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Bulletin of Mathematical Biology Jul 2020With advances in computing, agent-based models (ABMs) have become a feasible and appealing tool to study biological systems. ABMs are seeing increased incorporation into...
With advances in computing, agent-based models (ABMs) have become a feasible and appealing tool to study biological systems. ABMs are seeing increased incorporation into both the biology and mathematics classrooms as powerful modeling tools to study processes involving substantial amounts of stochasticity, nonlinear interactions, and/or heterogeneous spatial structures. Here we present a brief synopsis of the agent-based modeling approach with an emphasis on its use to simulate biological systems, and provide a discussion of its role and limitations in both the biology and mathematics classrooms.
Topics: Biology; Computer Simulation; Humans; Mathematics; Models, Biological; Systems Analysis
PubMed: 32725363
DOI: 10.1007/s11538-020-00778-z -
Biomaterials Oct 2019Optimal levels of chaos and fractality are distinctly associated with physiological health and function in natural systems. Chaos is a type of nonlinear dynamics that... (Review)
Review
Optimal levels of chaos and fractality are distinctly associated with physiological health and function in natural systems. Chaos is a type of nonlinear dynamics that tends to exhibit seemingly random structures, whereas fractality is a measure of the extent of organization underlying such structures. Growing bodies of work are demonstrating both the importance of chaotic dynamics for proper function of natural systems, as well as the suitability of fractal mathematics for characterizing these systems. Here, we review how measures of fractality that quantify the dose of chaos may reflect the state of health across various biological systems, including: brain, skeletal muscle, eyes and vision, lungs, kidneys, tumours, cell regulation, skin and wound repair, bone, vasculature, and the heart. We compare how reports of either too little or too much chaos and fractal complexity can be damaging to normal biological function, and suggest that aiming for the healthy dose of chaos may be an effective strategy for various biomedical applications. We also discuss rising examples of the implementation of fractal theory in designing novel materials, biomedical devices, diagnostics, and clinical therapies. Finally, we explain important mathematical concepts of fractals and chaos, such as fractal dimension, criticality, bifurcation, and iteration, and how they are related to biology. Overall, we promote the effectiveness of fractals in characterizing natural systems, and suggest moving towards using fractal frameworks as a basis for the research and development of better tools for the future of biomedical engineering.
Topics: Biocompatible Materials; Biomedical Engineering; Fractals; Health; Humans; Nonlinear Dynamics
PubMed: 31376747
DOI: 10.1016/j.biomaterials.2019.119363 -
PloS One 2018The multivariate nonlinear Granger causality developed by Bai et al. (2010) (Mathematics and Computers in simulation. 2010; 81: 5-17) plays an important role in...
The multivariate nonlinear Granger causality developed by Bai et al. (2010) (Mathematics and Computers in simulation. 2010; 81: 5-17) plays an important role in detecting the dynamic interrelationships between two groups of variables. Following the idea of Hiemstra-Jones (HJ) test proposed by Hiemstra and Jones (1994) (Journal of Finance. 1994; 49(5): 1639-1664), they attempt to establish a central limit theorem (CLT) of their test statistic by applying the asymptotical property of multivariate U-statistic. However, Bai et al. (2016) (2016; arXiv: 1701.03992) revisit the HJ test and find that the test statistic given by HJ is NOT a function of U-statistics which implies that the CLT neither proposed by Hiemstra and Jones (1994) nor the one extended by Bai et al. (2010) is valid for statistical inference. In this paper, we re-estimate the probabilities and reestablish the CLT of the new test statistic. Numerical simulation shows that our new estimates are consistent and our new test performs decent size and power.
Topics: Causality; Computer Simulation; Mathematical Concepts; Models, Statistical; Multivariate Analysis; Nonlinear Dynamics; Stochastic Processes
PubMed: 29304085
DOI: 10.1371/journal.pone.0185155 -
BMC Psychology Feb 2022The current evidence on an integrative role of the domain-specific early mathematical skills and number-specific executive functions (EFs) from informal to formal...
BACKGROUND
The current evidence on an integrative role of the domain-specific early mathematical skills and number-specific executive functions (EFs) from informal to formal schooling and their effect on mathematical abilities is so far unclear. The main objectives of this study were to (i) compare the domain-specific early mathematics, the number-specific EFs, and the mathematical abilities between preschool and primary school children, and (ii) examine the relationship among the domain-specific early mathematics, the number-specific EFs, and the mathematical abilities among preschool and primary school children.
METHODS
The current study recruited 6- and 7-year-old children (N = 505, n = 238, and n = 267). The domain-specific early mathematics as measured by symbolic and nonsymbolic tasks, number-specific EFs tasks, and mathematics tasks between these preschool and primary school children were compared. The relationship among domain-specific early mathematics, number-specific EFs, and mathematical abilities among preschool and primary school children was examined. MANOVA and structural equation modeling (SEM) were used to test research hypotheses.
RESULTS
The current results showed using MANOVA that primary school children were superior to preschool children over more complex tests of the domain-specific early mathematics; number-specific EFs; mathematical abilities, particularly for more sophisticated numerical knowledge; and number-specific EF components. The SEM revealed that both the domain-specific early numerical and the number-specific EFs significantly related to the mathematical abilities across age groups. Nevertheless, the number comparison test and mental number line of the domain-specific early mathematics significantly correlated with the mathematical abilities of formal school children. These results show the benefits of both the domain-specific early mathematics and the number-specific EFs in mathematical development, especially at the key stages of formal schooling. Understanding the relationship between EFs and early mathematics in improving mathematical achievements could allow a more powerful approach in improving mathematical education at this developmental stage.
Topics: Achievement; Child; Child Development; Child, Preschool; Cognition; Executive Function; Humans; Mathematics
PubMed: 35148787
DOI: 10.1186/s40359-022-00740-9 -
STAR Protocols Jun 2024It is well-understood that the science, technology, engineering, and mathematics (STEM) fields have unique challenges that discourage recruiting and retaining... (Review)
Review
It is well-understood that the science, technology, engineering, and mathematics (STEM) fields have unique challenges that discourage recruiting and retaining underrepresented minorities. Research programs aimed at undergraduates have arisen as a critical mechanism for fostering innovation and addressing the challenges faced by underrepresented minorities. Here, we review various undergraduate research programs designed to provide exposure to undergraduates, with a focus on underrepresented minorities in STEM disciplines. We provide insight into selected programs' objectives, key features, potential limitations, and outcomes. We also offer recommendations for future improvements of each research program, particularly in the context of mentorship. These programs range from broad-reaching initiatives (e.g., Leadership Alliance) to more specific programs targeting underrepresented students. By offering a nuanced understanding of each program's structure, we seek to provide a brief overview of the landscape of diversity-focused STEM initiatives and a guide on how to run a research program effectively.
Topics: Humans; Minority Groups; Students; Technology; Science; Mathematics; Research; Universities; Engineering
PubMed: 38748884
DOI: 10.1016/j.xpro.2024.102997 -
Masculinity in the public image of physics and mathematics: a new model comparing Japan and England.Public Understanding of Science... Oct 2021Women are a minority in science, technology, engineering and mathematics academic careers. In particular, few women in Japan choose to study physics and mathematics. In...
Women are a minority in science, technology, engineering and mathematics academic careers. In particular, few women in Japan choose to study physics and mathematics. In this study, we investigated the factors contributing to the masculine image of physics and mathematics based on the framework of our expanded model. We conducted online questionnaire surveys in Japan and England, and found that physics and mathematics occupations, and mathematical stereotypes were both related to a masculine image. Only in Japan were social factors, such as a person's attitude to intellectual women, related to viewing mathematics as 'masculine'. However, the experience of being told or having heard that the choice of a particular course of studies would make someone less attractive to the opposite sex was evident only in England. This finding suggests that social factors affect the masculine image of physics and mathematics, and that this could vary depending on the country.
Topics: Career Choice; Engineering; Female; Humans; Japan; Male; Masculinity; Mathematics; Physics; Science
PubMed: 33757362
DOI: 10.1177/09636625211002375 -
Research in Developmental Disabilities Sep 2020Profiles of mathematical learning disability (MLD) have been conceptualized in the literature, but empirical evidence to support them based on academic and cognitive...
BACKGROUND
Profiles of mathematical learning disability (MLD) have been conceptualized in the literature, but empirical evidence to support them based on academic and cognitive characteristics is lacking.
AIMS
We examined whether profiles of mathematics performance can empirically be identified and whether the identified profiles also differ in underlying cognitive skills.
METHODS AND PROCEDURES
Latent profile analysis in 281 fourth-graders. Basic arithmetic and advanced mathematics were used to identify profiles. Cognitive skills were then described for each profile of mathematics performance.
OUTCOMES AND RESULTS
Four profiles of mathematics performance were retrieved from the data, including one general low-achieving profile. Additional profiles of MLD were not found, possibly because individual variation was substantial.
CONCLUSIONS AND IMPLICATIONS
It is highly important to understand children's mathematics performance from an individual perspective, rather than by averaging these children over subgroups. These new insights can be used to better tend to the specific needs of children with mathematical difficulties.
Topics: Child; Humans; Learning Disabilities; Mathematics
PubMed: 32574935
DOI: 10.1016/j.ridd.2020.103704 -
Social Studies of Science Apr 2024Mathematics is often treated as different from other disciplines, since arguments in the field rely on deductive proof rather than empirical evidence as in the natural...
Mathematics is often treated as different from other disciplines, since arguments in the field rely on deductive proof rather than empirical evidence as in the natural sciences. A mathematical paper can therefore, at least in principle, be replicated simply by reading it. While this distinction is sometimes taken as the basis to claim that the results in mathematics are therefore certain, mathematicians themselves know that the published literature contains many mistakes. Reading a proof is not easy, and checking whether an argument constitutes a proof is surprisingly difficult. This article uses peer review of submissions to mathematics journals as a site where referees are explicitly concerned with checking whether a paper is correct and therefore could be published. Drawing on 95 qualitative interviews with mathematics journal editors, as well as a collection of more than 100 referee reports and other correspondence from peer review processes, this article establishes that while mathematicians acknowledge that peer review does not guarantee correctness, they still value it. For mathematicians, peer review 'adds a bit of certainty', especially in contrast to papers only submitted to preprint servers such as arXiv. Furthermore, during peer review there can be disagreements not just regarding the importance of a result, but also whether a particular argument constitutes a proof or not (in particular, whether there are substantial gaps in the proof). Finally, the mathematical community is seen as important when it comes to accepting arguments as proofs and assigning certainty to results. Publishing an argument in a peer-reviewed journal is often only the first step in having a result accepted. Results get accepted if they stand the test of time and are used by other mathematicians.
Topics: Peer Review; Mathematics; Dissent and Disputes
PubMed: 37776165
DOI: 10.1177/03063127231200274 -
Child Neuropsychology : a Journal on... Feb 2019Children born very preterm (VPT) are at risk for academic, behavioral, and/or emotional problems. Mathematics is a particular weakness and better understanding of the...
Children born very preterm (VPT) are at risk for academic, behavioral, and/or emotional problems. Mathematics is a particular weakness and better understanding of the relationship between preterm birth and early mathematics ability is needed, particularly as early as possible to aid in early intervention. Preschoolers born VPT (n = 58) and those born full term (FT; n = 29) were administered a large battery of measures within 6 months of beginning kindergarten. A multiple-mediation model was utilized to characterize the difference in skills underlying mathematics ability between groups. Children born VPT performed significantly worse than FT-born children on a measure of mathematics ability as well as full-scale IQ, verbal skills, visual-motor integration, phonological awareness, phonological working memory, motor skills, and executive functioning. Mathematics was significantly correlated with verbal skills, visual-motor integration, phonological processing, and motor skills across both groups. When entered into the mediation model, verbal skills, visual-motor integration, and phonological awareness were significant mediators of the group differences. This analysis provides insights into the pre-academic skills that are weak in preschoolers born VPT and their relationship to mathematics. It is important to identify children who will have difficulties as early as possible, particularly for VPT children who are at higher risk for academic difficulties. Therefore, this model may be used in evaluating VPT children for emerging difficulties as well as an indicator that if other weaknesses are found, an assessment of mathematics should be conducted.
Topics: Child; Child, Preschool; Cognition; Executive Function; Female; Humans; Infant, Extremely Premature; Infant, Newborn; Male; Mathematics
PubMed: 29233080
DOI: 10.1080/09297049.2017.1412413 -
Brazilian Journal of Anesthesiology... 2023Aspiration of gastric contents during induction of general anesthesia remains a significant cause of mortality and morbidity in anesthesia. Recent data show that... (Review)
Review
Aspiration of gastric contents during induction of general anesthesia remains a significant cause of mortality and morbidity in anesthesia. Recent data show that pulmonary aspiration still accounts for many cases with implications on mortality despite technical and technological evolution. Practical, ethical, and methodological issues prevent high-quality research in the setting of aspiration and rapid sequence induction/intubation, and significant controversy is ongoing. Patients' position, drugs choice, dosing and timing, use of cricoid force, and a reliable risk assessment are widely debated with significant questions still unanswered. We focus our discussion on three approaches to promote a better understanding of rapid sequence induction/intubation and airway management decision-making. Firstly, we review how we can use qualitative and quantitative assessment of fasting status and gastric content with the point-of-care ultrasound as an integral part of preoperative evaluation and planning. Secondly, we propose using imaging-based mathematical models to study different patient positions and aspiration mechanisms, including identifying aspiration triggers. Thirdly, we promote the development of a global data collection system aiming to obtain precise epidemiological data. Therefore, we fill the gap between evidence-based medicine and experts' opinion through easily accessible and diffused computer-based databases. A better understanding of aspiration epidemiology obtained through focused global data gathering systems, the widespread use of ultrasound-based prandial status evaluation, and development of advanced mathematical models might potentially guide safer airway management decision making in the 21 century.
Topics: Humans; Incidence; Anesthesia, General; Airway Management; Data Collection; Mathematics
PubMed: 34102227
DOI: 10.1016/j.bjane.2021.05.004