Counting, generating and sampling tree alignments

Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical sets of matches between identical pairs of trees. This ambiguity is uninformative, and detrimental to any probabilistic analysis.In this work, we consider tree alignments up to equivalence. Our first result is a precise asymptotic enumeration of tree alignments, obtained from a context-free grammar by mean of basic analytic combinatorics. Our second result focuses on alignments between two given ordered trees $S$ and $T$. By refining our grammar to align specific trees, we obtain a decomposition scheme for the space of alignments, and use it to design an efficient dynamic programming algorithm for sampling alignments under the Gibbs-Boltzmann probability distribution. This generalizes existing tree alignment algorithms, and opens the door for a probabilistic analysis of the space of suboptimal RNA secondary structures alignments.Comment: ALCOB - 3rd International Conference on Algorithms for Computational Biology - 2016, Jun 2016, Trujillo, Spain. 201

Sparse Dynamic Programming on DAGs with Small Width

The minimum path cover problem asks us to find a minimum-cardinality set of paths that cover all the nodes of a directed acyclic graph (DAG). We study the case when the size k of a minimum path cover is small, that is, when the DAG has a small width. This case is motivated by applications in pan-genomics, where the genomic variation of a population is expressed as a DAG. We observe that classical alignment algorithms exploiting sparse dynamic programming can be extended to the sequence-against-DAG case by mimicking the algorithm for sequences on each path of a minimum path cover and handling an evaluation order anomaly with reachability queries. Namely, we introduce a general framework for DAG-extensions of sparse dynamic programming. This framework produces algorithms that are slower than their counterparts on sequences only by a factor k. We illustrate this on two classical problems extended to DAGs: longest increasing subsequence and longest common subsequence. For the former, we obtain an algorithm with running time O(k vertical bar E vertical bar log vertical bar V vertical bar). This matches the optimal solution to the classical problem variant when the input sequence is modeled as a path. We obtain an analogous result for the longest common subsequence problem. We then apply this technique to the co-linear chaining problem, which is a generalization of the above two problems. The algorithm for this problem turns out to be more involved, needing further ingredients, such as an FM-index tailored for large alphabets and a two-dimensional range search tree modified to support range maximum queries. We also study a general sequence-to-DAG alignment formulation that allows affine gap costs in the sequence. The main ingredient of the proposed framework is a new algorithm for finding a minimum path cover of a DAG (V, E) in O(k vertical bar E vertical bar log vertical bar V vertical bar) time, improving all known time-bounds when k is small and the DAG is not too dense. In addition to boosting the sparse dynamic programming framework, an immediate consequence of this new minimum path cover algorithm is an improved space/time tradeoff for reachability queries in arbitrary directed graphs.Peer reviewe

Algorithms for pre-microrna classification and a GPU program for whole genome comparison

MicroRNAs (miRNAs) are non-coding RNAs with approximately 22 nucleotides that are derived from precursor molecules. These precursor molecules or pre-miRNAs often fold into stem-loop hairpin structures. However, a large number of sequences with pre-miRNA-like hairpin can be found in genomes. It is a challenge to distinguish the real pre-miRNAs from other hairpin sequences with similar stem-loops (referred to as pseudo pre-miRNAs). The first part of this dissertation presents a new method, called MirID, for identifying and classifying microRNA precursors. MirID is comprised of three steps. Initially, a combinatorial feature mining algorithm is developed to identify suitable feature sets. Then, the feature sets are used to train support vector machines to obtain classification models, based on which classifier ensemble is constructed. Finally, an AdaBoost algorithm is adopted to further enhance the accuracy of the classifier ensemble. Experimental results on a variety of species demonstrate the good performance of the proposed approach, and its superiority over existing methods. In the second part of this dissertation, A GPU (Graphics Processing Unit) program is developed for whole genome comparison. The goal for the research is to identify the commonalities and differences of two genomes from closely related organisms, via multiple sequencing alignments by using a seed and extend technique to choose reliable subsets of exact or near exact matches, which are called anchors. A rigorous method named Smith-Waterman search is applied for the anchor seeking, but takes days and months to map millions of bases for mammalian genome sequences. With GPU programming, which is designed to run in parallel hundreds of short functions called threads, up to 100X speed up is achieved over similar CPU executions

The super-n-motifs model : a novel alignment-free approach for representing and comparing RNA secondary structures

Abstract : Motivation: Comparing ribonucleic acid (RNA) secondary structures of arbitrary size uncovers structural patterns that can provide a better understanding of RNA functions. However, performing fast and accurate secondary structure comparisons is challenging when we take into account the RNA configuration (i.e. linear or circular), the presence of pseudoknot and G-quadruplex (G4) motifs and the increasing number of secondary structures generated by high-throughput probing techniques. To address this challenge, we propose the super-n-motifs model based on a latent analysis of enhanced motifs comprising not only basic motifs but also adjacency relations. The super-n-motifs model computes a vector representation of secondary structures as linear combinations of these motifs. Results: We demonstrate the accuracy of our model for comparison of secondary structures from linear and circular RNA while also considering pseudoknot and G4 motifs. We show that the supern- motifs representation effectively captures the most important structural features of secondary structures, as compared to other representations such as ordered tree, arc-annotated and string representations. Finally, we demonstrate the time efficiency of our model, which is alignment free and capable of performing large-scale comparisons of 10 000 secondary structures with an efficiency up to 4 orders of magnitude faster than existing approaches

Service robotics and machine learning for close-range remote sensing

L'abstract è presente nell'allegato / the abstract is in the attachmen

Counting, Generating, Analyzing and Sampling Tree Alignments

Pairwise ordered tree alignment are combinatorial objects that appear unimportant applications, such as RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical sets of matches between identical pairs of trees. This ambiguity is uninformative, and detrimental to any probabilistic analysis. In this work, we consider tree alignments up to equivalence. Our first result is a precise asymptotic enumeration of tree alignments, obtained from a context-free grammar by mean of basic analytic combinatorics. Our second result focuses on alignments between two given ordered trees SS and TT. By refining our grammar to align specific trees, we obtain a decomposition scheme for the space of alignments, and use it to design an efficient dynamic programming algorithm for sampling alignments under the Gibbs-Boltzmann probability distribution. This generalizes existing tree alignment algorithms, and opens the door for a probabilistic analysis of the space of suboptimal alignments