34,199 research outputs found
Inhomogeneous percolation models for spreading phenomena in random graphs
Percolation theory has been largely used in the study of structural
properties of complex networks such as the robustness, with remarkable results.
Nevertheless, a purely topological description is not sufficient for a correct
characterization of networks behaviour in relation with physical flows and
spreading phenomena taking place on them. The functionality of real networks
also depends on the ability of the nodes and the edges in bearing and handling
loads of flows, energy, information and other physical quantities. We propose
to study these properties introducing a process of inhomogeneous percolation,
in which both the nodes and the edges spread out the flows with a given
probability.
Generating functions approach is exploited in order to get a generalization
of the Molloy-Reed Criterion for inhomogeneous joint site bond percolation in
correlated random graphs. A series of simple assumptions allows the analysis of
more realistic situations, for which a number of new results are presented. In
particular, for the site percolation with inhomogeneous edge transmission, we
obtain the explicit expressions of the percolation threshold for many
interesting cases, that are analyzed by means of simple examples and numerical
simulations. Some possible applications are debated.Comment: 28 pages, 11 figure
Characterizing Distances of Networks on the Tensor Manifold
At the core of understanding dynamical systems is the ability to maintain and
control the systems behavior that includes notions of robustness,
heterogeneity, or regime-shift detection. Recently, to explore such functional
properties, a convenient representation has been to model such dynamical
systems as a weighted graph consisting of a finite, but very large number of
interacting agents. This said, there exists very limited relevant statistical
theory that is able cope with real-life data, i.e., how does perform analysis
and/or statistics over a family of networks as opposed to a specific network or
network-to-network variation. Here, we are interested in the analysis of
network families whereby each network represents a point on an underlying
statistical manifold. To do so, we explore the Riemannian structure of the
tensor manifold developed by Pennec previously applied to Diffusion Tensor
Imaging (DTI) towards the problem of network analysis. In particular, while
this note focuses on Pennec definition of geodesics amongst a family of
networks, we show how it lays the foundation for future work for developing
measures of network robustness for regime-shift detection. We conclude with
experiments highlighting the proposed distance on synthetic networks and an
application towards biological (stem-cell) systems.Comment: This paper is accepted at 8th International Conference on Complex
Networks 201
Robust Stability Analysis of Sparsely Interconnected Uncertain Systems
In this paper, we consider robust stability analysis of large-scale sparsely
interconnected uncertain systems. By modeling the interconnections among the
subsystems with integral quadratic constraints, we show that robust stability
analysis of such systems can be performed by solving a set of sparse linear
matrix inequalities. We also show that a sparse formulation of the analysis
problem is equivalent to the classical formulation of the robustness analysis
problem and hence does not introduce any additional conservativeness. The
sparse formulation of the analysis problem allows us to apply methods that rely
on efficient sparse factorization techniques, and our numerical results
illustrate the effectiveness of this approach compared to methods that are
based on the standard formulation of the analysis problem.Comment: Provisionally accepted to appear in IEEE Transactions on Automatic
Contro
Precise Packet Loss Pattern Generation by Intentional Interference
Abstract—Intermediate-quality links often cause vulnerable
connectivity in wireless sensor networks, but packet losses caused by such volatile links are not easy to trace. In order to equip link layer protocol designers with a reliable test and debugging tool, we develop a reactive interferer to generate packet loss patterns precisely. By using intentional interference to emulate parameterized lossy links with very low intrusiveness, our tool facilitates both robustness evaluation of protocols and flaw detection in protocol implementation
Dual-layer network representation exploiting information characterization
In this paper, a logical dual-layer representation approach is proposed to facilitate the analysis of directed and weighted complex networks. Unlike the single logical layer structure, which was widely used for the directed and weighted flow graph, the proposed approach replaces the single layer with a dual-layer structure, which introduces a provider layer and a requester layer. The new structure provides the characterization of the nodes by the information, which they provide to and they request from the network. Its features are explained and its implementation and visualization are also detailed. We also design two clustering methods with different strategies respectively, which provide the analysis from different points of view. The effectiveness of the proposed approach is demonstrated using a simplified example. By comparing the graph layout with the conventional directed graph, the new dual-layer representation reveals deeper insight into the complex networks and provides more opportunities for versatile clustering analysis.The National Institute for Health Research (NIHR) under its Programme Grants for Applied Research Programme (Grant Reference Number RP-PG-0310-1004)
A contrasting look at self-organization in the Internet and next-generation communication networks
This article examines contrasting notions of self-organization in the Internet and next-generation communication networks, by reviewing in some detail recent evidence regarding several of the more popular attempts to explain prominent features of Internet structure and behavior as "emergent phenomena." In these examples, what might appear to the nonexpert as "emergent self-organization" in the Internet actually results from well conceived (albeit perhaps ad hoc) design, with explanations that are mathematically rigorous, in agreement with engineering reality, and fully consistent with network measurements. These examples serve as concrete starting points from which networking researchers can assess whether or not explanations involving self-organization are relevant or appropriate in the context of next-generation communication networks, while also highlighting the main differences between approaches to self-organization that are rooted in engineering design vs. those inspired by statistical physics
Understanding Internet topology: principles, models, and validation
Building on a recent effort that combines a first-principles approach to modeling router-level connectivity with a more pragmatic use of statistics and graph theory, we show in this paper that for the Internet, an improved understanding of its physical infrastructure is possible by viewing the physical connectivity as an annotated graph that delivers raw connectivity and bandwidth to the upper layers in the TCP/IP protocol stack, subject to practical constraints (e.g., router technology) and economic considerations (e.g., link costs). More importantly, by relying on data from Abilene, a Tier-1 ISP, and the Rocketfuel project, we provide empirical evidence in support of the proposed approach and its consistency with networking reality. To illustrate its utility, we: 1) show that our approach provides insight into the origin of high variability in measured or inferred router-level maps; 2) demonstrate that it easily accommodates the incorporation of additional objectives of network design (e.g., robustness to router failure); and 3) discuss how it complements ongoing community efforts to reverse-engineer the Internet
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