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Evolutionary Psychology : An... 2022This is a brief history of my intellectual life from age 13 to 29 years-and beyond. It encompasses mathematics, US history, and evolutionary biology, especially social...
This is a brief history of my intellectual life from age 13 to 29 years-and beyond. It encompasses mathematics, US history, and evolutionary biology, especially social theory based on natural selection.
Topics: Adolescent; Adult; Biological Evolution; Biology; Humans; Mathematics; Selection, Genetic; Young Adult
PubMed: 35014559
DOI: 10.1177/14747049211067172 -
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 -
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 -
Annals of the New York Academy of... Jul 2022In this paper, we discuss several largely undisputed claims about mathematics anxiety (MA) and propose where MA research should focus, including theoretical...
In this paper, we discuss several largely undisputed claims about mathematics anxiety (MA) and propose where MA research should focus, including theoretical clarifications on what MA is and what constitutes its opposite pole; discussion of construct validity, specifically relations between self-descriptive, neurophysiological, and cognitive measures; exploration of the discrepancy between state and trait MA and theoretical and practical consequences; discussion of the prevalence of MA and the need for establishing external criteria for estimating prevalence and a proposal for such criteria; exploration of the effects of MA in different groups, such as highly anxious and high math-performing individuals; classroom and policy applications of MA knowledge; the effects of MA outside educational settings; and the consequences of MA on mental health and well-being.
Topics: Anxiety; Anxiety Disorders; Humans; Mathematics
PubMed: 35322431
DOI: 10.1111/nyas.14770 -
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 -
Neuroscience and Biobehavioral Reviews Mar 2024Numerical abilities are complex cognitive skills essential for dealing with requirements of the modern world. Although the brain structures and functions underlying... (Review)
Review
Numerical abilities are complex cognitive skills essential for dealing with requirements of the modern world. Although the brain structures and functions underlying numerical cognition in different species have long been appreciated, genetic and molecular techniques have more recently expanded the knowledge about the mechanisms underlying numerical learning. In this review, we discuss the status of the research related to the neurobiological bases of numerical abilities. We consider how genetic factors have been associated with mathematical capacities and how these link to the current knowledge of brain regions underlying these capacities in human and non-human animals. We further discuss the extent to which significant variations in the levels of specific neurotransmitters may be used as potential markers of individual performance and learning difficulties and take into consideration the therapeutic potential of brain stimulation methods to modulate learning and improve interventional outcomes. The implications of this research for formulating a more comprehensive view of the neural basis of mathematical learning are discussed.
Topics: Humans; Learning; Cognition; Brain; Mathematics; Neurobiology
PubMed: 38220032
DOI: 10.1016/j.neubiorev.2024.105545 -
PLoS Computational Biology May 2020Postdocs are a critical transition for early-career researchers. This transient period, between finishing a PhD and finding a permanent position, is when early-career...
Postdocs are a critical transition for early-career researchers. This transient period, between finishing a PhD and finding a permanent position, is when early-career researchers develop independent research programs and establish collaborative relationships that can make a successful career. Traditionally, postdocs physically relocate-sometimes multiple times-for these short-term appointments, which creates challenges that can disproportionately affect members of traditionally underrepresented groups in science, technology, engineering, and mathematics (STEM). However, many research activities involving analytical and quantitative work do not require a physical presence in a lab and can be accomplished remotely. Other fields have embraced remote work, yet many academics have been hesitant to hire remote postdocs. In this article, we present advice to both principal investigators (PIs) and postdocs for successfully navigating a remote position. Using the combined experience of the authors (as either remote postdocs or employers of remote postdocs), we provide a road map to overcome the real (and perceived) obstacles associated with remote work. With planning, communication, and creativity, remote postdocs can be a fully functioning and productive member of a research lab. Further, our rules can be useful for research labs generally and can help foster a more flexible and inclusive environment.
Topics: Career Choice; Education, Distance; Engineering; Humans; Mathematics; Preceptorship; Research Personnel; Science; Technology
PubMed: 32379759
DOI: 10.1371/journal.pcbi.1007809 -
Annals of the New York Academy of... Jul 2022Mathematics anxiety (MA) is negatively associated with mathematics performance. Although some aspects, such as mathematics self-concept (M self-concept), seem to...
Mathematics anxiety (MA) is negatively associated with mathematics performance. Although some aspects, such as mathematics self-concept (M self-concept), seem to modulate this association, the underlying mechanism is still unclear. In addition, the false gender stereotype that women are worse than men in mathematics can have a detrimental effect on women. The role that the endorsement of this stereotype (mathematics-gender stereotype (MGS) endorsement) can play may differ between men and women. In this study, we investigated how MA and mathematics self-concept relate to arithmetic performance when considering one's MGS endorsement and gender in a large sample (n = 923) of university students. Using a structural equation modeling approach, we found that MA and mathematics self-concept mediated the effect of MGS endorsement in both men and women. For women, MGS endorsement increased their MA level, while in men, it had the opposite effect (albeit weak). Specifically, in men, MGS endorsement influenced the level of the numerical components of MA, but, unlike women, it also positively influenced their mathematics self-concept. Moreover, men and women perceived the questions included in the considered instruments differently, implying that the scores obtained in these questionnaires may not be directly comparable between genders, which has even broader theoretical and methodological implications for MA research.
Topics: Anxiety; Anxiety Disorders; Female; Humans; Male; Mathematics; Self Concept; Stereotyping
PubMed: 35429357
DOI: 10.1111/nyas.14779 -
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 -
Journal of Vision Jan 2022Shape is an interesting property of objects because it is used in ordinary discourse in ways that seem to have little connection to how it is typically defined in... (Review)
Review
Shape is an interesting property of objects because it is used in ordinary discourse in ways that seem to have little connection to how it is typically defined in mathematics. The present article describes how the concept of shape can be grounded within Euclidean and non-Euclidean geometry and also to human perception. It considers the formal methods that have been proposed for measuring the differences among shapes and how the performance of those methods compares with shape difference thresholds of human observers. It discusses how different types of shape change can be perceptually categorized. It also evaluates the specific data structures that have been used to represent shape in models of both human and machine vision, and it reviews the psychophysical evidence about the extent to which those models are consistent with human perception. Based on this review of the literature, we argue that shape is not one thing but rather a collection of many object attributes, some of which are more perceptually salient than others. Because the relative importance of these attributes can be context dependent, there is no obvious single definition of shape that is universally applicable in all situations.
Topics: Form Perception; Humans; Mathematics
PubMed: 34982105
DOI: 10.1167/jov.22.1.1