Foundations  (F) Session 4

Abstract: Multiple sinks competition is investigated for a walker diffusing on directed complex networks. The asymmetry of the imposed spatial support makes the system non transitive. As a consequence, it is always possible to identify a suitable location for the second absorbing sink that screens at most the flux of agents directed against the first trap, whose position has been preliminarily assigned. The degree of mutual competition between pairs of nodes is analytically quantified through apt indicators that build on the topological characteristics of the hosting graph. Moreover, the positioning of the second trap can be chosen so as to minimize, at the same time the probability of being in turn shaded by a thirdly added trap. Supervised placing of absorbing traps on a asymmetric disordered and complex graph is hence possible, as follows a robust optimization protocol. This latter is here discussed and successfully tested against synthetic data. Close

Abstract: Most of the real world complex systems consist of multiple subsystems that interact with each other, which can be represented as multilayer networks. Implications of such multilayer topologies have been studied for system robustness, cascading failures, reaction-diffusion dynamics, etc., but little research has been conducted on the dynamical stability of multilayer networks. Here we study the stability of multilayer networks and its relationships with the stabilities of networks within individual layers. Specifically, we generated two random networks following the method of May's random ecological network model, and then coupled them to create a random multilayer network. Two parameters were systematically varied: the strength of within-layer connections, alpha, and the strength of inter-layer coupling, kappa. Stabilities of those networks were evaluated by calculating eigenvalues of their (supra-) adjacency matrices. Numerical analysis showed that, with alpha above a certain threshold, individual networks become unstable, as is well known from May's work. We also found, however, that the whole multilayer network can be unstable with alpha below the threshold, if the inter-layer coupling kappa is above another threshold. This form of instability was previously not known, and it indicates that a system made of individually stable layers may get destabilized because of too strong inter-layer coupling. We also investigated the effects of the network size in each layer. As the number of nodes increases, the thresholds of alpha and kappa both decrease, further manifesting the network instability induced by inter-layer coupling. Our study illustrates that the strength of inter-layer coupling has a critical role in the stability of the whole network. Close

Abstract: We would like to draw the network science community's attention to a scenario in which the graphlet correlation distance (GCD) method, introduced by Yaveroglu et al. [1], can give misleading results. The aim of the talk is to introduce attendees to the method and offer an appreciation of its subtleties. Graphlet correlation distance (GCD) has been proposed as an alignment-free method for the comparison of networks in systems biology and other domains. In particular, GCD has been shown to outperform other alignment-free methods, both in terms of accuracy and computational efficiency [1, 2]. The method correlates counts of graphlets, that is, induced subgraphs of a network that are of order 5 or less, for individual nodes of a network. A set of networks can then be clustered based upon a distance between their graphlet correlation matrices. In this talk we argue that GCD is very sensitive to low counts of graphlets; which, in turn, can bias results. Thus, when a set of networks contains negligible amounts of some graphlets, correlations between these underrepresented graphlets dominates the resulting partition. We illustrate this problem by constructing artificial networks which lack some graphlets in their makeup. We then add a statistically insignificant amount of edges to individual networks such that they now contain an instance of the missing graphlet. We conclude by proposing a modification to the method and then applying it to a dataset of street networks. [1] Yaveroğlu, Ömer Nebil, et al. "Revealing the hidden language of complex networks." Scientific reports 4 (2014). [2] Yaveroğlu, Ömer Nebil, Tijana Milenković, and Nataša Pržulj. "Proper evaluation of alignment-free network comparison methods." Bioinformatics 31.16 (2015): 2697-2704. Close

Abstract: Bipartite networks are currently regarded as providing a major insight into the organization of real-world systems, unveiling the mechanisms shaping the interactions occurring between separate groups of nodes. One of the major problems encountered when dealing with bipartite networks is obtaining a (monopartite) projection over the layer of interest, preserving as much as possible the information encoded into the original bipartite structure. In the present paper we propose an algorithm able to obtain statistically-validated projections of bipartite networks: our method com- pares the number of shared neighbors between two nodes on the same layer with the expectation from a recently null-models for bipartite networks, [1,2]. The output of our method is a p-value per couple of nodes, encoding the statistical significance of the observation: if the p-value is small, the observation is not explained by the null-model and it is statistically relevant. A validated projection can thus be obtained by choosing a threshold and linking the nodes passing the test. We also show an alternative approach, intended to retain all the information provided by the whole matrix of p-values: upon doing so, we are able to detect the (potentially) hierarchical relationships occurring between different subsets of elements. We test our procedure on the bipartite projection of the trade network (i.e. usual Economic Complexity framework) and on the bipartite social network of MovieLens100k between users and rated films. The resulting similarities between countries have interesting explanations in terms of the economic development of different nations; on the social side, our methods is able to cluster films respect to some non trivial features (cast, directors, sub-genres..). [1] Saracco F., et al. Randomizing bipartite networks: the case of the World Trade Web. Sci. Rep. 5(10595) [2] Saracco F., et al. Detecting the bipartite world trade web evolution across 2007: a motifs-based analysis, arXiv:1508.03533. Close

Abstract: Bubbly flows are frequently observed in nature or industrial applications. Is some cases, inception of such flows are undesirable, like boiling of coolant liquid which prevents effective heat loss. On other hand, there are processes, like bubble chemical reactors, where formation of bubbly flows are necessary but should be carried out in specific fashion. Prediction of such regimes are crucial for robust equipment design. It is not always possible to apply experimental methods for investigation of bubbly flows, thus modern numerical methods are of high importance and can be used to predict flow patterns, bubble formation and evolution for complex systems and set-ups. Numerical simulation of three-dimensional bubbly column will be presented in the scope of that work as a representative case of polydisperse bubbly flow. Numerical algorithm is based on the mathematical model which utilizes Euler-Euler approach for description of dispersed phases, supplemented by k-omega SST turbulence model for bubbly flows and extended for polydisperse flow description by multi-class approach. Main problem arises from coupling between carrier phase and multiple dispersed classes, which is overcome by specific numerical realization of the mathematical model. In-house computer code was developed on the basis of the proposed numerical algorithm. Main feature of that code is unstructured meshes, pseudo-time solution algorithm, modified phase-coupled SIMPLEC method, TVD-based interpolation schemes. Velocity and gas concentration distributions presented for bubbly flow column and compared with the existed experimental data (Sokolichin at al 1999). Column is represented as parallelepiped with gas injector (sparger) installed on the bottom surface with the offset towards one vertical wall. It was shown, that numerical simulation predicts well entire jet structure produced by buoyant bubbles, but also provides detailed information of flow near bubble inlet and close to vertical walls, with formation of thin regions with local maximum of bubble concentration. Close