A practical fpt algorithm for Flow Decomposition and transcript assembly

The Flow Decomposition problem, which asks for the smallest set of weighted paths that "covers" a flow on a DAG, has recently been used as an important computational step in transcript assembly. We prove the problem is in FPT when parameterized by the number of paths by giving a practical linear fpt algorithm. Further, we implement and engineer a Flow Decomposition solver based on this algorithm, and evaluate its performance on RNA-sequence data. Crucially, our solver finds exact solutions while achieving runtimes competitive with a state-of-the-art heuristic. Finally, we contextualize our design choices with two hardness results related to preprocessing and weight recovery. Specifically, $k$-Flow Decomposition does not admit polynomial kernels under standard complexity assumptions, and the related problem of assigning (known) weights to a given set of paths is NP-hard.Comment: Introduces software package Toboggan: Version 1.0. http://dx.doi.org/10.5281/zenodo.82163

Efficient Minimum Flow Decomposition via Integer Linear Programming

Extended version of RECOMB 2022 paperMinimum flow decomposition (MFD) is an NP-hard problem asking to decompose a network flow into a minimum set of paths (together with associated weights). Variants of it are powerful models in multiassembly problems in Bioinformatics, such as RNA assembly. Owing to its hardness, practical multiassembly tools either use heuristics or solve simpler, polynomial time-solvable versions of the problem, which may yield solutions that are not minimal or do not perfectly decompose the flow. Here, we provide the first fast and exact solver for MFD on acyclic flow networks, based on Integer Linear Programming (ILP). Key to our approach is an encoding of all the exponentially many solution paths using only a quadratic number of variables. We also extend our ILP formulation to many practical variants, such as incorporating longer or paired-end reads, or minimizing flow errors. On both simulated and real-flow splicing graphs, our approach solves any instance inPeer reviewe

Improving RNA Assembly via Safety and Completeness in Flow Decompositions

Extended version of RECOMB 2022 paperDecomposing a network flow into weighted paths is a problem with numerous applications, ranging from networking, transportation planning, to bioinformatics. In some applications we look for a decomposition that is optimal with respect to some property, such as the number of paths used, robustness to edge deletion, or length of the longest path. However, in many bioinformatic applications, we seek a specific decomposition where the paths correspond to some underlying data that generated the flow. In these cases, no optimization criteria guarantee the identification of the correct decomposition. Therefore, we propose to instead report the safe paths, which are subpaths of at least one path in every flow decomposition. In this work, we give the first local characterization of safe paths for flow decompositions in directed acyclic graphs, leading to a practical algorithm for finding the complete set of safe paths. In addition, we evaluate our algorithm on RNA transcript data sets against a trivial safe algorithm (extended unitigs), the recently proposed safe paths for path covers (TCBB 2021) and the popular heuristic greedy-width. On the one hand, we found that besides maintaining perfect precision, our safe and complete algorithm reports a significantly higher coverage (≈50 compared with the other safe algorithms. On the other hand, the greedy-width algorithm although reporting a better coverage, it also reports a significantly lower precision on complex graphs (for genes expressing a large number of transcripts). Overall, our safe and complete algorithm outperforms (by ≈20 greedy-width on a unified metric (F-score) considering both coverage and precision when the evaluated data set has a significant number of complex graphs. Moreover, it also has a superior time (4−5×) and space performance (1.2−2.2×), resulting in a better and more practical approach for bioinformatic applications of flow decomposition.Peer reviewe

Width Helps and Hinders Splitting Flows

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Width Helps and Hinders Splitting Flows

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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

Development of efficient De Bruijn graph-based algorithms for genome assembly

Programa Oficial de Doutoramento en Computación. 5009V01[Abstract] During the last two decades, thanks to the development of new sequencing techniques, the study of the genome has become very popular in order to discover the genetic variation present in both humans and other organisms. The predominant mode of genome analysis is through the assembly of reads in one or multiple chains for as long as possible. The most traditional way of assembly is the one that involves reads from a single genome. In this field, in the last decade, third-generation readings have emerged with new challenges for which there are no efficient solutions. The first contribution that has been made in this thesis is Compact-Flye, a tool for the efficient assembly of third-generation reads on the Flye algorithm. This tool is based on the ingenious use of compact data structures to improve typical assembly steps such as counting and indexing k-mers. Apart from the assembly of a genome, there are techniques that seek to assemble all the genomes contained in a given sample. This assembly is known as multiple sequence assembly or haplotype reconstruction, a subject also treated in this thesis. Our first approach to solving this has been viaDBG, which is the first solution based on de Bruijn graphs that offers results comparable to current techniques in viral genome assembly while maintaining the efficiency of these graphs. Our second contribution is ViQUF, which is a natural improvement on its predecessor. ViQUF completely changes the algorithm of viaDBG but continues to be based on the same structures, although with some variations that allow it not only to improve results in terms of time and quality, but also to provide additionalinformation such as an estimate of the relative presence of each species in the sample.[Resumen] Durante las últimas dos décadas, gracias al desarrollo de nuevas técnias secuenciación, el estudio del genoma ha ganado mucha popularidad de cara a conocer la variación genética presente tanto seres humanos como otros organismos. El modo predominante de análisis del genoma es a través del ensamblaje de lecturas en una o múltiples cadenas lo más largas posibles. La manera más tradicional de ensamblaje es el que implica lecturas provenientes de un solo genoma. En este campo, en la última década han surgido las lecturas de tercera generación con nuevos retos para los que no existen soluciones eficientes. La primera aportación que se ha realizado en esta tesis es Compact-Flye una herramienta para el ensamblaje eficiente de lecturas de tercera generación sobre el algoritmo Flye. Esta herramienta está basada en el uso igenioso de estructuras compactas de datos para mejorar etapas típicas del ensamblaje como el conteo e indexación de k-mers. Al margen del ensamblaje de un genoma existen técnicas que buscan ensamblar todos los genomas contenidos en una muestra determinada. Este ensamblaje es conocido como ensamblaje múltiple de secuencias o reconstrucción de haplotipos, tema también tratado en esta tesis. Nuestra primera aproximación para la resolución de este ha sido viaDBG, que es la primera solución basada en grafos de de Bruijn que ofrece resultados comparables a las técnicas vigentes en ensamblaje de genomas víricos, mientras que mantiene la eficiencia de estos grafos. Nuestra segunda aportación es ViQUF, que es una mejora natural de su predecesor. ViQUF cambia totalmente la algoritmia de viaDBG, pero sigue cimentándose en las mismas estructuras aunque con alguna variación que le permite no solo mejorar resultados en tiempo y calidad. Sino que además le permite aportar más información como estimaciones relativa de cada especie en la muestra.[Resumo] Durante as dúas últimas décadas, grazas ao desenvolvemento de novas técnicas de secuenciación, o estudo do xenoma fíxose moi popular para descubrir a variación xenética presente tanto nos humanos como noutros organismos. O modo predominante de análise do xenoma é a través da ensamblaxe de lecturas nunha ou varias cadeas o maior tempo posible. A forma máis tradicional de ensamblar é a que implica lecturas dun só xenoma. Neste campo, na última década xurdiron lecturas de terceira xeración con novos retos para os que non existen solucións eficientes. A primeira contribución que se fixo nesta tese é Compact-Flye, unha ferramenta para a montaxe eficiente de lecturas de terceira xeración sobre o algoritmo Flye. Esta ferramenta baséase no uso intelixente de estruturas de datos compactas para mellorar os pasos típicos de montaxe, como contar e indexar k-mers. Ademais da montaxe dun xenoma, existen técnicas que buscan ensamblar todos os xenomas contidos nunha determinada mostra. Este conxunto coñécese como conxunto de secuencias múltiples ou reconstrución de haplotipos, tema tamén tratado nesta tesis. O noso primeiro enfoque para resolver isto foi viaDBG, que é a primeira solución baseada en gráficos de Bruijn que ofrece resultados comparables ás técnicas actuais de ensamblaxe de xenoma viral, mantendo a eficiencia destes gráficos. A nosa segunda incorporación é ViQUF, que é unha mellora natural con respecto ao seu predecesor. ViQUF cambia completamente o algoritmo de viaDBG pero segue baseándose nas mesmas estruturas, aínda que con algunha variación que lle permite non só mellorar os resultados en tempo e calidade. Pero tamén permite achegar máis información como estimacións relativas de cada especie da mostra.Xunta de Galicia; ED431G 2019/01Xunta de Galicia; ED431C 2021/53Xunta de Galicia; IG240.2020.1.185Xunta de Galicia; IN852A 2018/14Quiero agradecer al Centro de Investigación de Galicia “CITIC”, financiado por la Xunta de Galicia y la Unión Europea (European Regional Development Fund- Galicia 2014-2020 Program), con la beca ED431G 2019/01. También agradecer a la Xunta de Galicia/FEDER-UE que ha financiado esta tesis a través de las becas [ED431C 2021/53; IG240.2020.1.185; IN852A 2018/14]; al Ministerio de Ciencia e Innovación con las becas [TIN2016- 78011-C4-1-R; FPU17/02742; PID2019-105221RB-C41; PID2020-114635RB-I00]; y a la academia de Finlandia [grants 308030 and 323233 (LS)]

Computational Methods for Sequencing and Analysis of Heterogeneous RNA Populations

Next-generation sequencing (NGS) and mass spectrometry technologies bring unprecedented throughput, scalability and speed, facilitating the studies of biological systems. These technologies allow to sequence and analyze heterogeneous RNA populations rather than single sequences. In particular, they provide the opportunity to implement massive viral surveillance and transcriptome quantification. However, in order to fully exploit the capabilities of NGS technology we need to develop computational methods able to analyze billions of reads for assembly and characterization of sampled RNA populations. In this work we present novel computational methods for cost- and time-effective analysis of sequencing data from viral and RNA samples. In particular, we describe: i) computational methods for transcriptome reconstruction and quantification; ii) method for mass spectrometry data analysis; iii) combinatorial pooling method; iv) computational methods for analysis of intra-host viral populations

Improving Comparative Genomic Studies:Definitions and Algorithms for Syntenic Blocks

Comparative genomics aims to understand the structure of genomes and the function of various genomic fragments, by transferring knowledge gained from well studied genomes, to the new object of study. Rapid and inexpensive high-throughput sequencing is making available more and more complete genome sequences. Despite the significant scientific advance, we still lack good models for the evolution of the genomic architecture, therefore analyzing these genomes presents formidable challenges. Early approaches used pairwise comparisons, but today researchers are attempting to leverage the larger potential of multiway comparisons. Current approaches are based on the identification of so called syntenic blocks: blocks of sequence that exhibit conserved features across the genomes under study. Syntenic blocks are in many ways analogous to genesâ -in many cases, the markers are used to constructing them are genes. Like genes they can exist in multiple copies, in which case we could define analogs of orthology and paralogy. However, whereas genes are studied at the sequence level, syntenic blocks are too large for that level of detail - it is their structure and function as a unit that makes them valuable for genome level comparative studies. Syntenic blocks are required for complex computations to scale to the billions of nucleotides present in many genomes; they enable comparisons across broad ranges of genomes because they filter outmuch of the individual variability; they highlight candidate regions for in-depth studies; and they facilitate whole-genome comparisons through visualization tools. The identification of such blocks is the first step in comparative studies, yet its effect on final results has not been well studied, nor has any formalization of syntenic blocks been proposed. Tools for the identification of syntenic blocks yield quite different results, thereby preventing a systematic assessment of the next steps in an analysis. Current tools do not include measurable quality objectives and thus cannot be benchmarked against themselves. Comparisons among tools have also been neglected - what few results are given use superficial measures unrelated to quality or consistency. In this thesis we address two major challenges, and present: (i) a theoretical model as well as an experimental basis for comparing syntenic blocks and thus also for improving the design of tools for the identification of syntenic blocks; (ii) a prototype model that serves as a basis for implementing effective synteny mining tools. We offer an overview of the milestones present in literature, on the development of concepts and tool related to synteny; we illustrate the application of the model and the measures by applying them to syntenic blocks produced by different contemporary tools on publicly available data sets. We have taken the first step towards a formal approach to the construction of syntenic blocks by developing a simple quality criterion based on sound evolutionary principles. Our experiments demonstrate widely divergent results among these tools, throwing into question the robustness of the basic approach in comparative genomics. Our findings highlight the need for a well founded, systematic approach to the decomposition of genomes into syntenic blocks and motivate the second part of the work - starting from the proposed model, we extend the concept with data dependent features and constraints, in order to test the concept on cases of interest

Landing site reachability and decision making for UAS forced landings

After a huge amount of success within the military, the benefits of the use of unmanned aerial systems over manned aircraft is obvious. They are becoming cheaper and their functions advancing to such a point that there is now a large drive for their use by civilian operators. However there are a number of significant challenges that are slowing their inevitable integration into the national airspace systems of countries. A large array of emergency situations will need to be dealt with autonomously by contingency management systems to prevent potentially deadly incidences. One such emergency situation that will need autonomous intervention, is the total loss of thrust from engine failure. The complex multi faceted task of landing the stricken aircraft at a potentially unprepared site is called a forced landing. This thesis presents methods to address a number of critical parts of a forced landing system for use by an unmanned aerial system. In order for an emergency landing site to be considered, it needs to be within glide range. In order to find a landing site s reachability from the point of engine failure the aircraft s glide performance and a glide path must be known. A method by which to calculate the glide performance, both from aircraft parameters or experiments is shown. These are based on a number of steady state assumptions to make them generic and quick to compute. Despite the assumptions, these are shown to have reasonable accuracy. A minimum height loss path to the landing site is defined, which takes account of a steady uniform wind. While this path is not the path to be flown it enables a measure of how reachable a landing site is, as any extra height the aircraft has once it gets to the site makes a site more reachable. It is shown that this method is fast enough to be run online and is generic enough for use on a range of aircraft. Based on identified factors that make a landing site more suitable, a multi criteria decision making Bayesian network is developed to decide upon which site a unmanned aircraft should land in. It can handle uncertainty and non-complete information while guaranteeing a fast reasonable decision, which is critical in this time sensitive situation. A high fidelity simulation environment and flight test platform are developed in order to test the performance of the developed algorithms. The test environments developed enable rapid prototyping of algorithms not just within the scope of this thesis, but on a range of vehicle types. In simulation the minimum height loss paths show good accuracy, for two completely different types of aircraft. The decision making algorithms show that they are capable of being ran online in a flight test. They make a reasonable decision and are capable of quickly reacting to changing conditions, enabling redirection to a more suitable landing site