5,151 research outputs found

    Dynamic Exploration of Networks: from general principles to the traceroute process

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    Dynamical processes taking place on real networks define on them evolving subnetworks whose topology is not necessarily the same of the underlying one. We investigate the problem of determining the emerging degree distribution, focusing on a class of tree-like processes, such as those used to explore the Internet's topology. A general theory based on mean-field arguments is proposed, both for single-source and multiple-source cases, and applied to the specific example of the traceroute exploration of networks. Our results provide a qualitative improvement in the understanding of dynamical sampling and of the interplay between dynamics and topology in large networks like the Internet.Comment: 13 pages, 6 figure

    Multilayer Networks

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    In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure

    Innovation creation and diffusion in a social network: an agent based approach

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    Market is not only the result of the behaviour of agents, as we can find other forms of contact and communication. Many of them are determined by proximity conditions in some kind of space: in this paper we pay a particular attention to relational space, that is the space determined by the relationships between individuals. The paper starts from a brief account on theoretical and empirical literature on social networks. Social networks represent people and their relationships as networks, in which individuals are nodes and the relationships between them are ties. In particular, graph theory is used in literature in order to demonstrate some properties of social networks summarised in the concept of Small Worlds. The concept may be used to explain how some phenomena involving relations among agents have effects on multiple different geographical scales, involving both the local and the global scale. The empirical section of the paper is introduced by a brief summary of simulation techniques in social science and economics as a way to investigate complexity. The model investigates the dynamics of a population of firms (potential innovators) and consumers interacting in a space defined as a social network. Consumers are represented in the model in order to create a competitive environment pushing enterprises into innovative process (we refer to Schumpeter’s definition): from interaction between consumers and firms innovation emerges as a relational good.Innovation; small world; computational economics; network; complexity

    Analysis of Static Cellular Cooperation between Mutually Nearest Neighboring Nodes

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    Cooperation in cellular networks is a promising scheme to improve system performance. Existing works consider that a user dynamically chooses the stations that cooperate for his/her service, but such assumption often has practical limitations. Instead, cooperation groups can be predefined and static, with nodes linked by fixed infrastructure. To analyze such a potential network, we propose a grouping method based on node proximity. With the Mutually Nearest Neighbour Relation, we allow the formation of singles and pairs of nodes. Given an initial topology for the stations, two new point processes are defined, one for the singles and one for the pairs. We derive structural characteristics for these processes and analyse the resulting interference fields. When the node positions follow a Poisson Point Process (PPP) the processes of singles and pairs are not Poisson. However, the performance of the original model can be approximated by the superposition of two PPPs. This allows the derivation of exact expressions for the coverage probability. Numerical evaluation shows coverage gains from different signal cooperation that can reach up to 15% compared to the standard noncooperative coverage. The analysis is general and can be applied to any type of cooperation in pairs of transmitting nodes.Comment: 17 pages, double column, Appendices A-D, 9 Figures, 18 total subfigures. arXiv admin note: text overlap with arXiv:1604.0464

    Complex Networks from Classical to Quantum

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    Recent progress in applying complex network theory to problems in quantum information has resulted in a beneficial crossover. Complex network methods have successfully been applied to transport and entanglement models while information physics is setting the stage for a theory of complex systems with quantum information-inspired methods. Novel quantum induced effects have been predicted in random graphs---where edges represent entangled links---and quantum computer algorithms have been proposed to offer enhancement for several network problems. Here we review the results at the cutting edge, pinpointing the similarities and the differences found at the intersection of these two fields.Comment: 12 pages, 4 figures, REVTeX 4-1, accepted versio

    Emergence of the mitochondrial reticulum from fission and fusion dynamics

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    Mitochondria form a dynamic tubular reticulum within eukaryotic cells. Currently, quantitative understanding of its morphological characteristics is largely absent, despite major progress in deciphering the molecular fission and fusion machineries shaping its structure. Here we address the principles of formation and the large-scale organization of the cell-wide network of mitochondria. On the basis of experimentally determined structural features we establish the tip-to-tip and tip-to-side fission and fusion events as dominant reactions in the motility of this organelle. Subsequently, we introduce a graph-based model of the chondriome able to encompass its inherent variability in a single framework. Using both mean-field deterministic and explicit stochastic mathematical methods we establish a relationship between the chondriome structural network characteristics and underlying kinetic rate parameters. The computational analysis indicates that mitochondrial networks exhibit a percolation threshold. Intrinsic morphological instability of the mitochondrial reticulum resulting from its vicinity to the percolation transition is proposed as a novel mechanism that can be utilized by cells for optimizing their functional competence via dynamic remodeling of the chondriome. The detailed size distribution of the network components predicted by the dynamic graph representation introduces a relationship between chondriome characteristics and cell function. It forms a basis for understanding the architecture of mitochondria as a cell-wide but inhomogeneous organelle. Analysis of the reticulum adaptive configuration offers a direct clarification for its impact on numerous physiological processes strongly dependent on mitochondrial dynamics and organization, such as efficiency of cellular metabolism, tissue differentiation and aging
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