Meanings given to algebraic symbolism in problem posing

Some errors in the learning of algebra suggest students have difficulties giving meaning to algebraic symbolism. In this paper, we use problem posing in order to analyze the students’ capacity to assign meaning to algebraic symbolism and the difficulties that students encounter in this process depending on the characteristics of the algebraic statements given. We designed a written questionnaire composed of eight closed algebraic statements expressed symbolically, which was administered to 55 students who had finished their compulsory education and that had some previous experience in problem posing. In our analysis of the data, we examine both syntactic and semantic structures of the problem posed. We note that in most cases students posed problems with syntactic structures different to those given. They did not include computations within variables, and changed the kinds of relationships connecting variables. Students easily posed problems for statements with additive structures. Other differences in the type of problems posed depend on the characteristics of the given statements

Genome-wide association study identifies WNT7B as a novel locus for central corneal thickness in Latinos

The cornea is the outermost layer of the eye and is a vital component of focusing incoming light on the retina. Central corneal thickness (CCT) is now recognized to have a significant role in ocular health and is a risk factor for various ocular diseases, such as keratoconus and primary open angle glaucoma. Most previous genetic studies utilized European and Asian subjects to identify genetic loci associated with CCT. Minority populations, such as Latinos, may aid in identifying additional loci and improve our understanding of the genetic architecture of CCT. In this study, we conducted a genome-wide association study (GWAS) in Latinos, a traditionally understudied population in genetic research, to further identify loci contributing to CCT. Study participants were genotyped using either the Illumina OmniExpress BeadChip (~730K markers) or the Illumina Hispanic/SOL BeadChip (~2.5 million markers). All study participants were 40 years of age and older. We assessed the association between individual single nucleotide polymorphisms (SNPs) and CCT using linear regression, adjusting for age, gender and principal components of genetic ancestry. To expand genomic coverage and to interrogate additional SNPs, we imputed SNPs from the 1000 Genomes Project reference panels. We identified a novel SNP, rs10453441 (P=6.01E-09), in an intron of WNT7B that is associated with CCT. Furthermore, WNT7B is expressed in the human cornea. We also replicated 11 previously reported loci, including IBTK, RXRA-COL5A1, COL5A1, FOXO1, LRRK1 and ZNF469 (P < 1.25E-3). These findings provide further insight into the genetic architecture of CCT and illustrate that the use of minority groups in GWAS will help identify additional loci

Urban Biodiversity and Landscape Ecology: Patterns, Processes and Planning

Effective planning for biodiversity in cities and towns is increasingly important as urban areas and their human populations grow, both to achieve conservation goals and because ecological communities support services on which humans depend. Landscape ecology provides important frameworks for understanding and conserving urban biodiversity both within cities and considering whole cities in their regional context, and has played an important role in the development of a substantial and expanding body of knowledge about urban landscapes and communities. Characteristics of the whole city including size, overall amount of green space, age and regional context are important considerations for understanding and planning for biotic assemblages at the scale of entire cities, but have received relatively little research attention. Studies of biodiversity within cities are more abundant and show that longstanding principles regarding how patch size, configuration and composition influence biodiversity apply to urban areas as they do in other habitats. However, the fine spatial scales at which urban areas are fragmented and the altered temporal dynamics compared to non-urban areas indicate a need to apply hierarchical multi-scalar landscape ecology models to urban environments. Transferring results from landscape-scale urban biodiversity research into planning remains challenging, not least because of the requirements for urban green space to provide multiple functions. An increasing array of tools is available to meet this challenge and increasingly requires ecologists to work with planners to address biodiversity challenges. Biodiversity conservation and enhancement is just one strand in urban planning, but is increasingly important in a rapidly urbanising world

Disentangling the genetic overlap and causal relationships between primary open-angle glaucoma, brain morphology and four major neurodegenerative disorders

BACKGROUND: Primary open-angle glaucoma (POAG) is an optic neuropathy characterized by progressive degeneration of the optic nerve that leads to irreversible visual impairment. Multiple epidemiological studies suggest an association between POAG and major neurodegenerative disorders (Alzheimer's disease, amyotrophic lateral sclerosis, frontotemporal dementia, and Parkinson's disease). However, the nature of the overlap between neurodegenerative disorders, brain morphology and glaucoma remains inconclusive. METHOD: In this study, we performed a comprehensive assessment of the genetic and causal relationship between POAG and neurodegenerative disorders, leveraging genome-wide association data from studies of magnetic resonance imaging of the brain, POAG, and four major neurodegenerative disorders. FINDINGS: This study found a genetic overlap and causal relationship between POAG and its related phenotypes (i.e., intraocular pressure and optic nerve morphology traits) and brain morphology in 19 regions. We also identified 11 loci with a significant local genetic correlation and a high probability of sharing the same causal variant between neurodegenerative disorders and POAG or its related phenotypes. Of interest, a region on chromosome 17 corresponding to MAPT, a well-known risk locus for Alzheimer's and Parkinson's disease, was shared between POAG, optic nerve degeneration traits, and Alzheimer's and Parkinson's diseases. Despite these local genetic overlaps, we did not identify strong evidence of a causal association between these neurodegenerative disorders and glaucoma. INTERPRETATION: Our findings indicate a distinctive and likely independent neurodegenerative process for POAG involving several brain regions although several POAG or optic nerve degeneration risk loci are shared with neurodegenerative disorders, consistent with a pleiotropic effect rather than a causal relationship between these traits. FUNDING: PG was supported by an NHMRC Investigator Grant (#1173390), SM by an NHMRC Senior Research Fellowship and an NHMRC Program Grant (APP1150144), DM by an NHMRC Fellowship, LP is funded by the NEI EY015473 and EY032559 grants, SS is supported by an NIH-Oxford Cambridge Fellowship and NIH T32 grant (GM136577), APK is supported by a UK Research and Innovation Future Leaders Fellowship, an Alcon Research Institute Young Investigator Award and a Lister Institute for Preventive Medicine Award

Mapping quantitative trait loci in line cross with repeat records

<p>Abstract</p> <p>Background</p> <p>Phenotypes with repeat records from one individual or multiple individuals were often encountered in practices of mapping QTL in linecross. The current genetic mapping method for a trait with repeat records is adopted by simply replacing the phenotype by the average value of the repeat records. This simple treatment has not sufficiently utilized the information from the replication and ignored the impacts of the permanent environmental effects on the accuracy of the estimated QTL.</p> <p>Results</p> <p>We propose to map QTL by using the repeatability model to directly analyze the repeat records rather than simply analyze the mean phenotype, improving the efficiency of QTL detecting because of adequately utilizing the information from data and allowing for the permanent environmental effects. A maximum likelihood method implemented via the expectation-maximization (EM) algorithm is applied to perform the parameter estimation of the repeatability model. The superiority of the mapping method based on the repeatability model over simple analysis using the mean phenotype was demonstrated by a series of simulations.</p> <p>Conclusion</p> <p>Our results suggest that the proposed method can serve as a powerful alternative to existing methods. By mean of the repeatability model, utilizing the repeat records on individual may improve the efficiency of QTL detecting in line cross.</p

GEIRA: gene-environment and gene–gene interaction research application

The GEIRA (Gene-Environment and Gene–Gene Interaction Research Application) algorithm and subsequent program is dedicated to genome-wide gene-environment and gene–gene interaction analysis. It implements concepts of both additive and multiplicative interaction as well as calculations based on dominant, recessive and co-dominant genetic models, respectively. Estimates of interactions are incorporated in a single table to make the output easily read. The algorithm is coded in both SAS and R. GEIRA is freely available to non-commercial users at http://www.epinet.se. Additional information, including user’s manual and example datasets is available online at http://www.epinet.se

A genome-wide association study for late-onset Alzheimer's disease using DNA pooling

Background: Late-onset Alzheimer's disease (LOAD) is an age related neurodegenerative disease with a high prevalence that places major demands on healthcare resources in societies with increasingly aged populations. The only extensively replicable genetic risk factor for LOAD is the apolipoprotein E gene. In order to identify additional genetic risk loci we have conducted a genome-wide association (GWA) study in a large LOAD case – control sample, reducing costs through the use of DNA pooling. Methods: DNA samples were collected from 1,082 individuals with LOAD and 1,239 control subjects. Age at onset ranged from 60 to 95 and Controls were matched for age (mean = 76.53 years, SD = 33), gender and ethnicity. Equimolar amounts of each DNA sample were added to either a case or control pool. The pools were genotyped using Illumina HumanHap300 and Illumina Sentrix HumanHap240S arrays testing 561,494 SNPs. 114 of our best hit SNPs from the pooling data were identified and then individually genotyped in the case – control sample used to construct the pools. Results: Highly significant association with LOAD was observed at the APOE locus confirming the validity of the pooled genotyping approach. For 109 SNPs outside the APOE locus, we obtained uncorrected p-values ≤ 0.05 for 74 after individual genotyping. To further test these associations, we added control data from 1400 subjects from the 1958 Birth Cohort with the evidence for association increasing to 3.4 × 10-6 for our strongest finding, rs727153. rs727153 lies 13 kb from the start of transcription of lecithin retinol acyltransferase (phosphatidylcholine – retinol O-acyltransferase, LRAT). Five of seven tag SNPs chosen to cover LRAT showed significant association with LOAD with a SNP in intron 2 of LRAT, showing greatest evidence of association (rs201825, p-value = 6.1 × 10-7). Conclusion: We have validated the pooling method for GWA studies by both identifying the APOE locus and by observing a strong enrichment for significantly associated SNPs. We provide evidence for LRAT as a novel candidate gene for LOAD. LRAT plays a prominent role in the Vitamin A cascade, a system that has been previously implicated in LOAD

Migraine in women: the role of hormones and their impact on vascular diseases

Migraine is a predominantly female disorder. Menarche, menstruation, pregnancy, and menopause, and also the use of hormonal contraceptives and hormone replacement treatment may influence migraine occurrence. Migraine usually starts after menarche, occurs more frequently in the days just before or during menstruation, and ameliorates during pregnancy and menopause. Those variations are mediated by fluctuation of estrogen levels through their influence on cellular excitability or cerebral vasculature. Moreover, administration of exogenous hormones may cause worsening of migraine as may expose migrainous women to an increased risk of vascular disease. In fact, migraine with aura represents a risk factor for stroke, cardiac disease, and vascular mortality. Studies have shown that administration of combined oral contraceptives to migraineurs may further increase the risk for ischemic stroke. Consequently, in women suffering from migraine with aura caution should be deserved when prescribing combined oral contraceptives

Genetic variation affects morphological retinal phenotypes extracted from UK Biobank optical coherence tomography images

Optical Coherence Tomography (OCT) enables non-invasive imaging of the retina and is used to diagnose and manage ophthalmic diseases including glaucoma. We present the first large-scale genome-wide association study of inner retinal morphology using phenotypes derived from OCT images of 31,434 UK Biobank participants. We identify 46 loci associated with thickness of the retinal nerve fibre layer or ganglion cell inner plexiform layer. Only one of these loci has been associated with glaucoma, and despite its clear role as a biomarker for the disease, Mendelian randomisation does not support inner retinal thickness being on the same genetic causal pathway as glaucoma. We extracted overall retinal thickness at the fovea, representative of foveal hypoplasia, with which three of the 46 SNPs were associated. We additionally associate these three loci with visual acuity. In contrast to the Mendelian causes of severe foveal hypoplasia, our results suggest a spectrum of foveal hypoplasia, in part genetically determined, with consequences on visual function

Genomic locus modulating corneal thickness in the mouse identifies POU6F2 as a potential risk of developing glaucoma

Central corneal thickness (CCT) is one of the most heritable ocular traits and it is also a phenotypic risk factor for primary open angle glaucoma (POAG). The present study uses the BXD Recombinant Inbred (RI) strains to identify novel quantitative trait loci (QTLs) modulating CCT in the mouse with the potential of identifying a molecular link between CCT and risk of developing POAG. The BXD RI strain set was used to define mammalian genomic loci modulating CCT, with a total of 818 corneas measured from 61 BXD RI strains (between 60–100 days of age). The mice were anesthetized and the eyes were positioned in front of the lens of the Phoenix Micron IV Image-Guided OCT system or the Bioptigen OCT system. CCT data for each strain was averaged and used to QTLs modulating this phenotype using the bioinformatics tools on GeneNetwork (www.genenetwork.org). The candidate genes and genomic loci identified in the mouse were then directly compared with the summary data from a human POAG genome wide association study (NEIGHBORHOOD) to determine if any genomic elements modulating mouse CCT are also risk factors for POAG.This analysis revealed one significant QTL on Chr 13 and a suggestive QTL on Chr 7. The significant locus on Chr 13 (13 to 19 Mb) was examined further to define candidate genes modulating this eye phenotype. For the Chr 13 QTL in the mouse, only one gene in the region (Pou6f2) contained nonsynonymous SNPs. Of these five nonsynonymous SNPs in Pou6f2, two resulted in changes in the amino acid proline which could result in altered secondary structure affecting protein function. The 7 Mb region under the mouse Chr 13 peak distributes over 2 chromosomes in the human: Chr 1 and Chr 7. These genomic loci were examined in the NEIGHBORHOOD database to determine if they are potential risk factors for human glaucoma identified using meta-data from human GWAS. The top 50 hits all resided within one gene (POU6F2), with the highest significance level of p = 10−6for SNP rs76319873. POU6F2 is found in retinal ganglion cells and in corneal limbal stem cells. To test the effect of POU6F2 on CCT we examined the corneas of a Pou6f2-null mice and the corneas were thinner than those of wild-type littermates. In addition, these POU6F2 RGCs die early in the DBA/2J model of glaucoma than most RGCs. Using a mouse genetic reference panel, we identified a transcription factor, Pou6f2, that modulates CCT in the mouse. POU6F2 is also found in a subset of retinal ganglion cells and these RGCs are sensitive to injury.</p