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Bio Systems Jul 2021
Topics: History, 20th Century; Humans; Mathematics; Models, Biological; Russia; Systems Biology
PubMed: 33785382
DOI: 10.1016/j.biosystems.2021.104416 -
Reviews in the Neurosciences May 2017Given that achievement in learning mathematics at school correlates with work and social achievements, it is important to understand the cognitive processes underlying... (Review)
Review
Given that achievement in learning mathematics at school correlates with work and social achievements, it is important to understand the cognitive processes underlying abilities to learn mathematics efficiently as well as reasons underlying the occurrence of mathematics anxiety (i.e. feelings of tension and fear upon facing mathematical problems or numbers) among certain individuals. Over the last two decades, many studies have shown that learning mathematical and numerical concepts relies on many cognitive processes, including working memory, spatial skills, and linguistic abilities. In this review, we discuss the relationship between mathematical learning and cognitive processes as well as the neural substrates underlying successful mathematical learning and problem solving. More importantly, we also discuss the relationship between these cognitive processes, mathematics anxiety, and mathematics learning disabilities (dyscalculia). Our review shows that mathematical cognition relies on a complex brain network, and dysfunction to different segments of this network leads to varying manifestations of mathematical learning disabilities.
Topics: Anxiety; Brain; Brain Mapping; Dyscalculia; Humans; Mathematics
PubMed: 28157694
DOI: 10.1515/revneuro-2016-0065 -
Physical Biology Jun 2019Whether the nom de guerre is Mathematical Oncology, Computational or Systems Biology, Theoretical Biology, Evolutionary Oncology, Bioinformatics, or simply Basic... (Review)
Review
Whether the nom de guerre is Mathematical Oncology, Computational or Systems Biology, Theoretical Biology, Evolutionary Oncology, Bioinformatics, or simply Basic Science, there is no denying that mathematics continues to play an increasingly prominent role in cancer research. Mathematical Oncology-defined here simply as the use of mathematics in cancer research-complements and overlaps with a number of other fields that rely on mathematics as a core methodology. As a result, Mathematical Oncology has a broad scope, ranging from theoretical studies to clinical trials designed with mathematical models. This Roadmap differentiates Mathematical Oncology from related fields and demonstrates specific areas of focus within this unique field of research. The dominant theme of this Roadmap is the personalization of medicine through mathematics, modelling, and simulation. This is achieved through the use of patient-specific clinical data to: develop individualized screening strategies to detect cancer earlier; make predictions of response to therapy; design adaptive, patient-specific treatment plans to overcome therapy resistance; and establish domain-specific standards to share model predictions and to make models and simulations reproducible. The cover art for this Roadmap was chosen as an apt metaphor for the beautiful, strange, and evolving relationship between mathematics and cancer.
Topics: Computational Biology; Computer Simulation; Humans; Mathematics; Medical Oncology; Models, Biological; Models, Theoretical; Neoplasms; Single-Cell Analysis; Systems Biology
PubMed: 30991381
DOI: 10.1088/1478-3975/ab1a09 -
Journal of Experimental Child Psychology Aug 2023Identifying the underpinnings of mathematics proficiency is relevant for all societies. A growing literature supports a relation between executive function (EF) and... (Randomized Controlled Trial)
Randomized Controlled Trial
Identifying the underpinnings of mathematics proficiency is relevant for all societies. A growing literature supports a relation between executive function (EF) and mathematics across a wide age range, but causal links are not well understood. In the current study, typically developing preschool children (N = 104) were randomly assigned to one of four training conditions: EF, Number, EF + Number, or an active Control. They participated in three brief training sessions and pretest and posttest sessions measuring EF and mathematics skills. EF training improved EF skills on a task similar to the training but did not extend to an untrained EF task. In addition, the EF training improved number skills but not general mathematics skills. The EF + Number training improved number and general mathematics skills but not EF skills. The EF + Number training did not yield significantly greater benefits for EF and mathematics beyond other training conditions. Finally, differential training effects emerged, such that children with lower pretest EF skills had greater EF benefits on only the trained EF skill. In addition, children from lower versus higher socioeconomic households had greater gains in numerical skills following EF training. No training condition improved verbal knowledge, suggesting that results were specific to the targeted skills. These results extend prior findings on the effectiveness of improving EF and mathematical skills through short-term trainings during early childhood.
Topics: Humans; Child, Preschool; Executive Function; Mathematics
PubMed: 36948040
DOI: 10.1016/j.jecp.2023.105663 -
Methods in Molecular Biology (Clifton,... 2018Basic mathematical descriptions are useful in phage ecology, applied phage ecology such as in the course of phage therapy, and also toward keeping track of expected... (Review)
Review
Basic mathematical descriptions are useful in phage ecology, applied phage ecology such as in the course of phage therapy, and also toward keeping track of expected phage-bacterial interactions as seen during laboratory manipulation of phages. The most basic mathematical descriptor of phages is their titer, that is, their concentration within stocks, experimental vessels, or other environments. Various phenomena can serve to modify phage titers, and indeed phage titers can vary as a function of how they are measured. An important aspect of how changes in titers can occur results from phage interactions with bacteria. These changes tend to vary in degree as a function of bacterial densities within environments, and particularly densities of those bacteria that are susceptible to or at least adsorbable by a given phage type. Using simple mathematical models one can describe phage-bacterial interactions that give rise particularly to phage adsorption events. With elaboration one can consider changes in both phage and bacterial densities as a function of both time and these interactions. In addition, phages along with their impact on bacteria can be considered as spatially constrained processes. In this chapter we consider the simpler of these concepts, providing in particular detailed verbal explanations toward facile mathematical insight. The primary goal is to stimulate a more informed use and manipulation of phages and phage populations within the laboratory as well as toward more effective phage application outside of the laboratory, such as during phage therapy. More generally, numerous issues and approaches to the quantification of phages are considered along with the quantification of individual, ecological, and applied properties of phages.
Topics: Adsorption; Bacteria; Bacteriophages; Mathematics; Models, Biological
PubMed: 29134583
DOI: 10.1007/978-1-4939-7343-9_1 -
Progress in Biophysics and Molecular... Oct 2016Theories organize knowledge and construct objectivity by framing observations and experiments. The elaboration of theoretical principles is examined in the light of the... (Review)
Review
Theories organize knowledge and construct objectivity by framing observations and experiments. The elaboration of theoretical principles is examined in the light of the rich interactions between physics and mathematics. These two disciplines share common principles of construction of concepts and of the proper objects of inquiry. Theory construction in physics relies on mathematical symmetries that preserve the key invariants observed and proposed by such theory; these invariants buttress the idea that the objects of physics are generic and thus interchangeable and they move along specific trajectories which are uniquely determined, in classical and relativistic physics. In contrast to physics, biology is a historical science that centers on the changes that organisms experience while undergoing ontogenesis and phylogenesis. Biological objects, namely organisms, are not generic but specific; they are individuals. The incessant changes they undergo represent the breaking of symmetries, and thus the opposite of symmetry conservation, a central component of physical theories. This instability corresponds to the changes of the environment and the phenotypes. Inspired by Galileo's principle of inertia, the "default state" of inert matter, we propose a "default state" for biological dynamics following Darwin's first principle, "descent with modification" that we transform into "proliferation with variation and motility" as a property that spans life, including cells in an organism. These dissimilarities between theories of the inert and of biology also apply to causality: biological causality is to be understood in relation to the distinctive role that constraints assume in this discipline. Consequently, the notion of cause will be reframed in a context where constraints to activity are seen as the core component of biological analyses. Finally, we assert that the radical materiality of life rules out distinctions such as "software vs. hardware."
Topics: Animals; Biology; Humans; Mathematics; Physics
PubMed: 27390105
DOI: 10.1016/j.pbiomolbio.2016.06.005 -
Cognitive Psychology Nov 2023Mathematical expressions consist of recursive combinations of numbers, variables, and operators. According to theoretical linguists, the syntactic mechanisms of natural... (Review)
Review
Mathematical expressions consist of recursive combinations of numbers, variables, and operators. According to theoretical linguists, the syntactic mechanisms of natural language also provide a basis for mathematics. To date, however, no theoretically rigorous investigation has been conducted to support such arguments. Therefore, this study uses a methodology based on theoretical linguistics to analyze the syntactic properties of mathematical expressions. Through a review of recent behavioral and neuroimaging studies on mathematical syntax, we report several inconsistencies with theoretical linguistics, such as the use of ternary structures. To address these, we propose that a syntactic category called Applicative plays a central role in analyzing mathematical expressions with seemingly ternary structures by combining binary structures. Besides basic arithmetic expressions, we also examine algebraic equations and complex expressions such as integral and differential calculi. This study is the first attempt at building a comprehensive framework for analyzing the syntactic structures of mathematical expressions.
Topics: Humans; Language; Linguistics; Mathematics
PubMed: 37748253
DOI: 10.1016/j.cogpsych.2023.101606 -
Physical Biology Jul 2023Mitochondria serve a wide range of functions within cells, most notably via their production of ATP. Although their morphology is commonly described as bean-like,... (Review)
Review
Mitochondria serve a wide range of functions within cells, most notably via their production of ATP. Although their morphology is commonly described as bean-like, mitochondria often form interconnected networks within cells that exhibit dynamic restructuring through a variety of physical changes. Further, though relationships between form and function in biology are well established, the extant toolkit for understanding mitochondrial morphology is limited. Here, we emphasize new and established methods for quantitatively describing mitochondrial networks, ranging from unweighted graph-theoretic representations to multi-scale approaches from applied topology, in particular persistent homology. We also show fundamental relationships between mitochondrial networks, mathematics, and physics, using ideas of graph planarity and statistical mechanics to better understand the full possible morphological space of mitochondrial network structures. Lastly, we provide suggestions for how examination of mitochondrial network form through the language of mathematics can inform biological understanding, and vice versa.
Topics: Mathematics; Lens, Crystalline; Mitochondria; Physics
PubMed: 37290456
DOI: 10.1088/1478-3975/acdcdb -
Biological Cybernetics Dec 2021Natural phenomena can be quantitatively described by means of mathematics, which is actually the only way of doing so. Physics is a convincing example of the...
Natural phenomena can be quantitatively described by means of mathematics, which is actually the only way of doing so. Physics is a convincing example of the mathematization of nature. This paper gives an answer to the question of how mathematization of nature is done and illustrates the answer. Here nature is to be taken in a wide sense, being a substantial object of study in, among others, large domains of biology, such as epidemiology and neurobiology, chemistry, and physics, the most outspoken example. It is argued that mathematization of natural phenomena needs appropriate core concepts that are intimately connected with the phenomena one wants to describe and explain mathematically. Second, there is a scale on and not beyond which a specific description holds. Different scales allow for different conceptual and mathematical descriptions. This is the scaling hypothesis, which has meanwhile been confirmed on many occasions. Furthermore, a mathematical description can, as in physics, but need not be universally valid, as in biology. Finally, the history of science shows that only an intensive gauging of theory, i.e., mathematical description, by experiment leads to progress. That is, appropriate core concepts and appropriate scales are a necessary condition for mathematizing nature, and so is its verification by experiment.
Topics: Mathematics; Neurobiology; Physics
PubMed: 34837542
DOI: 10.1007/s00422-021-00914-5 -
Mathematical Biosciences Dec 2022Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas...
Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas and hypotheses with data using statistical methods to determine the extent to which our hypotheses agree with reality. But doing so in a systematic way is becoming increasingly challenging as our hypotheses become more detailed, and our data becomes more complex. Mathematical methods are therefore gaining in importance across the life- and biomedical sciences. Mathematical models allow us to test our understanding, make testable predictions about future behaviour, and gain insights into how we can control the behaviour of biological systems. It has been argued that mathematical methods can be of great benefit to biologists to make sense of data. But mathematics and mathematicians are set to benefit equally from considering the often bewildering complexity inherent to living systems. Here we present a small selection of open problems and challenges in mathematical biology. We have chosen these open problems because they are of both biological and mathematical interest.
Topics: Models, Biological; Mathematics; Models, Theoretical; Biology
PubMed: 36377100
DOI: 10.1016/j.mbs.2022.108926