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Computational Intelligence and... 2022This study focuses on hybrid synchronization, a new synchronization phenomenon in which one element of the system is synced with another part of the system that is not...
This study focuses on hybrid synchronization, a new synchronization phenomenon in which one element of the system is synced with another part of the system that is not allowing full synchronization and nonsynchronization to coexist in the system. When , where and are the state vectors of the drive and response systems, respectively, and Wan ( = ∓1)), the two systems' hybrid synchronization phenomena are realized mathematically. Nonlinear control is used to create four alternative error stabilization controllers that are based on two basic tools: Lyapunov stability theory and the linearization approach.
Topics: Algorithms; Computer Simulation; Humans; Nonlinear Dynamics; Social Media
PubMed: 35222627
DOI: 10.1155/2022/4569879 -
Current Biology : CB Sep 2012
Topics: Animals; Behavior, Animal; Biology; England; Mathematics; Models, Theoretical; Sweden
PubMed: 23136669
DOI: 10.1016/j.cub.2012.06.077 -
Revista de Neurologia Jan 2014Mathematic difficulties are relatively frequent at school. With some frequency they appear associated to other troubles and learning disorders, thus provoking anxiety... (Review)
Review
INTRODUCTION
Mathematic difficulties are relatively frequent at school. With some frequency they appear associated to other troubles and learning disorders, thus provoking anxiety feelings in children. In case of not intervening on such difficulties their consequences may be extended until adulthood. Despite that, their intervention has not been widely administered, notably in the educational ambit. The main reason is that there is not a unique definition, which makes their detection not easy. However, some of the recent advances in neuroscience could improve this situation.
AIM
To review and summarize the main contributions provided by the neuroimaging techniques to the learning of numerical abilities and their difficulties, and how these techniques could be useful to intervene on the educational practice.
DEVELOPMENT
The ample advances of the neuroimaging techniques have allowed us the access to relevant information regarding the brain areas underlying each numerical task at childhood and at adulthood, and that made possible the design of intervention programs addressed to improve children' learning when there are any numerical difficulties. Some of the results obtained after the administration of these programs are positive, but they are not very generalizable yet.
CONCLUSIONS
In the future it should be expanded the use of neuroimaging techniques in order to implement the explanation of learning processes and detecting areas that, in case of not being correctly activated, could lead to any mathematic difficulties. Ultimately, research supported by these techniques should assist the development of programs devoted to intervene on mathematics in the educational field.
Topics: Adult; Brain Mapping; Child; Child, Preschool; Dominance, Cerebral; Dyscalculia; Education, Special; Forecasting; Frontal Lobe; Humans; Infant; Mathematics; Models, Neurological; Neuroimaging; Parietal Lobe
PubMed: 24399623
DOI: No ID Found -
Nature Jan 2024Proving mathematical theorems at the olympiad level represents a notable milestone in human-level automated reasoning, owing to their reputed difficulty among the...
Proving mathematical theorems at the olympiad level represents a notable milestone in human-level automated reasoning, owing to their reputed difficulty among the world's best talents in pre-university mathematics. Current machine-learning approaches, however, are not applicable to most mathematical domains owing to the high cost of translating human proofs into machine-verifiable format. The problem is even worse for geometry because of its unique translation challenges, resulting in severe scarcity of training data. We propose AlphaGeometry, a theorem prover for Euclidean plane geometry that sidesteps the need for human demonstrations by synthesizing millions of theorems and proofs across different levels of complexity. AlphaGeometry is a neuro-symbolic system that uses a neural language model, trained from scratch on our large-scale synthetic data, to guide a symbolic deduction engine through infinite branching points in challenging problems. On a test set of 30 latest olympiad-level problems, AlphaGeometry solves 25, outperforming the previous best method that only solves ten problems and approaching the performance of an average International Mathematical Olympiad (IMO) gold medallist. Notably, AlphaGeometry produces human-readable proofs, solves all geometry problems in the IMO 2000 and 2015 under human expert evaluation and discovers a generalized version of a translated IMO theorem in 2004.
Topics: Humans; Mathematics; Problem Solving; Natural Language Processing
PubMed: 38233616
DOI: 10.1038/s41586-023-06747-5 -
Seminars in Cancer Biology Jun 2011Erwin Schrödinger pointed out in his 1944 book "What is Life" that one defining attribute of biological systems seems to be their tendency to generate order from... (Review)
Review
Erwin Schrödinger pointed out in his 1944 book "What is Life" that one defining attribute of biological systems seems to be their tendency to generate order from disorder defying the second law of thermodynamics. Almost parallel to his findings, the science of complex systems was founded based on observations on physical and chemical systems showing that inanimate matter can exhibit complex structures although their interacting parts follow simple rules. This is explained by a process known as self-organization and it is now widely accepted that multi-cellular biological organisms are themselves self-organizing complex systems in which the relations among their parts are dynamic, contextual and interdependent. In order to fully understand such systems, we are required to computationally and mathematically model their interactions as promulgated in systems biology. The preponderance of network models in the practice of systems biology inspired by a reductionist, bottom-up view, seems to neglect, however, the importance of bidirectional interactions across spatial scales and domains. This approach introduces a shortcoming that may hinder research on emergent phenomena such as those of tissue morphogenesis and related diseases, such as cancer. Another hindrance of current modeling attempts is that those systems operate in a parameter space that seems far removed from biological reality. This misperception calls for more tightly coupled mathematical and computational models to biological experiments by creating and designing biological model systems that are accessible to a wide range of experimental manipulations. In this way, a comprehensive understanding of fundamental processes in normal development or of aberrations, like cancer, will be generated.
Topics: Animals; Humans; Morphogenesis; Nonlinear Dynamics; Systems Biology
PubMed: 21569848
DOI: 10.1016/j.semcancer.2011.04.004 -
PloS One 2022Stereotype threat has been proposed as one cause of gender differences in post-compulsory mathematics participation. Danaher and Crandall argued, based on a study...
Stereotype threat has been proposed as one cause of gender differences in post-compulsory mathematics participation. Danaher and Crandall argued, based on a study conducted by Stricker and Ward, that enquiring about a student's gender after they had finished a test, rather than before, would reduce stereotype threat and therefore increase the attainment of women students. Making such a change, they argued, could lead to nearly 5000 more women receiving AP Calculus AB credit per year. We conducted a preregistered conceptual replication of Stricker and Ward's study in the context of the UK Mathematics Trust's Junior Mathematical Challenge, finding no evidence of this stereotype threat effect. We conclude that the 'silver bullet' intervention of relocating demographic questions on test answer sheets is unlikely to provide an effective solution to systemic gender inequalities in mathematics education.
Topics: Educational Status; Female; Hospitals; Humans; Mathematics; Sex Factors; Stereotyping
PubMed: 35622813
DOI: 10.1371/journal.pone.0267699 -
PloS One 2023Algebra and geometry are important components of mathematics that are often considered gatekeepers for future success. However, most studies that have researched the...
Algebra and geometry are important components of mathematics that are often considered gatekeepers for future success. However, most studies that have researched the cognitive skills required for success in mathematics have only considered the domain of arithmetic. We extended models of mathematical skills to consider how executive function skills play both a direct role in secondary-school-level mathematical achievement as well as an indirect role via algebra and geometry, alongside arithmetic. We found that verbal and visuospatial working memory were indirectly associated with mathematical achievement via number fact knowledge, calculation skills, algebra and geometry. Inhibition was also indirectly associated with mathematical achievement via number fact knowledge and calculation skills. These findings highlight that there are multiple mechanisms by which executive function skills may be involved in mathematics outcomes. Therefore, using specific measures of mathematical processes as well as context-rich assessments of mathematical achievement is important to understand these mechanisms.
Topics: Executive Function; Memory, Short-Term; Academic Success; Inhibition, Psychological; Mathematics
PubMed: 37931003
DOI: 10.1371/journal.pone.0291796 -
PloS One 2020We analyse academic success using a genealogical approach to the careers of over 95,000 scientists in mathematics and associated fields in physics and chemistry. We look...
We analyse academic success using a genealogical approach to the careers of over 95,000 scientists in mathematics and associated fields in physics and chemistry. We look at the effect of Ph.D. supervisors (one's mentors) on the number of Ph.D. students that one supervises later on (one's mentees) as a measure of academic success. Supervisors generally provide important inputs in Ph.D. projects, which can have long-lasting effects on academic careers. Moreover, having multiple supervisors exposes one to a diversity of inputs. We show that Ph.D. students benefit from having multiple supervisors instead of a single one. The cognitive diversity of mentors has a subtler effect in that it increases both the likelihood of success (having many mentees later on) and failure (having no mentees at all later on). We understand the effect of diverse mentorship as a high-risk, high-gain strategy: the recombination of unrelated expertise often fails, but sometimes leads to true novelty.
Topics: Academic Success; Career Choice; Chemistry; Female; History, 18th Century; History, 19th Century; History, 20th Century; History, 21st Century; Humans; Male; Mathematics; Mentors; Physics; Research Personnel; Science; Students
PubMed: 33332441
DOI: 10.1371/journal.pone.0243913 -
Life Sciences Aug 2014Mathematical models are invaluable tools for understanding the relationships between components of a complex system. In the biological context, mathematical models help... (Review)
Review
Mathematical models are invaluable tools for understanding the relationships between components of a complex system. In the biological context, mathematical models help us understand the complex web of interrelations between various components (DNA, proteins, enzymes, signaling molecules etc.) in a biological system, gain better understanding of the system as a whole, and in turn predict its behavior in an altered state (e.g. disease). Mathematical modeling has enhanced our understanding of multiple complex biological processes like enzyme kinetics, metabolic networks, signal transduction pathways, gene regulatory networks, and electrophysiology. With recent advances in high throughput data generation methods, computational techniques and mathematical modeling have become even more central to the study of biological systems. In this review, we provide a brief history and highlight some of the important applications of modeling in biological systems with an emphasis on the study of excitable cells. We conclude with a discussion about opportunities and challenges for mathematical modeling going forward. In a larger sense, the review is designed to help answer a simple but important question that theoreticians frequently face from interested but skeptical colleagues on the experimental side: "What is the value of a model?"
Topics: Animals; Humans; Mathematics; Models, Biological; Physiological Phenomena; Physiology
PubMed: 25064823
DOI: 10.1016/j.lfs.2014.07.005 -
JAMA Network Open Apr 2020Children born preterm are at an elevated risk of academic underachievement. However, the extent to which performance across domain-specific subskills in reading and... (Meta-Analysis)
Meta-Analysis
IMPORTANCE
Children born preterm are at an elevated risk of academic underachievement. However, the extent to which performance across domain-specific subskills in reading and mathematics is associated with preterm birth remains unclear.
OBJECTIVE
To conduct a systematic review and meta-analysis of academic outcomes of school-aged children born preterm, compared with children born at term, appraising evidence for higher- and lower-order subskills in reading and mathematics.
DATA SOURCES
PubMed/MEDLINE, PsycINFO, and the Cumulative Index of Nursing and Allied Health Literature electronic databases from January 1, 1980, to July 30, 2018, were searched for population, exposure, and outcome terms such as child (population), preterm birth (exposure), and education* (outcome).
STUDY SELECTION
Peer-reviewed English-language publications that included preterm-born children and a comparison group of term-born children aged 5 to 18 years and born during or after 1980 and that reported outcomes on standardized assessments from cohort or cross-sectional studies were screened. Of the 9833 articles screened, 33 unique studies met the inclusion criteria.
DATA EXTRACTION AND SYNTHESIS
Data were analyzed from August 1 to September 29, 2018. The Preferred Reporting Items for Systematic Reviews and Meta-analyses (PRISMA) guidelines were followed. Two reviewers independently screened the databases and extracted sample characteristics and outcomes scores. Pooled mean differences (MDs) were analyzed using random-effects models.
MAIN OUTCOMES AND MEASURES
Performance on standardized assessment of higher-order subskills of reading comprehension and applied mathematics problems; lower-order reading subskills of decoding, pseudoword decoding, and word identification; and lower-order mathematics subskills of knowledge, calculation, and fluency.
RESULTS
Outcomes data were extracted for 4006 preterm and 3317 term-born children, totaling 7323 participants from 33 unique studies. Relative to children born at term, children born preterm scored significantly lower in reading comprehension (mean difference [MD], -7.96; 95% CI, -12.15 to -3.76; I2 = 81%) and applied mathematical problems (MD, -11.41; 95% CI, -17.57 to -5.26; I2 = 91%) assessments. Across the assessments of lower-order skills, children born preterm scored significantly lower than their term-born peers in calculation (MD, -10.57; 95% CI, -15.62 to -5.52; I2 = 92%), decoding (MD, -10.18; 95% CI, -16.83 to -3.53; I2 = 71%), mathematical knowledge (MD, -9.88; 95% CI, -11.68 to -8.08; I2 = 62%), word identification (MD, -7.44; 95% CI, -9.08 to -5.80; I2 = 69%), and mathematical fluency (MD, -6.89; 95% CI, -13.54 to -0.23; I2 = 72%). The associations remained unchanged after sensitivity analyses for reducing heterogeneity.
CONCLUSIONS AND RELEVANCE
These findings provide evidence that preterm birth is associated with academic underperformance in aggregate measures of reading and mathematics, as well as a variety of related subskills.
Topics: Academic Success; Adolescent; Case-Control Studies; Child; Child, Preschool; Comprehension; Cross-Sectional Studies; Data Management; Female; Humans; Male; Mathematics; Outcome Assessment, Health Care; Premature Birth; Reading
PubMed: 32242904
DOI: 10.1001/jamanetworkopen.2020.2027