Distance-generalized Core Decomposition

The $k$-core of a graph is defined as the maximal subgraph in which every vertex is connected to at least $k$ other vertices within that subgraph. In this work we introduce a distance-based generalization of the notion of $k$-core, which we refer to as the $(k,h)$-core, i.e., the maximal subgraph in which every vertex has at least $k$ other vertices at distance $\leq h$ within that subgraph. We study the properties of the $(k,h)$-core showing that it preserves many of the nice features of the classic core decomposition (e.g., its connection with the notion of distance-generalized chromatic number) and it preserves its usefulness to speed-up or approximate distance-generalized notions of dense structures, such as $h$-club. Computing the distance-generalized core decomposition over large networks is intrinsically complex. However, by exploiting clever upper and lower bounds we can partition the computation in a set of totally independent subcomputations, opening the door to top-down exploration and to multithreading, and thus achieving an efficient algorithm

Multiwave Mixing in Complex Molecular Media and Dynamic Modes of Light-Wave Transformation

The mechanism of multiwave mixing realized in solutions of complex organic compounds (dyes), in conditions when higher-order nonlinearities are exhibited along with the cubic one, has been analyzed theoretically and tested experimentally. Nonlinear recording of dynamic holograms enables signifcant improvement of the potentialities of holographic methods used for image conversion due to switching from phase conjugation to smoothing and amplification of the wavefront spatial structure. It has been demonstrated that a nonstationary energy exchange between the interacting waves is the cause for transition from the optical bistability mode to the mode of intensity self-oscillations

The evolution of interdisciplinarity in physics research

Science, being a social enterprise, is subject to fragmentation into groups that focus on specialized areas or topics. Often new advances occur through cross-fertilization of ideas between sub-fields that otherwise have little overlap as they study dissimilar phenomena using different techniques. Thus to explore the nature and dynamics of scientific progress one needs to consider the large-scale organization and interactions between different subject areas. Here, we study the relationships between the sub-fields of Physics using the Physics and Astronomy Classification Scheme (PACS) codes employed for self-categorization of articles published over the past 25 years (1985-2009). We observe a clear trend towards increasing interactions between the different sub-fields. The network of sub-fields also exhibits core-periphery organization, the nucleus being dominated by Condensed Matter and General Physics. However, over time Interdisciplinary Physics is steadily increasing its share in the network core, reflecting a shift in the overall trend of Physics research.Comment: Published version, 10 pages, 8 figures + Supplementary Informatio

Worldwide spreading of economic crisis

We model the spreading of a crisis by constructing a global economic network and applying the Susceptible-Infected-Recovered (SIR) epidemic model with a variable probability of infection. The probability of infection depends on the strength of economic relations between the pair of countries, and the strength of the target country. It is expected that a crisis which originates in a large country, such as the USA, has the potential to spread globally, like the recent crisis. Surprisingly we show that also countries with much lower GDP, such as Belgium, are able to initiate a global crisis. Using the {\it k}-shell decomposition method to quantify the spreading power (of a node), we obtain a measure of ``centrality'' as a spreader of each country in the economic network. We thus rank the different countries according to the shell they belong to, and find the 12 most central countries. These countries are the most likely to spread a crisis globally. Of these 12 only six are large economies, while the other six are medium/small ones, a result that could not have been otherwise anticipated. Furthermore, we use our model to predict the crisis spreading potential of countries belonging to different shells according to the crisis magnitude.Comment: 13 pages, 4 figures and Supplementary Materia

Hyperbolic Geometry of Complex Networks

We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong clustering in complex networks emerge naturally as simple reflections of the negative curvature and metric property of the underlying hyperbolic geometry. Conversely, we show that if a network has some metric structure, and if the network degree distribution is heterogeneous, then the network has an effective hyperbolic geometry underneath. We then establish a mapping between our geometric framework and statistical mechanics of complex networks. This mapping interprets edges in a network as non-interacting fermions whose energies are hyperbolic distances between nodes, while the auxiliary fields coupled to edges are linear functions of these energies or distances. The geometric network ensemble subsumes the standard configuration model and classical random graphs as two limiting cases with degenerate geometric structures. Finally, we show that targeted transport processes without global topology knowledge, made possible by our geometric framework, are maximally efficient, according to all efficiency measures, in networks with strongest heterogeneity and clustering, and that this efficiency is remarkably robust with respect to even catastrophic disturbances and damages to the network structure

Seeds Buffering for Information Spreading Processes

Seeding strategies for influence maximization in social networks have been studied for more than a decade. They have mainly relied on the activation of all resources (seeds) simultaneously in the beginning; yet, it has been shown that sequential seeding strategies are commonly better. This research focuses on studying sequential seeding with buffering, which is an extension to basic sequential seeding concept. The proposed method avoids choosing nodes that will be activated through the natural diffusion process, which is leading to better use of the budget for activating seed nodes in the social influence process. This approach was compared with sequential seeding without buffering and single stage seeding. The results on both real and artificial social networks confirm that the buffer-based consecutive seeding is a good trade-off between the final coverage and the time to reach it. It performs significantly better than its rivals for a fixed budget. The gain is obtained by dynamic rankings and the ability to detect network areas with nodes that are not yet activated and have high potential of activating their neighbours.Comment: Jankowski, J., Br\'odka, P., Michalski, R., & Kazienko, P. (2017, September). Seeds Buffering for Information Spreading Processes. In International Conference on Social Informatics (pp. 628-641). Springe

Partisan Asymmetries in Online Political Activity

We examine partisan differences in the behavior, communication patterns and social interactions of more than 18,000 politically-active Twitter users to produce evidence that points to changing levels of partisan engagement with the American online political landscape. Analysis of a network defined by the communication activity of these users in proximity to the 2010 midterm congressional elections reveals a highly segregated, well clustered partisan community structure. Using cluster membership as a high-fidelity (87% accuracy) proxy for political affiliation, we characterize a wide range of differences in the behavior, communication and social connectivity of left- and right-leaning Twitter users. We find that in contrast to the online political dynamics of the 2008 campaign, right-leaning Twitter users exhibit greater levels of political activity, a more tightly interconnected social structure, and a communication network topology that facilitates the rapid and broad dissemination of political information.Comment: 17 pages, 10 figures, 6 table

Emergence of influential spreaders in modified rumor models

The burst in the use of online social networks over the last decade has provided evidence that current rumor spreading models miss some fundamental ingredients in order to reproduce how information is disseminated. In particular, recent literature has revealed that these models fail to reproduce the fact that some nodes in a network have an influential role when it comes to spread a piece of information. In this work, we introduce two mechanisms with the aim of filling the gap between theoretical and experimental results. The first model introduces the assumption that spreaders are not always active whereas the second model considers the possibility that an ignorant is not interested in spreading the rumor. In both cases, results from numerical simulations show a higher adhesion to real data than classical rumor spreading models. Our results shed some light on the mechanisms underlying the spreading of information and ideas in large social systems and pave the way for more realistic diffusion models.Comment: 14 Pages, 6 figures, accepted for publication in Journal of Statistical Physic

Transition from fractal to non-fractal scalings in growing scale-free networks

Real networks can be classified into two categories: fractal networks and non-fractal networks. Here we introduce a unifying model for the two types of networks. Our model network is governed by a parameter $q$. We obtain the topological properties of the network including the degree distribution, average path length, diameter, fractal dimensions, and betweenness centrality distribution, which are controlled by parameter $q$. Interestingly, we show that by adjusting $q$, the networks undergo a transition from fractal to non-fractal scalings, and exhibit a crossover from `large' to small worlds at the same time. Our research may shed some light on understanding the evolution and relationships of fractal and non-fractal networks.Comment: 7 pages, 3 figures, definitive version accepted for publication in EPJ