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CBE Life Sciences Education 2014Although we agree with Theobold and Freeman (2014) that linear models are the most appropriate way in which to analyze assessment data, we show the importance of testing...
Although we agree with Theobold and Freeman (2014) that linear models are the most appropriate way in which to analyze assessment data, we show the importance of testing for interactions between covariates and factors.
Topics: Engineering; Humans; Mathematics; Research; Science; Students; Technology
PubMed: 25185220
DOI: 10.1187/cbe.14-05-0086 -
Science and Engineering Ethics Oct 2022While the consequences of mathematically-based software, algorithms and strategies have become ever wider and better appreciated, ethical reflection on mathematics has... (Review)
Review
While the consequences of mathematically-based software, algorithms and strategies have become ever wider and better appreciated, ethical reflection on mathematics has remained primitive. We review the somewhat disconnected suggestions of commentators in recent decades with a view to piecing together a coherent approach to ethics in mathematics. Calls for a Hippocratic Oath for mathematicians are examined and it is concluded that while lessons can be learned from the medical profession, the relation of mathematicians to those affected by their work is significantly different. There is something to be learned also from the codes of conduct of cognate but professionalised quantitative disciplines such as engineering and accountancy, as well as from legal principles bearing on professional work. We conclude with recommendations that professional societies in mathematics should sponsor an (international) code of ethics, institutional mission statements for mathematicians and syllabuses of ethics courses for incorporation into mathematics degrees.
Topics: Codes of Ethics; Ethics, Medical; Hippocratic Oath; Mathematics; Morals
PubMed: 36042113
DOI: 10.1007/s11948-022-00389-y -
Quarterly Journal of Experimental... Sep 2023Mathematics skills are associated with future employment, well-being, and quality of life. However, many adults and children fail to learn the mathematics skills they...
Mathematics skills are associated with future employment, well-being, and quality of life. However, many adults and children fail to learn the mathematics skills they require. To improve this situation, we need to have a better understanding of the processes of learning and performing mathematics. Over the past two decades, there has been a substantial growth in psychological research focusing on mathematics. However, to make further progress, we need to pay greater attention to the nature of, and multiple elements involved in, mathematical cognition. Mathematics is not a single construct; rather, overall mathematics achievement is comprised of proficiency with specific components of mathematics (e.g., number fact knowledge, algebraic thinking), which in turn recruit basic mathematical processes (e.g., magnitude comparison, pattern recognition). General cognitive skills and different learning experiences influence the development of each component of mathematics as well as the links between them. Here, I propose and provide evidence for a framework that structures how these components of mathematics fit together. This framework allows us to make sense of the proliferation of empirical findings concerning influences on mathematical cognition and can guide the questions we ask, identifying where we are missing both research evidence and models of specific mechanisms.
Topics: Child; Adult; Humans; Quality of Life; Cognition; Learning; Mathematics; Achievement
PubMed: 37129432
DOI: 10.1177/17470218231175325 -
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 -
The British Journal of Educational... Jun 2022Creativity requires both divergent and convergent thinking. Previous research established that divergent thinking relates to mathematics performance, but generally...
BACKGROUND
Creativity requires both divergent and convergent thinking. Previous research established that divergent thinking relates to mathematics performance, but generally ignored the role of convergent thinking and, hence, leaves it unclear how both might interact when children work on mathematical tasks. This study addressed this paucity in the research literature, with the goal of improving our understanding of the role of creative thinking in primary school mathematics.
AIMS
This study examined how divergent and convergent thinking contribute to mathematics performance, both directly and jointly, on single- and multiple-solution tasks.
SAMPLE
The study was conducted with 229 Dutch fifth graders of 12 primary schools.
METHOD
Divergent and convergent thinking were measured with a visual and verbal task. Path analysis was used including verbal and visual divergent and convergent thinking tasks in relation to single- and multiple-solution mathematics task performance. Working memory was included as a covariate.
RESULTS
Verbal convergent thinking positively predicted single- and multiple-solution task performance. Verbal divergent and convergent thinking interacted in relation to single-solution task performance, while visual divergent and convergent thinking interacted in relation to multiple-solution task performance.
CONCLUSIONS
Children's mathematics performance mainly relies on convergent thinking. The role of divergent thinking is twofold: it complements convergent thinking on multiple-solution tasks and compensates convergent thinking on single-solution tasks.
Topics: Child; Creativity; Humans; Mathematics; Memory, Short-Term; Task Performance and Analysis; Thinking
PubMed: 34496047
DOI: 10.1111/bjep.12459 -
Nature Reviews. Genetics Apr 2023Genome sequencing and analysis allow researchers to decode the functional information hidden in DNA sequences as well as to study cell to cell variation within a cell... (Review)
Review
Genome sequencing and analysis allow researchers to decode the functional information hidden in DNA sequences as well as to study cell to cell variation within a cell population. Traditionally, the primary bottleneck in genomic analysis pipelines has been the sequencing itself, which has been much more expensive than the computational analyses that follow. However, an important consequence of the continued drive to expand the throughput of sequencing platforms at lower cost is that often the analytical pipelines are struggling to keep up with the sheer amount of raw data produced. Computational cost and efficiency have thus become of ever increasing importance. Recent methodological advances, such as data sketching, accelerators and domain-specific libraries/languages, promise to address these modern computational challenges. However, despite being more efficient, these innovations come with a new set of trade-offs, both expected, such as accuracy versus memory and expense versus time, and more subtle, including the human expertise needed to use non-standard programming interfaces and set up complex infrastructure. In this Review, we discuss how to navigate these new methodological advances and their trade-offs.
Topics: Humans; Genomics; Genome; Chromosome Mapping; Data Analysis
PubMed: 36476810
DOI: 10.1038/s41576-022-00551-z -
Frontiers in Public Health 2022A long-standing human lifespan debate is revival, and the consensus is yet to come on whether the maximum human lifespan is reaching a limit or not. This study discusses...
A long-standing human lifespan debate is revival, and the consensus is yet to come on whether the maximum human lifespan is reaching a limit or not. This study discusses how mathematical constraints inherent in survival curves indicate a limit on maximum lifespans, implying that humans would have inevitable limits to lifespan growth.
Topics: Humans; Longevity; Mathematics
PubMed: 36684960
DOI: 10.3389/fpubh.2022.1037544 -
Anatomical Record (Hoboken, N.J. : 2007) Jan 2015
Topics: Anatomy; Animals; Finite Element Analysis; Humans; Mathematics; Models, Anatomic; Models, Biological
PubMed: 25529236
DOI: 10.1002/ar.23077 -
PLoS Computational Biology Feb 2023Neural mass models are used to simulate cortical dynamics and to explain the electrical and magnetic fields measured using electro- and magnetoencephalography....
Neural mass models are used to simulate cortical dynamics and to explain the electrical and magnetic fields measured using electro- and magnetoencephalography. Simulations evince a complex phase-space structure for these kinds of models; including stationary points and limit cycles and the possibility for bifurcations and transitions among different modes of activity. This complexity allows neural mass models to describe the itinerant features of brain dynamics. However, expressive, nonlinear neural mass models are often difficult to fit to empirical data without additional simplifying assumptions: e.g., that the system can be modelled as linear perturbations around a fixed point. In this study we offer a mathematical analysis of neural mass models, specifically the canonical microcircuit model, providing analytical solutions describing slow changes in the type of cortical activity, i.e. dynamical itinerancy. We derive a perturbation analysis up to second order of the phase flow, together with adiabatic approximations. This allows us to describe amplitude modulations in a relatively simple mathematical format providing analytic proof-of-principle for the existence of semi-stable states of cortical dynamics at the scale of a cortical column. This work allows for model inversion of neural mass models, not only around fixed points, but over regions of phase space that encompass transitions among semi or multi-stable states of oscillatory activity. Crucially, these theoretical results speak to model inversion in the context of multiple semi-stable brain states, such as the transition between interictal, pre-ictal and ictal activity in epilepsy.
Topics: Humans; Models, Neurological; Brain; Epilepsy; Mathematics; Magnetoencephalography; Nonlinear Dynamics
PubMed: 36763644
DOI: 10.1371/journal.pcbi.1010915 -
Bulletin of Mathematical Biology Jan 2023Pattern formation has been extensively studied in the context of evolving (time-dependent) domains in recent years, with domain growth implicated in ameliorating...
Pattern formation has been extensively studied in the context of evolving (time-dependent) domains in recent years, with domain growth implicated in ameliorating problems of pattern robustness and selection, in addition to more realistic modelling in developmental biology. Most work to date has considered prescribed domains evolving as given functions of time, but not the scenario of concentration-dependent dynamics, which is also highly relevant in a developmental setting. Here, we study such concentration-dependent domain evolution for reaction-diffusion systems to elucidate fundamental aspects of these more complex models. We pose a general form of one-dimensional domain evolution and extend this to N-dimensional manifolds under mild constitutive assumptions in lieu of developing a full tissue-mechanical model. In the 1D case, we are able to extend linear stability analysis around homogeneous equilibria, though this is of limited utility in understanding complex pattern dynamics in fast growth regimes. We numerically demonstrate a variety of dynamical behaviours in 1D and 2D planar geometries, giving rise to several new phenomena, especially near regimes of critical bifurcation boundaries such as peak-splitting instabilities. For sufficiently fast growth and contraction, concentration-dependence can have an enormous impact on the nonlinear dynamics of the system both qualitatively and quantitatively. We highlight crucial differences between 1D evolution and higher-dimensional models, explaining obstructions for linear analysis and underscoring the importance of careful constitutive choices in defining domain evolution in higher dimensions. We raise important questions in the modelling and analysis of biological systems, in addition to numerous mathematical questions that appear tractable in the one-dimensional setting, but are vastly more difficult for higher-dimensional models.
Topics: Mathematical Concepts; Computer Simulation; Models, Biological; Nonlinear Dynamics
PubMed: 36637542
DOI: 10.1007/s11538-022-01115-2