Overlap Graph Research Articles

HyLight: Strain aware assembly of low coverage metagenomes

Different strains of identical species can vary substantially in terms of their spectrum of biomedically relevant phenotypes. Reconstructing the genomes of microbial communities at the level of their strains poses significant challenges, because sequencing errors can obscure strain-specific variants. Next-generation sequencing (NGS) reads are too short to resolve complex genomic regions. Third-generation sequencing (TGS) reads, although longer, are prone to higher error rates or substantially more expensive. Limiting TGS coverage to reduce costs compromises the accuracy of the assemblies. This explains why prior approaches agree on losses in strain awareness, accuracy, tendentially excessive costs, or combinations thereof. We introduce HyLight, a metagenome assembly approach that addresses these challenges by implementing the complementary strengths of TGS and NGS data. HyLight employs strain-resolved overlap graphs (OG) to accurately reconstruct individual strains within microbial communities. Our experiments demonstrate that HyLight produces strain-aware and contiguous assemblies at minimal error content, while significantly reducing costs because utilizing low-coverage TGS data. HyLight achieves an average improvement of 19.05% in preserving strain identity and demonstrates near-complete strain awareness across diverse datasets. In summary, HyLight offers considerable advances in metagenome assembly, insofar as it delivers significantly enhanced strain awareness, contiguity, and accuracy without the typical compromises observed in existing approaches.

Efficient Genome Assembly Studies Using Overlap and Hamiltonian Graphs

These DNA sequencing is the intricate process of deciphering the specific arrangement of nitrogenous bases, also known as nucleotides, within a DNA molecule. Each organism possesses a unique nucleotide sequence that dictates its genetic blueprint, or genome, influencing both physical traits (phenotypes) and hereditary characteristics (genotypes) at the cellular level. In the realm of mathematics, graph theory delves into the study of mathematical constructs called graphs, composed of vertices (nodes) interconnected by either directed or undirected edges. Determining the precise order in which these nucleotides are linked empowers scientists and researchers to compare DNA across organisms, shedding light on their evolutionary relationships. This research delves into the pivotal role of graph theory in genome sequencing, exploring the diverse types of graphs utilized in this process. We propose innovative methods for employing graph theory in DNA sequencing and investigate the application of graphs such as overlap graphs and Hamiltonian graphs in genome sequencing, along with their associated advantages and limitations.

Person Re-Identification Using Local Relation-Aware Graph Convolutional Network.

Local feature extractions have been verified to be effective for person re-identification (re-ID) in recent literature. However, existing methods usually rely on extracting local features from single part of a pedestrian while neglecting the relationship of local features among different pedestrian images. As a result, local features contain limited information from one pedestrian image, and cannot benefit from other pedestrian images. In this paper, we propose a novel approach named Local Relation-Aware Graph Convolutional Network (LRGCN) to learn the relationship of local features among different pedestrian images. In order to completely describe the relationship of local features among different pedestrian images, we propose overlap graph and similarity graph. The overlap graph formulates the edge weight as the overlap node number in the node's neighborhoods so as to learn robust local features, and the similarity graph defines the edge weight as the similarity between the nodes to learn discriminative local features. To propagate the information for different kinds of nodes effectively, we propose the Structural Graph Convolution (SGConv) operation. Different from traditional graph convolution operations where all nodes share the same parameter matrix, SGConv learns different parameter matrices for the node itself and its neighbor nodes to improve the expressive power. We conduct comprehensive experiments to verify our method on four large-scale person re-ID databases, and the overall results show LRGCN exceeds the state-of-the-art methods.

Quantum algorithm for de novo DNA sequence assembly based on quantum walks on graphs

De novo DNA sequence assembly is based on finding paths in overlap graphs, which is a NP-hard problem. We developed a quantum algorithm for de novo assembly based on quantum walks in graphs. The overlap graph is partitioned repeatedly to smaller graphs that form a hierarchical structure. We use quantum walks to find paths in low rank graphs and a quantum algorithm that finds Hamiltonian paths in high hierarchical rank. We tested the partitioning quantum algorithm, as well as the quantum algorithm that finds Hamiltonian paths in high hierarchical rank and confirmed its correct operation using Qiskit. We developed a custom simulation for quantum walks to search for paths in low rank graphs. The approach described in this paper may serve as a basis for the development of efficient quantum algorithms that solve the de novo DNA assembly problem.

ClassGraph: Improving Metagenomic Read Classification with Overlap Graphs.

Current technologies allow the sequencing of microbial communities directly from the environment without prior culturing. One of the major problems when analyzing a microbial sample is to taxonomically annotate its reads to identify the species it contains. Most methods that are currently available focus on the classification of reads using a set of reference genomes and their k-mers. While in terms of precision these methods have reached percentages of correctness close to perfection, in terms of sensitivity (the actual number of classified reads), the performance is often poor. One reason is that the reads in a sample can be very different from the corresponding reference genomes; for example, viral genomes are usually highly mutated. To address this issue, in this article, we propose ClassGraph, a new taxonomic classification method that makes use of the read overlap graph and applies a label propagation algorithm to refine the results of existing tools. We evaluated its performance on simulated and real datasets with several taxonomic classification tools, and the results showed an improved sensitivity and F-measure, while maintaining high precision. ClassGraph is capable of improving the classification accuracy, especially in difficult cases such as virus and real datasets, where traditional tools can classify <40% of reads.

Identifying Taxonomic Units in Metagenomic DNA Streams on Mobile Devices.

With the emergence of portable DNA sequencers, such as Oxford Nanopore Technology MinION, metagenomic DNA sequencing can be performed in real-time and directly in the field. However, because metagenomic DNA analysis tasks, e.g., classification, taxonomic units assignment, etc., are compute and memory intensive, and the available methods are designed for batch processing, the current metagenomic tools are not well suited for mobile devices. In this work, we propose a new memory-efficient approach to identify Operational Taxonomic Units (OTUs) in metagenomic DNA streams on mobile devices. Our method is based on finding connected components in overlap graphs constructed over a real-time stream of long DNA reads as produced by the MinION platform. We propose an efficient algorithm to maintain connected components when an overlap graph is streamed and show how redundant information can be removed from the stream by transitive closures. We also propose how our algorithms can be integrated into a larger DNA analysis pipeline tailored for mobile computing. Through experiments on simulated and real-world metagenomic data, executed on the actual mobile device, we demonstrate that our resulting solution is able to recover OTUs with high precision. Our experiments also demonstrate the compounding benefits of introducing feedback loops in the DNA analysis pipeline.

Coverage-preserving sparsification of overlap graphs for long-read assembly.

Source code is available through GitHub (https://github.com/at-cg/ContainX) and Zenodo with doi: 10.5281/zenodo.7687543.

Integrating Heterogeneous Graphs Using Graph Transformer Encoder for Solving Math Word Problems

This paper introduces a novel method that integrates structural information with training deep neural models to solve math word problems. Prior works adopt the graph structure to represent rich information residing in the input sentences. However, they lack the consideration of different relation types between other parts of the sentences. To provide various types of structural information in a uniform way, we propose a graph transformer encoder to integrate heterogeneous graphs of various input representations. We developed two types of graph structures. First, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Dependency Graph</i> maintains long-distance lexical dependency between words and quantities. Second, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Question Overlap Graph</i> captures the gist within the problem body. The two graphs are encoded as a single graph for graph transformation. Experimental results show that our method produces competitive results compared to the baselines. Our model outperforms state-of-the-art models in Equation and Answer accuracy near three percent in SVAMP benchmark. Moreover, we discuss that integrating different types of textual characteristics may improve the quality of mathematical logic inference from natural language sentences.

On dominating set of some subclasses of string graphs

We provide constant factor approximation algorithms for the Minimum Dominating Set (MDS) problem on several subclasses of string graphs i.e. intersection graphs of simple curves on the plane. For k≥0, unitBk-VPG graphs are intersection graphs of simple rectilinear curves having at most k cusps (bends) and each segment of the curve being unit length. We give an 18-approximation algorithm for the MDS problem on unit B0-VPG graphs. This partially addresses a question of Katz et al. (2005) [24]. We also give an O(k4)-approximation algorithm for the MDS problem on unit Bk-VPG graphs. We show that there is an 8-approximation algorithm for the MDS problem on vertically-stabbedL-graphs. We also give a 656-approximation algorithm for the MDS problem on stabbed rectangle overlap graphs. This is the first constant-factor approximation algorithm for the MDS problem on stabbed rectangle overlap graphs and extends a result of Bandyapadhyay et al. (2019) [31]. We prove some hardness results to complement the above results.

LazyB: fast and cheap genome assembly

BackgroundAdvances in genome sequencing over the last years have lead to a fundamental paradigm shift in the field. With steadily decreasing sequencing costs, genome projects are no longer limited by the cost of raw sequencing data, but rather by computational problems associated with genome assembly. There is an urgent demand for more efficient and and more accurate methods is particular with regard to the highly complex and often very large genomes of animals and plants. Most recently, “hybrid” methods that integrate short and long read data have been devised to address this need.ResultsLazyB is such a hybrid genome assembler. It has been designed specificially with an emphasis on utilizing low-coverage short and long reads. LazyB starts from a bipartite overlap graph between long reads and restrictively filtered short-read unitigs. This graph is translated into a long-read overlap graph G. Instead of the more conventional approach of removing tips, bubbles, and other local features, LazyB stepwisely extracts subgraphs whose global properties approach a disjoint union of paths. First, a consistently oriented subgraph is extracted, which in a second step is reduced to a directed acyclic graph. In the next step, properties of proper interval graphs are used to extract contigs as maximum weight paths. These path are translated into genomic sequences only in the final step. A prototype implementation of LazyB, entirely written in python, not only yields significantly more accurate assemblies of the yeast and fruit fly genomes compared to state-of-the-art pipelines but also requires much less computational effort.ConclusionsLazyB is new low-cost genome assembler that copes well with large genomes and low coverage. It is based on a novel approach for reducing the overlap graph to a collection of paths, thus opening new avenues for future improvements.AvailabilityThe LazyB prototype is available at https://github.com/TGatter/LazyB.

Generalised online colouring problems in overlap graphs

In this paper we consider an online version of different colouring problems in overlap graphs, motivated by some stacking problems. The instance is a system of time intervals presented in non-decreasing order of the left endpoint. We consider the usual colouring problem as well as b-bounded colouring (colour class have a maximum capacity b) and the same problems in the complement graph. We also consider the case where at most b intervals of the same colour can intersect. For all these versions we obtain a logarithmic competitive ratio w.r.t. the maximum ratio of interval lengths while the best known ratio for the usual colouring was linear. To our knowledge it is the first time the other variants are considered in online overlap graphs. Moreover, in the offline case, a pre-processing allows us to deduce a logarithmic approximation ratio w.r.t. the maximum number of pairwise disjoint intervals in the system. Our method is based on a partition of the overlap graph into permutation graphs, leading to a competitive-preserving reduction of the problem in overlap graphs to the same problem in permutation graphs. We think that this new partition problem by itself is of interest for future work.

Genome-scale de novo assembly using ALGA.

MotivationThere are very few methods for de novo genome assembly based on the overlap graph approach. It is considered as giving more exact results than the so-called de Bruijn graph approach but in much greater time and of much higher memory usage. It is not uncommon that assembly methods involving the overlap graph model are not able to successfully compute greater datasets, mainly due to memory limitation of a computer. This was the reason for developing in last decades mainly de Bruijn-based assembly methods, fast and fairly accurate. However, the latter methods can fail for longer or more repetitive genomes, as they decompose reads to shorter fragments and lose a part of information. An efficient assembler for processing big datasets and using the overlap graph model is still looked out.ResultsWe propose a new genome-scale de novo assembler based on the overlap graph approach, designed for short-read sequencing data. The method, ALGA, incorporates several new ideas resulting in more exact contigs produced in short time. Among these ideas, we have creation of a sparse but quite informative graph, reduction of the graph including a procedure referring to the problem of minimum spanning tree of a local subgraph, and graph traversal connected with simultaneous analysis of contigs stored so far. What is rare in genome assembly, the algorithm is almost parameter-free, with only one optional parameter to be set by a user. ALGA was compared with nine state-of-the-art assemblers in tests on genome-scale sequencing data obtained from real experiments on six organisms, differing in size, coverage, GC content and repetition rate. ALGA produced best results in the sense of overall quality of genome reconstruction, understood as a good balance between genome coverage, accuracy and length of resulting sequences. The algorithm is one of tools involved in processing data in currently realized national project Genomic Map of Poland.Availability and implementationALGA is available at http://alga.put.poznan.pl.Supplementary information Supplementary data are available at Bioinformatics online.

Macro and mesofauna soil food webs in two temperate grasslands: responses to forestation with Eucalyptus

We studied the effects of land use change from grassland to Eucalyptus spp. plantation on macro and mesofauna soil food webs in two sites in the Rolling Pampas. We expected to find differences in the parameters that characterize the structure of soil food webs, as the implantation of Eucalyptus implies changes in the characteristics of the resources and the microhabitat conditions. We also expected to find differences in the communities in terms of diversity, abundance, and species present. The treatments were: grasslands; 10-year-old Eucalyptus plantations and 20-year-old Eucalyptus plantations. Seasonal samplings were performed for the extraction of soil fauna in winter, spring, summer and autumn. For the analysis of food webs, we worked with “trophic species'': groups of organisms that have the same prey and the same predators. A total of 25 food webs were laid out using bibliographical information of feeding habits from the identified taxa. From each food web, we obtained a predator overlap graph, in which the consumers that share the same source or prey are linked by an arrow. In addition, the Shannon-Wiener index was calculated. We found that trophic species densities were different among the treatments: communities from grassland and the younger plantations were dominated by earthworms and other secondary decomposers, while the community in the older plantation showed a greater contribution of primary decomposers (Shymphyla, Isopoda and Diplopoda). No significant differences between treatments were found in the parameters that characterize the structure of soil food webs, i.e. connections number, number of trophic species nor connectivity. However, the diversity of the community was lower in the youngest plantations than in the other treatments, and it shows evidence of compartmentalization in the predator overlap graphs. Our findings suggest that the meso and macrofauna communities in the 10-years-old plantations represent a transition between the communities from grasslands and the oldest plantations. We conclude that the effects of forestation with Eucalyptus on soil fauna communities are evident through changes in functional groups rather than changes in the parameters that characterize the structure of soil food webs.

An overlap graph model for large‐scale group decision making with social trust information considering the multiple roles of experts

AbstractSocial network analysis is an efficient tool to investigate the relationships of decision‐makers in large‐scale group decision making (LSGDM). Existing social network‐based LSGDM studies generally assumed that each decision‐maker has a single role or belongs to only one subgroup. The assumption that a decision‐maker has multiple roles or belongs to multiple subgroups is rarely taken into consideration. In this regard, this study proposes an overlap graph model (OGM) in which decision‐makers can participate in the decision‐making process in multiple roles to solve LSGDM problems with social trust information. In the OGM, decision‐makers are firstly divided into two types: multiple‐role decision‐makers and single‐role decision‐makers. Since it is unpractical for a decision‐maker to evaluate all others in a LSGDM problem, we then investigate how to construct a complete social trust network based on an Agent mechanism. A two‐stage consensus reaching process is proposed to reduce the discrepancies among decision‐makers: The first stage is for single‐role decision‐makers within a subgroup while the second stage is for Agents and multiple‐role decision‐makers. Finally, an illustrative example regarding selecting treatment plans for critical patients in COVID‐19 is provided to test the applicability and rationality of the proposed model.

The feasible region for consecutive patterns of permutations is a cycle polytope

We study proportions of consecutive occurrences of permutations of a given size. Specifically, the feasible limits of such proportions on large permutations form a region, called feasible region. We show that this feasible region is a polytope, more precisely the cycle polytope of a specific graph called overlap graph. This allows us to compute the dimension, vertices and faces of the polytope. Finally, we prove that the limits of classical occurrences and consecutive occurrences are independent, in some sense made precise in the extended abstract. As a consequence, the scaling limit of a sequence of permutations induces no constraints on the local limit and vice versa.

Inference of viral quasispecies with a paired de Bruijn graph

RNA viruses exhibit a high mutation rate and thus they exist in infected cells as a population of closely related strains called viral quasispecies. The viral quasispecies assembly problem asks to characterize the quasispecies present in a sample from high-throughput sequencing data. We study the de novo version of the problem, where reference sequences of the quasispecies are not available. Current methods for assembling viral quasispecies are either based on overlap graphs or on de Bruijn graphs. Overlap graph-based methods tend to be accurate but slow, whereas de Bruijn graph-based methods are fast but less accurate. We present viaDBG, which is a fast and accurate de Bruijn graph-based tool for de novo assembly of viral quasispecies. We first iteratively correct sequencing errors in the reads, which allows us to use large k-mers in the de Bruijn graph. To incorporate the paired-end information in the graph, we also adapt the paired de Bruijn graph for viral quasispecies assembly. These features enable the use of long-range information in contig construction without compromising the speed of de Bruijn graph-based approaches. Our experimental results show that viaDBG is both accurate and fast, whereas previous methods are either fast or accurate but not both. In particular, viaDBG has comparable or better accuracy than SAVAGE, while being at least nine times faster. Furthermore, the speed of viaDBG is comparable to PEHaplo but viaDBG is able to retrieve also low abundance quasispecies, which are often missed by PEHaplo. viaDBG is implemented in C++ and it is publicly available at https://bitbucket.org/bfreirec1/viadbg. All datasets used in this article are publicly available at https://bitbucket.org/bfreirec1/data-viadbg/. Supplementary data are available at Bioinformatics online.

The relationship between demoralization and depressive symptoms among patients from the general hospital: network and exploratory graph analysis

IntroductionDepression and demoralization are highly prevalent among individuals with physical illnesses but their relationship is still unclear. ObjectiveTo examine the relationship between clinical features of depression and demoralization with the network approach to psychopathology. MethodsParticipants were recruited from the medical wards of a University Hospital in Italy. The Demoralization Scale (DS) was used to assess demoralization, while the Patient Health Questionnaire-9 (PHQ-9) to assess depressive symptoms. The structure of the depression-demoralization symptom network was examined and complemented by the analysis of topological overlap and Exploratory Graph Analysis (EGA) to identify the most relevant groupings (communities) of symptoms and their connections. The stability of network models was estimated with bootstrap procedures and results were compared with factor analysis. ResultsLife feeling pointless, low mood/discouragement, hopelessness and feeling trapped were among the most central features of the network. EGA identified four communities: (1) Neurovegetative Depression, (2) Loss of purpose, (3) Frustrated Isolation and (4) Low mood and morale. Loss of purpose and low mood/morale were largely connected with other communities through anhedonia, hopelessness and items related to isolation and lack of emotional control. Results from EGA displayed good stability and were comparable to those from factor analysis. LimitationsCross-sectional design; sample heterogeneity ConclusionsAmong general hospital inpatients, features of depression and demoralization are independent, with the exception of low mood and self-reproach. The identification of symptom groupings around entrapment and helplessness may provide a basis for a dimensional characterization of depressed/demoralized patients, with possible implications for treatment.

SOGNet: Scene Overlap Graph Network for Panoptic Segmentation

The panoptic segmentation task requires a unified result from semantic and instance segmentation outputs that may contain overlaps. However, current studies widely ignore modeling overlaps. In this study, we aim to model overlap relations among instances and resolve them for panoptic segmentation. Inspired by scene graph representation, we formulate the overlapping problem as a simplified case, named scene overlap graph. We leverage each object's category, geometry and appearance features to perform relational embedding, and output a relation matrix that encodes overlap relations. In order to overcome the lack of supervision, we introduce a differentiable module to resolve the overlap between any pair of instances. The mask logits after removing overlaps are fed into per-pixel instance id classification, which leverages the panoptic supervision to assist in the modeling of overlap relations. Besides, we generate an approximate ground truth of overlap relations as the weak supervision, to quantify the accuracy of overlap relations predicted by our method. Experiments on COCO and Cityscapes demonstrate that our method is able to accurately predict overlap relations, and outperform the state-of-the-art performance for panoptic segmentation. Our method also won the Innovation Award in COCO 2019 challenge.

Overlap graphs and de Bruijn graphs: data structures for de novogenome assembly in the big data era

BackgroundDe novo genome assembly relies on two kinds of graphs: de Bruijn graphs and overlap graphs. Overlap graphs are the basis for the Celera assembler, while de Bruijn graphs have become the dominant technical device in the last decade. Those two kinds of graphs are collectively called assembly graphs.ResultsIn this review, we discuss the most recent advances in the problem of constructing, representing and navigating assembly graphs, focusing on very large datasets. We will also explore some computational techniques, such as the Bloom filter, to compactly store graphs while keeping all functionalities intact.ConclusionsWe complete our analysis with a discussion on the algorithmic issues of assembling from long reads ( e.g., PacBio and Oxford Nanopore). Finally, we present some of the most relevant open problems in this field.

Generalizing Design of Support Measures for Counting Frequent Patterns in Graphs.

Frequent subgraph mining (FSM) from graphs is an active subject in computer science research. One major challenge in FSM is the development of support measures, which are basically functions that map a pattern to its frequency count in a database. Current state-of-the-art in this topic features a hypergraph-based framework for modeling pattern occurrences which unifies the two main flavors of support measures: the overlap-graph based maximum independent set measure (MIS) and minimum image/instance based (MNI) measures. For the purpose of exploring the middle ground between these two groups and guiding the development of new support measures, we present general sufficient conditions for designing new support measures in hypergraph framework, which can be applied to MNI and other support measures that are not included in the overlap graph framework. We utilize the sufficient conditions to generalize MNI and minimum-instance measure (MI) for designing user-defined linear-time measures. Furthermore, we show that a maximum independent subedge set (MISS) measure developed from the sufficient conditions can fill the gap between MIS and MI in computation complexity and support count.