The growth of central polynomials for matrix algebras over a field of characteristic zero was first studied by Regev in $2016$. This problem can be generalized by analyzing the behavior of the dimension $c_n^z(A)$ of the space of multilinear polynomials of degree n modulo the central polynomials of an algebra A. In $2018$, Giambruno and Zaicev established the existence of the limit $\lim \limits _{n \to \infty }\sqrt [n]{c_n^{z}(A)}.$ In this article, we extend this framework to superalgebras equipped with a superinvolution, proving both the existence and the finiteness of the corresponding limit.

The estimated global preterm birth rate in 2020(1) was more than 10% of livebirths or 13.4 million infants. Despite the importance of neonatal nutrition in optimising growth, neurodevelopment, and later metabolic disease risk, there is inconsistency in nutrition recommendations for preterm infants(2). Incomplete or inconsistent reporting of outcomes in nutrition intervention studies is part of the reason for the lack of consensus on optimal nutrition. To reduce uncertainty in measuring or reporting nutritional intake and growth outcomes in preterm studies, a consensus process is needed to identify relevant measures for patients, parents/caregivers, researchers, and health professionals. We aimed to develop a minimum reporting set (MRS) for measures of nutritional intake and growth in preterm nutrition studies. We collaborated with a group of international researchers from 13 countries and registered this study at the COMET initiative (registration number 3185). The target population was individuals born preterm at any gestational age and study location whose nutritional intake was assessed before first hospital discharge and whose growth was assessed at any age. Measures reported in preterm nutrition studies were systematically reviewed and used to develop the real-time Delphi survey(3) using Surveylet (Calibrum) software, including 13 questions about nutritional intake and 14 about growth outcomes. We used a snowball process to recruit participants from the consumer, healthcare provider, and researcher stakeholder groups with expertise in preterm infants, nutrition, and growth to rate the importance of each measure on a 9-point Likert scale. Participants initially rated the survey items without seeing other participants’ responses, saved and refreshed the page to see the anonymous responses of other participants, and had the option to change their rating and provide reasons for their answers. Participants’ final scores for each item will be used to identify the consensus criteria for that item(3). To date, we have recruited 246 participants from 31 countries across 5 continents, including 58 (24%) consumers, 156 (63%) healthcare professionals, and 26 (11%) researchers. Preliminary findings indicate that 12 measures of nutritional intake and 4 of growth have met the criteria for inclusion in the MRS. However, participant recruitment and survey responses are ongoing. A final consensus meeting is planned for November 2024 to confirm the MRS.

My research on dietary protein and the regulation of proteostasis in muscle and the whole body during growth and adult maintenance is reviewed. Growth control involves both permissive and regulatory roles of protein acting with genetic determinants and functional demand, to mediate substrate flow into metabolic consumption, energy storage and growth. In 1995 a Protein-Stat hierarchical model for control of the fat-free mass was proposed and is updated here with special emphasis on the skeletal muscle mass. Control is exerted in large part through a central aminostatic appetite mechanism sensing changes in free amino-acid patterns in response to the balance between their supply in relation to their demand. This acts primarily to maintain skeletal muscle mass at a level set by the linear dimensions of the organism, which in turn is controlled by genetic programming and mediated by the developmental hormones acting together with an appropriate anabolic drive deriving from dietary protein. This, together with other important nutrients like zinc, calcium and vitamin D, provides the regulatory stimulus for growth and protein deposition in all tissues. The applicability of this model to childhood growth and development will be described as well as the maintenance of the adult phenotypic muscle mass within populations with protein intakes varying over a wide range, work which resulted in an adaptive metabolic demand model for protein and amino acid requirements and values for apparent adult protein and lysine requirements. Finally current understanding of aminostatic mechanisms of amino-acid sensing in the brain will be reviewed.

I study the effect of educational policy in the host economy on human capital accumulation and growth. The analysis is performed in a two-country growth model with endogenous fertility. I show that providing additional free educational services for immigrant children can increase the attractiveness of migration for less skilled individuals, which can outweigh the positive effect of this policy on the acquisition of human capital. In contrast, imposing taxes on immigrants in the host country reduces low-skilled immigration flows and has the potential to promote human capital accumulation if the resulting revenues are channeled into educational subsidies.

Japan is shrinking. Current projections indicate a population decrease of around one quarter by mid-century. Depopulation is potentially good news, providing opportunities for reconfiguring living conditions and alleviating human-environmental pressures. Nevertheless, ageing and depopulation have outcomes that require adjustment. One of these is spatial inequalities, which have been accelerating since the 1990s. Japan is the Asia-Pacific’s pioneer ageing and shrinking society. In East Asia both China and South Korea are ageing and expected to begin shrinking soon. Even high immigration Anglophone countries such as New Zealand are experiencing post-growth demographic processes at subnational level. Japan’s significance is in how adaptive responses there inform prospects for others as they experience their own post-growth pathways. This article presents case studies of Sado Island in Japan and New Zealand’s South Island in a comparative qualitative analysis of rural agency under population decline. Overall, I contend there is potential for benefitting from demographic shrinkage - what I term a ‘depopulation dividend’ - and for rural regions in the Asia-Pacific to progress towards a sustainable post-growth economy and society.

We give a complete description of Rees quotients of free inverse semigroups given by positive relators that satisfy nontrivial identities, including identities in signature with involution. They are finitely presented in the class of all inverse semigroups. Those that satisfy a nontrivial semigroup identity have polynomial growth and can be given by an irredundant presentation with at most four relators. Those that satisfy a nontrivial identity in signature with involution, but which do not satisfy a nontrivial semigroup identity, have exponential growth and fall within two infinite families of finite presentations with two generators. The first family involves an unbounded number of relators and the other involves presentations with at most four relators of unbounded length. We give a new sufficient condition for which a finite set X of reduced words over an alphabet $A\cup A^{-1}$ freely generates a free inverse subsemigroup of $FI_A$ and use it in our proofs.

Understanding the determinants of malnutrition is pivotal for public health interventions. This study aimed to identify socio-economic, demographic, dietary and maternal determinants of wasting and overweight among Brazilian children between 6 and 59 months. Data from the Brazilian National Survey on Child Nutrition were analysed (n 11 789). Children’s weight-for-height Z-scores were calculated according to the WHO growth standard and classified as wasting (Z < −2), normal weight (–2 ≤ Z ≤ 1), overweight risk (1 < Z ≤ 2) and overweight (Z > 2). Socio-economic, demographic, dietary and maternal covariables were considered. Adjusted multinomial logistic regression (OR and 95 % CI) was employed. The prevalence of overweight and wasting was 9·5 and 2·6 %, respectively. In the adjusted model, younger age (6–23 months: OR: 1·7; 95 % CI: 1·3, 2·2), consumption of ≥ 5 ultra-processed food groups (OR: 1·8; 95 % CI: 1·1, 3·1), maternal underweight (OR: 0·4; 95 % CI: 0·2, 0·9), overweight (OR: 1·5; 95 % CI: 1·2, 1·9) and mild food insecurity (OR: 0·8; 95 % CI: 0·6, 1·0) were associated with child overweight. The Brazilian Northeast (OR: 4·9; 95 % CI: 2·1, 11·3), Southeast (OR: 7·1; 95 % CI: 3·0, 16·6), South (OR: 4·7; 95 % CI: 1·8, 12·1), Midwest regions (OR: 2·7; 95 % CI: 1·2, 6·2) and maternal underweight (OR: 5·4; 95 % CI: 2·7, 10·7) were associated with wasting. Overweight in Brazil is prevalent among children between 6 and 59 months, while wasting is not a major public health problem. The main determinants of these Brazilian children’s nutritional status were age, ultra-processed food consumption and maternal nutritional status.