Multiple evolutionary rate classes in animal genome evolution

The proportion of functional sequence in the human genome is currently a subject of debate. The most widely accepted figure is that approximately 5% is under purifying selection. In Drosophila, estimates are an order of magnitude higher, though this corresponds to a similar quantity of sequence. These estimates depend on the difference between the distribution of genomewide evolutionary rates and that observed in a subset of sequences presumed to be neutrally evolving. Motivated by the widening gap between these estimates and experimental evidence of genome function, especially in mammals, we developed a sensitive technique for evaluating such distributions and found that they are much more complex than previously apparent. We found strong evidence for at least nine well-resolved evolutionary rate classes in an alignment of four Drosophila species and at least seven classes in an alignment of four mammals, including human. We also identified at least three rate classes in human ancestral repeats. By positing that the largest of these ancestral repeat classes is neutrally evolving, we estimate that the proportion of nonneutrally evolving sequence is 30% of human ancestral repeats and 45% of the aligned portion of the genome. However, we also question whether any of the classes represent neutrally evolving sequences and argue that a plausible alternative is that they reflect variable structure-function constraints operating throughout the genomes of complex organisms.

The rademacher complexity of coregularized kernel classes

In the multi-view approach to semisupervised learning, we choose one predictor from each of multiple hypothesis classes, and we co-regularize our choices by penalizing disagreement among the predictors on the unlabeled data. We examine the co-regularization method used in the co-regularized least squares (CoRLS) algorithm, in which the views are reproducing kernel Hilbert spaces (RKHS's), and the disagreement penalty is the average squared difference in predictions. The final predictor is the pointwise average of the predictors from each view. We call the set of predictors that can result from this procedure the co-regularized hypothesis class. Our main result is a tight bound on the Rademacher complexity of the co-regularized hypothesis class in terms of the kernel matrices of each RKHS. We find that the co-regularization reduces the Rademacher complexity by an amount that depends on the distance between the two views, as measured by a data dependent metric. We then use standard techniques to bound the gap between training error and test error for the CoRLS algorithm. Experimentally, we find that the amount of reduction in complexity introduced by co regularization correlates with the amount of improvement that co-regularization gives in the CoRLS algorithm.

Data modeling in elementary and middle school classes : a shared experience

This paper argues for a renewed focus on statistical reasoning in the elementary school years, with opportunities for children to engage in data modeling. Data modeling involves investigations of meaningful phenomena, deciding what is worthy of attention, and then progressing to organizing, structuring, visualizing, and representing data. Reported here are some findings from a two-part activity (Baxter Brown’s Picnic and Planning a Picnic) implemented at the end of the second year of a current three-year longitudinal study (grade levels 1-3). Planning a Picnic was also implemented in a grade 7 class to provide an opportunity for the different age groups to share their products. Addressed here are the grade 2 children’s predictions for missing data in Baxter Brown’s Picnic, the questions posed and representations created by both grade levels in Planning a Picnic, and the metarepresentational competence displayed in the grade levels’ sharing of their products for Planning a Picnic.

Using turning technologies to engage tutors and facilitate effective marking and moderation in large classes

Audience Response Systems (ARS) have been successfully used by academics to facilitate student learning and engagement, particularly in large lecture settings. However, in large core subjects a key challenge is not only to engage students, but also to engage large and diverse teaching teams in order to ensure a consistent approach to grading assessments. This paper provides an insight into the ways in which ARS can be used to encourage participation by tutors in marking and moderation meetings. It concludes that ARS can improve the consistency of grading and the quality of feedback provided to students.

Variational Bayes and the reduced dependence approximation for the autologistic model on an irregular grid with applications

Discrete Markov random field models provide a natural framework for representing images or spatial datasets. They model the spatial association present while providing a convenient Markovian dependency structure and strong edge-preservation properties. However, parameter estimation for discrete Markov random field models is difficult due to the complex form of the associated normalizing constant for the likelihood function. For large lattices, the reduced dependence approximation to the normalizing constant is based on the concept of performing computationally efficient and feasible forward recursions on smaller sublattices which are then suitably combined to estimate the constant for the whole lattice. We present an efficient computational extension of the forward recursion approach for the autologistic model to lattices that have an irregularly shaped boundary and which may contain regions with no data; these lattices are typical in applications. Consequently, we also extend the reduced dependence approximation to these scenarios enabling us to implement a practical and efficient non-simulation based approach for spatial data analysis within the variational Bayesian framework. The methodology is illustrated through application to simulated data and example images. The supplemental materials include our C++ source code for computing the approximate normalizing constant and simulation studies.

Using technology to facilitate grading consistency in large classes

University classes in marketing are often large, and therefore require teams of teachers to cover all of the necessary activities. A major problem with teaching teams is the inconsistency that results from myriad individuals offering subjective opinions. This innovation uses the latest moderation techniques along with Audience Response Technology (ART) to enhance the learning experience by providing more consistent and reliable grading in large classes. Assessment items are moderated before they are graded in meetings that employ ART. Results show the process is effective when the teaching team is very large, or there is a diverse range of experienced and inexperienced teachers. This “behind the scenes” innovation is not immediately apparent to students, but results in more consistent grades, more useful feedback for students, and more confident graders.

The Galerkin finite element approximation of the fractional cable equation

The cable equation is one of the most fundamental equations for modeling neuronal dynamics. Cable equations with a fractional order temporal derivative have been introduced to model electrotonic properties of spiny neuronal dendrites. In this paper, the fractional cable equation involving two integro-differential operators is considered. The Galerkin finite element approximations of the fractional cable equation are proposed. The main contribution of this work is outlined as follow: • A semi-discrete finite difference approximation in time is proposed. We prove that the scheme is unconditionally stable, and the numerical solution converges to the exact solution with order O(Δt). • A semi-discrete difference scheme for improving the order of convergence for solving the fractional cable equation is proposed, and the numerical solution converges to the exact solution with order O((Δt)2). • Based on the above semi-discrete difference approximations, Galerkin finite element approximations in space for a full discretization are also investigated. • Finally, some numerical results are given to demonstrate the theoretical analysis.