In search of lost introns

Many fundamental questions concerning the emergence and subsequent evolution of eukaryotic exon-intron organization are still unsettled. Genome-scale comparative studies, which can shed light on crucial aspects of eukaryotic evolution, require adequate computational tools. We describe novel computational methods for studying spliceosomal intron evolution. Our goal is to give a reliable characterization of the dynamics of intron evolution. Our algorithmic innovations address the identification of orthologous introns, and the likelihood-based analysis of intron data. We discuss a compression method for the evaluation of the likelihood function, which is noteworthy for phylogenetic likelihood problems in general. We prove that after $O(nL)$ preprocessing time, subsequent evaluations take $O(nL/\log L)$ time almost surely in the Yule-Harding random model of $n$-taxon phylogenies, where $L$ is the input sequence length. We illustrate the practicality of our methods by compiling and analyzing a data set involving 18 eukaryotes, more than in any other study to date. The study yields the surprising result that ancestral eukaryotes were fairly intron-rich. For example, the bilaterian ancestor is estimated to have had more than 90% as many introns as vertebrates do now

M-Best-Diverse Labelings for Submodular Energies and Beyond

Abstract We consider the problem of finding M best diverse solutions of energy minimization problems for graphical models. Contrary to the sequential method of Batra et al., which greedily finds one solution after another, we infer all M solutions jointly. It was shown recently that such jointly inferred labelings not only have smaller total energy but also qualitatively outperform the sequentially obtained ones. The only obstacle for using this new technique is the complexity of the corresponding inference problem, since it is considerably slower algorithm than the method of Batra et al. In this work we show that the joint inference of M best diverse solutions can be formulated as a submodular energy minimization if the original MAP-inference problem is submodular, hence fast inference techniques can be used. In addition to the theoretical results we provide practical algorithms that outperform the current state-of-the-art and can be used in both submodular and non-submodular case

Shapecollage: Occlusion-Aware, Example-Based Shape Interpretation

This paper presents an example-based method to interpret a 3D shape from a single image depicting that shape. A major difficulty in applying an example-based approach to shape interpretation is the combinatorial explosion of shape possibilities that occur at occluding contours. Our key technical contribution is a new shape patch representation and corresponding pairwise compatibility terms that allow for flexible matching of overlapping patches, avoiding the combinatorial explosion by allowing patches to explain only the parts of the image they best fit. We infer the best set of localized shape patches over a graph of keypoints at multiple scales to produce a discontinuous shape representation we term a shape collage. To reconstruct a smooth result, we fit a surface to the collage using the predicted confidence of each shape patch. We demonstrate the method on shapes depicted in line drawing, diffuse and glossy shading, and textured styles.National Science Foundation (U.S.) (Grant 1111415)United States. Office of Naval Research (Grant N00014-09-1-1051)National Institutes of Health (U.S.) (Grant R01-EY019262