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The functions of RNAs, like proteins, are determined by their structures, which, in turn, are determined by their sequences. Comparison/alignment of RNA molecules provides an effective means to predict their functions and understand their evolutionary relationships. For RNA sequence alignment, most methods developed for protein and DNA sequence alignment can be directly applied. RNA 3-dimensional structure alignment, on the other hand, tends to be more difficult than protein structure alignment due to the lack of regular secondary structures as observed in proteins. Most of the existing RNA 3D structure alignment methods use only the backbone geometry and ignore the sequence information. Using both the sequence and backbone geometry information in RNA alignment may not only produce more accurate classification, but also deepen our understanding of the sequence–structure–function relationship of RNA molecules. In this study, we developed a new RNA alignment method based on elastic shape analysis (ESA). ESA treats RNA structures as three dimensional curves with sequence information encoded on additional dimensions so that the alignment can be performed in the joint sequence–structure space. The similarity between two RNA molecules is quantified by a formal distance, geodesic distance. Based on ESA, a rigorous mathematical framework can be built for RNA structure comparison. Means and covariances of full structures can be defined and computed, and probability distributions on spaces of such structures can be constructed for a group of RNAs. Our method was further applied to predict functions of RNA molecules and showed superior performance compared with previous methods when tested on benchmark datasets. The programs are available at http://stat.fsu.edu/ ∼jinfeng/ESA.html.

Within this paper, we provide an expert opinion on five evidence-based psychological strategies that could help endurance participants overcome slowing down and stopping during performance: goal setting, motivational self-talk, relaxation, distraction, and pacing. We argue that these strategies are well-suited for delivery as brief-contact, educational interventions that could be accessible to large numbers of participants who do not have access to a sport and exercise psychologist. These interventions could be delivered using websites, online videos, workshops, or magazine articles. We propose a novel use for implementation intentions (i.e. if-then planning) to develop endurance participants’ conditional knowledge of when to use specific strategies. In addition, although research evidence suggests that these psychological strategies may be efficacious for overcoming thoughts of slowing down or stopping, there are important limitations in the research evidence. In particular, there is a dearth of ecologically valid, field-based effectiveness studies. Finally, we consider situations where attempts to resist slowing down or stopping during endurance activity may not be advisable. Scenarios include when there is an increased likelihood of injury, or when environmental conditions increase the risk of life-threatening events.

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