Mathematical Tutorials in Introductory Physics

Students in introductory calculus-based physics not only have difficulty understanding the fundamental physical concepts, they often have difficulty relating those concepts to the mathematics they have learned in math courses. This produces a barrier to their robust use of concepts in complex problem solving. As a part of the Activity-Based Physics project, we are carrying out research on these difficulties and are developing instructional materials in the tutorial framework developed at the University of Washington by Lillian C. McDermott and her collaborators. In this paper, we present a discussion of student difficulties and the development of a mathematical tutorial on the subject of pulses moving on strings.Comment: 8 pages, 2 figures, 1 table, 12 references and note

Investigating Student Understanding of Quantum Mechanics: Spontaneous Models of Conductivity

Students are taught several models of conductivity, both at the introductory and the advanced level. From early macroscopic models of current flow in circuits, through the discussion of microscopic particle descriptions of electrons flowing in an atomic lattice, to the development of microscopic non-localized band diagram descriptions in advanced physics courses, they need to be able to distinguish between commonly used, though sometimes contradictory, physical models. In investigations of student reasoning about models of conduction, we find that students often are unable to account for the existence of free electrons in a conductor and create models that lead to incorrect predictions and responses contradictory to expert descriptions of the physics. We have used these findings as a guide to creating curriculum materials that we show can be effective helping students to apply the different conduction models more effectively.Comment: 12 pages, 9 figures, 36 references and note

Understanding and Affecting Student Reasoning About Sound Waves

Student learning of sound waves can be helped through the creation of group-learning classroom materials whose development and design rely on explicit investigations into student understanding. We describe reasoning in terms of sets of resources, i.e. grouped building blocks of thinking that are commonly used in many different settings. Students in our university physics classes often used sets of resources that were different from the ones we wish them to use. By designing curriculum materials that ask students to think about the physics from a different view, we bring about improvement in student understanding of sound waves. Our curriculum modifications are specific to our own classes, but our description of student learning is more generally useful for teachers. We describe how students can use multiple sets of resources in their thinking, and raise questions that should be considered by both instructors and researchers.Comment: 23 pages, 4 figures, 3 tables, 28 references, 7 notes. Accepted for publication in the International Journal of Science Educatio

Discovery and genotyping of structural variation from long-read haploid genome sequence data

In an effort to more fully understand the full spectrum of human genetic variation, we generated deep single-molecule, real-time (SMRT) sequencing data from two haploid human genomes. By using an assembly-based approach (SMRT-SV), we systematically assessed each genome independently for structural variants (SVs) and indels resolving the sequence structure of 461,553 genetic variants from 2 bp to 28 kbp in length. We find that &gt;89% of these variants have been missed as part of analysis of the 1000 Genomes Project even after adjusting for more common variants (MAF &gt; 1%). We estimate that this theoretical human diploid differs by as much as ∼16 Mbp with respect to the human reference, with long-read sequencing data providing a fivefold increase in sensitivity for genetic variants ranging in size from 7 bp to 1 kbp compared with short-read sequence data. Although a large fraction of genetic variants were not detected by short-read approaches, once the alternate allele is sequence-resolved, we show that 61% of SVs can be genotyped in short-read sequence data sets with high accuracy. Uncoupling discovery from genotyping thus allows for the majority of this missed common variation to be genotyped in the human population. Interestingly, when we repeat SV detection on a pseudodiploid genome constructed in silico by merging the two haploids, we find that ∼59% of the heterozygous SVs are no longer detected by SMRT-SV. These results indicate that haploid resolution of long-read sequencing data will significantly increase sensitivity of SV detection.</jats:p

On positivity of Ehrhart polynomials

Ehrhart discovered that the function that counts the number of lattice points in dilations of an integral polytope is a polynomial. We call the coefficients of this polynomial Ehrhart coefficients, and say a polytope is Ehrhart positive if all Ehrhart coefficients are positive (which is not true for all integral polytopes). The main purpose of this article is to survey interesting families of polytopes that are known to be Ehrhart positive and discuss the reasons from which their Ehrhart positivity follows. We also include examples of polytopes that have negative Ehrhart coefficients and polytopes that are conjectured to be Ehrhart positive, as well as pose a few relevant questions.Comment: 40 pages, 7 figures. To appear in in Recent Trends in Algebraic Combinatorics, a volume of the Association for Women in Mathematics Series, Springer International Publishin

Winter and spring controls on the summer food web of the coastal West Antarctic Peninsula

Understanding the mechanisms by which climate variability affects multiple trophic levels in food webs is essential for determining ecosystem responses to climate change. Here we use over two decades of data collected by the Palmer Long Term Ecological Research program (PAL-LTER) to determine how large-scale climate and local physical forcing affect phytoplankton, zooplankton and an apex predator along the West Antarctic Peninsula (WAP). We show that positive anomalies in chlorophyll-a (chl-a) at Palmer Station, occurring every 4-6 years, are constrained by physical processes in the preceding winter/spring and a negative phase of the Southern Annular Mode (SAM). Favorable conditions for phytoplankton included increased winter ice extent and duration, reduced spring/summer winds, and increased water column stability via enhanced salinity-driven density gradients. Years of positive chl-a anomalies are associated with the initiation of a robust krill cohort the following summer, which is evident in Adelie penguin diets, thus demonstrating tight trophic coupling. Projected climate change in this region may have a significant, negative impact on phytoplankton biomass, krill recruitment and upper trophic level predators in this coastal Antarctic ecosystem