Spring Embedder Research Articles

Regulation of regeneration in Arabidopsis thaliana

We employed several algorithms with high efficacy to analyze the public transcriptomic data, aiming to identify key transcription factors (TFs) that regulate regeneration in Arabidopsis thaliana. Initially, we utilized CollaborativeNet, also known as TF-Cluster, to construct a collaborative network of all TFs, which was subsequently decomposed into many subnetworks using the Triple-Link and Compound Spring Embedder (CoSE) algorithms. Functional analysis of these subnetworks led to the identification of nine subnetworks closely associated with regeneration. We further applied principal component analysis and gene ontology (GO) enrichment analysis to reduce the subnetworks from nine to three, namely subnetworks 1, 12, and 17. Searching for TF-binding sites in the promoters of the co-expressed and co-regulated (CCGs) genes of all TFs in these three subnetworks and Triple-Gene Mutual Interaction analysis of TFs in these three subnetworks with the CCGs involved in regeneration enabled us to rank the TFs in each subnetwork. Finally, six potential candidate TFs—WOX9A, LEC2, PGA37, WIP5, PEI1, and AIL1 from subnetwork 1—were identified, and their roles in somatic embryogenesis (GO:0010262) and regeneration (GO:0031099) were discussed, so were the TFs in Subnetwork 12 and 17 associated with regeneration. The TFs identified were also assessed using the CIS-BP database and Expression Atlas. Our analyses suggest some novel TFs that may have regulatory roles in regeneration and embryogenesis and provide valuable data and insights into the regulatory mechanisms related to regeneration. The tools and the procedures used here are instrumental for analyzing high-throughput transcriptomic data and advancing our understanding of the regulation of various biological processes of interest.

FCoSE: A Fast Compound Graph Layout Algorithm with Constraint Support.

Visual analysis of relational information is vital in most real-life analytics applications. Automatic layout is a key requirement for effective visual display of such information. This article introduces a new layout algorithm named fCoSE for compound graphs showing varying levels of groupings or abstractions with support for user-specified placement constraints. fCoSE builds on a previous compound spring embedder layout algorithm and makes use of the spectral graph drawing technique for producing a quick draft layout, followed by phases where constraints are enforced and compound structures are properly shown while polishing the layout with respect to commonly accepted graph layout criteria. Experimental evaluation verifies that fCoSE produces quality layouts and is fast enough for interactive applications with small to medium-sized graphs by combining the speed of spectral graph drawing technique with the quality of force-directed layout algorithms while satisfying specified constraints and properly displaying compound structures. An implementation of fCoSE along with documentation and a demo page is freely available on GitHub at https://github.com/iVis-at-Bilkent/cytoscape.js-fcose.

CoSEP: A compound spring embedder layout algorithm with support for ports

This paper describes a new automatic layout algorithm named CoSEP for compound graphs with port constraints. The algorithm works by extending the physical model of a previous algorithm named CoSE by defining additional force types and heuristics for constraining edges to connect to certain user-defined locations on end nodes. Similar to its predecessor, CoSEP also accounts for non-uniform node dimensions and arbitrary levels of nesting via compound nodes. Our experiments show that CoSEP significantly improves the quality of the layouts for compound graphs with port constraints with respect to commonly accepted graph drawing criteria while running reasonably fast, suitable for use in interactive applications for small to medium-sized (up to 500 nodes) graphs. A complete JavaScript implementation of CoSEP as a Cytoscape.js extension along with a demo page is freely available at https://github.com/iVis-at-Bilkent/cytoscape.js-cosep .

An algorithm for automated layout of process description maps drawn in SBGN.

Motivation: Evolving technology has increased the focus on genomics. The combination of today’s advanced techniques with decades of molecular biology research has yielded huge amounts of pathway data. A standard, named the Systems Biology Graphical Notation (SBGN), was recently introduced to allow scientists to represent biological pathways in an unambiguous, easy-to-understand and efficient manner. Although there are a number of automated layout algorithms for various types of biological networks, currently none specialize on process description (PD) maps as defined by SBGN.Results: We propose a new automated layout algorithm for PD maps drawn in SBGN. Our algorithm is based on a force-directed automated layout algorithm called Compound Spring Embedder (CoSE). On top of the existing force scheme, additional heuristics employing new types of forces and movement rules are defined to address SBGN-specific rules. Our algorithm is the only automatic layout algorithm that properly addresses all SBGN rules for drawing PD maps, including placement of substrates and products of process nodes on opposite sides, compact tiling of members of molecular complexes and extensively making use of nested structures (compound nodes) to properly draw cellular locations and molecular complex structures. As demonstrated experimentally, the algorithm results in significant improvements over use of a generic layout algorithm such as CoSE in addressing SBGN rules on top of commonly accepted graph drawing criteria.Availability and implementation: An implementation of our algorithm in Java is available within ChiLay library (https://github.com/iVis-at-Bilkent/chilay).Contact: ugur@cs.bilkent.edu.tr or dogrusoz@cbio.mskcc.orgSupplementary information: Supplementary data are available at Bioinformatics online.

A Force Directed Layout Algorithm for Biological Networks

this paper, we present a layout algorithm for clustered graphs which is a modified force directed algorithm. We have used Spring Embedder algorithm by Eades as base for our algorithm and modified it to suit the constraints of general biological graphs. Our main contribution is adopting spring embedder algorithm to maintain clustered structure of original graph with inherent depth of nesting and handling different node sizes. Results show that our layout algorithm draws graphs with acceptable quality with respect to aesthetic criteria for graph drawing. The algorithm has been integrated with systems biology visualization suit called eSkin, which allows lay outing and analyze biological graphs.

Social networks as the context for understanding employment services utilization among homeless youth

Little is known about the factors associated with use of employment services among homeless youth. Social network characteristics have been known to be influential in motivating people's decision to seek services. Traditional theoretical frameworks applied to studies of service use emphasize individual factors over social contexts and interactions. Using key social network, social capital, and social influence theories, this paper developed an integrated theoretical framework that capture the social network processes that act as barriers or facilitators of use of employment services by homeless youth, and understand empirically, the salience of each of these constructs in influencing the use of employment services among homeless youth. We used the “Event based-approach” strategy to recruit a sample of 136 homeless youth at one drop-in agency serving homeless youth in Los Angeles, California in 2008. The participants were queried regarding their individual and network characteristics. Data were entered into NetDraw 2.090 and the spring embedder routine was used to generate the network visualizations. Logistic regression was used to assess the influence of the network characteristics on use of employment services. The study findings suggest that social capital is more significant in understanding why homeless youth use employment services, relative to network structure and network influence. In particular, bonding and bridging social capital were found to have differential effects on use of employment services among this population. The results from this study provide specific directions for interventions aimed to increase use of employment services among homeless youth.

CiSE: A Circular Spring Embedder Layout Algorithm

We present a new algorithm for automatic layout of clustered graphs using a circular style. The algorithm tries to determine optimal location and orientation of individual clusters intrinsically within a modified spring embedder. Heuristics such as reversal of the order of nodes in a cluster and swap of neighboring node pairs in the same cluster are employed intermittently to further relax the spring embedder system, resulting in reduced inter-cluster edge crossings. Unlike other algorithms generating circular drawings, our algorithm does not require the quotient graph to be acyclic, nor does it sacrifice the edge crossing number of individual clusters to improve respective positioning of the clusters. Moreover, it reduces the total area required by a cluster by using the space inside the associated circle. Experimental results show that the execution time and quality of the produced drawings with respect to commonly accepted layout criteria are quite satisfactory, surpassing previous algorithms. The algorithm has also been successfully implemented and made publicly available as part of a compound and clustered graph editing and layout tool named CHISIO.

Position-Specific HIV Risk in a Large Network of Homeless Youths

We examined interconnections among runaway and homeless youths (RHYs) and how aggregated network structure position was associated with HIV risk in this population. We collected individual and social network data from 136 RHYs. On the basis of these data, we generated a sociomatrix, accomplished network visualization with a "spring embedder," and examined k-cores. We used multivariate logistic regression models to assess associations between peripheral and nonperipheral network position and recent unprotected sexual intercourse. Small numbers of nominations at the individual level aggregated into a large social network with a visible core, periphery, and small clusters. Female youths were more likely to be in the core, as were youths who had been homeless for 2 years or more. Youths at the periphery were less likely to report unprotected intercourse and had been homeless for a shorter duration. HIV risk was a function of risk-taking youths' connections with one another and was associated with position in the overall network structure. Social network-based prevention programs, young women's housing and health programs, and housing-first programs for peripheral youths could be effective strategies for preventing HIV among this population.

Drawing Meshed One-Line Diagrams of Electric Power Systems using a Modified Controlled Spring Embedder Algorithm Enhanced with Geospatial Data

Problem statement: One-line diagrams are widely used in electrical power systems to provide a graphical view of state of the system and to assess its performance. Several methodologies and algorithms have been proposed to automatically draw the power system’s one-line diagram and provide satisfactory results for radial or small-size meshed networks. Nevertheless, actual power systems models are generally associated to strongly meshed networks and in this case, the usage of the mentioned methodologies can yield unsatisfactory solutions, with a great number of line crossings. Approach: This study proposes a method that generates bus/branch one-line diagrams of meshed power systems, based on a modified version of the Controlled Spring Embedder algorithm enhanced by the usage of physical laws and geospatial data. Results: The methodology was tested using a portion of the Brazilian interconnected power system that corresponds to a meshed bus/branch model with 58 nodes and 64 branches. The graphical portrayal was obtained from the branches list of the network, firstly without the presence of geographical information and then considering it. Conclusion: The proposed algorithm was able to evolve a graphical portrayal of the bus/branch electric model of a power system, yielding satisfactory results. In special, geospatial data have proved to be fundamental information, allowing the elimination of branch crossings and providing consistent representations for a specific electrical network in 95% of the simulated cases.

An efficient biological pathway layout algorithm combining grid-layout and spring embedder for complicated cellular location information

BackgroundGraph drawing is one of the important techniques for understanding biological regulations in a cell or among cells at the pathway level. Among many available layout algorithms, the spring embedder algorithm is widely used not only for pathway drawing but also for circuit placement and www visualization and so on because of the harmonized appearance of its results. For pathway drawing, location information is essential for its comprehension. However, complex shapes need to be taken into account when torus-shaped location information such as nuclear inner membrane, nuclear outer membrane, and plasma membrane is considered. Unfortunately, the spring embedder algorithm cannot easily handle such information. In addition, crossings between edges and nodes are usually not considered explicitly.ResultsWe proposed a new grid-layout algorithm based on the spring embedder algorithm that can handle location information and provide layouts with harmonized appearance. In grid-layout algorithms, the mapping of nodes to grid points that minimizes a cost function is searched. By imposing positional constraints on grid points, location information including complex shapes can be easily considered. Our layout algorithm includes the spring embedder cost as a component of the cost function. We further extend the layout algorithm to enable dynamic update of the positions and sizes of compartments at each step.ConclusionsThe new spring embedder-based grid-layout algorithm and a spring embedder algorithm are applied to three biological pathways; endothelial cell model, Fas-induced apoptosis model, and C. elegans cell fate simulation model. From the positional constraints, all the results of our algorithm satisfy location information, and hence, more comprehensible layouts are obtained as compared to the spring embedder algorithm. From the comparison of the number of crossings, the results of the grid-layout-based algorithm tend to contain more crossings than those of the spring embedder algorithm due to the positional constraints. For a fair comparison, we also apply our proposed method without positional constraints. This comparison shows that these results contain less crossings than those of the spring embedder algorithm. We also compared layouts of the proposed algorithm with and without compartment update and verified that latter can reach better local optima.

Node overlap removal in clustered directed acyclic graphs

Graph drawing and visualization represent structural information as diagrams of abstract graphs and networks. An important subset of graphs is directed acyclic graphs (DAGs). This paper presents a new E-Spring algorithm, extended from the popular spring embedder model, which eliminates node overlaps in clustered DAGs. In this framework, nodes are modeled as non-uniform charged particles with weights, and a final drawing is derived by adjusting the positions of the nodes according to a combination of spring forces and repulsive forces derived from electrostatic forces between the nodes. The drawing process needs to reach a stable state when the average distances of separation between nodes are near optimal. We introduce a stopping condition for such a stable state, which reduces equilibrium distances between nodes and therefore results in a significantly reduced area for DAG visualization. It imposes an upper bound on the repulsive forces between nodes based on graph geometry. The algorithm employs node interleaving to eliminate any residual node overlaps. These new techniques have been validated by visualizing eBay buyer–seller relationships and has resulted in overall area reductions in the range of 45–79%.

Anchored Map: Graph Drawing Technique to Support Network Mining

Because network diagrams drawn using the spring embedder are not easy to read, this paper proposes the use of “anchored maps” in which some nodes are fixed as anchors. The readability of network diagrams is discussed, anchored maps are proposed, and a method for drawing anchored maps is explained. The method uses indices to decide the orders of anchors because those orders markedly affect the readability of the network diagrams. Examples showing the effectiveness of the anchored maps are also shown.

Improved Layout of Phylogenetic Networks

Split networks are increasingly being used in phylogenetic analysis. Usually, a simple equal angle algorithm is used to draw such networks, producing layouts that leave much room for improvement. Addressing the problem of producing better layouts of split networks, this paper presents an algorithm for maximizing the area covered by the network, describes an extension of the equal-daylight algorithm to networks, looks into using a spring embedder and discusses how to construct rooted split networks.

Drawing graphs using modular decomposition

In this paper we present an algorithm for drawing an undirected graph G which takes advantage of the structure of the modular decomposition tree of G. Specifically, our algorithm works by traversing the modular decomposition tree of the input graph G on n vertices and m edges, in a bottom-up fashion until it reaches the root of the tree, while at the same time intermediate drawings are computed. In order to achieve aesthetically pleasing results, we use grid and circular placement techniques, and utilize an appropriate modification of a well-known spring embedder algorithm. It turns out, that for some classes of graphs, our algorithm runs in O(n+m) time, while in general, the running time is bounded in terms of the processing time of the spring embedder algorithm. The result is a drawing that reveals the structure of the graph G and preserves certain aesthetic criteria.

Algorithms for automatic generation of one-line diagrams

Three placement algorithms are presented that may be employed for the automatic generation of one-line diagrams of power systems. To demonstrate the ability of these algorithms, a one-line diagram auto generation software program (ODAG) has been developed. ODAG has been implemented using the Java programming language so that it is network accessible over the Internet as a one-line diagram design tool. Algorithms implemented in ODAG include Spring Embedder, Rooted Tree and Controlled Spring Embedder with Grid Aligning. They autogenerate one-line diagram layouts that are aesthetically pleasing with acceptable readability and user friendliness. Two networks have been used as examples in the paper to illustrate the one-line diagrams autogenerated by these algorithms.