progressiveMauve: Multiple Genome Alignment with Gene Gain, Loss and Rearrangement

Multiple genome alignment remains a challenging problem. Effects of recombination including rearrangement, segmental duplication, gain, and loss can create a mosaic pattern of homology even among closely related organisms.We describe a new method to align two or more genomes that have undergone rearrangements due to recombination and substantial amounts of segmental gain and loss (flux). We demonstrate that the new method can accurately align regions conserved in some, but not all, of the genomes, an important case not handled by our previous work. The method uses a novel alignment objective score called a sum-of-pairs breakpoint score, which facilitates accurate detection of rearrangement breakpoints when genomes have unequal gene content. We also apply a probabilistic alignment filtering method to remove erroneous alignments of unrelated sequences, which are commonly observed in other genome alignment methods. We describe new metrics for quantifying genome alignment accuracy which measure the quality of rearrangement breakpoint predictions and indel predictions. The new genome alignment algorithm demonstrates high accuracy in situations where genomes have undergone biologically feasible amounts of genome rearrangement, segmental gain and loss. We apply the new algorithm to a set of 23 genomes from the genera Escherichia, Shigella, and Salmonella. Analysis of whole-genome multiple alignments allows us to extend the previously defined concepts of core- and pan-genomes to include not only annotated genes, but also non-coding regions with potential regulatory roles. The 23 enterobacteria have an estimated core-genome of 2.46Mbp conserved among all taxa and a pan-genome of 15.2Mbp. We document substantial population-level variability among these organisms driven by segmental gain and loss. Interestingly, much variability lies in intergenic regions, suggesting that the Enterobacteriacae may exhibit regulatory divergence.The multiple genome alignments generated by our software provide a platform for comparative genomic and population genomic studies. Free, open-source software implementing the described genome alignment approach is available from http://gel.ahabs.wisc.edu/mauve

Teaching and Learning of Calculus

This survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Since the diversity of the research in the field makes it difficult to produce an exhaustive state-of-the-art summary, the authors discuss recent developments that go beyond this survey and put forward new research questions

A model for analyzing the explanatory writing of undergraduate students when solving mathematical tasks

In light of the recent interest in mathematical competencies and the ways in which students communicate their ideas, this study aims to explore how undergraduate students communicate their ideas about mathematical tasks through written texts. Forty-three first-year undergraduate students participated in this study. They were given a graph of a function and tangent line and were asked to estimate the value of the derivative at the tangent point justifying their answer. We analyzed the justification of students to the given task by referring to the cooperative principle and to the Anthropological Theory of the Didactic. For the former, we employed the four Grice maxims: Quantity, Quality, Relation and Manner. For the latter, we employed the main components of praxeologies: the type of task, the technique needed to solve the task, the technology as knowledge needed to explain the technique, and a theory as basis to justify the technology. A model of the students’ communication about mathematical ideas emerges and is described with reference to data analysis. The model sheds light on the relationship between the discourse of a student solving a mathematical task and how she performs the related problem-solving activity

The Method of Varying Inquiry for stimulating learning

This paper introduces a model built upon the Method of Varying Inquiry, offering a didactical approach to problem posing and solving activities that stimulates inquiry-based learning in mathematics classrooms. The model combines the inquiry-based framework with the variation theory and with specific didactical and theoretical elements (the mathematics laboratory approach and the construct of virtuous cycle) to support both the design of effective environments for students’ inquiry processes and the theoretical justification of this design. By means of an example, we show how the model can provide teachers with specific criteria that could guide them both in designing tasks specifically aimed at engaging students in ongoing inquiry-based learning processes, and in planning effective ways of managing students’ interactions during these processes

Use of secondary prevention drugs for cardiovascular disease in the community in high-income, middle-income, and low-income countries (the PURE Study): a prospective epidemiological survey

Background: Although most cardiovascular disease occurs in low-income and middle-income countries, little is known about the use of effective secondary prevention medications in these communities. We aimed to assess use of proven effective secondary preventive drugs (antiplatelet drugs, beta blockers, angiotensin-converting-enzyme [ACE] inhibitors or angiotensin-receptor blockers [ARBs], and statins) in individuals with a history of coronary heart disease or stroke. Methods: In the Prospective Urban Rural Epidemiological (PURE) study, we recruited individuals aged 35-70 years from rural and urban communities in countries at various stages of economic development. We assessed rates of previous cardiovascular disease (coronary heart disease or stroke) and use of proven effective secondary preventive drugs and blood-pressure-lowering drugs with standardised questionnaires, which were completed by telephone interviews, household visits, or on Patient\u27s presentation to clinics. We report estimates of drug use at national, community, and individual levels. Findings: We enrolled 153 996 adults from 628 urban and rural communities in countries with incomes classified as high (three countries), upper-middle (seven), lower-middle (three), or low (four) between January, 2003, and December, 2009. 5650 participants had a self-reported coronary heart disease event (median 5.0 years previously [IQR 2.0-10.0]) and 2292 had stroke (4.0 years previously [2.0-8.0]). Overall, few individuals with cardiovascular disease took antiplatelet drugs (25.3%), beta blockers (17.4%), ACE inhibitors or ARBs (19.5%), or statins (14.6%). Use was highest in high-income countries (antiplatelet drugs 62.0%, beta blockers 40.0%, ACE inhibitors or ARBs 49.8%, and statins 66.5%), lowest in low-income countries (8.8%, 9.7%, 5.2%, and 3.3%, respectively), and decreased in line with reduction of country economic status (p(trend)\u3c0.0001 for every drug type). Fewest Patients received no drugs in high-income countries (11.2%), compared with 45.1% in upper middle-income countries, 69.3% in lower middle-income countries, and 80.2% in low-income countries. Drug use was higher in urban than rural areas (antiplatelet drugs 28.7% urban vs 21.3% rural, beta blockers 23.5% vs 15.6%, ACE inhibitors or ARBs 22.8% vs 15.5%, and statins 19.9% vs 11.6%, all p\u3c0.0001), with greatest variation in poorest countries (p(interaction)\u3c0.0001 for urban vs rural differences by country economic status). Country-level factors (eg, economic status) affected rates of drug use more than did individual-level factors (eg, age, sex, education, smoking status, body-mass index, and hypertension and diabetes statuses).Interpretation Because use of secondary prevention medications is low worldwide-especially in low-income countries and rural areas-systematic approaches are needed to improve the long-term use of basic, inexpensive, and effective drugs