Pairwise Distances and the Problem of Multiple Optima.

Discrete optimization problems arise in many biological contexts and, in many cases, we seek to make inferences from the optimal solutions. However, the number of optimal solutions is frequently very large and making inferences from any single solution may result in conclusions that are not supported by other optimal solutions. We describe a general approach for efficiently (polynomial time) and exactly (without sampling) computing statistics on the space of optimal solutions. These statistics provide insights into the space of optimal solutions that can be used to support the use of a single optimum (e.g., when the optimal solutions are similar) or justify the need for selecting multiple optima (e.g., when the solution space is large and diverse) from which to make inferences. We demonstrate this approach on two well-known problems and identify the properties of these problems that make them amenable to this method.

Maximum-scoring path sets on pangenome graphs of constant treewidth.

We generalize a problem of finding maximum-scoring segment sets, previously studied by Csurös (IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2004, 1, 139-150), from sequences to graphs. Namely, given a vertex-weighted graph G and a non-negative startup penalty c, we can find a set of vertex-disjoint paths in G with maximum total score when each path's score is its vertices' total weight minus c. We call this new problem maximum-scoring path sets (MSPS). We present an algorithm that has a linear-time complexity for graphs with a constant treewidth. Generalization from sequences to graphs allows the algorithm to be used on pangenome graphs representing several related genomes and can be seen as a common abstraction for several biological problems on pangenomes, including searching for CpG islands, ChIP-seq data analysis, analysis of region enrichment for functional elements, or simple chaining problems.

Maternal genetics and diet modulate vitamin A homeostasis of the offspring and affect the susceptibility to obesity in adulthood in mice.

Perinatal nutrition exerts a profound influence on adult metabolic health. This study aimed to investigate whether increased maternal vitamin A (VA) supply can lead to beneficial metabolic phenotypes in the offspring. The researchers utilized mice deficient in the intestine-specific homeobox (ISX) transcription factor, which exhibit increased intestinal VA retinoid production from dietary ß-carotene (BC). ISX-deficient dams were fed a VA-sufficient or a BC-enriched diet during the last week of gestation and the whole lactation period. Total retinol levels in milk and weanling livers were 2 to 2.5-fold higher in the offspring of BC-fed dams (BC offspring), indicating increased VA supplies during late gestation and lactation. The corresponding VAS and BC offspring (males and females) were compared at weaning and adulthood after being fed either a standard or high-fat diet (HFD) with regular VA content for 13 weeks from weaning. HFD-induced increases in adiposity metrics, such as fat depot mass and adipocyte diameter, were more pronounced in males than females and were attenuated or suppressed in the BC offspring. Notably, the BC offspring were protected from HFD-induced increases in circulating triacylglycerol levels and hepatic steatosis. These protective effects were associated with reduced food efficiency, enhanced capacity for thermogenesis and mitochondrial oxidative metabolism in adipose tissues, and increased adipocyte hyperplasia rather than hypertrophy in the BC offspring. In conclusion, maternal VA nutrition influenced by genetics may confer metabolic benefits to the offspring, with mild increases in late gestation and lactation protecting against obesity and metabolic dysregulation in adulthood.

Modulation of metabolic and immunoregulatory pathways in the gut transcriptome of Atlantic salmon (Salmo salar L.) after early nutritional programming during first feeding with plant-based diet.

Introduction: Plant-based nutritional programming is the concept of exposing fish at very early life stages to a plant-based diet for a short duration to improve physiological responses when exposed to a similar plant-rich diet at a later developmental stage. The mechanisms of action underlying nutritional programming have not been fully deciphered, and the responses may be controlled at multiple levels. Methods: This 22-week study examines gut transcriptional changes after nutritional programming. Triplicate groups of Atlantic salmon were fed with a plant (V) vs. a marine-rich (M, control) diet for 2 weeks (stimulus phase) at the first exogenous feeding. Both stimulus fish groups (M and V fish) were then fed the M diet for 12 weeks (intermediate phase) and lastly fed the V diet (challenge phase) for 6 weeks, generating two dietary regimes (MMV and VMV) across phases. This study used a whole-transcriptome approach to analyse the effects of the V diet at the end of stimulus (short-term effects) and 22 weeks post-first feeding (long-term effects). After the stimulus, due to its developmental stage, the whole intestine was used, whereas, after the challenge, pyloric caeca and middle and distal intestines were examined. Results and discussion: At the stimulus end, genes with increased expression in V fish enriched pathways including regulatory epigenetic responses and lipid metabolism, and genes involved in innate immune response were downregulated. In the middle intestine at the end of the challenge, expression levels of genes of lipid, carbohydrate, and energy metabolism were increased in V fish, while M fish revealed increased expression of genes associated with autoimmune and acute adaptive immune response. The distal intestine of V fish showed increased expression of genes associated with immune response and potential immune tolerance. Conversely, the distal intestine of M fish at challenge revealed upregulation of lipid and carbohydrate metabolic pathways, tissue degeneration, and apoptotic responses. The present study demonstrated nutritional programming-associated changes in the intestinal transcriptome, with altered expression of genes involved in both immune responses and different metabolic processes. While there were limited changes in growth between the groups, the results show that there were transcriptional differences, suggesting a programming response, although the mechanism of this response still requires to be fully elucidated.

Understanding perspectives of HIV/AIDS affected households on food and nutrition interventions and social protection programmes in Zimbabwe.

Introduction: The study was aimed at understanding the needs and perspectives of HIV affected households on food and nutrition security intervention programmes. Methods: The study used qualitative methods that include focus groups discussions and key informant interviews to solicit for lived experiences of People Living With HIV (PLWHIV). Results: The results revealed that intervention programmes by both government and development partners (donors) can be divided into four (4) categories: food and nutrition security, livelihood, health, and social protection. Interventions that targeted health included the provision of HIV antiretroviral drugs to PLWHIV and counselling to both PLWHIV and affected persons. Intervention programmes targeted at social protection included provision of food aid and cash transfers. Discussion: The recommendations based on the research findings are that intervention programmes should focus more on resilience building as a way of building capacity of PLWHIV. This way, sustainability of intervention programmes is improved. As such, it is important to ensure, through policy, that all intervention programmes have a component of capacity building to improve resilience of participants and programme sustainability. Furthermore, there is a need to improve targeting for beneficiaries of intervention programmes and clearly define the "vulnerable" group.

Xihuang pills targeting the Warburg effect through inhibition of the Wnt/ß-catenin pathway in prostate cancer.

Objective: Prostate cancer, marked by a high incidence and mortality rate, presents a significant challenge, especially in the context of castration-resistant prostate cancer (CRPC) with limited treatment options due to drug resistance. This study aims to explore the anti-tumor effects of Xihuang Pills (XHP) on CRPC, focusing on metabolic reprogramming and the Wnt/ß-catenin pathway. Methods: In vitro and in vivo biofunctional assays were employed to assess the efficacy and mechanisms of XHP. Subcutaneous xenografts of PC3 in mice served as an in vivo model to evaluate XHP's anti-tumor activity. Tumor volume, weight, proliferation, and apoptosis were monitored. Various assays, including CCK8, TUNEL assay, QRT-PCR, and Western Blotting, were conducted to measure metabolic reprogramming, proliferation, apoptosis, and cell cycle in prostate cancer cells. RNA-seq analysis predicted XHP's impact on prostate cancer, validating the expression of Wnt/ß-catenin-related proteins and mRNA. Additionally, 58 compounds in XHP were identified via LC-MS/MS, and molecular docking analysis connected these compounds to key genes. Results: In vitro and in vivo experiments demonstrated that XHP significantly inhibited CRPC cell viability, induced apoptosis, and suppressed invasion and migration. mRNA sequencing revealed differentially expressed genes, with functional enrichment analysis indicating modulation of key biological processes. XHP treatment downregulated Wnt signaling pathway-related genes, including CCND2, PRKCG, and CCN4. Moreover, XHP effectively inhibited glucose uptake and lactate production, leading to reduced HIF-1α and glycolytic enzymes (GLUT1, HK2, PKM2), suggesting its potential in attenuating the Warburg effect. Molecular docking analysis suggested a plausible interaction between XHP's active compounds and Wnt1 protein, indicating a mechanism through which XHP modulates the Wnt/ß-catenin pathway. Conclusion: XHP demonstrated remarkable efficacy in suppressing the growth, proliferation, apoptosis, migration, and invasiveness of prostate tumors. The interaction between XHP's active constituents and Wnt1 was evident, leading to the inhibition of Wnt1 and downstream anti-carcinogenic factors, thereby influencing the ß-catenin/HIF-1α-mediated glycolysis.

High-Fat Diets Fed during Pregnancy Cause Changes to Pancreatic Tissue DNA Methylation and Protein Expression in the Offspring: A Multi-Omics Approach.

Maternal obesity, caused by diets rich in fats and sugars during pregnancy, can predispose offspring to metabolic diseases such as diabetes. We hypothesized that obesity during pregnancy leads to increased DNA methylation and reduced protein expression in factors regulating ß-cell function and apoptosis. Female C57BL/6J mice were fed a high-fat diet (HFD; 42% fat content; n = 3) or a control diet (CON; 16% fat content; n = 3) for fourteen weeks before and during pregnancy. Offspring were euthanized at 8 weeks and pancreatic tissue was collected. Isolated DNA was analyzed using whole-genome bisulfite sequencing. Protein expression was quantified using LC-MS. No significant differences in body weight were observed between HFD and control pups (p = 0.10). Whole-genome bisulfite sequencing identified 91,703 and 88,415 differentially methylated regions (DMRs) in CON vs. HFD male and female offspring. A total of 34 and 4 proteins were determined to have changes in expression that correlated with changes in DNA methylation in CON vs. HFD males and females, respectively. The majority of these factors were grouped into the metabolic function category via pathway analyses. This study illustrates the complex relationship between epigenetics, diet, and sex-specific responses, therefore offering insights into potential therapeutic targets and areas for further research.

Fast Low-Sidelobe Pattern Synthesis Using the Symmetry of Array Geometry.

Array pattern synthesis with low sidelobe levels is widely used in practice. An effective way to incorporate sensor patterns in the design procedure is to use numerical optimization methods. However, the dimension of the optimization variables is very high for large-scale arrays, leading to high computational complexity. Fortunately, sensor arrays used in practice usually have symmetric structures that can be utilized to accelerate the optimization algorithms. This paper studies a fast pattern synthesis method by using the symmetry of array geometry. In this method, the problem of amplitude weighting is formulated as a second-order cone programming (SOCP) problem, in which the dynamic range of the weighting coefficients can also be taken into account. Then, by utilizing the symmetric property of array geometry, the dimension of the optimization problem as well as the number of constraints can be reduced significantly. As a consequence, the computational efficiency is greatly improved. Numerical experiments show that, for a uniform rectangular array (URA) with 1024 sensors, the computational efficiency is improved by a factor of 158, while for a uniform hexagonal array (UHA) with 1261 sensors, the improvement factor is 284.

Exploring Selenoprotein P in Liver Cancer: Advanced Statistical Analysis and Machine Learning Approaches.

Selenoprotein P (SELENOP) acts as a crucial mediator, distributing selenium from the liver to other tissues within the body. Despite its established role in selenium metabolism, the specific functions of SELENOP in the development of liver cancer remain enigmatic. This study aims to unravel SELENOP's associations in hepatocellular carcinoma (HCC) by scrutinizing its expression in correlation with disease characteristics and investigating links to hormonal and lipid/triglyceride metabolism biomarkers as well as its potential as a prognosticator for overall survival and predictor of hypoxia. SELENOP mRNA expression was analyzed in 372 HCC patients sourced from The Cancer Genome Atlas (TCGA), utilizing statistical methodologies in R programming and machine learning techniques in Python. SELENOP expression significantly varied across HCC grades (p < 0.000001) and among racial groups (p = 0.0246), with lower levels in higher grades and Asian individuals, respectively. Gender significantly influenced SELENOP expression (p < 0.000001), with females showing lower altered expression compared to males. Notably, the Spearman correlation revealed strong positive connections of SELENOP with hormonal markers (AR, ESR1, THRB) and key lipid/triglyceride metabolism markers (PPARA, APOC3, APOA5). Regarding prognosis, SELENOP showed a significant association with overall survival (p = 0.0142) but explained only a limited proportion of variability (~10%). Machine learning suggested its potential as a predictive biomarker for hypoxia, explaining approximately 18.89% of the variance in hypoxia scores. Future directions include validating SELENOP's prognostic and diagnostic value in serum for personalized HCC treatment. Large-scale prospective studies correlating serum SELENOP levels with patient outcomes are essential, along with integrating them with clinical parameters for enhanced prognostic accuracy and tailored therapeutic strategies.

Enhancing affordability and profit in a non-cooperative, coordinated, hypothetical pediatric vaccine market via sequential optimization.

This study considers a hypothetical global pediatric vaccine market where multiple coordinating entities make optimal procurement decisions on behalf of countries with different purchasing power. Each entity aims to improve affordability for its countries while maintaining a profitable market for vaccine producers. This study analyzes the effect of several factors on affordability and profitability, including the number of non-cooperative coordinating entities making procuring decisions, the number of market segments in which countries are grouped for tiered pricing purposes, how producers recover fixed production costs, and the procuring order of the coordinating entities. The study relies on a framework where entities negotiate sequentially with vaccine producers using a three-stage optimization process that solves a MIP and two LP problems to determine the optimal procurement plans and prices per dose that maximize savings for the entities' countries and profit for the vaccine producers. The study's results challenge current vaccine market dynamics and contribute novel alternative strategies to orchestrate the interaction of buyers, producers, and coordinating entities for enhancing affordability in a non-cooperative market. Key results show that the order in which the coordinating entities negotiate with vaccine producers and how the latter recuperate their fixed cost investments can significantly affect profitability and affordability. Furthermore, low-income countries can meet their demands more affordably by procuring vaccines through tiered pricing via entities coordinating many market segments. In contrast, upper-middle and high-income countries increase their affordability by procuring through entities with fewer and more extensive market segments. A procurement order that prioritizes entities based on the descending income level of their countries offers higher opportunities to increase affordability and profit when producers offer volume discounts.

Influence of leptin administration to pregnant mice on fetal gene expression and adaptation to sweet and fatty food in adult offspring of different sexes.

Elevated leptin in pregnant mice improves metabolism in offspring fed high-calorie diet and its influence may be sex-specific. Molecular mechanisms mediating leptin programming action are unknown. We aimed to investigate programming actions of maternal leptin on the signaling function of the placenta and fetal liver and on adaptation to high-calorie diet in male and female offspring. Female C57BL/6J mice received leptin injections in mid-pregnancy. Gene expression was assessed in placentas and in the fetal brain and liver at the end of pregnancy. Metabolic parameters and gene expression in the liver, brown fat and hypothalamus were assessed in adult male and female offspring that had consumed sweet and fatty diet (SFD: chow, lard, sweet biscuits) for 2 weeks. Females had lower blood levels of leptin, glucose, triglycerides and cholesterol than males. Consuming SFD, females had increased Ucp1 expression in brown fat, while males had accumulated fat, decreased blood triglycerides and liver Fasn expression. Leptin administration to mothers increased Igf1 and Dnmt3b expression in fetal liver, decreased post-weaning growth rate, and increased hypothalamic Crh expression in response to SFD in both sexes. Only in male offspring this administration decreased expression of Fasn and Gck in the mature liver, increased fat mass, blood levels of glucose, triglycerides and cholesterol and Dmnt3a expression in the fetal liver. The results suggest that the influence of maternal leptin on the expression of genes encoding growth factors and DNA methyltransferases in the fetal liver may mediate its programming effect on offspring metabolic phenotypes.

Epigenetic regulation by hypoxia, N-acetylcysteine and hydrogen sulphide of the fetal vasculature in growth restricted offspring: A study in humans and chicken embryos.

Fetal growth restriction (FGR) is a common outcome in human suboptimal gestation and is related to prenatal origins of cardiovascular dysfunction in offspring. Despite this, therapy of human translational potential has not been identified. Using human umbilical and placental vessels and the chicken embryo model, we combined cellular, molecular, and functional studies to determine whether N-acetylcysteine (NAC) and hydrogen sulphide (H2S) protect cardiovascular function in growth-restricted unborn offspring. In human umbilical and placental arteries from control or FGR pregnancy and in vessels from near-term chicken embryos incubated under normoxic or hypoxic conditions, we determined the expression of the H2S gene CTH (i.e. cystathionine γ-lyase) (via quantitative PCR), the production of H2S (enzymatic activity), the DNA methylation profile (pyrosequencing) and vasodilator reactivity (wire myography) in the presence and absence of NAC treatment. The data show that FGR and hypoxia increased CTH expression in the embryonic/fetal vasculature in both species. NAC treatment increased aortic CTH expression and H2S production and enhanced third-order femoral artery dilator responses to the H2S donor sodium hydrosulphide in chicken embryos. NAC treatment also restored impaired endothelial relaxation in human third-to-fourth order chorionic arteries from FGR pregnancies and in third-order femoral arteries from hypoxic chicken embryos. This NAC-induced protection against endothelial dysfunction in hypoxic chicken embryos was mediated via nitric oxide independent mechanisms. Both developmental hypoxia and NAC promoted vascular changes in CTH DNA and NOS3 methylation patterns in chicken embryos. Combined, therefore, the data support that the effects of NAC and H2S offer a powerful mechanism of human translational potential against fetal cardiovascular dysfunction in complicated pregnancy. KEY POINTS: Gestation complicated by chronic fetal hypoxia and fetal growth restriction (FGR) increases a prenatal origin of cardiovascular disease in offspring, increasing interest in antenatal therapy to prevent against a fetal origin of cardiovascular dysfunction. We investigated the effects between N-acetylcysteine (NAC) and hydrogen sulphide (H2S) in the vasculature in FGR human pregnancy and in chronically hypoxic chicken embryos. Combining cellular, molecular, epigenetic and functional studies, we show that the vascular expression and synthesis of H2S is enhanced in hypoxic and FGR unborn offspring in both species and this acts to protect their vasculature. Therefore, the NAC/H2S pathway offers a powerful therapeutic mechanism of human translational potential against fetal cardiovascular dysfunction in complicated pregnancy.

Inuit youth health and wellbeing programming in Canada.

Inuit youth face challenges in maintaining their wellbeing, stemming from continued impacts of colonisation. Recent work documented that urban centres, such as Winnipeg Canada, have large Inuit populations comprised of a high proportion of youth. However, youth lack culturally appropriate health and wellbeing services. This review aimed to scan peer-reviewed and grey literature on Inuit youth health and wellbeing programming in Canada. This review is to serve as an initial phase in the development of Inuit-centric youth programming for the Qanuinngitsiarutiksait program of research. Findings will support further work of this program of research, including the development of culturally congruent Inuit-youth centric programming in Winnipeg. We conducted an environmental scan and used an assessment criteria to assess the effectiveness of the identified programs. Results showed that identified programs had Inuit involvement in creation framing programming through Inuit knowledge and mostly informed by the culture as treatment approach. Evaluation of programs was diffcult to locate, and it was hard to discren between programming, pilots or explorative studies. Despite the growing urban population, more non-urban programming was found. Overall, research contributes to the development of effective strategies to enhance the health and wellbeing of Inuit youth living in Canada.

Prediction of optical properties of rare-earth doped phosphate glasses using gene expression programming.

The progression of optical materials and their associated applications necessitates a profound comprehension of their optical characteristics, with the Judd-Ofelt (JO) theory commonly employed for this purpose. However, the computation of JO parameters (Ω2, Ω4, Ω6) entails wide experimental and theoretical endeavors, rendering traditional calculations often impractical. To address these challenges, the correlations between JO parameters and the bulk matrix composition within a series of Rare-Earth ions doped sulfophosphate glass systems were explored in this research. In this regard, a novel soft computing technique named genetic expression programming (GEP) was employed to derive formulations for JO parameters and bulk matrix composition. The predictor variables integrated into the formulations consist of JO parameters. This investigation demonstrates the potential of GEP as a practical tool for defining functions and classifying important factors to predict JO parameters. Thus, precise characterization of such materials becomes crucial with minimal or no reliance on experimental work.

Parental genetic effects on the offspring`s phenotype without direct transmission of the parental gene itself - pathophysiology and clinical evidence.

Parental genes can influence the phenotype of their offspring through genomic-epigenomic interactions even without the direct inheritance of specific parental genotypes. Maternal genetic variations can affect the ovarian and intrauterine environments and potentially alter lactation behaviors, impacting offspring nutrition and health outcomes independently of the fetal genome. Similarly, paternal genetic changes can affect the endocrine system and vascular functions in the testes, influencing sperm quality and seminal fluid composition. These changes can initiate early epigenetic modifications in sperm, including alterations in microRNAs, tRNA-derived small RNAs, and DNA methylation patterns. These epigenetic modifications might induce further changes in target organs of the offspring, leading to modified gene expression and phenotypic outcomes without transmitting the original parental genetic alterations. This review presents clinical evidence supporting this hypothesis and discusses the potential underlying molecular mechanisms. Parental gene-offspring epigenome-offspring phenotype interactions have been observed in neurocognitive disorders as well as cardio-renal diseases.

Predictors of Shock-Reduction Programming and Its Impact on Implantable Cardioverter-Defibrillator Therapies and Mortality: The CERTITUDE Registry.

BACKGROUND: Shock-reduction implantable cardioverter-defibrillator programming (SRP) was associated with fewer therapies and improved survival in randomized controlled trials, but real-world studies investigating SRP and associated outcomes are limited. METHODS AND RESULTS: The BIOTRONIK CERTITUDE registry was linked with the Medicare database. We included all patients with an implantable cardioverter-defibrillator implanted between August 22, 2012 and September 30, 2021 in the United States. SRP was defined as programming to either a therapy rate cutoff ≥188 beats per minute or number of intervals to detection ≥30/40 for treatment. Among 6781 patients (mean 74±9 years; 27% women), 3393 (50%) had SRP. Older age, secondary prevention indication, and device implantation in the southern or western United States were associated with lower use of SRP. The cumulative incidence rate of implantable cardioverter-defibrillator shocks was lower in the SRP group (5.1% shocks/patient year) compared with the non-SRP group (7.2% shocks/patient year) (adjusted hazard ratio [HR], 0.83 [95% CI, 0.73-0.96]; P=0.005). Over a median follow-up of 2.9 years, 739 deaths occurred in the SRP group and 822 deaths occurred in the non-SRP group (adjusted HR, 0.97 [95% CI, 0.88-1.07]; P=0.569). SRP was associated with a lower all-cause mortality among patients without ischemic heart disease compared with patients with ischemic heart disease (adjusted HR, 0.64 [95% CI, 0.48-0.87] versus adjusted HR, 1.02 [95% CI, 0.92-1.14]; Pinteraction=0.004). CONCLUSIONS: Adoption of SRP is low in real-world clinical practice. Age, clinical variables, and geographic factors are associated with use of SRP. In this study, SRP-associated decrease in mortality was limited to patients without ischemic heart disease.

Assessing carbon tax using a CGE model with firm heterogeneity: An application to Vietnam.

Vietnam's government is considering introducing a carbon market as part of its decarbonization strategy. The carbon tax is an option for the government to regulate greenhouse gas emissions. We evaluate the potential macroeconomic and climate impacts of carbon tax policy in Vietnam using a unique data set and simulation analysis with a multi-sector dynamic computable general equilibrium model. The model allows for firm heterogeneity: domestic firms and foreign-invested enterprises. The results show that with plausible tax rates, emissions can be reduced to levels 1.3-2.8 percent below the target value of emissions in 2030. The cost is a loss in GDP by 1.2-2.7 percent in 2030. The results also show that foreign-invested enterprises tend to increase emissions in the medium run even with a carbon tax while a carbon tax is more effective when applied to domestic firms. In addition, a substantial reduction in emissions from the energy sector and improvement in energy efficiency are keys to success in carbon abatement.

Maternal α-casein deficiency extends the lifespan of offspring and programmes their body composition.

Early nutrition has significant effects on physiological outcomes during adult life. We have analysed the effect of maternal α-casein (CSN1S1) deficiency on the physiological fate of dams and their offspring. α-casein deficiency reduces maternal milk protein concentration by more than 50% and attenuates the growth of pups to 27% (p < 0.001) of controls at the point of weaning. This is associated with a permanent reduction in adult body weight (- 31% at 25 weeks). Offspring nursed by α-casein deficient dams showed a significantly increased lifespan (+ 20%, χ2: 10.6; p = 0.001). Liver transcriptome analysis of offspring nursed by α-casein deficient dams at weaning revealed gene expression patterns similar to those found in dwarf mice (reduced expression of somatotropic axis signalling genes, increased expression of xenobiotic metabolism genes). In adult mice, the expression of somatotropic axis genes returned to control levels. This demonstrates that, in contrast to dwarf mice, attenuation of the GH-IGF signalling axis in offspring nursed by α-casein deficient dams is transient, while the changes in body size and lifespan are permanent. Offspring nursed by α-casein deficient dams showed permanent changes in body composition. Absolute and relative adipose tissue weights (p < 0.05), the percentage of body fat (p < 0.001) as well as adipocyte size in epididymal white adipose tissue are all reduced. Serum leptin levels were 25% of those found in control mice (p < 0.001). Liver lipid content and lipid composition were significantly altered in response to postnatal nutrition. This demonstrates the nutrition in early life programmes adult lipid metabolism, body composition and lifespan.

Optimal refinement of strata to balance covariates.

What is the best way to split one stratum into two to maximally reduce the within-stratum imbalance in many covariates? We formulate this as an integer program and approximate the solution by randomized rounding of a linear program. A linear program may assign a fraction of a person to each refined stratum. Randomized rounding views fractional people as probabilities, assigning intact people to strata using biased coins. Randomized rounding is a well-studied theoretical technique for approximating the optimal solution of certain insoluble integer programs. When the number of people in a stratum is large relative to the number of covariates, we prove the following new results: (i) randomized rounding to split a stratum does very little randomizing, so it closely resembles the linear programming relaxation without splitting intact people; (ii) the linear relaxation and the randomly rounded solution place lower and upper bounds on the unattainable integer programming solution; and because of (i), these bounds are often close, thereby ratifying the usable randomly rounded solution. We illustrate using an observational study that balanced many covariates by forming matched pairs composed of 2016 patients selected from 5735 using a propensity score. Instead, we form 5 propensity score strata and refine them into 10 strata, obtaining excellent covariate balance while retaining all patients. An R package optrefine at CRAN implements the method. Supplementary materials are available online.