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The Citrus tristeza virus (CTV) is one of the most economically devastating citrus diseases worldwide. The spread of CTV in eastern Spain was studied by Gottwald et al. with the goal of determining the spatio-temporal mechanisms of spread. Since the subjects in this study are individual trees, it is natural to think of infections as Bernoulli trials. This approach is difficult however, due to the spatial and temporal dependence of the observations. Consequently, a system of ordinary differential equations (ODE) was used to model the probabilities of infection as well as the spatial and temporal dependence. Given the parameters in the ODE, the probabilities of infection are treated as conditionally independent. Using the conditional independence we then specify the joint likelihood function as a Poisson binomial distribution. For the purpose of model selection and hypothesis testing we, employed accumulated prediction error (APE) which has connections to both Bayesian and frequentist frameworks. We demonstrated the robustness of our method in accounting for spatio-temporal dependencies in the data by accurately predicting the spatial distribution of the disease through Join Counts.

Comparison of ribonucleic acid (RNA) molecules is important for revealing their evolutionary relationships, predicting their functions and predicting their structures. Many methods have been developed for comparing RNAs using either sequence or three-dimensional (3D) structure (backbone geometry) information. Sequences and 3D structures contain non-overlapping sets of information that both determine RNA functions. When comparing RNA 3D structures, both types of information need to be taken into account. However, few methods compare RNA structures using both sequence and 3D structure information. Recently, we have developed a new method based on elastic shape analysis (ESA) that compares RNA molecules by combining both sequence and 3D structure information. ESA treats RNA structures as 3D curves with sequence information encoded on additional coordinates 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. In this study, we implement a web server for the method, called RASS, to make it publicly available to research community. The web server is located at http://cloud.stat.fsu.edu/RASS/.

In recent years, RNAs have been found to have diverse functions beyond being a messenger in gene transcription. The functions of non-coding RNAs are determined by their structures. Structure comparison/alignment of RNAs provides an effective means to predict their functions. Despite many previous studies on RNA structure alignment, it is still a challenging problem to predict the function of RNA molecules based on their structure information. In this study, we developed a new RNA structure alignment method based on elastic shape analysis (ESA). ESA treats RNA structures as three dimensional curves and performs flexible alignment between two RNA molecules by bending and stretching one of the molecules to match the other. The amount of bending and stretching 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 can be computed and probability distributions can be constructed for a group of RNA structures. We further applied the method to predict functions of RNA molecules. Our method achieved good performance when tested on benchmark datasets.

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.