Markov Chain Methods For Analyzing Complex Transport Networks

We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph representations of transport networks allowing for the effective network design, network performance evaluation, embedding, partitioning, and network fault tolerance analysis. Random walks embed graphs into Euclidean space in which distances and angles acquire a clear statistical interpretation. Being defined on the dual graph representations of transport networks random walks describe the equilibrium configurations of not random commodity flows on primary graphs. This theory unifies many network concepts into one framework and can also be elegantly extended to describe networks represented by directed graphs and multiple interacting networks.Comment: 26 pages, 4 figure

Interest communities and flow roles in directed networks: the Twitter network of the UK riots

Directionality is a crucial ingredient in many complex networks in which information, energy or influence are transmitted. In such directed networks, analysing flows (and not only the strength of connections) is crucial to reveal important features of the network that might go undetected if the orientation of connections is ignored. We showcase here a flow-based approach for community detection in networks through the study of the network of the most influential Twitter users during the 2011 riots in England. Firstly, we use directed Markov Stability to extract descriptions of the network at different levels of coarseness in terms of interest communities, i.e., groups of nodes within which flows of information are contained and reinforced. Such interest communities reveal user groupings according to location, profession, employer, and topic. The study of flows also allows us to generate an interest distance, which affords a personalised view of the attention in the network as viewed from the vantage point of any given user. Secondly, we analyse the profiles of incoming and outgoing long-range flows with a combined approach of role-based similarity and the novel relaxed minimum spanning tree algorithm to reveal that the users in the network can be classified into five roles. These flow roles go beyond the standard leader/follower dichotomy and differ from classifications based on regular/structural equivalence. We then show that the interest communities fall into distinct informational organigrams characterised by a different mix of user roles reflecting the quality of dialogue within them. Our generic framework can be used to provide insight into how flows are generated, distributed, preserved and consumed in directed networks.Comment: 32 pages, 14 figures. Supplementary Spreadsheet available from: http://www2.imperial.ac.uk/~mbegueri/Docs/riotsCommunities.zip or http://rsif.royalsocietypublishing.org/content/11/101/20140940/suppl/DC

Flow-Based Network Analysis of the Caenorhabditis elegans Connectome

We exploit flow propagation on the directed neuronal network of the nematode C. elegans to reveal dynamically relevant features of its connectome. We find flow-based groupings of neurons at different levels of granularity, which we relate to functional and anatomical constituents of its nervous system. A systematic in silico evaluation of the full set of single and double neuron ablations is used to identify deletions that induce the most severe disruptions of the multi-resolution flow structure. Such ablations are linked to functionally relevant neurons, and suggest potential candidates for further in vivo investigation. In addition, we use the directional patterns of incoming and outgoing network flows at all scales to identify flow profiles for the neurons in the connectome, without pre-imposing a priori categories. The four flow roles identified are linked to signal propagation motivated by biological input-response scenarios

Reduced-Order Equivalent-Circuit Models Of Thermal Systems Including Thermal Radiation

We established a general, automatic, and versatile procedure to derive an equivalent circuit for a thermal system using temperature data obtained from FE simulations. The EC topology was deduced from the FE mesh using a robust and general graph-partitioning algorithm. The method was shown to yield models that are independent of the boundary conditions for complicated 3D thermal systems such as an electronic chip. The results are strongly correlated with the geometry, and the EC can be extended to yield variable medium-order models. Moreover, a variety of heat sources and boundary conditions can be accommodated, and the EC models are inherently modular. A reliable method to compute thermal resistors connecting different regions was developed. It appropriately averages several estimates of a thermal resistance where each estimate is obtained using data obtained under different boundary or heating conditions. The concept of fictitious heat sources was used to increase the number of simulation datasets. The method was shown to yield models that are independent of the BCs for complicated 2-D thermal systems such as a 2D cavity. A reliable method to compute thermal resistors connecting different regions was developed. In general, the number of regions required for getting an accurate reduced-order model depends on the complexity of the system to be modeled. We have extended the reduced-order modeling procedure to include a view-factor based thermal radiation heat transfer model by including voltage controlled current sources in the equivalent circuit

Detecting Activations over Graphs using Spanning Tree Wavelet Bases

We consider the detection of activations over graphs under Gaussian noise, where signals are piece-wise constant over the graph. Despite the wide applicability of such a detection algorithm, there has been little success in the development of computationally feasible methods with proveable theoretical guarantees for general graph topologies. We cast this as a hypothesis testing problem, and first provide a universal necessary condition for asymptotic distinguishability of the null and alternative hypotheses. We then introduce the spanning tree wavelet basis over graphs, a localized basis that reflects the topology of the graph, and prove that for any spanning tree, this approach can distinguish null from alternative in a low signal-to-noise regime. Lastly, we improve on this result and show that using the uniform spanning tree in the basis construction yields a randomized test with stronger theoretical guarantees that in many cases matches our necessary conditions. Specifically, we obtain near-optimal performance in edge transitive graphs, $k$-nearest neighbor graphs, and $\epsilon$-graphs

Dual communities in spatial networks

Both human-made and natural supply systems, such as power grids and leaf venation networks, are built to operate reliably under changing external conditions. Many of these spatial networks exhibit community structures. Here, we show that a relatively strong connectivity between the parts of a network can be used to define a different class of communities: dual communities. We demonstrate that traditional and dual communities emerge naturally as two different phases of optimized network structures that are shaped by fluctuations and that they suppress failure spreading, which underlines their importance in understanding the shape of real-world supply networks

SUNLAB: a Functional-Structral Model for Genotypic and Phenotypic Characterization of the Sunflower Crop

International audienceA new functional-structural model SUNLAB for the crop sunflower (Helianthus annuus L.) is developed. It is dedicated to simulate the organogenesis, morphogenesis, biomass accumulation and biomass partitioning to organs in sunflower growth. It is adapted to model phenotypic response to diverse environment factors including temperature stress and water deficiency, and adapted to different genotypic variants. The model is confronted to experimental data and estimated parameter values of two genotypes "Melody" and "Prodisol" are presented. SUNLAB parameters seem to show genotypic variability, which potentially makes the model an interesting intermediate to discriminate between genotypes. Statistical tests on estimated parameter values suggest that some parameters are common between genotypes and others are genotypic specific. Since SUNLAB simulate individual leaf area and biomass as two state variables, an interesting corollary is that it also simulates dynamically the specific leaf area (SLA) variable. Further studies are performed to evaluate model performances with more genotypes and more discriminating environments to test and expand model's adaptability and usabilit

Trade Complexity and Productivity

We exploit a panel dataset of Hungarian firms merged with product-level trade data for the period 1992-2003 to investigate the relation between firms' trading activities (importing, exporting or both) and productivity. We find important self-selection effects of the most productive firms induced by the existence of heterogeneous sunk costs of trade, for both importers and exporters. We relate these sunk costs of trade to the relationship-specific nature of the trade activities, entailing a certain degree of technological and organizational complexity. We also show that, to the extent that imports and exports are correlated within firms, failing to control for the importing activity leads to overstated average productivity premia of exporters.Trade Openness, Firms' Heterogeneity, Productivity