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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 -
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 -
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 -
CBE Life Sciences Education 2010
Topics: Biology; Cooperative Behavior; Curriculum; Mathematics; Research
PubMed: 20810940
DOI: 10.1187/cbe.10-06-0084 -
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 -
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 -
Annual Review of Biophysics May 2022In stark contrast to foldable proteins with a unique folded state, intrinsically disordered proteins and regions (IDPs) persist in perpetually disordered ensembles. Yet... (Review)
Review
In stark contrast to foldable proteins with a unique folded state, intrinsically disordered proteins and regions (IDPs) persist in perpetually disordered ensembles. Yet an IDP ensemble has conformational features-even when averaged-that are specific to its sequence. In fact, subtle changes in an IDP sequence can modulate its conformational features and its function. Recent advances in theoretical physics reveal a set of elegant mathematical expressions that describe the intricate relationships among IDP sequences, their ensemble conformations, and the regulation of their biological functions. These equations also describe the molecular properties of IDP sequences that predict similarities and dissimilarities in their functions and facilitate classification of sequences by function, an unmet challenge to traditional bioinformatics. These physical sequence-patterning metrics offer a promising new avenue for advancing synthetic biology at a time when multiple novel functional modes mediated by IDPs are emerging.
Topics: Intrinsically Disordered Proteins; Mathematics; Protein Conformation
PubMed: 35119946
DOI: 10.1146/annurev-biophys-120221-095357 -
Journal of Biomedical Informatics Jun 2022Significant technological advances made in recent years have shepherded a dramatic increase in utilization of digital technologies for biomedicine- everything from the... (Review)
Review
Significant technological advances made in recent years have shepherded a dramatic increase in utilization of digital technologies for biomedicine- everything from the widespread use of electronic health records to improved medical imaging capabilities and the rising ubiquity of genomic sequencing contribute to a "digitization" of biomedical research and clinical care. With this shift toward computerized tools comes a dramatic increase in the amount of available data, and current tools for data analysis capable of extracting meaningful knowledge from this wealth of information have yet to catch up. This article seeks to provide an overview of emerging mathematical methods with the potential to improve the abilities of clinicians and researchers to analyze biomedical data, but may be hindered from doing so by a lack of conceptual accessibility and awareness in the life sciences research community. In particular, we focus on topological data analysis (TDA), a set of methods grounded in the mathematical field of algebraic topology that seeks to describe and harness features related to the "shape" of data. We aim to make such techniques more approachable to non-mathematicians by providing a conceptual discussion of their theoretical foundations followed by a survey of their published applications to scientific research. Finally, we discuss the limitations of these methods and suggest potential avenues for future work integrating mathematical tools into clinical care and biomedical informatics.
Topics: Data Analysis; Diagnostic Imaging
PubMed: 35508272
DOI: 10.1016/j.jbi.2022.104082 -
Trends in Neuroscience and Education Dec 2022One frequent learning obstacle in mathematics is conceptual interference. However, the majority of research on conceptual interference has focused on science. In this...
BACKGROUND
One frequent learning obstacle in mathematics is conceptual interference. However, the majority of research on conceptual interference has focused on science. In this functional magnetic resonance imaging (fMRI) study, we examined the conceptual interference effects in both mathematics and science and the moderating influence of mathematical expertise.
METHODS
Thirty adult mathematicians and 31 gender-, age-, and intelligence-matched non-mathematicians completed a speeded reasoning tasks with statements from mathematics and science. Statements were either congruent (true or false according to both scientifically and naïve theories) or incongruent (differed in their truth value).
FINDINGS
Both groups exhibited more errors and a slower response time when evaluating incongruent compared to congruent statements in the science and mathematics task, but mathematicians were less affected by naïve theories. In mathematics, the left dorsolateral prefrontal cortex was activated when inhibiting naïve theories, while in science it was the dorsolateral and the ventrolateral prefrontal cortex bilaterally. Mathematical expertise did not moderate the conceptual interference effect at the neural level.
CONCLUSION
This study demonstrates that naïve theories in mathematics are still present in mathematicians, even though they are less affected by them in performance than novices. In addition, the differential brain activation in the mathematics and science task indicates that the extent of inhibitory control processes to resolve conceptual interference depends on the quality of the involved concepts.
Topics: Magnetic Resonance Imaging; Brain Mapping; Mathematics; Brain; Reaction Time
PubMed: 36470624
DOI: 10.1016/j.tine.2022.100194 -
Journal of the Royal Society, Interface Feb 2021One-shot anonymous unselfishness in economic games is commonly explained by social preferences, which assume that people care about the monetary pay-offs of others.... (Review)
Review
One-shot anonymous unselfishness in economic games is commonly explained by social preferences, which assume that people care about the monetary pay-offs of others. However, during the last 10 years, research has shown that different types of unselfish behaviour, including cooperation, altruism, truth-telling, altruistic punishment and trustworthiness are in fact better explained by preferences for following one's own personal norms-internal standards about what is right or wrong in a given situation. Beyond better organizing various forms of unselfish behaviour, this moral preference hypothesis has recently also been used to increase charitable donations, simply by means of interventions that make the morality of an action salient. Here we review experimental and theoretical work dedicated to this rapidly growing field of research, and in doing so we outline mathematical foundations for moral preferences that can be used in future models to better understand selfless human actions and to adjust policies accordingly. These foundations can also be used by artificial intelligence to better navigate the complex landscape of human morality.
Topics: Altruism; Artificial Intelligence; Cooperative Behavior; Humans; Mathematics; Morals; Punishment
PubMed: 33561377
DOI: 10.1098/rsif.2020.0880