Time changes of symmetric diffusions and Feller measures

We extend the classical Douglas integral, which expresses the Dirichlet integral of a harmonic function on the unit disk in terms of its value on boundary, to the case of conservative symmetric diffusion in terms of Feller measure, by using the approach of time change of Markov processes.Comment: Published at http://dx.doi.org/10.1214/009117904000000649 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Rejoinder: Conditional Growth Charts

Rejoinder: Conditional Growth Charts [math.ST/0702634]Comment: Published at http://dx.doi.org/10.1214/009053606000000678 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

On Recommendation of Learning Objects using Felder-Silverman Learning Style Model

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The e-learning recommender system in learning institutions is increasingly becoming the preferred mode of delivery, as it enables learning anytime, anywhere. However, delivering personalised course learning objects based on learner preferences is still a challenge. Current mainstream recommendation algorithms, such as the Collaborative Filtering (CF) and Content-Based Filtering (CBF), deal with only two types of entities, namely users and items with their ratings. However, these methods do not pay attention to student preferences, such as learning styles, which are especially important for the accuracy of course learning objects prediction or recommendation. Moreover, several recommendation techniques experience cold-start and rating sparsity problems. To address the challenge of improving the quality of recommender systems, in this paper a novel recommender algorithm for machine learning is proposed, which combines students actual rating with their learning styles to recommend Top-N course learning objects (LOs). Various recommendation techniques are considered in an experimental study investigating the best technique to use in predicting student ratings for e-learning recommender systems. We use the Felder-Silverman Learning Styles Model (FSLSM) to represent both the student learning styles and the learning object profiles. The predicted rating has been compared with the actual student rating. This approach has been experimented on 80 students for an online course created in the MOODLE Learning Management System, while the evaluation of the experiments has been performed with the Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). The results of the experiment verify that the proposed approach provides a higher prediction rating and significantly increases the accuracy of the recommendation

A dual catalytic strategy for carbon-phosphorus cross-coupling via gold and photoredox catalysis.

A new method for the P-arylation of aryldiazonium salts with H-phosphonates via dual gold and photoredox catalysis is described. The reaction proceeds smoothly at room temperature in the absence of base and/or additives, and offers an efficient approach to arylphosphonates. The reaction is proposed to proceed through a photoredox-promoted generation of an electrophilic arylgold(III) intermediate that undergoes coupling with the H-phosphonate nucleophile