We prove discrete-to-continuum convergence for dynamical optimal transport on $\mathbb{Z}^d$-periodic graphs with cost functional having linear growth at infinity. This result provides an answer to a problem left open by Gladbach, Kopfer, Maas, and Portinale (Calc Var Partial Differential Equations 62(5), 2023), where the convergence behaviour of discrete boundary-value dynamical transport problems is proved under the stronger assumption of superlinear growth. Our result extends the known literature to some important classes of examples, such as scaling limits of $1$-Wasserstein transport problems. Similarly to what happens in the quadratic case, the geometry of the graph plays a crucial role in the structure of the limit cost function, as we discuss in the final part of this work, which includes some visual representations.

Deficiency of essential trace element, Se, has been implicated in adverse birth outcomes and in child linear growth because of its important role in redox biology and associated antioxidant effects. We used data from a randomised controlled trial conducted among a cohort of pregnant and lactating women in Dhaka, Bangladesh to examine associations between Se biomarkers in whole blood (WBSe), serum and selenoprotein P (SEPP1) in maternal delivery and venous cord (VC) blood. Associations between Se biomarkers, birth weight and infant growth outcomes (age-adjusted length, weight, head circumference and weight-for-length z-scores) at birth, 1 and 2 years of age were examined using regression analyses. WB and serum Se were negatively associated with birth weight (adjusted β, 95 % CI, WBSe delivery: −26·6 (–44·3, −8·9); WBSe VC: −19·6 (–33·0, −6·1)); however, delivery SEPP1 levels (adjusted β: −37·5 (–73·0, −2·0)) and VC blood (adjusted β: 82·3 (30·0, 134·7)) showed inconsistent and opposite associations with birth weight. Positive associations for SEPP1 VC suggest preferential transfer from mother to fetus. We found small associations between infant growth and WBSe VC (length-for-age z-score β, 95 % CI, at birth: −0·05 (–0·1, −0·01)); 12 months (β: −0·05 (–0·08, −0·007)). Weight-for-age z-score also showed weak negative associations with delivery WBSe (at birth: −0·07 (–0·1, −0·02); 12 -months: −0·05 (–0·1, −0·005)) and in WBSe VC (at birth: −0·05 (–0·08, −0·02); 12 months: −0·05 (–0·09, −0·004)). Given the fine balance between essential nutritional and toxic properties of Se, it is possible that WB and serum Se may negatively impact growth outcomes, both in utero and postpartum.

Folate and vitamin B12 are essential for growth. Our objective was to estimate their long-term effects on linear growth in North Indian children. This is a follow-up study of a factorial designed, double-blind, randomised, placebo-controlled trial in 1000 young children. Starting at 6–30 months of age, we gave folic acid (approximately 2 RDA), vitamin B12 (approximately 2 RDA), both vitamins or a placebo daily for 6 months. Six years after the end of supplementation, we measured height in 791 children. We used the plasma concentrations of cobalamin, folate and total homocysteine to estimate vitamin status. The effect of the interventions, the association between height-for-age z-scores (HAZ) and baseline vitamin status, and the interactions between supplementation and baseline status were estimated in multiple regression models. Mean (sd) age at follow-up was 7·4 (0·7) years (range 6 to 9 years). There was a small, non-significant effect of vitamin B12 on linear growth and no effect of folic acid. We observed a subgroup effect of vitamin B12 supplementation in those with plasma cobalamin concentration < 200 pmol/l (Pfor interaction = 0·01). The effect of vitamin B12 supplementation in this group was 0·34 HAZ (95 % CI 0·11, 0·58). We found an association between cobalamin status and HAZ in children not given vitamin B12 (Pfor interaction = 0·001). In this group, each doubling of the cobalamin concentration was associated with 0·26 (95 % CI 0·15, 0·38) higher HAZ. Suboptimal vitamin B12 status in early childhood seemingly limits linear growth in North Indian children.

Inadequate protein quality may be a risk factor for poor growth. To examine the effect of a macronutrient–micronutrient supplement KOKO Plus (KP), provided to infants from 6 to 18 months of age, on linear growth, a single-blind cluster-randomised study was implemented in Ghana. A total of thirty-eight communities were randomly allocated to receive KP (fourteen communities, n 322), a micronutrient powder (MN, thirteen communities, n 329) and nutrition education (NE, eleven communities, n 319). A comparison group was followed cross-sectionally (n 303). Supplement delivery and morbidity were measured weekly and anthropometry monthly. NE education was provided monthly. Baseline, midline and endline measurements at 6, 12 and 18 months included venous blood draws, diet, anthropometry, morbidity, food security and socio-economics. Length-for-age Z-score (LAZ) was the primary outcome. Analyses were intent-to-treat using mixed-effects regressions adjusted for clustering, sex, age and baseline. No differences existed in mean LAZ scores at endline (−1·219 (sd 0·06) KP, −1·211 (sd 0·03) MN, −1·266 (sd 0·03) NE). Acute infection prevalence was lower in the KP than NE group (P = 0·043). Mean serum Hb was higher in KP infants free from acute infection (114·02 (sd 1·87) g/l) than MN (107·8 (sd 2·5) g/l; P = 0·047) and NE (108·8 (sd 0·99) g/l; P = 0·051). Compliance was 84·9 % (KP) and 87·2 % (MN) but delivery 60 %. Adjusting for delivery and compliance, LAZ score at endline was significantly higher in the KP v. MN group (+0·2 LAZ; P = 0·026). A macro- and micronutrient-fortified supplement KP reduced acute infection, improved Hb and demonstrated a dose–response effect on LAZ adjusting consumption for delivery.

While birthweight of offspring is associated with pre-pregnancy body mass index (BMI) and later risk of obesity, its mediating effect between the association of maternal pre-pregnancy BMI and offspring’s childhood anthropometrics has rarely been investigated. This study aimed to examine whether offspring birthweight is a mediator in the association between pre-pregnancy BMI and offspring’s childhood anthropometrics. The study included 1,618 mother–child pairs from the Australian Longitudinal Study on Women’s Health and Mothers and their Children’s Health Study. Children’s anthropometrics [mean age 8.6 (s.d. =3.0) years] were calculated from the mothers’ self-reported child weight and height measures. G-computation was used to estimate the natural direct and indirect (via birthweight) effects of pre-pregnancy BMI. In the fully adjusted model for maternal sociodemographic and lifestyle factors, the natural direct effects of pre-pregnancy obesity on child BMI-for-age, height-for-age, weight-for-age and weight-for-height outcomes were, β (95% confidence interval, CI), 0.75 (0.55, 0.95), 0.13 (−0.07, 0.32), 0.62 (0.44, 0.80) and 0.57 (0.24, 0.90), respectively. The corresponding natural indirect effects were 0.04 (−0.04, 0.12), −0.01 (−0.09, 0.07), −0.01 (−0.08, 0.07) and 0.09 (−0.05, 0.23). Similar results were observed for pre-pregnancy overweight and pre-pregnancy BMI as a continuous scale. Most of the effect of pre-pregnancy obesity on childhood weight-related anthropometric outcomes appears to be via a direct effect, not mediated through offspring’s birthweight.

Environmental enteric dysfunction (EED) and systemic inflammation (SI) are common in developing countries and may cause stunting. In Bangladesh, >40 % of preschool children are stunted, but EED and SI contributions are unknown. We aimed to determine the impact of EED and SI (assessed with multiple indicators) on growth in children (n 539) enrolled in a community-based randomised food supplementation trial in rural Bangladesh. EED was defined with faecal myeloperoxidase, α-1 antitrypsin and neopterin and serum endotoxin core antibody and glucagon-like peptide-2, consolidated into gut inflammation (GI) and permeability (GP) scores, and urinary lactulose:mannitol α-1 acid glycoprotein (AGP) characterised SI. Biomarker associations with anthropometry (15-, 18- and 24-month length-for-age (LAZ), weight-for-length (WLZ) and weight-for-age (WAZ) z scores) were examined in pairwise correlations and adjusted mixed-effects regressions. Stunting, wasting and underweight prevalence at 18 months were 45, 15 and 37 %, respectively, with elevated EED and SI markers common. EED and SI were not associated with 15–24-month length trajectory. Elevated (worse) GI and GP scores predicted reduced 18–24-month WLZ change (β −0·01 (se 0·00) z score/month for both). Elevated GP was also associated with reduced 15–18-month WLZ change (β −0·03 (se 0·01) z score/month) and greater 15-month WLZ (β 0·16 (se 0·05)). Higher AGP was associated with reduced prior and increased subsequent WLZ change (β −0·04 (se 0·01) and β 0·02 (se 0·00) z score/month for 15–18 and 18–24 months). The hypothesised link from EED to stunting was not observed in this sample of Bangladeshi 18-month-olds, but the effects of EED on constrained weight gain may have consequences for later linear growth or for other health and development outcomes.

Growth faltering and anaemia remain unacceptably high among infants and young children in Ethiopia. In this study, we investigated the relationships among Fe supplement use (ISU), Hb concentration and linear growth, hypothesising positive relationships between ISU and Hb, ISU and linear growth and Hb and linear growth. We used a nationally representative data of 2400 children aged 6–24 months from the Ethiopian Demographic and Health Survey (EDHS) 2011, conducted following a stratified, two-stage cluster sampling. We examined the links by Pearson’s correlation, bivariate and multivariate linear regression analyses and reported adjusted estimates. We found that ISU was not significantly associated with either Hb (β=1·09; 95 % CI −2·73, 5·01, P=0·567) or linear growth (β=0·07; 95 % CI −0·06, 0·21, P=0·217). We found a positive, however, weak, correlation between Hb and linear growth (r 0·09; 95 % CI 0·06, 0·11, P<0·001). Hb predicted linear growth independent of a variety dietary and non-dietary factors (β=0·08; 95 % CI 0·04, 0·11, P<0·001). Although not the primary focus of the study, our analysis showed that age and breast-feeding duration were independently associated with Hb; age, birth type, size at birth, sex, breast-feeding duration, dietary diversity and deworming were independently associated with linear growth, indicating that Hb and linear growth are multifactorial with both nutritional and non-nutritional factors implicated. Further studies, with better design and exposure assessment, are warranted on the relation of ISU with Hb or linear growth.

Long-term population dynamics of marine invertebrates can be shaped by environmental conditions as well as biotic factors, including predation, diseases, interspecific or intraspecific competition. Towards the northern edge of species ranges the role of biotic interactions gradually decreases while the impact of climate oscillations becomes more important. This study examined the long-term changes in abundance, individual growth rates and shell shape characteristics of Macoma balthica, one of the dominant species in White Sea soft-bottom intertidal communities. To test the role of predators in changes in clam abundance, we examined the number of moonsnails Amauropsis islandica. Macoma balthica exhibited spatially synchronous population dynamics at six sites in Kandalaksha Bay, where densities of clams varied between 140 and 8500 ind. m−2 during the 21-year period of observations. Statistical modelling using generalized additive models (GAM) shows that a combination of mild winter and warm summer led to an increase in M. balthica density the following year. Predation by A. islandica had no impact on changes in M. balthica density. Growth rates of M. balthica were higher during a cool decade, but clams that lived in a warmer period were characterized by more globose shells. Our results suggest that the climate oscillations can be regarded as the key factor causing the shift in abundance of M. balthica in the White Sea during the last two decades via recruitment and survival.

Dietary diversity involves adequate intake of macronutrient and micronutrient. The inclusion of animal source foods (ASF) in the diet helps prevent multiple nutrient deficiencies and any resultant, linear growth retardation. The objective of the current study was to assess the relationship between dietary diversity, ASF consumption and height-for-age z-score (HAZ) among children aged 12–59 months old across a 1-year observation. This longitudinal observational study without controls was conducted among four age groups: 12–23 months (n 57), 24–35 months (n 56), 36–47 months (n 58) and 48–59 months (n 56). Anthropometry and dietary intake were measured during each of four visits at 16–20-week intervals. The general characteristics and other observations were only collected at baseline and endline. During the year-long study period, approximately 27 % of the children ate a diverse diet (consumed ≥6 out of 9 food groups) according to ≥3 visits. ASF consumption was high, particularly for eggs, poultry, processed meats and liquid milk. Yet, micronutrient intake inadequacy, especially of Zn, Ca, Fe and vitamin A, was highly prevalent. A multivariate regression analysis showed that the consumption of a diverse diet and ASF was not significantly associated with the HAZ at endline, after controlling for demographic characteristics and the baseline HAZ. The consumption of a diverse diet was significantly associated with Ca intake adequacy. Moreover, ASF consumption was significantly associated with adequate intake of protein and micronutrients, particularly vitamin A, Ca and Zn. Thus, the recommendation is to continue and strengthen the promotion of consuming a diverse diet that includes ASF in supporting the linear growth of young children.

The amino acid arginine is a well-known growth hormone (GH) stimulator and GH is an important modulator of linear growth. The aim of the present study was to investigate the effect of dietary arginine on growth velocity in children between 7 and 13 years of age. Data from the Copenhagen School Child Intervention Study during 2001–2 (baseline), and at 3-year and 7-year follow-up, were used. Arginine intake was estimated via a 7 d precoded food diary at baseline and 3-year follow-up. Data were analysed in a multilevel structure in which children were embedded within schools. Random intercept and slopes were defined to estimate the association between arginine intake and growth velocity, including the following covariates: sex; age; baseline height; energy intake; puberty stage at 7-year follow-up and intervention/control group. The association between arginine intake and growth velocity was significant for the third and fourth quintile of arginine intake (2·5–2·8 and 2·8–3·2 g/d, respectively) compared with the first quintile ( < 2·2 g/d) (P for trend = 0·04). Protein intake (excluding arginine) was significantly associated with growth velocity; however, the association was weaker than the association between arginine intake and growth velocity (P for trend = 0·14). The results of the present study suggest a dose-dependent physiological role of habitual protein intake, and specifically arginine intake, on linear growth in normally growing children. However, since the study was designed in healthy children, we cannot firmly conclude whether arginine supplementation represents a relevant clinical strategy. Further research is needed to investigate whether dietary arginine may represent a nutritional strategy potentially advantageous for the prevention and treatment of short stature.

Poor fetal growth and associated prepubertal growth acceleration are linked to increased risk of cardiometabolic dysfunction in later life, but whether obesity is integral to ‘catch-up’ growth and its ensuing risks are unknown. In microswine offspring exposed to perinatal maternal protein restriction (MPR), we measured body and organ sizes (during MPR); linear growth and weight gain (birth to 5 months of age); feed intake and utilization efficiency (5–14 weeks); and body composition at 6 and 11 weeks of age (by dual-energy X-ray absorptiometry, DEXA). During MPR, low protein offspring (LPO) showed asymmetric growth restriction with reduced body weight (Wt):length (Lth) at birth and elevated heart Wt:liver Wt ratio by 2 weeks of age. In LPO, after slow early postnatal growth (0–5 weeks), subsequent linear growth on ad libitum normal feed was absolutely accelerated (cm/week; P < 0.001) over 6–11 weeks but normal thereafter, whereas absolute weight gain (kg/week) was similar to controls but accelerated relative to lower LPO nadir weights. Concurrently, rates of fat and lean tissue accrual in LPO over 6–11 weeks were similar to normal protein offspring in absolute terms (g/5 weeks) but increased relative to lower mass at 6 weeks, yielding normal lean:Lth but reduced fat:Lth ratios at 11 weeks. LPO had higher relative feed intake (g/kg/meal) in both sexes and higher feed efficiency in females over 5–11 weeks of age. Findings suggest that postnatal linear growth acceleration preserved thinness in juvenile LPO. Given separately reported abnormalities of vascular (Bagby et al., 2011) and adipocyte function in juvenile LPO, (DuPriest et al., 2011) findings demonstrate that perinatal MPR programs catch-up growth and cardiovascular abnormalities independently of obesity.

Let $k$ be a field of characteristic $0,\,R\,=\,k\left[ {{x}_{1}},\,\ldots ,\,{{x}_{d}} \right]$ be a polynomial ring, and $m$ its maximal homogeneous ideal. Let $I\,\subset \,R$ be a homogeneous ideal in $R$ . Let $\lambda (M)$ denote the length of an $R$ -module $M$ . In this paper, we show that

$$\underset{x\to \infty }{\mathop{\lim }}\,\,\frac{\lambda \left( H_{m}^{0}\left( R/{{I}^{n}} \right) \right)}{{{n}^{d}}}\,=\,\underset{x\to \infty }{\mathop{\lim }}\,\,\frac{\lambda \left( \text{Ext}_{R}^{d}\left( R/{{I}^{n}},\,R\left( -d \right) \right) \right)}{{{n}^{d}}}$$

always exists. This limit has been shown to be $e(I)/d!$ for $m$ -primary ideals $I$ in a local Cohen–Macaulay ring, where $e(I)$ denotes the multiplicity of $I$ . But we find that this limit may not be rational in general. We give an example for which the limit is an irrational number thereby showing that the lengths of these extension modules may not have polynomial growth.

The relationship between ponderal, linear and lower leg growth in children recovering from severe malnutrition remains unclear. We report on the early growth of 141 severely malnourished Bangladeshi children aged 6 to 36 months of age who were followed for 90 d. Mean (SD) weight for height (WHZ) and height for age (HAZ) catch-up growth Z scores over the 90 d were 1.6 (0.85) and 0.47 (0.325) respectively. mean (SD) lower leg length growth was 10.35 (4.5) mm. Change in HAZ was significantly associated with initial WHZ, but linear growth occurred in the presence of severe wasting and no threshold WHZ score was identified. Lower leg length gain correlated throughout with ponderal indices but with change in HAZ score only after day 45. Only initial WHZ score and maternal height predicted for linear growth and only accounted for 20 % of total variance. We conclude that linear growth occurs early in severely malnourished children but that knemometry behaves as a ponderal index acutely.