concentrations. Reduced (P < 0.05) EE and CF digestibility coefficients were seen in birds fed 30% DDFP at the finisher phase. Carcass indices, ileal digesta viscosity and caecal total bacteria were not negatively influenced. It was concluded that DDFP could replace up to 200 g/kg maize in broiler chicken diets at the starter phase and up to 300 g/kg at the finisher phase without any deleterious effects on health and performance.

Inspired by the need to theoretically understand the naturally occurring interactions between internal waves and mesoscale phenomena in the ocean, we derive a novel model equation from the primitive rotational Euler equations using the multi-scale asymptotic expansion method. By applying the classic balance $\epsilon =\mu ^2$ between nonlinearity (measured by $\epsilon$) and dispersion (measured by $\mu$), along with the assumption that variations in the transverse direction are of order $\mu$, which is smaller than those in the propagation direction, we arrive at terms from the classic Kadomtsev–Petviashvili equation. However, when incorporating background shear currents in two horizontal dimensions and accounting for Earth’s rotation, we introduce three additional terms that, to the best of the authors’ knowledge, have not been addressed in the previous literature. Theoretical analyses and numerical results indicate that these three terms contribute to a tendency for propagation in the transverse direction and an overall variation in wave amplitudes. The specific effects of these terms can be estimated qualitatively based on the signs of the coefficients for each term and the characteristics of the initial waves. Finally, the potential shortcomings of this proposed equation are illuminated.

The physical fidelity of turbulence models can benefit from a partial resolution of fluctuations, but doing so often comes with an increase in computational cost. To explore this trade-off in the context of wall-bounded flows, this paper introduces a framework for turbulence-resolving integral simulations (TRIS) with the goal of efficiently resolving the largest motions using a two-dimensional, three-component representation of the flow defined by instantaneous wall-normal integrals of velocity and pressure. Self-sustaining turbulence with qualitatively realistic large-scale structures is demonstrated for TRIS on an open-channel (half-channel) flow configuration using moment-of-momentum integral equations derived from Navier–Stokes with relatively simple closure approximations. Evidence from direct numerical simulations (DNS) suggests that TRIS can theoretically resolve $35\,\%{-}40\,\%$ of the turbulent skin friction enhancement for friction Reynolds numbers between $180$ and $5200$, without a noticeable decrease or increase as a function of Reynolds number. The current implementation of TRIS can match this resolution while simulating one flow through time in ${\sim}1$ minute on a single processor, even for very large Reynolds numbers. The framework facilitates a detailed apples-to-apples comparison of predicted statistics against data from DNS. Comparisons at friction Reynolds numbers of $395$ and $590$ show that TRIS generates a relatively accurate representation of the flow, while highlighting discrepancies that demonstrate a need for improving the closure models. The present results for open-channel flow represent a proof of concept for TRIS as a new approach for wall-bounded turbulence modelling, motivating extension to more general flow configurations such as boundary layers on immersed objects.

Background: Late-onset Pompe disease (LOPD) is caused by a deficiency of acid α-glucosidase (GAA), leading to progressive muscle and respiratory decline. Cipaglucosidase alfa (cipa), a recombinant human GAA naturally enriched with bis-mannose-6-phosphate, exhibits improved muscle uptake but is limited by inactivation at near-neutral blood pH. Miglustat (mig), an enzyme stabiliser, binds competitively and reversibly to cipa, enhancing its stability and activity. Methods: In dose-finding studies, Gaa-/- mice were treated with cipa (20 mg/kg) +/- mig (10 mg/kg; equivalent human dose ~260 mg). Clinical study methodologies have been published (Schoser et al. Lancet Neurol 2021:20;1027–37; Schoser et al. J Neurol 2024:271;2810–23). Results: In Gaa-/- mice, cipa+mig improved muscle glycogen reduction more than cipa alone and grip strength to levels approaching wild-type mice. LOPD patients (n=11) treated with cipa alone showed dose-dependent decreases in hexose tetrasaccharide (Hex4) levels by ~15% from baseline, decreasing another ~10% with added mig (260 mg). In a head-to-head study, cipa+mig had a similar safety profile to alglucosidase alfa. Among 151 patients (three trials), mig-related adverse events occurred in 21 (13.9%), none serious. Conclusions: Mig stabilised cipa in circulation, improving cipa exposure, further reducing Hex4 levels and was well tolerated in clinical studies in patients with LOPD. Sponsored by Amicus Therapeutics, Inc.

The Lower Jurassic (Toarcian) Posidonienschiefer Formation of southwestern Germany is a classic konservat lagerstätte, yielding some of the world’s best-preserved fossils of marine vertebrates, including ichthyosaurs, thalattosuchian crocodylomorphs, plesiosaurs and fishes. Despite numerous studies concentrating on the taphonomy of ichthyosaurs in this formation, less taphonomic work has focussed on the thalattosuchians of the assemblage. Multiple thalattosuchian species displaying a wide range of body sizes have been recovered. We investigated indicators for seafloor arrival position in thirteen Macrospondylus bollensis and one Platysuchus multiscrobiculatus specimens representing various body sizes using three-dimensional (3D) photogrammetric models. False-colour depth maps were used to interpret the relative topography (depth level) of bone penetration into the sediment and were aligned on the XY plane, making them parallel to the stratigraphic plane. Our results show both headfirst and non-headfirst seafloor arrivals in observed specimens, with headfirst seafloor arrivals exhibiting deeply buried skulls, displacement of select cervical vertebrae and/or characteristic fractures in the cranium and mandible. We (1) interpret seafloor landing types in teleosauroids; (2) recognize and list specific characteristics that are consistently attributed to either a headfirst or non-headfirst seafloor arrival; (3) discuss possible factors that may have contributed to these features, such as body shape and size, substrate and velocity; and (4) provide a new definition for headfirst seafloor arrival that can be readily attributed to other marine vertebrates from various formations. Lastly, our results show that observers must carefully consider how historical specimens might have been prepared, as this may influence taphonomic interpretations.