Bleach gel: a simple agarose gel for analyzing RNA quality

RNA-based applications requiring high-quality, non-degraded RNA are a foundational element of many research studies. As such, it is paramount that the integrity of experimental RNA is validated prior to cDNA synthesis or other downstream applications. In the absence of expensive equipment such as microfluidic electrophoretic devices, and as an alternative to the costly and time-consuming standard formaldehyde gel, RNA quality can be quickly analyzed by adding small amounts of commercial bleach to TAE buffer-based agarose gels prior to electrophoresis. In the presence of low concentrations of bleach, the secondary structure of RNA is denatured and potential contaminating RNases are destroyed. Because of this, the 'bleach gel' is a functional approach that addresses the need for an inexpensive and safe way to evaluate RNA integrity and will improve the ability of researchers to rapidly analyze RNA quality.     

Non-Cayley Vertex-Transitive Graphs of Order Twice the Product of Two Odd Primes

For a positive integer n, does there exist a vertex-transitive graph Γ on n vertices which is not a Cayley graph, or, equivalently, a graph Γ on n vertices such that Aut Γ is transitive on vertices but none of its subgroups are regular on vertices? Previous work (by Alspach and Parsons, Frucht, Graver and Watkins, Marusic and Scapellato, and McKay and the second author) has produced answers to this question if n is prime, or divisible by the square of some prime, or if n is the product of two distinct primes. In this paper we consider the simplest unresolved case for even integers, namely for integers of the form n = 2pq, where 2 < q < p, and p and q are primes. We give a new construction of an infinite family of vertex-transitive graphs on 2pq vertices which are not Cayley graphs in the case where p ≡ 1 (mod q). Further, if p ? 1 (mod q), p ≡ q ≡ 3(mod 4), and if every vertex-transitive graph of order pq is a Cayley graph, then it is shown that, either 2pq = 66, or every vertex-transitive graph of order 2pq admitting a transitive imprimitive group of automorphisms is a Cayley graph.     

NMR and X-ray crystallography, complementary tools in structural proteomics of small proteins

NMR spectroscopy and X-ray crystallography, the two primary experimental methods for protein structure determination at high resolution, have different advantages and disadvantages in terms of sample preparation and data collection and analysis. It is therefore of interest to assess their complementarity when applied to small proteins. Structural genomics/proteomics projects provide an ideal opportunity to make such comparisons as they generate data in a systematic manner for large enough numbers of proteins to allow firm conclusions to be drawn. Here we report a comparison for 263 unique proteins screened by both NMR spectroscopy and X-ray crystallography in our structural proteomics pipeline. Only 21 targets (8%) were deemed amenable to both methods based on an initial 2D 15N-HSQC NMR spectrum and optimized crystallization trials. However, the use of both methods in the pipeline increased the total number of targets amenable to structure determination to 107, with 43 amenable to NMR only and 43 amenable to X-ray crystallographic methods only. We did not observe a correlation between 15N-HSQC spectral quality and the success of the same protein in crystallization screens. Similar results were found for an independent set of 159 proteins as reported in the accompanying paper by Snyder et al. Thus, we conclude that both methods are highly complementary, and in order to increase the number of proteins suited for structure determination, we suggest that both methods be used in parallel in screening of all small proteins for structure determination.     

Diagonally neighbour transitive codes and frequency permutation arrays

Constant composition codes have been proposed as suitable coding schemes to solve the narrow band and impulse noise problems associated with powerline communication, while at the same time maintaining a constant power output. In particular, a certain class of constant composition codes called frequency permutation arrays have been suggested as ideal, in some sense, for these purposes. In this paper we characterise a family of neighbour transitive codes in Hamming graphs in which frequency permutation arrays play a central rode. We also classify all the permutation codes generated by groups in this family.     

Identification of Error Types in Preservice Teachers' Attempts to Create Fraction Story Problems for Specified Operations

The purpose of this research was to determine if recognizable error types exist in the work of preservice teachers required to create story problems for specific fraction operations. Students were given a particular single‐operation fraction expression and asked to do the calculation and then create a story problem that would require the use of both the expression and calculation to answer the story problem. Distinct error types, determined by mathematical and grammatical characteristics, were identified by the researchers. These error types were then used to analyze an additional set of work samples to determine frequency rates of error types. Future research will involve evaluating the efficacy of specific instructional methods with the goal of reducing the frequency of certain error types.     

Locally s-distance transitive graphs and pairwise transitive designs

The study of locally s-distance transitive graphs initiated by the authors in previous work, identified that graphs with a star quotient are of particular interest. This paper shows that the study of locally s-distance transitive graphs with a star quotient is equivalent to the study of a particular family of designs with strong symmetry properties that we call nicely affine and pairwise transitive. We show that a group acting regularly on the points of such a design must be abelian and give general construction for this case.     

Preparing K‐8 Preservice Teachers in a Content Course for Standards‐Based Mathematics Pedagogy

Many K–8 preservice teachers have not experienced learning mathematics in a standards‐based classroom. This article describes a mathematics content course designed to provide preservice teachers experiences in learning mathematics that will help build a solid foundation for a standards‐based methods course. The content course focuses on developing preservice teachers' mathematical knowledge, as well as helping them realize what it means to learn mathematics that is taught using the pedagogy in the Principles and Standards for School Mathematics ( National Council of Teachers of Mathematics, 2000 ). Furthermore, findings are presented from a study on this course that describe students' pre‐ and postcourse beliefs, attitudes, and perceptions of what it means to learn and teach mathematics. These findings provide evidence that the students in the study are beginning to understand what is meant by a standards‐based classroom. Data were collected from surveys and interviews. Quotes from the students who aspire to be elementary teachers are used throughout the article to support the points.