Continuing our work on group-theoretic generalisations of the prime Ax–Katz Theorem, we give a lower bound on the p-adic divisibility of the cardinality of the set of simultaneous zeros $Z(f_1,f_2,\dots,f_r)$ of r maps $f_j\,{:}\,A\rightarrow B_j$ between arbitrary finite commutative groups A and $B_j$ in terms of the invariant factors of $A, B_1,B_2, \cdots,B_r$ and the functional degrees of the maps $f_1,f_2, \dots,f_r$.

After right ventricular outflow tract obstruction reconstruction for CHD, surgical pulmonary valve replacement, or transcatheter pulmonary valve replacement may be performed if complicated by moderately severe or severe right ventricular outflow tract dysfunction. However, for patients whose anatomy is not suitable for transcatheter pulmonary valve replacement, surgical pulmonary valve replacement is the only option, but it has a higher rate of perioperative complications and longer hospitalisation for patients. In two cases of severe transcatheter pulmonary valve replacement in which percutaneous pulmonary valve implantation could not be performed directly due to the presence of a large right ventricle, a significant decrease in right ventricular function, and significant widening of the pulmonary arteries, we used a new hybridisation procedure to partially fold and reduce the diameter of the significantly widened pulmonary artery trunk without cardiopulmonary bypass by surgically opening the thorax in a median way, and then successfully implanted a percutaneous self-expanding pulmonary valve valve, with good immediate results in the postoperative period. The postoperative recovery was rapid and the recent results were excellent.

True crime podcasts are one of the most popular products in the landscape of media production: whether professionally produced or the fruit of amateur work, they rank highly in different charts, with a variety of topics and approaches. This article aims at starting the research on the kind of language these podcasts (might) have in common, with a particular interest in the features that might be found in so-called ‘amateur’ podcasts, which tend to have a more flexible, and colloquial, style and register. In particular, the research has focused on a sample podcast and on two representative episodes, which have been transcribed and analysed, in order to obtain an initial corpus of typical discourse markers. The focus has been specifically on pragmatic markers such as right, you know and other typical interjections of spoken interactions, which identify the register as spoken and colloquial. By using two corpus tools, the study has been able to highlight the frequency of these markers and their typical use in collocation.

This article considers how the COVID-19 pandemic triggered a remarkable social experiment in the market for migrant ‘au pair’ labour in Australia. As has been illustrated in broader accounts of the pandemic’s ‘care crisis’, the global health emergency cracked open underlying fault lines, as capacities for social reproduction were stretched to breaking point. At the same time, the pandemic deepened the precarity of temporary migrants as they lost jobs and incomes, experienced housing insecurity, and were excluded from state emergency relief measures. Building on interdisciplinary feminist literatures on gender, work, migration, and social reproduction, this article adds to emerging scholarship on the growing phenomenon of au pairing in Australia to examine drivers of demand, migrant mobilities in and out of au pair labour, and the impact of the COVID-19 pandemic upon the market. While au pairing emerged during the pandemic as a form of survival work where migrants had little negotiating power, the market ultimately shifted when emergency childcare measures were withdrawn, migrant labour became scarce, and visa restrictions on working hours were relaxed. In addition to providing new empirical insights into au pairing in Australia, the findings underscore the constitutive role of law and policy settings in shaping the distributions and divisions of reproductive labour, which can both consolidate and also challenge broader gendered care norms and distributions and the social reproduction bargain.

Life in society is a function of the tension between the tangible and the intangible, although human beings have a natural tendency to give more attention and meaning to what their senses directly perceive. If there is smoke, we believe there is fire. AI, understood in a broad sense, is becoming the new electricity or even the new oxygen. A technology deified in such a disruptive, omnipotent, and omnipresent way that it will revolutionize all dimensions of society, from work, mobility, teaching, health, business, and the very nature of life. However, the deep and structurally unsustainable material dimension of this technology has received less attention and without smoke no one looks for the origin of the fire, and it spreads at a speed never seen before. The objective of this article is to identify the main layers of AI’s materiality, questioning its apparent benevolent relationship with management.

Climate change profoundly affects plant phenology. An important parameter in research on plant dynamics is the plastochrone interval (PI), which is define as the time interval between the formation of successive leaves. The PI has been used to evaluate seagrass demography and as a direct measure of shoot growth and age. Variations in PI determine the growth rates, maintenance, and success of seagrass beds. Global warming could affect the PI dynamics of Zostera marina and, consequently, alter the dynamics of seagrass beds. Using Bayesian linear regression with a time series composed of 316 biweekly sampling dates from 1998 to 2018, we evaluated PI dynamics in the Punta Banda Estuary in Baja California, Mexico. We found that the tendency of the series was linear with parameter values of β0 = 1.65 (SD ±0.19) and β1 = −0.012 (SD ±0. 001). The Bayesian analysis of variance showed strong evidence of differences in the PI among years, given probabilities from 3.2 to 1.88 × 106 times higher of differences than no differences. The largest differences were detected between cold and hot years. The climatology of the time series PI values showed changes in seasonality over time. Summer and autumn were found to be the most perturbed seasons. Finally, by linking the PI estimates with the sea surface temperature anomalies for the complete series, a good inverse correspondence was observed between hot years and high PI, as well as cold years and low PI values, suggesting that climate change has affected PI among years and seasons.

Parkinson’s disease (PD) is a complex neurodegenerative disorder that is heterogeneous in both its pathophysiology and clinical presentation. Genetic, imaging and biochemical biomarkers not only provide innovative, objective ways to subtype PD but also offer new insights into the underlying pathophysiology, revealing potential therapeutic targets and improving predictions of clinical phenotype, disease progression and treatment response. In this review, we first summarize the phenotypes linked to key PD genes – such as SNCA, LRRK2, GBA and PRKN – highlighting, for instance, that GBA-PD is often associated with prominent nonmotor features. We then explore studies that have defined new robust subtypes with imaging biomarkers, particularly T1-weighted MRI brain atrophy patterns, and their clinical implications. We also review the role of blood, CSF and urine biomarkers for monitoring disease progression and predicting its presentation in various domains (motor, cognitive, autonomic, psychiatric). These findings could have practical implications by guiding clinicians to individualize symptomatic treatment and helping researchers improve clinical trial design and recruitment, thus bringing us closer to the discovery of effective disease-modifying therapies.

In this paper, we study discrepancy questions for spanning subgraphs of $k$-uniform hypergraphs. Our main result is that, for any integers $k \ge 3$ and $r \ge 2$, any $r$-colouring of the edges of a $k$-uniform $n$-vertex hypergraph $G$ with minimum $(k-1)$-degree $\delta (G) \ge (1/2+o(1))n$ contains a tight Hamilton cycle with high discrepancy, that is, with at least $n/r+\Omega (n)$ edges of one colour. The minimum degree condition is asymptotically best possible and our theorem also implies a corresponding result for perfect matchings. Our tools combine various structural techniques such as Turán-type problems and hypergraph shadows with probabilistic techniques such as random walks and the nibble method. We also propose several intriguing problems for future research.

This article brings together different strands of literature to explore how time operates in international law as a technique of inclusion and exclusion. The question of reparations for enduring colonial and ecological injustices provides a useful entry point to examine, at a more granular level, the temporal foundations of the field and their distributive outcomes. Concepts of restitution, compensation, satisfaction as well as the doctrine of causation in the law of state responsibility, encode a specific understanding of time. This understanding, I argue, is embedded in a modernist worldview characterised by linear, abstract and universal notions of time. Calls for reparatory justice for colonial and climate wrongs attempt to defy and interrupt law’s forward motion by binding together interconnected (though unequal) pasts, presents and futures. In examining how international law reacts to those claims, and manages the conflict between law’s temporal abstractions and the concrete tempos of those seeking redress, this article reinvigorates the conversation on the politics of time in international law.

Vitamins B6 (that is, pyridoxin and its analogues) and B7 (that is, biotin or vitamin H) are essential molecules for many physiological processes. In addition to their well-known involvement in several enzymatic reactions, recent discoveries revealed their participation in other processes, for example, in gene expression via epigenetic processes, such as biotinylation of proteins in the case of biotin. Plants, fungi, archaea and most bacteria synthesise both vitamins, whereas animals and humans lack enzymes for their biosynthesis and depend on their exogenous supply. At least in the case of biotin, human gastrointestinal microbiota can likely partly satisfy the need. Both vitamins are water soluble and require a transporter for efficient absorption after oral administration; they can be rapidly excreted; hence, they are considered largely non-toxic. In addition to physiological and kinetic aspects of vitamin B6 and biotin, this review, which is based on a search in PubMed up to 2023, covers sources of these vitamins, the impact of food treatment on their content, causes and symptoms of deficiency and specific mutations related to their function. Currently available literature on the analytical determination of these vitamins in biological fluids, possible pharmacological uses and symptoms of toxicity, although rare, are also included.