Network Capacity Bound for Personalized PageRank in Multimodal Networks

In a former paper the concept of Bipartite PageRank was introduced and a theorem on the limit of authority flowing between nodes for personalized PageRank has been generalized. In this paper we want to extend those results to multimodal networks. In particular we introduce a hypergraph type that may be used for describing multimodal network where a hyperlink connects nodes from each of the modalities. We introduce a generalisation of PageRank for such graphs and define the respective random walk model that can be used for computations. we finally state and prove theorems on the limit of outflow of authority for cases where individual modalities have identical and distinct damping factors.Comment: 28 pages. arXiv admin note: text overlap with arXiv:1702.0373

Visualisation and ordering of many-objective populations

Copyright © 2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.We introduce novel methods of visualising and ordering multi-and many-objective populations. We compare individuals by the probability that one will beat another in a tournament on a randomly selected objective. This defines a weighted directed graph representing the population. We introduce a novel graphical representation of the many objective population based on Pareto shells. We examine leagues, Pareto shells, preference ordering, average rank, outflow, the stationary distribution and the power index for ordering the population finding that the average rank is equivalent to outflow and that these together with the power index are generally superior. Finally, we show how to seriate objectives to enhance the interpretability of heatmap visualisations

Interactions between financial and environmental networks in OECD countries

We analyse a multiplex of networks between OECD countries during the decade 2002-2010, which consists of five financial layers, given by foreign direct investment, equity securities, short-term, long-term and total debt securities, and five environmental layers, given by emissions of N O x, P M 10 SO 2, CO 2 equivalent and the water footprint associated with international trade. We present a new measure of cross-layer correlations between flows in different layers based on reciprocity. For the assessment of results, we implement a null model for this measure based on the exponential random graph theory. We find that short-term financial flows are more correlated with environmental flows than long-term investments. Moreover, the correlations between reverse financial and environmental flows (i.e. flows of different layers going in opposite directions) are generally stronger than correlations between synergic flows (flows going in the same direction). This suggests a trade-off between financial and environmental layers, where, more financialised countries display higher correlations between outgoing financial flows and incoming environmental flows from lower financialised countries, which could have important policy implications. Five countries are identified as hubs in this finance-environment multiplex: The United States, France, Germany, Belgium-Luxembourg and the United Kingdom.Comment: Supplementary Information provide