Deconstructing the Big Valley Search Space Hypothesis

The big valley hypothesis suggests that, in combinatorial optimisation, local optima of good quality are clustered and surround the global optimum. We show here that the idea of a single valley does not always hold. Instead the big valley seems to de-construct into several valleys, also called ‘funnels’ in theoretical chemistry. We use the local optima networks model and propose an effective procedure for extracting the network data. We conduct a detailed study on four selected TSP instances of moderate size and observe that the big valley decomposes into a number of sub-valleys of different sizes and fitness distributions. Sometimes the global optimum is located in the largest valley, which suggests an easy to search landscape, but this is not generally the case. The global optimum might be located in a small valley, which offers a clear and visual explanation of the increased search difficulty in these cases. Our study opens up new possibilities for analysing and visualising combinatorial landscapes as complex networks

The role of endogenous and exogenous mechanisms in the formation of R&D networks

We develop an agent-based model of strategic link formation in Research and Development (R&D)networks. Empirical evidence has shown that the growth of these networks is driven by mechanisms whichare both endogenous to the system (that is, depending on existing alliances patterns) and exogenous (that is, driven by an exploratory search for newcomer firms). Extant research to date has not investigated both mechanisms simultaneously in a comparative manner. To overcome this limitation, we develop a general modeling framework to shed light on the relative importance of these two mechanisms. We test our model against a comprehensive dataset, listing cross-country and cross-sectoral R&D alliances from 1984 to 2009. Our results show that by fitting only three macroscopic properties of the network topology, this framework is able to reproduce a number of micro-level measures, including the distributions of degree, local clustering, path length and component size, and the emergence of network clusters. Furthermore, by estimating the link probabilities towards newcomers and established firms from the data, we find that endogenous mechanisms are predominant over the exogenous ones in the network formation, thus quantifying the importance of existing structures in selecting partner firms

A unified data representation theory for network visualization, ordering and coarse-graining

Representation of large data sets became a key question of many scientific disciplines in the last decade. Several approaches for network visualization, data ordering and coarse-graining accomplished this goal. However, there was no underlying theoretical framework linking these problems. Here we show an elegant, information theoretic data representation approach as a unified solution of network visualization, data ordering and coarse-graining. The optimal representation is the hardest to distinguish from the original data matrix, measured by the relative entropy. The representation of network nodes as probability distributions provides an efficient visualization method and, in one dimension, an ordering of network nodes and edges. Coarse-grained representations of the input network enable both efficient data compression and hierarchical visualization to achieve high quality representations of larger data sets. Our unified data representation theory will help the analysis of extensive data sets, by revealing the large-scale structure of complex networks in a comprehensible form.Comment: 13 pages, 5 figure

Discovering hidden relationships between renal diseases and regulated genes through 3D network visualizations

Abstract Background In a recent study, two-dimensional (2D) network layouts were used to visualize and quantitatively analyze the relationship between chronic renal diseases and regulated genes. The results revealed complex relationships between disease type, gene specificity, and gene regulation type, which led to important insights about the underlying biological pathways. Here we describe an attempt to extend our understanding of these complex relationships by reanalyzing the data using three-dimensional (3D) network layouts, displayed through 2D and 3D viewing methods. Findings The 3D network layout (displayed through the 3D viewing method) revealed that genes implicated in many diseases (non-specific genes) tended to be predominantly down-regulated, whereas genes regulated in a few diseases (disease-specific genes) tended to be up-regulated. This new global relationship was quantitatively validated through comparison to 1000 random permutations of networks of the same size and distribution. Our new finding appeared to be the result of using specific features of the 3D viewing method to analyze the 3D renal network. Conclusions The global relationship between gene regulation and gene specificity is the first clue from human studies that there exist common mechanisms across several renal diseases, which suggest hypotheses for the underlying mechanisms. Furthermore, the study suggests hypotheses for why the 3D visualization helped to make salient a new regularity that was difficult to detect in 2D. Future research that tests these hypotheses should enable a more systematic understanding of when and how to use 3D network visualizations to reveal complex regularities in biological networks.http://deepblue.lib.umich.edu/bitstream/2027.42/112972/1/13104_2010_Article_700.pd

Beyond Statistical Significance: Implications of Network Structure on Neuronal Activity

It is a common and good practice in experimental sciences to assess the statistical significance of measured outcomes. For this, the probability of obtaining the actual results is estimated under the assumption of an appropriately chosen null-hypothesis. If this probability is smaller than some threshold, the results are deemed statistically significant and the researchers are content in having revealed, within their own experimental domain, a “surprising” anomaly, possibly indicative of a hitherto hidden fragment of the underlying “ground-truth”. What is often neglected, though, is the actual importance of these experimental outcomes for understanding the system under investigation. We illustrate this point by giving practical and intuitive examples from the field of systems neuroscience. Specifically, we use the notion of embeddedness to quantify the impact of a neuron's activity on its downstream neurons in the network. We show that the network response strongly depends on the embeddedness of stimulated neurons and that embeddedness is a key determinant of the importance of neuronal activity on local and downstream processing. We extrapolate these results to other fields in which networks are used as a theoretical framework

ForceAtlas2, a Continuous Graph Layout Algorithm for Handy Network Visualization Designed for the Gephi Software

International audienceGephi is a network visualization software used in various disciplines (social network analysis, biology, genomics…). One of its key features is the ability to display the spatialization process, aiming at transforming the network into a map, and ForceAtlas2 is its default layout algorithm. The latter is developed by the Gephi team as an all-around solution to Gephi users' typical networks (scale-free, 10 to 10,000 nodes). We present here for the first time its functioning and settings. ForceAtlas2 is a force-directed layout close to other algorithms used for network spatialization. We do not claim a theoretical advance but an attempt to integrate different techniques such as the Barnes Hut simulation, degree-dependent repulsive force, and local and global adaptive temperatures. It is designed for the Gephi user experience (it is a continuous algorithm), and we explain which constraints it implies. The algorithm benefits from much feedback and is developed in order to provide many possibilities through its settings. We lay out its complete functioning for the users who need a precise understanding of its behaviour, from the formulas to graphic illustration of the result. We propose a benchmark for our compromise between performance and quality. We also explain why we integrated its various features and discuss our design choices

Wiederauffindung von wiederverwendbaren Software-Dokumenten: Repraesentationsmethoden und Suchverfahren

Available from TIB Hannover: RR 8166(95-01) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEBayerische Forschungsstiftung, Muenchen (Germany)DEGerman