Node Overlap Research Articles

Evolutionary games on multilayer networks: coordination and equilibrium selection

We study mechanisms of synchronisation, coordination, and equilibrium selection in two-player coordination games on multilayer networks. We investigate three possible update rules: the replicator dynamics (RD), the best response (BR), and the unconditional imitation (UI). Players interact on a two-layer random regular network. The population on each layer plays a different game, with layer I preferring the opposite strategy to layer II. We measure the difference between the two games played on the layers by a difference in payoffs, and the inter-connectedness by a node overlap parameter. We discover a critical value of the overlap below which layers do not synchronise, i.e. they display different levels of coordination. Above this threshold both layers typically coordinate on the same strategy. Surprisingly, there is a symmetry breaking in the selection of equilibrium—for RD and UI there is a phase where only the payoff-dominant equilibrium is selected. It is not observed, however, for BR update rule. Our work is an example of previously observed differences between the update rules. Nonetheless, we took a novel approach with the game being played on two inter-connected layers. As we show, the multilayer structure enhances the abundance of the Pareto-optimal equilibrium in coordination games with imitative update rules.

Node Overlap Removal Algorithms: an Extended Comparative Study

In the context of graph layout, many algorithms have been designed to remove node overlapping, and many quality criteria and associated metrics have been proposed to evaluate those algorithms. Unfortunately, a complete comparison of the algorithms based on some metrics that evaluate their quality has never been provided and it is thus difficult for a visualisation designer to select the algorithm that best suits their needs. In this paper, we review 22 metrics available in the literature, classify them according to the quality criteria they try to capture, and select a representative one for each class. Based on the selected metrics,we compare 9 node overlap removal algorithms. Our experiment involves 854 synthetic and real-world graphs. Finally, we propose a JavaScript library containing both the algorithms and the criteria, and we provide a Web platform, AGORA, in which one can upload graphs, apply the algorithms and compare/download the results.

A comprehensive analysis of delayed insertions in metric access methods

Similarity queries are fundamental operations for applications that deal with complex data. This paper presents MIA (Metric Indexing Assisted by auxiliary memory with limited capacity), a new delayed insertion approach that can be employed to create enhanced dynamic metric access methods through short-term memories. We present a comprehensive evaluation of delayed insertion methods for metric access methods while comparing MIA to dynamic forced reinsertions. Our experimental results show that metric access methods can benefit from these strategies, decreasing the node overlap, the number of distance calculations, the number of disk accesses, and the execution time to run k-nearest neighbor queries.

LAZY R-tree: The R-tree with lazy splitting algorithm

The spatial index is a data structure formed according to the position and shape of the spatial object or the relationship between the spatial objects according to certain rules, and the spatial data is managed by an effective spatial data structure. The quality of a spatial index directly affects the performance of spatial queries. The R-tree index structure is a highly efficient spatial index. According to the R-tree query rule, when performing spatial query, most data that is not related to the query condition can be filtered out, and finally, a few leaf nodes can be accessed to query the data satisfying the condition. Its query performance is affected by factors such as non-leaf node overlap and node space utilisation. This article proposes a lazy splitting method to improve the R-tree construction process. The scheme works as follows: (1) When a node overflows, it creates an overflow node for that node and all overflow nodes are saved in a hash table. (2) If the node continues to insert data, the data are added to its overflow node. (3) When an overflow node is saturated, the node and its overflow node are split into two saturated nodes. We use both simulated and actual data to perform experiments. The experimental results show that an R-tree constructed by the lazy algorithm is superior to an R-tree constructed using the original R-tree PM algorithm or the corner-based splitting (CBS) algorithm based on the number of splits created, the node space used and the efficiency of region queries and k-nearest neighbour (kNN) queries.

An Automated Displaced Proportional Circle Map Using Delaunay Triangulation and an Algorithm for Node Overlap Removal

Proportional circle maps are a popular method for visualizing quantitative data on a map. Circles are scaled proportionally based on the data provided; larger circles represent larger quantities. The circles require two values, a location and a numeric quantity. For data that have a wide range of values, the resulting map will produce clutter and overlap in which large symbols obscure the information contained in smaller circles. Some previous solutions to this problem are modifying and improving the contrast between symbols, or using stacking algorithms so all symbols are visible. This article proposes the displaced proportional symbol map, which displaces the symbol's location based on the amount of overlap between neighbouring circles. At the same time, it preserves the location of non-overlapping symbols, which distinguishes it from the circular cartogram. The displacement is automated through the proximity stress model algorithm for node overlap removal. This algorithm was originally designed for graph layouts with overlapping nodes, but was modified here for circular symbols and map layout. The result is a map with improved clarity and the ability to add labelling to a cluttered proportional circle map.

NOS: a software suite to compute node overlap and segregation in ecological networks

Investigating the structure of ecological networks can help unravel the mechanisms promoting and maintaining biodiversity. Recently, Strona and Veech 2015 (A new measure of ecological network structure based on node overlap and segregation. – Methods Ecol. Evol. 6: 907–915) introduced a new metric (Ɲ̅, pronounced ‘nos’), that allows assessment of structural patterns in networks ranging from complete node segregation to perfect nestedness, and that also provides a visual and quantitative assessment of the degree of network modularity. The Ɲ̅ metric permits testing of a wide range of hypotheses regarding the tendency for species to share interacting partners by taking into account ecologically plausible species interactions based on constraints such as trophic levels and habitat preference. Here we introduce NOS, a software suite (including a web interface freely accessible at  http://nos.alwaysdata.net , an executable program, and Python and R packages) that makes it possible to exploit the full potential of this method. Besides computing node overlap and segregation (Ɲ̅), the software provides different functions to automatically identify a set of possible resource–consumer interactions in food webs based on trophic levels. As an example of application, we analyzed two well‐resolved high‐latitude marine food webs, showing that an explicit a priori consideration of trophic levels is fundamental for a proper assessment of food web structure.

Node Overlap Removal by Growing a Tree

Node overlap removal is a necessary step in many scenarios including laying out a graph, or visualizing a tag cloud. Our contribution is a new overlap removal algorithm that iteratively builds a Minimum Spanning Tree on a Delaunay triangulation of the node centers and removes the node overlaps by "growing" the tree. The algorithm is simple to implement, yet it produces high quality layouts. According to our experiments it runs several times faster than the current state-of-the-art methods.

Forbidden versus permitted interactions: Disentangling processes from patterns in ecological network analysis.

Several studies have identified the tendency for species to share interacting partners as a key property to the functioning and stability of ecological networks. However, assessing this pattern has proved challenging in several regards, such as finding proper metrics to assess node overlap (sharing), and using robust null modeling to disentangle significance from randomness. Here, we bring attention to an additional, largely neglected challenge in assessing species’ tendency to share interacting partners. In particular, we discuss and illustrate with two different case studies how identifying the set of “permitted” interactions for a given species (i.e. interactions that are not impeded, e.g. by lack of functional trait compatibility) is paramount to understand the ecological and co‐evolutionary processes at the basis of node overlap and segregation patterns.

Ultrametricity of optimal transport substates for multiple interacting paths over a square lattice network.

We model a set of point-to-point transports on a network as a system of polydisperse interacting self-avoiding walks (SAWs) over a finite square lattice. The ends of each SAW may be located both at random, uniformly distributed, positions or with one end fixed at a lattice corner. The total energy of the system is computed as the sum over all SAWs, which may represent either the time needed to complete the transport over the network, or the resources needed to build the networking infrastructure. We focus especially on the second aspect by assigning a concave cost function to each site to encourage path overlap. A simulated annealing optimization, based on a modified Berg-Foerster-Aragao de Carvalho-Caracciolo-Froehlich (BFACF) algorithm developed for polymers, is used to probe the complex conformational substate structure at zero temperature. We characterize the average cost gains (and path-length variations) for increasing polymer density with respect to a Dijkstra routing and find a nonmonotonic behavior as recently found for random networks. We observe the emergence of ergodicity breaking and of nontrivial overlap distributions among replicas when switching from a convex to a concave cost function (e.g., x^{γ}, where x represents the node overlap). Finally, we show that the space of ground states for γ<1 is compatible with an ultrametric structure, as seen in many complex systems such as some spin glasses.

A new measure of ecological network structure based on node overlap and segregation

Summary Despite substantial recent progress, ecologists continue to search for methods of measuring the structure of ecological networks. Several studies have focused on nestedness, a pattern reflecting the tendency of network nodes to share interaction partners. Here, we introduce a new statistical procedure to measure both this kind of structure and the opposite one (i.e. species' tendency against sharing interacting partners) that we call ‘node segregation’. In addition, our procedure provides also a straightforward measure of modularity, that is, the tendency of a network to be compartmented into separated clusters of interacting nodes. This new analytical measure of network structure assesses the average deviation between the observed number of neighbours shared by any pair of nodes (species), and the expected number, that is computed using a probabilistic approach based on simple combinatorics. The measure can be applied to both bipartite networks (such as plant–pollinators) and unimode networks (such as food webs). We tested our approach on several sets of hypothetical and real‐world networks. We demonstrate that our approach makes it possible to identify different kinds of non‐random network configurations (nestedness, node segregation and modularity). In addition, we show that nestedness in ecological networks is less common than previously thought, and that most ecological networks (including the majority of mutualistic ones) tend towards patterns of segregated associations. Our analyses show that the new measure of node overlap and segregation can efficiently identify different structural patterns. The results of our analyses conducted on real networks highlight the need to carefully reconsider the assumption that ecological networks are stable due to their inherent nestedness.

Clustered Graph Hierarchical Layout Algorithm for Systems Biology Models

In this article we describe a complete method to the layout clustered graph in hierarchical fashion. We have adopted Sugiyama[11] framework for hierarchical layout and modified its phases to produce the clustered graph layout. The algorithm is based on Sanders compound graph layout algorithm. Our main contribution is positioning of nodes with different sizes without any node overlap while maintaining straight lines for long edges. Experimental results show that the executiontime and quality of the produced drawings with respect to commonly accepted layoutcriteria are quite satisfactory.This algorithm is intended to integrate as a part of system biology software Cell-in-Silico, for drawing biological pathways with compartmental constraints and arbitrary nesting of graphs and molecular complexes. General Terms Data Visualization, Layout Algorithm.

Efficient collection of sensor data via a new accelerated random walk

SummaryMotivated by the problem of efficiently collecting data from wireless sensor networks via a mobile sink, we present an accelerated random walk on random geometric graphs (RGG). Random walks in wireless sensor networks can serve as fully local, lightweight strategies for sink motion that significantly reduce energy dissipation but introduce higher latency in the data collection process. In most cases, random walks are studied on graphs like Gn,p and grid. Instead, we here choose the RGG model, which abstracts more accurately spatial proximity in a wireless sensor network. We first evaluate an adaptive walk (the random walk with inertia) on the RGG model; its performance proved to be poor and led us to define and experimentally evaluate a novel random walk that we call γ‐stretched random walk. Its basic idea is to favour visiting distant neighbours of the current node towards reducing node overlap and accelerate the cover time. We also define a new performance metric called proximity cover time that, along with other metrics such as visit overlap statistics and proximity variation, we use to evaluate the performance properties and features of the various walks. Copyright © 2013 John Wiley &amp; Sons, Ltd.

Mathematical genealogy and department prestige

The Mathematics Genealogy Project (http://www. genealogy.ams.org/) is a database of over 150 000 scholars with advanced degrees in mathematics and related fields. Entries include dissertation titles, adviser(s), graduation years, degree-granting institutions, and advisees. The MGP is popular among mathematicians, and it can be used to trace academic lineages through luminaries like Courant, Hilbert, and Wiener to historical predecessors such as Gauss, Euler, and even Kant. For example, MGP data was used recently to study the role of mentorship in protege performance. We consider recent branches of this mathematical family tree by projecting the MGP data for degrees granted since 1973 onto a network whose nodes represent academic institutions in the United States. An individual who earns a doctorate from institution A (during the selected period) and later advises students at institution B is represented by a directed edge of unit weight pointing from B to A. The total edge weight from B to A counts the number of such advisers. This network representation can be used to estimate the mathematical prestige of each university using various “centrality” scores of the corresponding node (see Fig. 1). We represent “hub” and “authority” scores using node size and color (red to blue), respectively. Institutions with high authority scores have high-valued hubs pointing to them, and high-valued hub nodes point to high-valued authorities. A university with a high authority score is a strong source of prestigious Ph.D. students and a university with a high hub score is a strong destination. In the legend of Fig. 1, we list the top 20 institutions in order of their authority scores. We use a “geographically inspired” layout to balance node locations and node overlap. A Kamada-Kawai visualization places the high-authority universities in the network’s center. In Fig. 2, we compare authority scores with three rankings of mathematics departments for the 58 universities that appear in the top 40 of at least one of the rankings or have one of the top-40 authority scores. As expected, higher authority scores correlate with higher prestige (i.e., smaller rank numbers). However, scatter is obviously present, particularly with the 2010 National Research Council (NRC) rankings. We thank Mitch Keller at the MGP for providing data. This work was supported by the NSF (PJM: DMS-0645369) and the James S. McDonnell Foundation (MAP: #220020177).

Automated temporal tracking and segmentation of lymphoma on serial CT examinations

It is challenging to reproducibly measure and compare cancer lesions on numerous follow-up studies; the process is time-consuming and error-prone. In this paper, we show a method to automatically and reproducibly identify and segment abnormal lymph nodes in serial computed tomography (CT) exams. Our method leverages initial identification of enlarged (abnormal) lymph nodes in the baseline scan. We then identify an approximate region for the node in the follow-up scans using nonrigid image registration. The baseline scan is also used to locate regions of normal, non-nodal tissue surrounding the lymph node and to map them onto the follow-up scans, in order to reduce the search space to locate the lymph node on the follow-up scans. Adaptive region-growing and clustering algorithms are then used to obtain the final contours for segmentation. We applied our method to 24 distinct enlarged lymph nodes at multiple time points from 14 patients. The scan at the earlier time point was used as the baseline scan to be used in evaluating the follow-up scan, resulting in 70 total test cases (e.g., a series of scans obtained at 4 time points results in 3 test cases). For each of the 70 cases, a "reference standard" was obtained by manual segmentation by a radiologist. Assessment according to response evaluation criteria in solid tumors (RECIST) using our method agreed with RECIST assessments made using the reference standard segmentations in all test cases, and by calculating node overlap ratio and Hausdorff distance between the computer and radiologist-generated contours. Compared to the reference standard, our method made the correct RECIST assessment for all 70 cases. The average overlap ratio was 80.7 ± 9.7% s.d., and the average Hausdorff distance was 3.2 ± 1.8 mm s.d. The concordance correlation between automated and manual segmentations was 0.978 (95% confidence interval 0.962, 0.984). The 100% agreement in our sample between our method and the standard with regard to RECIST classification suggests that the true disagreement rate is no more than 6%. Our automated lymph node segmentation method achieves excellent overall segmentation performance and provides equivalent RECIST assessment. It potentially will be useful to streamline and improve cancer lesion measurement and tracking and to improve assessment of cancer treatment response.

Phylogenetic Molecular Ecological Network of Soil Microbial Communities in Response to Elevated CO 2

ABSTRACTUnderstanding the interactions among different species and their responses to environmental changes, such as elevated atmospheric concentrations of CO2, is a central goal in ecology but is poorly understood in microbial ecology. Here we describe a novel random matrix theory (RMT)-based conceptual framework to discern phylogenetic molecular ecological networks using metagenomic sequencing data of 16S rRNA genes from grassland soil microbial communities, which were sampled from a long-term free-air CO2 enrichment experimental facility at the Cedar Creek Ecosystem Science Reserve in Minnesota. Our experimental results demonstrated that an RMT-based network approach is very useful in delineating phylogenetic molecular ecological networks of microbial communities based on high-throughput metagenomic sequencing data. The structure of the identified networks under ambient and elevated CO2 levels was substantially different in terms of overall network topology, network composition, node overlap, module preservation, module-based higher-order organization, topological roles of individual nodes, and network hubs, suggesting that the network interactions among different phylogenetic groups/populations were markedly changed. Also, the changes in network structure were significantly correlated with soil carbon and nitrogen contents, indicating the potential importance of network interactions in ecosystem functioning. In addition, based on network topology, microbial populations potentially most important to community structure and ecosystem functioning can be discerned. The novel approach described in this study is important not only for research on biodiversity, microbial ecology, and systems microbiology but also for microbial community studies in human health, global change, and environmental management.

Efficient, Proximity-Preserving Node Overlap Removal

When drawing graphs whose nodes contain text or graphics, the nontrivial node sizes must be taken into account, either as partof the initial layout or as a post-processing step. The core problem in avoiding or removing overlaps is to retain the structural information inherent in a layout while minimizing the additional area required. Thispaper presents a new node overlap removal algorithm that does well at retaining a graph’s shape while using little additional area and time. As part ofthe analysis, we consider and evaluate two measures of dissimilarity for two layouts of the same graph.

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%.