Stability of Influence Maximization

The present article serves as an erratum to our paper of the same title, which was presented and published in the KDD 2014 conference. In that article, we claimed falsely that the objective function defined in Section 1.4 is non-monotone submodular. We are deeply indebted to Debmalya Mandal, Jean Pouget-Abadie and Yaron Singer for bringing to our attention a counter-example to that claim. Subsequent to becoming aware of the counter-example, we have shown that the objective function is in fact NP-hard to approximate to within a factor of $O(n^{1-\epsilon})$ for any $\epsilon > 0$. In an attempt to fix the record, the present article combines the problem motivation, models, and experimental results sections from the original incorrect article with the new hardness result. We would like readers to only cite and use this version (which will remain an unpublished note) instead of the incorrect conference version.Comment: Erratum of Paper "Stability of Influence Maximization" which was presented and published in the KDD1

Availability of food resources and habitat structure shape the individual‐resource network of a Neotropical marsupial

1. Spatial and temporal variation in networks has been reported in different studies. However, the many effects of habitat structure and food resource availability variation on network structures have remained poorly investigated, especially in individual‐ based networks. This approach can shed light on individual specialization of resource use and how habitat variations shape trophic interactions. 2. To test hypotheses related to habitat variability on trophic interactions, we investigated seasonal and spatial variation in network structure of four populations of the marsupial Gracilinanus agilis in the highly seasonal tropical savannas of the Brazilian Cerrado. 3. We evaluated such variation with network nestedness and modularity considering both cool‐dry and warm‐wet seasons, and related such variations with food resource availability and habitat structure (considered in the present study as environmental variation) in four sites of savanna woodland forest. 4. Network analyses showed that modularity (but not nestedness) was consistently lower during the cool‐dry season in all G. agilis populations. Our results indicated that nestedness is related to habitat structure, showing that this metric increases in sites with thick and spaced trees. On the other hand, modularity was positively related to diversity of arthropods and abundance of fruits. 5. We propose that the relationship between nestedness and habitat structure is an outcome of individual variation in the vertical space and food resource use by G. agilis in sites with thick and spaced trees. Moreover, individual specialization in resource‐rich and population‐dense periods possibly increased the network modularity of G. agilis. Therefore, our study reveals that environment variability considering spatial and temporal components is important for shaping network structure of populations

Qualitative Comparison of Community Detection Algorithms

Community detection is a very active field in complex networks analysis, consisting in identifying groups of nodes more densely interconnected relatively to the rest of the network. The existing algorithms are usually tested and compared on real-world and artificial networks, their performance being assessed through some partition similarity measure. However, artificial networks realism can be questioned, and the appropriateness of those measures is not obvious. In this study, we take advantage of recent advances concerning the characterization of community structures to tackle these questions. We first generate networks thanks to the most realistic model available to date. Their analysis reveals they display only some of the properties observed in real-world community structures. We then apply five community detection algorithms on these networks and find out the performance assessed quantitatively does not necessarily agree with a qualitative analysis of the identified communities. It therefore seems both approaches should be applied to perform a relevant comparison of the algorithms.Comment: DICTAP 2011, The International Conference on Digital Information and Communication Technology and its Applications, Dijon : France (2011

Micro-behaviors and structural properties of knowledge networks: toward a 'one size fits one'cluster policy

The economic returns of cluster policies have been recently called into question. Based on a “one size fits all” approach consisting in boosting R&D collaborations and reinforcing network density, cluster policies are suspected to have failed in reaching their objectives. The paper proposes to go back to the micro foundations of clusters in order to disentangle the links between the long run performance of clusters and their structural properties. We use a simple agent-based model to shed light on how individual motives to build knowledge relationships can give rise to emerging structures with different properties, which imply different innovation and renewal capacities. The simulation results are discussed in a micro-macro perspective, and motivate suggestions to reorient cluster policy guidelines towards more targeted public-funded incentives for R&D collaboration

Untangling a Polygon

The following problem was raised by M. Watanabe. Let P be a self-intersecting closed polygon with n vertices in general position. How manys steps does it take to untangle P, i.e., to turn it into a simple polygon, if in each step we can arbitrarily relocate one of its vertices. It is shown that in some cases one has to move all but at most O((n log n)2/3) vertices. On the other hand, every polygon $P$ can be untangled in at most n − Ω(√n) steps. Some related questions are also considered