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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 -
Annals of the New York Academy of... Dec 2019We are used to thinking of mathematics as a symbolic activity. Here I argue that it may also be seen as a performative one. Making an analogy with music, I draw...
We are used to thinking of mathematics as a symbolic activity. Here I argue that it may also be seen as a performative one. Making an analogy with music, I draw attention to the ways in which mathematics may not only be written down but also played out.
Topics: Algorithms; Fractals; History, 18th Century; History, 19th Century; History, 20th Century; History, Ancient; Humans; Mathematics; Models, Theoretical; Music; Physics
PubMed: 31658380
DOI: 10.1111/nyas.14269 -
Biological Cybernetics Dec 2021The Wilson-Cowan equations were developed to provide a simplified yet powerful description of neural network dynamics. As such, they embraced nonlinear dynamics, but in...
The Wilson-Cowan equations were developed to provide a simplified yet powerful description of neural network dynamics. As such, they embraced nonlinear dynamics, but in an interpretable form. Most importantly, it was the first mathematical formulation to emphasize the significance of interactions between excitatory and inhibitory neural populations, thereby incorporating both cooperation and competition. Subsequent research by many has documented the Wilson-Cowan significance in such diverse fields as visual hallucinations, memory, binocular rivalry, and epilepsy. The fact that these equations are still being used to elucidate a wide range of phenomena attests to their validity as a dynamical approximation to more detailed descriptions of complex neural computations.
Topics: Neural Networks, Computer; Nonlinear Dynamics
PubMed: 34797411
DOI: 10.1007/s00422-021-00912-7 -
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 -
Research in Developmental Disabilities Dec 2020This paper reviews and discusses research on arithmetical strengths and weaknesses in children with specific developmental cognitive disabilities. It focusses on... (Review)
Review
This paper reviews and discusses research on arithmetical strengths and weaknesses in children with specific developmental cognitive disabilities. It focusses on children with dyslexia, developmental language disorder, attention deficit hyperactivity disorder and autism. In general, studies show that arithmetical weaknesses are commoner in children with any of these disorders than in controls. Autism is sometimes associated with specific strengths in arithmetic; but even in autism, it is commoner for arithmetic to be a relative weakness than a relative strength. There may be some genetic reasons why there is an overlap between mathematical difficulties and other developmental learning difficulties; but much of the reason seems to be that specific aspects of arithmetic are often influenced by other factors, including language comprehension, phonological awareness, verbal and spatial working memory and long-term memory, and executive functions. The findings discussed here will be discussed in relation to Pennington's (2006) Multiple Deficit Model.
Topics: Attention Deficit Disorder with Hyperactivity; Child; Cognition; Cognition Disorders; Dyslexia; Humans; Mathematics; Memory, Short-Term
PubMed: 33035783
DOI: 10.1016/j.ridd.2020.103778 -
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 -
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 -
Reviews in the Neurosciences Apr 2020Many students suffer from anxiety when performing numerical calculations. Mathematics anxiety is a condition that has a negative effect on educational outcomes and... (Review)
Review
Many students suffer from anxiety when performing numerical calculations. Mathematics anxiety is a condition that has a negative effect on educational outcomes and future employment prospects. While there are a multitude of behavioral studies on mathematics anxiety, its underlying cognitive and neural mechanism remain unclear. This article provides a systematic review of cognitive studies that investigated mathematics anxiety. As there are no prior neural network models of mathematics anxiety, this article discusses how previous neural network models of mathematical cognition could be adapted to simulate the neural and behavioral studies of mathematics anxiety. In other words, here we provide a novel integrative network theory on the links between mathematics anxiety, cognition, and brain substrates. This theoretical framework may explain the impact of mathematics anxiety on a range of cognitive and neuropsychological tests. Therefore, it could improve our understanding of the cognitive and neurological mechanisms underlying mathematics anxiety and also has important applications. Indeed, a better understanding of mathematics anxiety could inform more effective therapeutic techniques that in turn could lead to significant improvements in educational outcomes.
Topics: Anxiety; Brain; Cognition; Connectome; Humans; Mathematics
PubMed: 31730536
DOI: 10.1515/revneuro-2019-0068