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Acta Psychologica Aug 2022Although a great deal of research has shown a relationship between numerosity sense and mathematical ability, some studies have failed to do so. The main source of this...
Although a great deal of research has shown a relationship between numerosity sense and mathematical ability, some studies have failed to do so. The main source of this inconsistency could be the varied ways of measuring mathematical abilities. The current investigation explored several types of mathematical ability, from basic number processing and arithmetic computation to numerical reasoning and arithmetic learning. We hypothesized that the correlation between numerosity sense and mathematical ability depends on mathematical fluency. A total of 415 college students (178 males and 237 females, mean age = 20.42 years, range = 18.58-22.92 years) were recruited to complete seven mathematical tasks and two numerosity tasks, as well as other tasks that measured cognitive covariates. The results showed that after controlling for age, gender, and related general cognitive factors, numerosity sense still predicted substantial variation in parity judgment, visual digit comparison, and computation, but it did not predict variation in numerosity estimation, auditory digit comparison, number series completion, or digit associate learning. The results suggest that numerosity sense correlates with mathematical abilities that accompany fluency.
Topics: Adolescent; Adult; Aptitude; Cognition; Female; Humans; Judgment; Male; Mathematical Concepts; Mathematics; Problem Solving; Young Adult
PubMed: 35772311
DOI: 10.1016/j.actpsy.2022.103655 -
PloS One 2022In opinion dynamics, as in general usage, polarisation is subjective. To understand polarisation, we need to develop more precise methods to measure the agreement in...
In opinion dynamics, as in general usage, polarisation is subjective. To understand polarisation, we need to develop more precise methods to measure the agreement in society. This paper presents four mathematical measures of polarisation derived from graph and network representations of societies and information-theoretic divergences or distance metrics. Two of the methods, min-max flow and spectral radius, rely on graph theory and define polarisation in terms of the structural characteristics of networks. The other two methods represent opinions as probability density functions and use the Kullback-Leibler divergence and the Hellinger distance as polarisation measures. We present a series of opinion dynamics simulations from two common models to test the effectiveness of the methods. Results show that the four measures provide insight into the different aspects of polarisation and allow real-time monitoring of social networks for indicators of polarisation. The three measures, the spectral radius, Kullback-Leibler divergence and Hellinger distance, smoothly delineated between different amounts of polarisation, i.e. how many cluster there were in the simulation, while also measuring with more granularity how close simulations were to consensus. Min-max flow failed to accomplish such nuance.
Topics: Computer Simulation; Mathematics; Social Segregation
PubMed: 36194573
DOI: 10.1371/journal.pone.0275283 -
Scientific Reports Jul 2022Investigating how the brain may constrain academic achievement is not only relevant to understanding brain structure but also to providing insight into the origins of...
Investigating how the brain may constrain academic achievement is not only relevant to understanding brain structure but also to providing insight into the origins of individual differences in these academic abilities. In this pre-registered study, we investigated whether the variability of sulcal patterns, a qualitative feature of the brain determined in-utero and not affected by brain maturation and learning, accounted for individual differences in reading and mathematics. Participants were 97 typically developing 10-year-olds. We examined (a) the association between the sulcal pattern of the IntraParietal Sulcus (IPS) and mathematical ability; (b) the association between the sulcal pattern of the Occipito Temporal Sulcus (OTS) and reading ability; and (c) the overlap and specificity of sulcal morphology of IPS and OTS and their associations with mathematics and reading. Despite its large sample, the present study was unable to replicate a previously observed relationship between the IPS sulcal pattern and mathematical ability and a previously observed association between the left posterior OTS sulcal pattern and reading. We found a weak association between right IPS sulcal morphology and symbolic number abilities and a weak association between left posterior OTS and reading. However, both these associations were the opposite of previous reports. We found no evidence for a possible overlap or specificity in the effect of sulcal morphology on mathematics and reading. Possible explanations for this weak association between sulcal morphology and academic achievement and suggestions for future research are discussed.
Topics: Academic Success; Brain Mapping; Humans; Magnetic Resonance Imaging; Mathematics; Parietal Lobe
PubMed: 35854034
DOI: 10.1038/s41598-022-15335-y -
Philosophical Transactions. Series A,... Dec 2021In the nearly seven decades since the publication of Alan Turing's work on morphogenesis, enormous progress has been made in understanding both the mathematical and... (Review)
Review
In the nearly seven decades since the publication of Alan Turing's work on morphogenesis, enormous progress has been made in understanding both the mathematical and biological aspects of his proposed reaction-diffusion theory. Some of these developments were nascent in Turing's paper, and others have been due to new insights from modern mathematical techniques, advances in numerical simulations and extensive biological experiments. Despite such progress, there are still important gaps between theory and experiment, with many examples of biological patterning where the underlying mechanisms are still unclear. Here, we review modern developments in the mathematical theory pioneered by Turing, showing how his approach has been generalized to a range of settings beyond the classical two-species reaction-diffusion framework, including evolving and complex manifolds, systems heterogeneous in space and time, and more general reaction-transport equations. While substantial progress has been made in understanding these more complicated models, there are many remaining challenges that we highlight throughout. We focus on the mathematical theory, and in particular linear stability analysis of 'trivial' base states. We emphasize important open questions in developing this theory further, and discuss obstacles in using these techniques to understand biological reality. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.
Topics: Diffusion; Mathematics; Models, Biological; Morphogenesis
PubMed: 34743603
DOI: 10.1098/rsta.2020.0268 -
Molecules (Basel, Switzerland) Jun 2023Since chemistry, materials science, and crystallography deal with three-dimensional structures, they use mathematics such as geometry and symmetry. In recent years, the...
Since chemistry, materials science, and crystallography deal with three-dimensional structures, they use mathematics such as geometry and symmetry. In recent years, the application of topology and mathematics to material design has yielded remarkable results. It can also be seen that differential geometry has been applied to various fields of chemistry for a relatively long time. There is also the possibility of using new mathematics, such as the crystal structure database, which represents big data, for computational chemistry (Hirshfeld surface analysis). On the other hand, group theory (space group and point group) is useful for crystal structures, including determining their electronic properties and the symmetries of molecules with relatively high symmetry. However, these strengths are not exhibited in the low-symmetry molecules that are actually handled. A new use of mathematics for chemical research is required that is suitable for the age when computational chemistry and artificial intelligence can be used.
Topics: Artificial Intelligence; Mathematics; Crystallography
PubMed: 37298985
DOI: 10.3390/molecules28114509 -
Mathematical Biosciences and... Dec 2018This paper reviews some recent works on impulsive delayed systems (IDSs). The prime focus is the fundamental results and recent progress in theory and applications.... (Review)
Review
This paper reviews some recent works on impulsive delayed systems (IDSs). The prime focus is the fundamental results and recent progress in theory and applications. After reviewing the relative literatures, this paper provides a comprehensive and intuitive overview of IDSs. Five aspects of IDSs are surveyed including basic theory, stability analysis, impulsive control, impulsive perturbation, and delayed impulses. Then the research prospect is given, which provides a reference for further study of IDSs theory.
Topics: Computer Simulation; Mathematical Concepts; Neural Networks, Computer; Nonlinear Dynamics; Stochastic Processes; Systems Theory; Time Factors
PubMed: 30418796
DOI: 10.3934/mbe.2018069 -
Psychological Research Jul 2022There is a notion that mathematical equations can be considered aesthetic objects. However, whereas some aesthetic experiences are triggered primarily by the sensory...
There is a notion that mathematical equations can be considered aesthetic objects. However, whereas some aesthetic experiences are triggered primarily by the sensory properties of objects, for mathematical equations aesthetic judgments extend beyond their sensory qualities and are also informed by semantics and knowledge. Therefore, to the extent that expertise in mathematics represents the accumulation of domain knowledge, it should influence aesthetic judgments of equations. In a between-groups study design involving university students who majored in mathematics (i.e., experts) or not (i.e., laypeople), we found support for the hypothesis that mathematics majors exhibit more agreement in their aesthetic judgments of equations-reflecting a greater degree of shared variance driven by formal training in the domain. Furthermore, their judgments were driven more strongly by familiarity and meaning than was the case for laypeople. These results suggest that expertise via advanced training in mathematics alters (and sharpens) aesthetic judgments of mathematical equations.
Topics: Esthetics; Humans; Judgment; Mathematics; Semantics
PubMed: 34495389
DOI: 10.1007/s00426-021-01592-5 -
Journal of Neurology, Neurosurgery, and... Jan 2016Computational Psychiatry aims to describe the relationship between the brain's neurobiology, its environment and mental symptoms in computational terms. In so doing, it... (Review)
Review
Computational Psychiatry aims to describe the relationship between the brain's neurobiology, its environment and mental symptoms in computational terms. In so doing, it may improve psychiatric classification and the diagnosis and treatment of mental illness. It can unite many levels of description in a mechanistic and rigorous fashion, while avoiding biological reductionism and artificial categorisation. We describe how computational models of cognition can infer the current state of the environment and weigh up future actions, and how these models provide new perspectives on two example disorders, depression and schizophrenia. Reinforcement learning describes how the brain can choose and value courses of actions according to their long-term future value. Some depressive symptoms may result from aberrant valuations, which could arise from prior beliefs about the loss of agency ('helplessness'), or from an inability to inhibit the mental exploration of aversive events. Predictive coding explains how the brain might perform Bayesian inference about the state of its environment by combining sensory data with prior beliefs, each weighted according to their certainty (or precision). Several cortical abnormalities in schizophrenia might reduce precision at higher levels of the inferential hierarchy, biasing inference towards sensory data and away from prior beliefs. We discuss whether striatal hyperdopaminergia might have an adaptive function in this context, and also how reinforcement learning and incentive salience models may shed light on the disorder. Finally, we review some of Computational Psychiatry's applications to neurological disorders, such as Parkinson's disease, and some pitfalls to avoid when applying its methods.
Topics: Computational Biology; Humans; Mathematics; Mental Disorders; Psychiatry
PubMed: 26157034
DOI: 10.1136/jnnp-2015-310737 -
Journal of Biomedical Optics Jan 2024Quantitative photoacoustic tomography (QPAT) exploits the photoacoustic effect with the aim of estimating images of clinically relevant quantities related to the... (Review)
Review
SIGNIFICANCE
Quantitative photoacoustic tomography (QPAT) exploits the photoacoustic effect with the aim of estimating images of clinically relevant quantities related to the tissue's optical absorption. The technique has two aspects: an acoustic part, where the initial acoustic pressure distribution is estimated from measured photoacoustic time-series, and an optical part, where the distributions of the optical parameters are estimated from the initial pressure.
AIM
Our study is focused on the optical part. In particular, computational modeling of light propagation (forward problem) and numerical solution methodologies of the image reconstruction (inverse problem) are discussed.
APPROACH
The commonly used mathematical models of how light and sound propagate in biological tissue are reviewed. A short overview of how the acoustic inverse problem is usually treated is given. The optical inverse problem and methods for its solution are reviewed. In addition, some limitations of real-life measurements and their effect on the inverse problems are discussed.
RESULTS
An overview of QPAT with a focus on the optical part was given. Computational modeling and inverse problems of QPAT were addressed, and some key challenges were discussed. Furthermore, the developments for tackling these problems were reviewed. Although modeling of light transport is well-understood and there is a well-developed framework of inverse mathematics for approaching the inverse problem of QPAT, there are still challenges in taking these methodologies to practice.
CONCLUSIONS
Modeling and inverse problems of QPAT together were discussed. The scope was limited to the optical part, and the acoustic aspects were discussed only to the extent that they relate to the optical aspect.
Topics: Algorithms; Tomography, X-Ray Computed; Image Processing, Computer-Assisted; Models, Theoretical; Mathematics
PubMed: 38125717
DOI: 10.1117/1.JBO.29.S1.S11509 -
Advances in Physiology Education Mar 2019Science, technology, engineering, and math (STEM) continue to work to increase the diversity of the fields, yet there are still significant historical and societal... (Review)
Review
Science, technology, engineering, and math (STEM) continue to work to increase the diversity of the fields, yet there are still significant historical and societal hurdles to be overcome before we reach full representation throughout STEM. The concept of science identity has become a point of interest in this process; it has been suggested that development of one's identity as a scientist is critical to persistence in the field. Metaphors that are rooted in bodily experience can provide a starting point to understand abstract concepts, including science identity and how we as STEM educators respond to increasing diversity within our fields. Given the history of STEM being predominantly populated by people who are white and male, disorientation or discomfort with increasing diversity is not unexpected, and many women and people of color report discrimination and marginalization as a part of their experience in STEM. Here I present a neuroscience-based metaphor that can serve as a starting point for understanding some of the potential disorientation or discomfort that we may experience as we engage with the increasing diversity of STEM and acknowledge this experience as a normal but temporary part of the process of growth and development as a field. I encourage the development and use of further discipline-based metaphors to enhance our discussion and understanding of this important work.
Topics: Biomedical Research; Cultural Diversity; Engineering; Female; Humans; Male; Mathematics; Metaphor; Motion Sickness; Science; Technology
PubMed: 30540205
DOI: 10.1152/advan.00185.2018