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BACKGROUND AND AIMS: A variety of maternal heart conditions are associated with abnormal placentation and reduced foetal growth. However, their impact on offspring's long-term cardiovascular health is poorly studied. This study aims to investigate the association between intrauterine exposure to pre-existing maternal cardiovascular disease (CVD) and offspring CVD occurring from infancy to early adulthood, using paternal CVD as a negative control. METHODS: This nationwide cohort study used register data of live singletons without major malformations or congenital heart disease born between 1992 and 2019 in Sweden. Hazard ratios (HRs) and 95% confidence intervals (CIs) were estimated using Cox proportional hazards models, adjusted for essential maternal characteristics. Paternal CVD served as a negative control for assessment of unmeasured genetic and environmental confounding. RESULTS: Of the 2 597 786 offspring analysed (49.1% female), 26 471 (1.0%) were born to mothers with pre-existing CVD. During a median follow-up of 14 years (range 1-29 years), 17 382 offspring were diagnosed with CVD. Offspring of mothers with CVD had 2.09 times higher adjusted HR of CVD (95% CI 1.83, 2.39) compared with offspring of mothers without CVD. Compared with maternal CVD, paternal CVD showed an association of smaller magnitude (HR 1.49, 95% CI 1.32, 1.68). Increased hazards of offspring CVD were also found when stratifying maternal CVD into maternal arrhythmia (HR 2.94, 95% CI 2.41, 3.58), vascular (HR 1.59, 95% CI 1.21, 2.10), and structural heart diseases (HR 1.48, 95% CI 1.08, 2.02). CONCLUSIONS: Maternal CVD was associated with an increased risk of CVD in offspring during childhood and young adulthood. Paternal comparison suggests that genetic or shared familial factors may not fully explain this association.
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The presaccadic preview of a peripheral target enhances the efficiency of its postsaccadic processing, termed the extrafoveal preview effect. Peripheral visual performance-and thus the quality of the preview-varies around the visual field, even at isoeccentric locations: It is better along the horizontal than vertical meridian and along the lower than upper vertical meridian. To investigate whether these polar angle asymmetries influence the preview effect, we asked human participants to preview four tilted gratings at the cardinals, until a central cue indicated which one to saccade to. During the saccade, the target orientation either remained or slightly changed (valid/invalid preview). After saccade landing, participants discriminated the orientation of the (briefly presented) second grating. Stimulus contrast was titrated with adaptive staircases to assess visual performance. Expectedly, valid previews increased participants' postsaccadic contrast sensitivity. This preview benefit, however, was inversely related to polar angle perceptual asymmetries; largest at the upper, and smallest at the horizontal meridian. This finding reveals that the visual system compensates for peripheral asymmetries when integrating information across saccades, by selectively assigning higher weights to the less-well perceived preview information. Our study supports the recent line of evidence showing that perceptual dynamics around saccades vary with eye movement direction.
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Movimentos Sacádicos , Campos Visuais , Percepção Visual , Humanos , Movimentos Sacádicos/fisiologia , Adulto , Percepção Visual/fisiologia , Feminino , Masculino , Campos Visuais/fisiologia , Estimulação Luminosa/métodos , Adulto Jovem , Sensibilidades de Contraste/fisiologiaRESUMO
In this study a real case multi-objective material and supplier selection problem in cardboard box production industries is studied. This problem for the first time optimizes the objective functions such as total wastage amounts remained from all raw sheets, total costs of the system including purchasing cost and transportation cost (including fixed and variable costs) of the raw sheets, and total overplus of produced cardboard boxes. To be closer to the real situations, as a novelty, the problem is formulated in belief-degree-based uncertain environment with normal distribution where this type of uncertainty applies the ideas of experts. A solution approach including two steps is proposed to solve the problem. In the first step, the proposed uncertain formulation is converted to a crisp form using a typical chance constrained programming scheme. In the second step, a new goal programming approach containing a piecewise penalty function is developed in order to solve the obtained multi-objective crisp formulation. In this approach, based on the ideas of experts, multiple goals are considered with different penalty values. A case study from cardboard box industries is considered to evaluate the proposed formulations and solution approach. According to the obtained results, the proposed solution approach is compared to similar approaches of the literature and its efficiency is studied.
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Basin water pollution caused by livestock, poultry and fish breeding is still a serious problem for remote villages, however, reliable regional breeding management programming have the potentials to improve pollution status. This paper focuses on the optimal model design and water quality analysis of the livestock, poultry and fish breeding system for Wenchang City, China. Methods of multi-objective programming (MOP), interval parameter programming (IPP), fuzzy-stochastic parameter programming (FSPP), and chance constrained programming (CCP) were incorporated into the developed model to tackle multi uncertainties described by interval values, probability distributions, fuzzy membership function. Based on the estimation of local breeding potential and current situation of surface water section, a multi-objective mixed fuzzy-stochastic nonlinear programming optimization model is presented with one-dimensional water quality model. In order to evaluate the environmental carrying capacity of livestock, poultry and fishery manure, predict its development trend and investigate the implementation effect of different emission reduction policies, this paper designs quantization system of the urban water environmental carrying capacity for the model. The results indicated that the water environment pollutant absorption capacity and carrying capacity of Wenchang city have approached the limit especially the towns in the northeast of City which limited the overall development space of the City. The modeling results are valuable for supporting the adjustment of the existing livestock, poultry and fish breeding schemes within a complicated system benefit and surface water quality situation under uncertainty.
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Environmental factors in the early life stages can lead the descendant to adaptations in gene expression, permanently impacting several structures and organs. The amount and quality of fatty acids in the maternal diet in pregnancy and lactation were found to impact offspring metabolism. So, maternal diet and insulin resistance can affect the male and female descendants through distinct pathways and at different time points. We hypothesized that maternal high-fat diet (HFD) intake before conception and an adequate amount of different fatty acids intake during pregnancy and lactation could influence the energy homeostasis system of 21-day-old offspring. Female rats received control diet (C) or HFD (HF) for 8 weeks before pregnancy. During pregnancy and lactation C group remained with same diet (C-C), HF group were distributed into 4 groups and received C diet (HF-C), normolipidic diet based on saturated fatty acids (HF-S) or based on polyunsaturated fatty acids n-3 (HF-P) or remained in same diet (HF-HF). Maternal HFD in preconception, pregnancy, and lactation (HF-HF) led to lower glucagon-like peptide-1 levels in male (HF-HF21) compared to other groups (C-C21, HF-C21, and HF-P21) and compared to HF-HF21 females. Neuropeptide YY levels were higher in the HF-HF21, HF-C21, and HF-S21 male offspring compared to HF-P21. HF-P21 was similar to C-C21. Positive correlations were found among the energy homeostasis markers genes expressed in the offspring hypothalamus. Maternal diet changes to adequate quantities of fatty acids during pregnancy and lactation showed less impaired results but was not entirely avoided. A maternal diet based on PUFA n-3 during pregnancy and lactation seems to reverse the damage of an HFD in preconception. These results of homeostasis energy system disturbance in the offspring at weaning give us clues about changes that precede the onset of the disease in adult life - adding notes to the knowledge for future investigations of prevention and treatment of chronic diseases.
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PURPOSE: There is increasing recognition of the importance of transparency and reproducibility in scientific research. This study aimed to quantify the extent to which programming code is publicly shared in pharmacoepidemiology, and to develop a set of recommendations on this topic. METHODS: We conducted a literature review identifying all studies published in Pharmacoepidemiology and Drug Safety (PDS) between 2017 and 2022. Data were extracted on the frequency and types of programming code shared, and other key open science practices (clinical codelist sharing, data sharing, study preregistration, and stated use of reporting guidelines and preprinting). We developed six recommendations for investigators who choose to share code and gathered feedback from members of the International Society for Pharmacoepidemiology (ISPE). RESULTS: Programming code sharing by articles published in PDS ranged from 1.8% in 2017 to 9.5% in 2022. It was more prevalent among articles with a methodological focus, simulation studies, and papers which also shared record-level data. CONCLUSION: Programming code sharing is rare but increasing in pharmacoepidemiology studies published in PDS. We recommend improved reporting of whether code is shared and how available code can be accessed. When sharing programming code, we recommend the use of permanent digital identifiers, appropriate licenses, and, where possible, adherence to good software practices around the provision of metadata and documentation, computational reproducibility, and data privacy.
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Disseminação de Informação , Farmacoepidemiologia , Farmacoepidemiologia/métodos , Humanos , Disseminação de Informação/métodos , Software , Reprodutibilidade dos Testes , Guias como AssuntoRESUMO
The goal of this study was to understand how neighborhood greenspace access may support or hinder the effectiveness of community programs and policies (CPPs) aimed at reducing racial and ethnic inequities in screen time among 4598 US children. We found higher CPP intensity was significantly associated with fewer screen time behaviors in high greenspace neighborhoods, but not neighborhoods with low or moderate greenspace. Moreover, there were significant differences in greenspace access by neighborhood-level race and ethnicity. Implementing CPPs without regard for racial and ethnic greenspace inequities may be an underlying cause in the perpetuation of inequities in childhood screen time.
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Emerging evidence that intrauterine exposures to environmental stressors can 'programme' epigenetic modifications in offspring, leading to long-lasting health risks, has generated debate about whether prospective mothers have a specific 'epigenetic' moral responsibility. However, to date, proposals for maternal epigenetic responsibility have failed to grapple adequately with the uncertainty of scientific evidence, and specifically, whether the causal basis for intrauterine epigenetic effects is sufficiently established to ground claims of moral responsibility. Causality is widely considered a necessary condition for the attribution of moral responsibility. In this paper, we show that much foetal programming science in humans has yet to establish a causal epigenetic connection between intrauterine exposures and subsequent offspring health impacts. This research struggles to establish that the relationship between such exposures and offspring health risks is in fact causal, neither has it been able to evince the causal significance of exposures during pregnancy to such outcomes. We argue that these two challenges to establishing causality in foetal programming research seriously undercut the idea that prospective mothers may have a moral responsibility to ensure the epigenetics of their offspring.
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A neural network model is constructed to solve convex quadratic multi-objective programming problem (CQMPP). The CQMPP is first converted into an equivalent single-objective convex quadratic programming problem by the mean of the weighted sum method, where the Pareto optimal solution (POS) are given by diversifying values of weights. Then, for given various values weights, multiple projection neural networks are employded to search for Pareto optimal solutions. Based on employing Lyapunov theory, the proposed neural network approach is established to be stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the single-objective problem. The simulation results also show that the presented model is feasible and efficient.
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Given a family of linear constraints and a linear objective function one can consider whether to apply a Linear Programming (LP) algorithm or use a Linear Superiorization (LinSup) algorithm on this data. In the LP methodology one aims at finding a point that fulfills the constraints and has the minimal value of the objective function over these constraints. The Linear Superiorization approach considers the same data as linear programming problems but instead of attempting to solve those with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward feasible points with reduced (not necessarily minimal) objective function values. Previous studies compared LP and LinSup in terms of their respective outputs and the resources they use. In this paper we investigate these two approaches in terms of their sensitivity to condition numbers of the system of linear constraints. Condition numbers are a measure for the impact of deviations in the input data on the output of a problem and, in particular, they describe the factor of error propagation when given wrong or erroneous data. Therefore, the ability of LP and LinSup to cope with increased condition numbers, thus with ill-posed problems, is an important matter to consider which was not studied until now. We investigate experimentally the advantages and disadvantages of both LP and LinSup on examplary problems of linear programming with multiple condition numbers and different problem dimensions.
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This study identifies the optimal combination of active and passive thermoplastic materials for producing multi-material programmable 3D structures. These structures can undergo shape changes with varying radii of curvature over time when exposed to hot water. The research focuses on examining the thermal, thermomechanical, and mechanical properties of active (PLA) and passive (PRO-PLA, ABS, and TPU) materials. It also includes the experimental determination of the radius of curvature of the programmed 3D structures. The pairing of active PLA with passive PRO-PLA was found to be the most effective for creating complex programmable 3D structures capable of two-sided transformation. This efficacy is attributed to the adequate apparent shear strength, significant differences in thermomechanical shrinkage between the two materials, identical printing parameters for both materials, and the lowest bending storage modulus of PRO-PLA among the passive materials within the activation temperature range. Multi-material 3D printing has also proven to be a suitable method for producing programmable 3D structures for practical applications such as phone stands, phone cases, door hangers, etc. It facilitates the programming of the active material and ensures the dimensional stability of the passive components of programmable 3D structures during thermal activation.
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Background: In large supplementary feeding programs for children, it is challenging to create and sustain contextual, acceptable, nutritionally complete, and diverse supplemental foods. For example, the Indian Supplementary Nutrition Program (SNP) supplements the dietary intake of children, pregnant and lactating women, and severely acutely malnourished (SAM) children by offering dry take home rations (THRs) or hot cooked meals (HCMs) across India, but an optimization tool is necessary to create local contextual recipes for acceptable and nutritionally adequate products. Objectives: This study aimed to create a linear programming (LP) model to optimize diverse food provisions for a SNP to meet its program guidelines, using locally available foods, within budgetary allocations. Methods: A LP algorithm with appropriate constraints was used to generate an optimal THR based on raw foods, or an optimal weekly HCM menu comprised of a lunch meal with mid-morning snacks, based on user choices of foods and recipes. The database of foods used was created by a prospective survey conducted across all states of India for this purpose, such that the recipe and food optimization was diverse and specific to the guidelines for each beneficiary group. Results: An interactive web-based app, which can optimize feeding programs at any population level, was developed for use by program implementers and is hosted at https://www.datatools.sjri.res.in/SNP/. In the Indian example analyzed here, the recommended optimized diets met the guidelines for diversified and nutritionally complete SNP provision but at a cost that was almost 25% higher than the present Indian budget allocation. Conclusions: The optimization model developed demonstrates that contextual SNP diets can be created to meet macronutrient and most essential micronutrient needs of large-scale feeding programs, but appropriate diversification entails additional costs.
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OBJECTIVE: In order to facilitate the tracing of infectious diseases in a small area and to effectively carry out disease control and epidemiological investigations, this research proposes a novel spatiotemporal model to estimate effective reproduction number(Re)for infectious diseases, based on the fundamental concept of contact tracing. METHODS: This study utilizes the incidence of hand, foot, and mouth disease (HFMD) among children in Bishan District, Chongqing, China from 2015 to 2019. The study incorporates the epidemiological characteristics of HFMD and aims to construct a Spatiotemporal Correlation Discrimination of HFMD. Utilizing ARC ENGINE and C# programming for the creation of a spatio-temporal database dedicated to HFMD to facilitate data collection and analysis. The scientific validity of the proposed method was verified by comparing the effective reproduction number obtained by the traditional SEIR model. RESULTS: We have ascertained the optimal search radius for the spatiotemporal search model to be 1.5 km. Upon analyzing the resulting Re values, which range from 1.14 to 4.75, we observe a skewed distribution pattern from 2015 to 2019. The median and quartile Re value recorded is 2.42 (1.98, 2.72). Except for 2018, the similarity coefficient r of the years 2015, 2016, 2017, and 2019 were all close to 1, and p <0.05 in the comparison of the two models, indicating that the Re values obtained by using the search model and the traditional SEIR model are correlated and closely related. The results exhibited similarity between the Re curves of both models and the epidemiological characteristics of HFMD. Finally, we illustrated the regional distribution of Re values obtained by the search model at various time intervals on Geographic Information System (GIS) maps which highlighted variations in the incidence of diseases across different communities, neighborhoods, and even smaller areas. CONCLUSION: The model comprehensively considers both temporal variation and spatial heterogeneity in disease transmission and accounts for each individual's distinct time of onset and spatial location. This proposed method differs significantly from existing mathematical models used for estimating Re in that it is founded on reasonable scientific assumptions and computer algorithms programming that take into account real-world spatiotemporal factors. It is particularly well-suited for estimating the Re of infectious diseases in relatively stable mobile populations within small geographical areas.
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Doença de Mão, Pé e Boca , Análise Espaço-Temporal , Doença de Mão, Pé e Boca/epidemiologia , Humanos , China/epidemiologia , Número Básico de Reprodução/estatística & dados numéricos , Incidência , Criança , Doenças Transmissíveis/epidemiologia , Pré-Escolar , Feminino , Masculino , Modelos EpidemiológicosRESUMO
Accurately predicting the Modulus of Resilience (MR) of subgrade soils, which exhibit non-linear stress-strain behaviors, is crucial for effective soil assessment. Traditional laboratory techniques for determining MR are often costly and time-consuming. This study explores the efficacy of Genetic Programming (GEP), Multi-Expression Programming (MEP), and Artificial Neural Networks (ANN) in forecasting MR using 2813 data records while considering six key parameters. Several Statistical assessments were utilized to evaluate model accuracy. The results indicate that the GEP model consistently outperforms MEP and ANN models, demonstrating the lowest error metrics and highest correlation indices (R2). During training, the GEP model achieved an R2 value of 0.996, surpassing the MEP (R2 = 0.97) and ANN (R2 = 0.95) models. Sensitivity and SHAP (SHapley Additive exPlanations) analysis were also performed to gain insights into input parameter significance. Sensitivity analysis revealed that confining stress (21.6%) and dry density (26.89%) are the most influential parameters in predicting MR. SHAP analysis corroborated these findings, highlighting the critical impact of these parameters on model predictions. This study underscores the reliability of GEP as a robust tool for precise MR prediction in subgrade soil applications, providing valuable insights into model performance and parameter significance across various machine-learning (ML) approaches.
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Bentonite plastic concrete (BPC) is extensively used in the construction of water-tight structures like cut-off walls in dams, etc., because it offers high plasticity, improved workability, and homogeneity. Also, bentonite is added to concrete mixes for the adsorption of toxic metals. The modified design of BPC, as compared to normal concrete, requires a reliable tool to predict its strength. Thus, this study presents a novel attempt at the application of two innovative evolutionary techniques known as multi-expression programming (MEP) and gene expression programming (GEP) and a boosting-based algorithm known as AdaBoost to predict the 28-day compressive strength ( ) of BPC based on its mixture composition. The MEP and GEP algorithms expressed their outputs in the form of an empirical equation, while AdaBoost failed to do so. The algorithms were trained using a dataset of 246 points gathered from published literature having six important input factors for predicting. The developed models were subject to error evaluation, and the results revealed that all algorithms satisfied the suggested criteria and had a correlation coefficient (R) greater than 0.9 for both the training and testing phases. However, AdaBoost surpassed both MEP and GEP in terms of accuracy and demonstrated a lower testing RMSE of 1.66 compared to 2.02 for MEP and 2.38 for GEP. Similarly, the objective function value for AdaBoost was 0.10 compared to 0.176 for GEP and 0.16 for MEP, which indicated the overall good performance of AdaBoost compared to the two evolutionary techniques. Also, Shapley additive analysis was done on the AdaBoost model to gain further insights into the prediction process, which revealed that cement, coarse aggregate, and fine aggregate are the most important factors in predicting the strength of BPC. Moreover, an interactive graphical user interface (GUI) has been developed to be practically utilized in the civil engineering industry for prediction of BPC strength.
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This paper studies an optimal synchronous control protocol design for nonlinear multi-agent systems under partially known dynamics and uncertain external disturbance. Under some mild assumptions, Hamilton-Jacobi-Isaacs equation is derived by the performance index function and system dynamics, which serves as an equivalent formulation. Distributed policy iteration adaptive dynamic programming is developed to obtain the numerical solution to the Hamilton-Jacobi-Isaacs equation. Three theoretical results are given about the proposed algorithm. First, the iterative variables is proved to converge to the solution to Hamilton-Jacobi-Isaacs equation. Second, the L2-gain performance of the closed loop system is achieved. As a special case, the origin of the nominal system is asymptotically stable. Third, the obtained control protocol constitutes an Nash equilibrium solution. Neural network-based implementation is designed following the main results. Finally, two numerical examples are provided to verify the effectiveness of the proposed method.
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The global obesity epidemic, with its associated comorbidities and increased risk of early mortality, underscores the urgent need for enhancing our understanding of the origins of this complex disease. It is increasingly clear that metabolism is programmed early in life and that metabolic programming can have life-long health consequences. As a critical metabolic organ sensitive to early-life stimuli, proper development of adipose tissue (AT) is crucial for life-long energy homeostasis. Early-life nutrients, especially fatty acids (FA), significantly influence the programming of AT and shape its function and metabolism. Of growing interest are the dynamic responses during pre- and postnatal development to proinflammatory omega-6 (n6) and anti-inflammatory omega-3 (n3) FA exposures in AT. In the US maternal diet, the ratio of 'pro-inflammatory' n6- to 'anti-inflammatory' n3-FA has grown dramatically due to the greater prevalence of n6-FA. Notably, AT macrophages (ATM) form a significant population within adipose stromal cells, playing not only an instrumental role in AT formation and maintenance, but also acting as key mediators of cell-to-cell lipid and cytokine signaling. Despite rapid advances in ATM and immunometabolism fields, research has focused on responses to obesogenic diets and during adulthood. Consequently, there is a significant gap in identifying the mechanisms contributing metabolic health, especially regarding lipid exposures during the establishment of ATM physiology. Our review highlights the current understanding of ATM diversity, their critical role in AT, and their potential role in early-life metabolic programming, as well as the broader implications for metabolism and health.
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Healthcare processes are complex and involve uncertainties to influence the service quality and health of patients. Patient transportation takes place between the hospitals or between the departments within the hospital (i.e., Inter- or Intra-Hospital Transportation respectively). The focus of our paper is route planning for transporting patients within the hospital. The route planning task is complex due to multiple factors such as regulations, fairness considerations (i.e., balanced workload amongst transporters), and other dynamic factors (i.e., transport delays, wait times). Transporters perform the physical transportation of patients within the hospital. In principle, each job allocation respects the transition time between the subsequent jobs. The primary objective was to determine the feasible number of transporters, and then generate the route plan for all determined transporters by distributing all transport jobs (i.e., from retrospective data) within each shift. Secondary objectives are to minimize the sum of total travel time and sum of total idle time of all transporters and minimize the deviations in total travel time amongst transporters. Our method used multi-staged Local Search Metaheuristics to attain the primary objective. Metaheuristics incorporate Mixed Integer Linear Programming to allocate fairly the transport jobs by formulating optimization constraints with bounds for satisfying the secondary objectives. The obtained results using formulated optimization constraints represent better efficacy in multi-objective route planning of Intra-Hospital Transportation of patients.
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Programação Linear , Transporte de Pacientes , Humanos , AlgoritmosRESUMO
There is no safe level of air pollution for human health. Traffic-related particulate matter (PM2.5) is a major in-utero toxin, mechanisms of action of which are not fully understood. BALB/c dams were exposed to an Australian level of traffic PM2.5 (5 µg/mouse/day, intranasal, 6 weeks before mating, during gestation and lactation). Male offspring had reduced memory in adulthood, whereas memory was normal in female littermates, similar to human responses. Maternal PM2.5 exposure resulted in oxidative stress and abnormal mitochondria in male, but not female, brains. RNA-sequencing analysis showed unique sex-related changes in newborn brains. Two X-chromosome-linked histone lysine demethylases, Kdm6a and Kdm5c, demonstrated higher expression in female compared to male littermates, in addition to upregulated genes with known functions to support mitochondrial function, synapse growth and maturation, cognitive function, and neuroprotection. No significant changes in Kdm6a and Kdm5c were found in male littermates, nor other genes, albeit significantly impaired memory function after birth. In primary foetal cortical neurons, PM2.5 exposure suppressed neuron and synaptic numbers and induced oxidative stress, which was prevented by upregulation of Kdm6a or Kdm5c. Therefore, timely epigenetic adaptation by histone demethylation to open DNA for translation before birth may be the key to protecting females against prenatal PM2.5 exposure-induced neurological disorders, which fail to occur in males associated with their poor cognitive outcomes.
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Modern project managers cope with significant challenges to schedule and control projects considering dynamic environments, frequent uncertainties, strict project deadlines, and stricter sustainable requirements above all. Sustainability taking into account resource utilization has been recently associated with project management. Hence, this paper presents a new mixed-integer linear programming (MILP) model with two objectives for a resource-constrained project scheduling problem (RCPSP) with multiple skills and multiple modes, assuming preemptive and non-preemptive activities in an uncertain environment. Given the importance of sustainable developments in projects, the considered objectives are to maximize job opportunities and minimize project duration, resource costs, and total energy consumption. To deal with the model, an AUGNMECON2VIKOR algorithm is utilized to create Pareto solutions. In this model, project activities can be crashed by allocating extra resources. Furthermore, multi-skill resources are used to perform project activities. This study also investigates the impact of these resources on project scheduling. To deal with uncertain circumstances, a fuzzy chance-constrained programming method is employed to develop a robust possibilistic programming model. With respect to the increasing significance of sustainability in project management, this study pioneers the examination of the impact of sustainable factors on project scheduling. Finally, the proposed formulation is validated using instances from the well-known PSPLIB and MMLIB test sets. Finally, a comparison is drawn between the presented solution method considering AUGMECON2VIKOR and AUGMECON2.