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Proceedings of the National Academy of... Nov 2020Exponentially growing systems are prevalent in nature, spanning all scales from biochemical reaction networks in single cells to food webs of ecosystems. How exponential...
Exponentially growing systems are prevalent in nature, spanning all scales from biochemical reaction networks in single cells to food webs of ecosystems. How exponential growth emerges in nonlinear systems is mathematically unclear. Here, we describe a general theoretical framework that reveals underlying principles of long-term growth: scalability of flux functions and ergodicity of the rescaled systems. Our theory shows that nonlinear fluxes can generate not only balanced growth but also oscillatory or chaotic growth modalities, explaining nonequilibrium dynamics observed in cell cycles and ecosystems. Our mathematical framework is broadly useful in predicting long-term growth rates from natural and synthetic networks, analyzing the effects of system noise and perturbations, validating empirical and phenomenological laws on growth rate, and studying autocatalysis and network evolution.
Topics: Biological Phenomena; Ecosystem; Growth; Models, Biological; Models, Theoretical; Nonlinear Dynamics
PubMed: 33093194
DOI: 10.1073/pnas.2013061117 -
Kidney International Oct 1983The potential of computing and mathematics to make major contributions to nephrology by making information retrieval and presentation more accurate, more complete, and...
The potential of computing and mathematics to make major contributions to nephrology by making information retrieval and presentation more accurate, more complete, and more rapid and by providing immediate access to computational and graphic facilities is emphasized in this symposium issue. The realization that disordered physiology due to disease may not prevent the course of an illness being described in mathematical terms should encourage physicians, and others interested in pathophysiology, to integrate mathematics and statistics into their thinking and their practice.
Topics: Computers; Decision Making; Humans; Mathematics; Medical Records; Models, Biological; Nephrology; Statistics as Topic
PubMed: 6645214
DOI: 10.1038/ki.1983.178 -
Philosophical Transactions. Series A,... May 2006Computational modelling of biological processes and systems has witnessed a remarkable development in recent years. The search-term (modelling OR modeling) yields over... (Review)
Review
Computational modelling of biological processes and systems has witnessed a remarkable development in recent years. The search-term (modelling OR modeling) yields over 58000 entries in PubMed, with more than 34000 since the year 2000: thus, almost two-thirds of papers appeared in the last 5-6 years, compared to only about one-third in the preceding 5-6 decades. The development is fuelled both by the continuously improving tools and techniques available for bio-mathematical modelling and by the increasing demand in quantitative assessment of element inter-relations in complex biological systems. This has given rise to a worldwide public domain effort to build a computational framework that provides a comprehensive theoretical representation of integrated biological function-the Physiome. The current and next issues of this journal are devoted to a small sub-set of this initiative and address biocomputation and modelling in physiology, illustrating the breadth and depth of experimental data-based model development in biological research from sub-cellular events to whole organ simulations.
Topics: Computer Simulation; Mathematics; Models, Biological; Physiology; Systems Biology
PubMed: 16608698
DOI: 10.1098/rsta.2006.1757 -
Studies in History and Philosophy of... Aug 2023In this paper we show how simple text-driven variations of given statements in mathematics can lead to interesting new problems and push forward a whole theory around...
In this paper we show how simple text-driven variations of given statements in mathematics can lead to interesting new problems and push forward a whole theory around simple initial questions. We exemplify this in two cases. Case 1 deals with problem-posing activities suitable for pupils and case 2 is a rational reconstruction of the organisation of mathematical knowledge within problems of graph colorings. Mathematicians learn to systematically look for subsequent problems around a given problem. We argue that this toy-model captures a nontrivial part of professional mathematical research within the pure fields and conjecture that it even grasps high level developments in mathematics. By doing this, we implicitly encourage a very simplistic view on criteria, so to speak a "cowpath" approach to progress in mathematics. The term "cowpath" is borrowed from architecture and software design, where it is commonly used. While we can contemplate which pathways are ideal, we may also just plant grass and see where people choose to walk. Those pathways are also self-enforcing, since we are less hesitant to walk on those rather than criss-cross the landscape.
Topics: Humans; Mathematics; Learning; Knowledge
PubMed: 37329627
DOI: 10.1016/j.shpsa.2023.05.006 -
Mathematical Biosciences and... Apr 2011
Topics: Biology; Biomedical Engineering; Computer Simulation; Mathematics; Models, Biological
PubMed: 21631126
DOI: 10.3934/mbe.2011.8.2i -
Bulletin of Mathematical Biology Jul 2022The processes underpinning solid tumour growth involve the interactions between various healthy and tumour tissue components and the vasculature, and can be affected in...
The processes underpinning solid tumour growth involve the interactions between various healthy and tumour tissue components and the vasculature, and can be affected in different ways by cancer treatment. In particular, the growth-limiting mechanisms at play may influence tumour responses to treatment. In this paper, we propose a simple ordinary differential equation model of solid tumour growth to investigate how tumour-specific mechanisms of growth arrest may affect tumour response to different combination cancer therapies. We consider the interactions of tumour cells with the physical space in which they proliferate and a nutrient supplied by the tumour vasculature, with the aim of representing two distinct growth arrest mechanisms. More specifically, we wish to consider growth arrest due to (1) nutrient deficiency, which corresponds to balancing cell proliferation and death rates, and (2) competition for space, which corresponds to cessation of proliferation without cell death. We perform numerical simulations of the model and a steady-state analysis to determine the possible tumour growth scenarios described by the model. We find that there are three distinct growth regimes: the nutrient- and spatially limited regimes and a bi-stable regime, in which both growth arrest mechanisms are simultaneously active. Thus, the proposed model has the features required to investigate and distinguish tumour responses to different cancer treatments.
Topics: Computer Simulation; Humans; Mathematical Concepts; Mathematics; Models, Biological; Neoplasms
PubMed: 35773547
DOI: 10.1007/s11538-022-01034-2 -
International Journal of Environmental... Dec 2021Mathematical competency in the profession of nursing has increasingly become a central focus as more nursing students appear to struggle with basic concepts of...
Mathematical competency in the profession of nursing has increasingly become a central focus as more nursing students appear to struggle with basic concepts of arithmetic, mental estimation, and critical reasoning. This paper highlights how one School of Nursing in Ontario, Canada implemented a Dosage Calculation Competency Test model which involved an online, self-directed, prerequisite approach to improve student mathematical competency and confidence. The purpose of this research case study was to document, through shared participant perceptions, the creation, implementation, and subsequent modifications to a Dosage Calculation Competency Test model in light of student needs and advances in online learning and assessment. The research design combined a quantitative survey of Year 1-4 nursing students, followed by a series of qualitative, semi-structured interviews with nursing students and program instructors. The study took place within a School of Nursing undergraduate program in Ontario, Canada. Forty-four participants, including students from all four years of the nursing program, completed the survey, followed by individual interviews with nine students and six faculty instructors. Survey (the open-response items) and interview data were analyzed thematically using (ATLAS.ti, Berlin, Germany). The authors recount the new DCCT model's development, implementation, and subsequent modifications and further discuss student/instructor perceptions of learning types, math confidence, and competency. The paper concludes with a series of seven key recommendations for nursing programs.
Topics: Curriculum; Education, Nursing, Baccalaureate; Humans; Learning; Mathematics; Ontario; Students, Nursing
PubMed: 34948717
DOI: 10.3390/ijerph182413106 -
Journal of Personality and Social... Aug 2020In 1992, the Study of Mathematically Precocious Youth (SMPY) surveyed 714 first- and second-year graduate students (48.5% female) attending U.S. universities ranked in...
In 1992, the Study of Mathematically Precocious Youth (SMPY) surveyed 714 first- and second-year graduate students (48.5% female) attending U.S. universities ranked in the top-15 by science, technology, engineering, and mathematics (STEM) field. This study investigated whether individual differences assessed early in their graduate school career were associated with becoming a STEM leader 25 years later (e.g., STEM full professors at research-intensive universities, STEM CEOs, and STEM leaders in government) versus not becoming a STEM leader. We also studied whether there were any important gender differences in relation to STEM leadership. For both men and women, small to medium effect size differences in interests, values, and personality distinguished STEM leaders from nonleaders. Lifestyle and work preferences also distinguished STEM leaders who were more exclusively career-focused and preferred to work-and did work-more hours than nonleaders. Also, there were small to large gender differences in abilities, interests, and lifestyle preferences. Men had more intense interests in STEM and were more career-focused. Women had more diverse educational and occupational interests, and they were more interested in activities outside of work. Early in graduate school, therefore, there are signs that predict who will become a STEM leader-even among elite STEM graduate students. Given the many ways in which STEM leadership can be achieved, the gender differences uncovered within this high-potential sample suggest that men and women are likely to assign different priorities to these opportunities. (PsycInfo Database Record (c) 2020 APA, all rights reserved).
Topics: Achievement; Education, Graduate; Engineering; Faculty; Female; Humans; Individuality; Leadership; Longitudinal Studies; Male; Mathematics; Middle Aged; Science; Students; Technology; Universities
PubMed: 30869985
DOI: 10.1037/pspp0000239 -
PloS One 2018Our work applies Universal Design criteria for producing and using Mathematics videos for primary education students, at a time when many countries are shifting towards...
Our work applies Universal Design criteria for producing and using Mathematics videos for primary education students, at a time when many countries are shifting towards inclusive education policies. We have focused on how the accessibility criteria used for students with visual impairments might affect non-disabled students. For this, we reviewed applicable Universal Design principles as well as best practices in multimedia learning. We took into account the roles, procedures, tools and standards involved in the multimedia lifecycle. We then undertook an experiment consisting of producing two videos about prime numbers with the same pedagogical contents; one video was accessible for students with visual impairments and the other one was not accessible to them. We conducted a trial in real world school settings with 228 non-disabled children, who were randomly assigned a version, either accessible or not accessible, and were then asked to take a test to measure objective aspects of their learning concerning retention and transfer as well as several subjective aspects, including the attractiveness of the videos. Results indicate that there were no significant differences in the scores obtained by students using either video, although the group who watched the accessible video obtained higher score medians in the retention questions. Moreover, students found the accessible video significantly more attractive (p = 0.042). Our study provides recommendations for different stakeholders and stages within the process of producing multimedia mathematics materials that are accessible to primary students with visual impairments, as well as evidence demonstrating that everybody can benefit from the recommendations for developing good quality, accessible multimedia material.
Topics: Child; Educational Measurement; Female; Humans; Male; Mathematical Concepts; Mathematics; Random Allocation; Students; Video Recording; Vision Disorders
PubMed: 30485351
DOI: 10.1371/journal.pone.0208117 -
Scientific Reports Apr 2024Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a novel virus known as coronavirus 2 (SARS-CoV-2) that affects the pulmonary structure and results in the...
Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a novel virus known as coronavirus 2 (SARS-CoV-2) that affects the pulmonary structure and results in the coronavirus illness 2019 (COVID-19). Tuberculosis (TB) and COVID-19 codynamics have been documented in numerous nations. Understanding the complexities of codynamics is now critically necessary as a consequence. The aim of this research is to construct a co-infection model of TB and COVID-19 in the context of fractional calculus operators, white noise and probability density functions, employing a rigorous biological investigation. By exhibiting that the system possesses non-negative and bounded global outcomes, it is shown that the approach is both mathematically and biologically practicable. The required conditions are derived, guaranteeing the eradication of the infection. Sensitivity analysis and bifurcation of the submodel are also investigated with system parameters. Furthermore, existence and uniqueness results are established, and the configuration is tested for the existence of an ergodic stationary distribution. For discovering the system's long-term behavior, a deterministic-probabilistic technique for modeling is designed and operated in MATLAB. By employing an extensive review, we hope that the previously mentioned approach improves and leads to mitigating the two diseases and their co-infections by examining a variety of behavioral trends, such as transitions to unpredictable procedures. In addition, the piecewise differential strategies are being outlined as having promising potential for scholars in a range of contexts because they empower them to include particular characteristics across multiple time frame phases. Such formulas can be strengthened via classical technique, power-law, exponential decay, generalized Mittag-Leffler kernels, probability density functions and random procedures. Furthermore, we get an accurate description of the probability density function encircling a quasi-equilibrium point if the effect of TB and COVID-19 minimizes the propagation of the codynamics. Consequently, scholars can obtain better outcomes when analyzing facts using random perturbations by implementing these strategies for challenging issues. Random perturbations in TB and COVID-19 co-infection are crucial in controlling the spread of an epidemic whenever the suggested circulation is steady and the amount of infection eliminated is closely correlated with the random perturbation level.
Topics: Humans; SARS-CoV-2; COVID-19; Coinfection; Tuberculosis; Mathematics
PubMed: 38632309
DOI: 10.1038/s41598-024-59261-7