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Scientific Reports Aug 2023In contrast to traditional expertise domains like chess and music, very little is known about the cognitive mechanisms in broader, more education-oriented domains like...
In contrast to traditional expertise domains like chess and music, very little is known about the cognitive mechanisms in broader, more education-oriented domains like mathematics. This is particularly true for the role of mathematical experts' knowledge for domain-specific information processing in memory as well as for domain-specific and domain-general creativity. In the present work, we compared 115 experts in mathematics with 109 gender, age, and educational level matched novices in their performance in (a) a newly developed mathematical memory task requiring encoding and recall of structured and unstructured information and (b) tasks drawing either on mathematical or on domain-general creativity. Consistent with other expertise domains, experts in mathematics (compared to novices) showed superior short-term memory capacity for complex domain-specific material when presented in a structured, meaningful way. Further, experts exhibited higher mathematical creativity than novices, but did not differ from them in their domain-general creativity. Both lines of findings demonstrate the importance of experts' knowledge base in processing domain-specific material and provide new insights into the characteristics of mathematical expertise.
Topics: Mental Recall; Cognition; Memory, Short-Term; Creativity; Mathematics
PubMed: 37532807
DOI: 10.1038/s41598-023-39309-w -
Isis; An International Review Devoted... Sep 2011This essay argues that the diversity of the history of mathematics community in the United Kingdom has influenced the development of the subject and is a significant...
This essay argues that the diversity of the history of mathematics community in the United Kingdom has influenced the development of the subject and is a significant factor behind the different concerns often evident in work on the history of mathematics when compared with that of historians of science. The heterogeneous nature of the community, which includes many who are not specialist historians, and the limited opportunities for academic careers open to practitioners have had a profound effect on the discipline, leading to a focus on elite mathematics and great mathematicians. More recently, reflecting earlier developments in the history of science, an increased interest in the context and culture of the practice of mathematics has become evident.
Topics: History, 19th Century; History, 20th Century; History, 21st Century; Interdisciplinary Communication; Mathematics; Science; United Kingdom
PubMed: 22073776
DOI: 10.1086/661626 -
Chaos (Woodbury, N.Y.) Mar 2022One of the simplest mathematical models in the study of nonlinear systems is the Kuramoto model, which describes synchronization in systems from swarms of insects to...
One of the simplest mathematical models in the study of nonlinear systems is the Kuramoto model, which describes synchronization in systems from swarms of insects to superconductors. We have recently found a connection between the original, real-valued nonlinear Kuramoto model and a corresponding complex-valued system that permits describing the system in terms of a linear operator and iterative update rule. We now use this description to investigate three major synchronization phenomena in Kuramoto networks (phase synchronization, chimera states, and traveling waves), not only in terms of steady state solutions but also in terms of transient dynamics and individual simulations. These results provide new mathematical insight into how sophisticated behaviors arise from connection patterns in nonlinear networked systems.
Topics: Chimera; Models, Theoretical; Nonlinear Dynamics
PubMed: 35364855
DOI: 10.1063/5.0078791 -
Medical Science Monitor : International... May 2003The importance of 'small-worlds', fractals and complex networks to medicine are discussed. The interrelationship between the concepts is highlighted.... (Review)
Review
The importance of 'small-worlds', fractals and complex networks to medicine are discussed. The interrelationship between the concepts is highlighted. 'Small-worlds'--where large populations are linked at the level of the individual have considerable importance for understanding disease transmission. Complex networks where linkages are based on the concept 'the rich get richer' are fundamental in the medical sciences--from enzymatic interactions at the subcellular level to social interactions such as sexual liaisons. Mathematically 'the rich get richer' can be modeled as a power law. Fractal architecture and time sequences can also be modeled by power laws and are ubiquitous in nature with many important examples in medicine. The potential of fractal life support--the return of physiological time sequences to devices such as mechanical ventilators and cardiopulmonary bypass pumps--is presented in the context of a failing complex network. Experimental work suggests that using fractal time sequences improves support of failing organs. Medicine, as a science has much to gain by embracing the interrelated concepts of 'small-worlds', fractals and complex networks. By so doing, medicine will move from the historical reductionist approach toward a more holistic one.
Topics: Fractals; Humans; Life Support Systems; Mathematics; Models, Biological
PubMed: 12761464
DOI: No ID Found -
PloS One 2021The registered report was targeted at identifying latent profiles of competence development in reading and mathematics among N = 15,012 German students in upper...
The registered report was targeted at identifying latent profiles of competence development in reading and mathematics among N = 15,012 German students in upper secondary education sampled in a multi-stage stratified cluster design across German schools. These students were initially assessed in grade 9 and provided competence assessments on three measurement occasions across six years using tests especially developed for the German National Educational Panel Study (NEPS). Using Latent Growth Mixture Models, Using Latent Growth Mixture Models, we aimed at identifying multiple profiles of competence development. Specifically, we expected to find at least one generalized (i.e., reading and mathematical competence develop similarly) and two specialized profiles (i.e., one of the domains develops faster) of competence development and that these profiles are explained by the specialization of interest and of vocational education of students. Contrary to our expectations, we did not find multiple latent profiles of competence development. The model describing our data best was a single-group latent growth model confirming a competence development profile, which can be described as specializing in mathematical competences, indicating a higher increase in mathematical competences as compared to reading competences in upper secondary school. Since only one latent profile was identified, potential predictors (specialization of vocational education and interest) for different profiles of competence development were not examined.
Topics: Adolescent; Education; Female; Germany; Humans; Male; Mathematics; Mental Competency; Reading; Schools; Students; Young Adult
PubMed: 34597338
DOI: 10.1371/journal.pone.0258152 -
Journal of Theoretical Biology Aug 2020Characterising biochemical reaction network structure in mathematical terms enables the inference of functional biochemical consequences from network structure with...
Characterising biochemical reaction network structure in mathematical terms enables the inference of functional biochemical consequences from network structure with existing mathematical techniques and spurs the development of new mathematics that exploits the peculiarities of biochemical network structure. The structure of a biochemical network may be specified by reaction stoichiometry, that is, the relative quantities of each molecule produced and consumed in each reaction of the network. A biochemical network may also be specified at a higher level of resolution in terms of the internal structure of each molecule and how molecular structures are transformed by each reaction in a network. The stoichiometry for a set of reactions can be compiled into a stoichiometric matrix N∈Z, where each row corresponds to a molecule and each column corresponds to a reaction. We demonstrate that a stoichiometric matrix may be split into the sum of m-rank(N) moiety transition matrices, each of which corresponds to a subnetwork accessible to a structurally identifiable conserved moiety. The existence of this moiety matrix splitting is a property that distinguishes a stoichiometric matrix from an arbitrary rectangular matrix.
Topics: Cell Physiological Phenomena; Mathematics
PubMed: 32333975
DOI: 10.1016/j.jtbi.2020.110276 -
Mathematical Biosciences and... 2013
Topics: Biology; History, 20th Century; History, 21st Century; Humans; Mathematics
PubMed: 24245630
DOI: 10.3934/mbe.2013.10.1499 -
Journal of Experimental Child Psychology Jul 2016Executive function (EF) has been highlighted as a potentially important factor for mathematical understanding. The relation has been well established in school-aged...
Executive function (EF) has been highlighted as a potentially important factor for mathematical understanding. The relation has been well established in school-aged children but has been less explored at younger ages. The current study investigated the relation between EF and mathematics in preschool-aged children. Participants were 142 typically developing 3- and 4-year-olds. Controlling for verbal ability, a significant positive correlation was found between EF and general math abilities in this age group. Importantly, we further examined this relation causally by varying the EF load on a magnitude comparison task. Results suggested a developmental pattern where 3-year-olds' performance on the magnitude comparison task was worst when EF was taxed the most. Conversely, 4-year-olds performed well on the magnitude task despite varying EF demands, suggesting that EF might play a critical role in the development of math concepts.
Topics: Child Development; Child, Preschool; Comprehension; Executive Function; Female; Humans; Male; Mathematics
PubMed: 27082019
DOI: 10.1016/j.jecp.2016.01.002 -
Philosophical Transactions. Series A,... Jun 2022Fluid dynamics is a research area lying at the crossroads of physics and applied mathematics with an ever-expanding range of applications in natural sciences and...
Fluid dynamics is a research area lying at the crossroads of physics and applied mathematics with an ever-expanding range of applications in natural sciences and engineering. However, despite decades of concerted research efforts, this area abounds with many fundamental questions that still remain unanswered. At the heart of these problems often lie mathematical models, usually in the form of partial differential equations, and many of the open questions concern the validity of these models and what can be learned from them about the physical problems. In recent years, significant progress has been made on a number of open problems in this area, often using approaches that transcend traditional discipline boundaries by combining modern methods of modelling, computation and mathematical analysis. The two-part theme issue aims to represent the breadth of these approaches, focusing on problems that are mathematical in nature but help to understand aspects of real physical importance such as fluid dynamical stability, transport, mixing, dissipation and vortex dynamics. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.
Topics: Hydrodynamics; Mathematics; Models, Theoretical; Physics
PubMed: 35527635
DOI: 10.1098/rsta.2021.0057 -
Philosophical Transactions. Series A,... Jun 2022Fluid dynamics is a research area lying at the crossroads of physics and applied mathematics with an ever-expanding range of applications in natural sciences and...
Fluid dynamics is a research area lying at the crossroads of physics and applied mathematics with an ever-expanding range of applications in natural sciences and engineering. However, despite decades of concerted research efforts, this area abounds with many fundamental questions that still remain unanswered. At the heart of these problems often lie mathematical models, usually in the form of partial differential equations, and many of the open questions concern the validity of these models and what can be learned from them about the physical problem. In recent years, significant progress has been made on a number of open problems in this area, often using approaches that transcend traditional discipline boundaries by combining modern methods of modelling, computation and mathematical analysis. The two-part theme issue aims to represent the breadth of these approaches, focusing on problems that are mathematical in nature but help to understand aspects of real physical importance such as fluid dynamical stability, transport, mixing, dissipation and vortex dynamics. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'.
Topics: Hydrodynamics; Mathematics; Models, Theoretical; Physics
PubMed: 35465715
DOI: 10.1098/rsta.2021.0056