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Concept: Discrete mathematics


Currently, most paired link based scaffolding algorithms intrinsically mask the sequences between two linked contigs and bypass their direct link information embedded in the original de Bruijn assembly graph. Such disadvantage substantially complicates the scaffolding process and leads to the inability of resolving repetitive contig assembly. Here we present a novel algorithm, inGAP-sf, for effectively generating high-quality and continuous scaffolds. inGAP-sf achieves this by using a new strategy based on the combination of direct link and paired link graphs, in which direct link is used to increase graph connectivity and to decrease graph complexity and paired link is employed to supervise the traversing process on the direct link graph. Such advantage greatly facilitates the assembly of short-repeat enriched regions. Moreover, a new comprehensive decision model is developed to eliminate the noise routes accompanying with the introduced direct link. Through extensive evaluations on both simulated and real datasets, we demonstrated that inGAP-sf outperforms most of the genome scaffolding algorithms by generating more accurate and continuous assembly, especially for short repetitive regions.

Concepts: Algorithm, Graph theory, Graph, Discrete mathematics, Planar graph, Vertex-transitive graph


Network motifs are small connected sub-graphs that have recently gathered much attention to discover structural behaviors of large and complex networks. Finding motifs with any size is one of the most important problems in complex and large networks. It needs fast and reliable algorithms and tools for achieving this purpose. CytoKavosh is one of the best choices for finding motifs with any given size in any complex network. It relies on a fast algorithm, Kavosh, which makes it faster than other existing tools. Kavosh algorithm applies some well known algorithmic features and includes tricky aspects, which make it an efficient algorithm in this field. CytoKavosh is a Cytoscape plug-in which supports us in finding motifs of given size in a network that is formerly loaded into the Cytoscape work-space (directed or undirected). High performance of CytoKavosh is achieved by dynamically linking highly optimized functions of Kavosh’s C++ to the Cytoscape Java program, which makes this plug-in suitable for analyzing large biological networks. Some significant attributes of CytoKavosh is efficiency in time usage and memory and having no limitation related to the implementation in motif size. CytoKavosh is implemented in a visual environment Cytoscape that is convenient for the users to interact and create visual options to analyze the structural behavior of a network. This plug-in can work on any given network and is very simple to use and generates graphical results of discovered motifs with any required details. There is no specific Cytoscape plug-in, specific for finding the network motifs, based on original concept. So, we have introduced for the first time, CytoKavosh as the first plug-in, and we hope that this plug-in can be improved to cover other options to make it the best motif-analyzing tool.

Concepts: Algorithm, Graph theory, Social network, Network theory, Network science, Complex network, Discrete mathematics, Algorithmic efficiency


Reverse engineering gene networks and identifying regulatory interactions are integral to understanding cellular decision making processes. Advancement in high throughput experimental techniques has initiated innovative data driven analysis of gene regulatory networks. However, inherent noise associated with biological systems requires numerous experimental replicates for reliable conclusions. Furthermore, evidence of robust algorithms directly exploiting basic biological traits are few. Such algorithms are expected to be efficient in their performance and robust in their prediction.

Concepts: Algorithm, Decision making, Engineering, Feedback, Gene regulatory network, Systems biology, Discrete mathematics, Algorithmic efficiency


We created a system using a triad of change management, electronic surveillance, and algorithms to detect sepsis and deliver highly sensitive and specific decision support to the point of care using a mobile application. The investigators hypothesized that this system would result in a reduction in sepsis mortality.

Concepts: Decision theory, Decision support system, Decision engineering, Data warehouse, Halting problem, Discrete mathematics, Knowledge engineering, Self service software


To improve understanding of the internal structure of the proximal phalanx (P1), response of the bone to load and possible relation to the pathogenesis of fractures in P1.

Concepts: Finite element method, Hilbert space, Set theory, Partial differential equation, Finite element method in structural mechanics, Discrete mathematics


Given a multiset of colors as the query and a list-colored graph, i.e. an undirected graph with a set of colors assigned to each of its vertices, in the NP-hard list-colored graph motif problem the goal is to find the largest connected subgraph such that one can select a color from the set of colors assigned to each of its vertices to obtain a subset of the query. This problem was introduced to find functional motifs in biological networks. We present a branch-and-bound algorithm named RANGI for finding and enumerating list-colored graph motifs. As our experimental results show, RANGI’s pruning methods and heuristics make it quite fast in practice compared to the algorithms presented in the literature. We also present a parallel version of RANGI that achieves acceptable scalability.

Concepts: Algorithm, Mathematics, Graph theory, Graph, Discrete mathematics, Glossary of graph theory, Planar graph, Branch and bound


In this paper, we propose an efficient algorithm to detect dense subgraphs of a weighted graph. The proposed algorithm, called Shrinking and Expansion Algorithm (SEA), iterates between two phases, namely, expansion phase and shrink phase, until convergence. For a current subgraph, the expansion phase adds the most related vertices based on the average affinity between each vertex and the subgraph. The shrink phase considers all pairwise relations in the current subgraph and filters out vertices whose average affinities to other vertices are smaller than the average affinity of the result subgraph. In both phases, SEA operates on small subgraphs, thus it is very efficient. Significant dense subgraphs are robustly enumerated by running SEA from each vertex of the graph. We evaluate SEA on two different applications: solving correspondence problems and cluster analysis. Both theoretic analysis and experimental results show that SEA is very efficient and robust, especially when there exist large amount of noises in edge weights.

Concepts: Cluster analysis, Phase, Graph theory, The Current, Proposal, Discrete mathematics, Glossary of graph theory, Vertex


In directed graphs, relationships are asymmetric and these asymmetries contain essential structural information about the graph. Directed relationships lead to a new type of clustering that is not feasible in undirected graphs. We propose a spectral co-clustering algorithm called di-sim for asymmetry discovery and directional clustering. A Stochastic co-Blockmodel is introduced to show favorable properties of di-sim To account for the sparse and highly heterogeneous nature of directed networks, di-sim uses the regularized graph Laplacian and projects the rows of the eigenvector matrix onto the sphere. A nodewise asymmetry score and di-sim are used to analyze the clustering asymmetries in the networks of Enron emails, political blogs, and the Caenorhabditis elegans chemical connectome. In each example, a subset of nodes have clustering asymmetries; these nodes send edges to one cluster, but receive edges from another cluster. Such nodes yield insightful information (e.g., communication bottlenecks) about directed networks, but are missed if the analysis ignores edge direction.

Concepts: Caenorhabditis elegans, Caenorhabditis, Rhabditidae, Graph theory, Matrix, Binary relation, Network theory, Discrete mathematics


Graphs are mathematical structures to model several biological data. Applications to analyze them require to apply solutions for the subgraph isomorphism problem, which is NP-complete. Here, we investigate the existing strategies to reduce the subgraph isomorphism algorithm running time with emphasis on the importance of the order with which the graph vertices are taken into account during the search, called variable ordering, and its incidence on the total running time of the algorithms. We focus on two recent solutions, which are based on an effective variable ordering strategy. We discuss their comparison both with the variable ordering strategies reviewed in the paper and the other algorithms present in the ICPR2014 contest on graph matching algorithms for pattern search in biological databases.

Concepts: Mathematics, Graph theory, Order theory, Binary relation, Discrete mathematics, NP-complete, Graph rewriting, Subgraph isomorphism problem


Multiple criteria decision analysis swing weighting (SW) and discrete choice experiments (DCE) are appropriate methods for capturing patient preferences on treatment benefit-risk trade-offs. This paper presents a qualitative comparison of the 2 methods.

Concepts: Critical thinking, Decision theory, Educational psychology, Decision making software, Operations research, Thought, Choice, Discrete mathematics