Mathematical Aspects of the Periodic Law

We review different studies of the Periodic Law and the set of chemical elements from a mathematical point of view. This discussion covers the first attempts made in the 19th century up to the present day. Mathematics employed to study the periodic system includes number theory, information theory, order theory, set theory and topology. Each theory used shows that it is possible to provide the Periodic Law with a mathematical structure. We also show that it is possible to study the chemical elements taking advantage of their phenomenological properties, and that it is not always necessary to reduce the concept of chemical elements to the quantum atomic concept to be able to find interpretations for the Periodic Law. Finally, a connection is noted between the lengths of the periods of the Periodic Law and the philosophical Pythagorean doctrine.Comment: 20 pages, PDF fil

On the use of the group SO(4,2) in atomic and molecular physics

In this paper the dynamical noninvariance group SO(4,2) for a hydrogen-like atom is derived through two different approaches. The first one is by an established traditional ascent process starting from the symmetry group SO(3). This approach is presented in a mathematically oriented original way with a special emphasis on maximally superintegrable systems, N-dimensional extension and little groups. The second approach is by a new symmetry descent process starting from the noninvariance dynamical group Sp(8,R) for a four-dimensional harmonic oscillator. It is based on the little known concept of a Lie algebra under constraints and corresponds in some sense to a symmetry breaking mechanism. This paper ends with a brief discussion of the interest of SO(4,2) for a new group-theoretical approach to the periodic table of chemical elements. In this connection, a general ongoing programme based on the use of a complete set of commuting operators is briefly described. It is believed that the present paper could be useful not only to the atomic and molecular community but also to people working in theoretical and mathematical physics.Comment: 31 page

Generalization Strategies in Finding the <i>n</i>th Term Rule for Simple Quadratic Sequences

In this study, we identify ways in which a sample of 18 graduates with mathematics-related first degrees found the nth term for quadratic sequences from the first values of a sequence of data, presented on a computer screen in various formats: tabular, scattered data pairs and sequential. Participants’ approaches to identifying the nth term were recorded with eye-tracking technology. Our aims are to identify their strategies and to explore whether and how format influences these strategies. Qualitative analysis of eye-tracking data offers several strategies: Sequence of Differences, Building a Relationship, Known Formula, Linear Recursive and Initial Conjecture. Sequence of Differences was the most common strategy, but Building a Relationship was more likely to lead to the right formula. Building from Square and Factor Search were the most successful methods of Building a Relationship. Findings about the influence of format on the range of strategies were inconclusive but analysis indicated sporadic evidence of possible influences

Viewing scenes of the history of chemistry through the opera glass

Artistic creation has always reflected the spirit of the moment and opera has not been an exception. There are several examples of operas which appeared at key moments of the development of science, portraying them. Additionally there are also operas that emerged after scientific events or the lifetime of the scientists they were inspired on. In what concerns chemistry, the first category could be exemplified by the apothecary operas (already discussed by the author in a previous paper of this journal) while the others could be illustrated by recent operas such as Dr. Atomic or Madame Curie. Continuing our endeavor of establishing relations between opera and chemistry, and considering that history of science plays an important role in the process of teaching and learning sciences, some milestones of the history of chemistry are here revisited through the opera glass. The operas analyzed have been grouped in the following categories: Operas of Fire and Metallurgy, Operas of the Philosophers of Antiquity, Operas of Alchemy, Operas of the Age of Enlightenment, Operas of the Revolutions and Operas of Entropy.Thanks are due to the Foundation for Science and Technology (FCT–Portugal) and FEDER (European Fund for Regional Development)-COMPETE/QREN/EU for financial support through the research unity PEst-C/QUI/UI686/2013.

De Novo Truncating Mutations in WASF1 Cause Intellectual Disability with Seizures.

Next-generation sequencing has been invaluable in the elucidation of the genetic etiology of many subtypes of intellectual disability in recent years. Here, using exome sequencing and whole-genome sequencing, we identified three de novo truncating mutations in WAS protein family member 1 (WASF1) in five unrelated individuals with moderate to profound intellectual disability with autistic features and seizures. WASF1, also known as WAVE1, is part of the WAVE complex and acts as a mediator between Rac-GTPase and actin to induce actin polymerization. The three mutations connected by Matchmaker Exchange were c.1516C>T (p.Arg506Ter), which occurs in three unrelated individuals, c.1558C>T (p.Gln520Ter), and c.1482delinsGCCAGG (p.Ile494MetfsTer23). All three variants are predicted to partially or fully disrupt the C-terminal actin-binding WCA domain. Functional studies using fibroblast cells from two affected individuals with the c.1516C>T mutation showed a truncated WASF1 and a defect in actin remodeling. This study provides evidence that de novo heterozygous mutations in WASF1 cause a rare form of intellectual disability

Phenotypic Characterization of EIF2AK4 Mutation Carriers in a Large Cohort of Patients Diagnosed Clinically With Pulmonary Arterial Hypertension.

BACKGROUND: Pulmonary arterial hypertension (PAH) is a rare disease with an emerging genetic basis. Heterozygous mutations in the gene encoding the bone morphogenetic protein receptor type 2 (BMPR2) are the commonest genetic cause of PAH, whereas biallelic mutations in the eukaryotic translation initiation factor 2 alpha kinase 4 gene (EIF2AK4) are described in pulmonary veno-occlusive disease/pulmonary capillary hemangiomatosis. Here, we determine the frequency of these mutations and define the genotype-phenotype characteristics in a large cohort of patients diagnosed clinically with PAH. METHODS: Whole-genome sequencing was performed on DNA from patients with idiopathic and heritable PAH and with pulmonary veno-occlusive disease/pulmonary capillary hemangiomatosis recruited to the National Institute of Health Research BioResource-Rare Diseases study. Heterozygous variants in BMPR2 and biallelic EIF2AK4 variants with a minor allele frequency of <1:10 000 in control data sets and predicted to be deleterious (by combined annotation-dependent depletion, PolyPhen-2, and sorting intolerant from tolerant predictions) were identified as potentially causal. Phenotype data from the time of diagnosis were also captured. RESULTS: Eight hundred sixty-four patients with idiopathic or heritable PAH and 16 with pulmonary veno-occlusive disease/pulmonary capillary hemangiomatosis were recruited. Mutations in BMPR2 were identified in 130 patients (14.8%). Biallelic mutations in EIF2AK4 were identified in 5 patients with a clinical diagnosis of pulmonary veno-occlusive disease/pulmonary capillary hemangiomatosis. Furthermore, 9 patients with a clinical diagnosis of PAH carried biallelic EIF2AK4 mutations. These patients had a reduced transfer coefficient for carbon monoxide (Kco; 33% [interquartile range, 30%-35%] predicted) and younger age at diagnosis (29 years; interquartile range, 23-38 years) and more interlobular septal thickening and mediastinal lymphadenopathy on computed tomography of the chest compared with patients with PAH without EIF2AK4 mutations. However, radiological assessment alone could not accurately identify biallelic EIF2AK4 mutation carriers. Patients with PAH with biallelic EIF2AK4 mutations had a shorter survival. CONCLUSIONS: Biallelic EIF2AK4 mutations are found in patients classified clinically as having idiopathic and heritable PAH. These patients cannot be identified reliably by computed tomography, but a low Kco and a young age at diagnosis suggests the underlying molecular diagnosis. Genetic testing can identify these misclassified patients, allowing appropriate management and early referral for lung transplantation

Telomerecat: A ploidy-agnostic method for estimating telomere length from whole genome sequencing data.

Telomere length is a risk factor in disease and the dynamics of telomere length are crucial to our understanding of cell replication and vitality. The proliferation of whole genome sequencing represents an unprecedented opportunity to glean new insights into telomere biology on a previously unimaginable scale. To this end, a number of approaches for estimating telomere length from whole-genome sequencing data have been proposed. Here we present Telomerecat, a novel approach to the estimation of telomere length. Previous methods have been dependent on the number of telomeres present in a cell being known, which may be problematic when analysing aneuploid cancer data and non-human samples. Telomerecat is designed to be agnostic to the number of telomeres present, making it suited for the purpose of estimating telomere length in cancer studies. Telomerecat also accounts for interstitial telomeric reads and presents a novel approach to dealing with sequencing errors. We show that Telomerecat performs well at telomere length estimation when compared to leading experimental and computational methods. Furthermore, we show that it detects expected patterns in longitudinal data, repeated measurements, and cross-species comparisons. We also apply the method to a cancer cell data, uncovering an interesting relationship with the underlying telomerase genotype

Phenotypic Characterization of <i>EIF2AK4</i> Mutation Carriers in a Large Cohort of Patients Diagnosed Clinically With Pulmonary Arterial Hypertension

Background: Pulmonary arterial hypertension (PAH) is a rare disease with an emerging genetic basis. Heterozygous mutations in the gene encoding the bone morphogenetic protein receptor type 2 ( BMPR2 ) are the commonest genetic cause of PAH, whereas biallelic mutations in the eukaryotic translation initiation factor 2 alpha kinase 4 gene ( EIF2AK4 ) are described in pulmonary veno-occlusive disease/pulmonary capillary hemangiomatosis. Here, we determine the frequency of these mutations and define the genotype-phenotype characteristics in a large cohort of patients diagnosed clinically with PAH. Methods: Whole-genome sequencing was performed on DNA from patients with idiopathic and heritable PAH and with pulmonary veno-occlusive disease/pulmonary capillary hemangiomatosis recruited to the National Institute of Health Research BioResource–Rare Diseases study. Heterozygous variants in BMPR2 and biallelic EIF2AK4 variants with a minor allele frequency of &lt;1:10 000 in control data sets and predicted to be deleterious (by combined annotation-dependent depletion, PolyPhen-2, and sorting intolerant from tolerant predictions) were identified as potentially causal. Phenotype data from the time of diagnosis were also captured. Results: Eight hundred sixty-four patients with idiopathic or heritable PAH and 16 with pulmonary veno-occlusive disease/pulmonary capillary hemangiomatosis were recruited. Mutations in BMPR2 were identified in 130 patients (14.8%). Biallelic mutations in EIF2AK4 were identified in 5 patients with a clinical diagnosis of pulmonary veno-occlusive disease/pulmonary capillary hemangiomatosis. Furthermore, 9 patients with a clinical diagnosis of PAH carried biallelic EIF2AK4 mutations. These patients had a reduced transfer coefficient for carbon monoxide (K co ; 33% [interquartile range, 30%–35%] predicted) and younger age at diagnosis (29 years; interquartile range, 23–38 years) and more interlobular septal thickening and mediastinal lymphadenopathy on computed tomography of the chest compared with patients with PAH without EIF2AK4 mutations. However, radiological assessment alone could not accurately identify biallelic EIF2AK4 mutation carriers. Patients with PAH with biallelic EIF2AK4 mutations had a shorter survival. Conclusions: Biallelic EIF2AK4 mutations are found in patients classified clinically as having idiopathic and heritable PAH. These patients cannot be identified reliably by computed tomography, but a low K co and a young age at diagnosis suggests the underlying molecular diagnosis. Genetic testing can identify these misclassified patients, allowing appropriate management and early referral for lung transplantation. </jats:sec

Large expert-curated database for benchmarking document similarity detection in biomedical literature search

Document recommendation systems for locating relevant literature have mostly relied on methods developed a decade ago. This is largely due to the lack of a large offline gold-standard benchmark of relevant documents that cover a variety of research fields such that newly developed literature search techniques can be compared, improved and translated into practice. To overcome this bottleneck, we have established the RElevant LIterature SearcH consortium consisting of more than 1500 scientists from 84 countries, who have collectively annotated the relevance of over 180 000 PubMed-listed articles with regard to their respective seed (input) article/s. The majority of annotations were contributed by highly experienced, original authors of the seed articles. The collected data cover 76% of all unique PubMed Medical Subject Headings descriptors. No systematic biases were observed across different experience levels, research fields or time spent on annotations. More importantly, annotations of the same document pairs contributed by different scientists were highly concordant. We further show that the three representative baseline methods used to generate recommended articles for evaluation (Okapi Best Matching 25, Term Frequency-Inverse Document Frequency and PubMed Related Articles) had similar overall performances. Additionally, we found that these methods each tend to produce distinct collections of recommended articles, suggesting that a hybrid method may be required to completely capture all relevant articles. The established database server located at https://relishdb.ict.griffith.edu.au is freely available for the downloading of annotation data and the blind testing of new methods. We expect that this benchmark will be useful for stimulating the development of new powerful techniques for title and title/abstract-based search engines for relevant articles in biomedical research.Peer reviewe