2,022 research outputs found
Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications (Extended Version)
Although the ``scale-free'' literature is large and growing, it gives neither
a precise definition of scale-free graphs nor rigorous proofs of many of their
claimed properties. In fact, it is easily shown that the existing theory has
many inherent contradictions and verifiably false claims. In this paper, we
propose a new, mathematically precise, and structural definition of the extent
to which a graph is scale-free, and prove a series of results that recover many
of the claimed properties while suggesting the potential for a rich and
interesting theory. With this definition, scale-free (or its opposite,
scale-rich) is closely related to other structural graph properties such as
various notions of self-similarity (or respectively, self-dissimilarity).
Scale-free graphs are also shown to be the likely outcome of random
construction processes, consistent with the heuristic definitions implicit in
existing random graph approaches. Our approach clarifies much of the confusion
surrounding the sensational qualitative claims in the scale-free literature,
and offers rigorous and quantitative alternatives.Comment: 44 pages, 16 figures. The primary version is to appear in Internet
Mathematics (2005
Connectivity measures for internet topologies.
The topology of the Internet has initially been modelled as an undirected graph, where vertices correspond to so-called Autonomous Systems (ASs),and edges correspond to physical links between pairs of ASs. However, in order to capture the impact of routing policies, it has recently become apparent that one needs to classify the edges according to the existing economic relationships (customer-provider, peer-to-peer or siblings) between the ASs. This leads to a directed graph model in which traffic can be sent only along so-called valley-free paths. Four different algorithms have been proposed in the literature for inferring AS relationships using publicly available data from routing tables. We investigate the differences in the graph models produced by these algorithms, focussing on connectivity measures. To this aim, we compute the maximum number of vertex-disjoint valley-free paths between ASs as well as the size of a minimum cut separating a pair of ASs. Although these problems are solvable in polynomial time for ordinary graphs, they are NP-hard in our setting. We formulate the two problems as integer programs, and we propose a number of exact algorithms for solving them. For the problem of finding the maximum number of vertex-disjoint paths, we discuss two algorithms; the first one is a branch-and-price algorithm based on the IP formulation, and the second algorithm is a non LP based branch-and-bound algorithm. For the problem of finding minimum cuts we use a branch-and-cut algo rithm, based on the IP formulation of this problem. Using these algorithms, we obtain exact solutions for both problems in reasonable time. It turns out that there is a large gap in terms of the connectivity measures between the undirected and directed models. This finding supports our conclusion that economic relationships need to be taken into account when building a topology of the Internet.Research; Internet;
Knowledge-based machine vision systems for space station automation
Computer vision techniques which have the potential for use on the space station and related applications are assessed. A knowledge-based vision system (expert vision system) and the development of a demonstration system for it are described. This system implements some of the capabilities that would be necessary in a machine vision system for the robot arm of the laboratory module in the space station. A Perceptics 9200e image processor, on a host VAXstation, was used to develop the demonstration system. In order to use realistic test images, photographs of actual space shuttle simulator panels were used. The system's capabilities of scene identification and scene matching are discussed
PowerSpy: Location Tracking using Mobile Device Power Analysis
Modern mobile platforms like Android enable applications to read aggregate
power usage on the phone. This information is considered harmless and reading
it requires no user permission or notification. We show that by simply reading
the phone's aggregate power consumption over a period of a few minutes an
application can learn information about the user's location. Aggregate phone
power consumption data is extremely noisy due to the multitude of components
and applications that simultaneously consume power. Nevertheless, by using
machine learning algorithms we are able to successfully infer the phone's
location. We discuss several ways in which this privacy leak can be remedied.Comment: Usenix Security 201
The Internet AS-Level Topology: Three Data Sources and One Definitive Metric
We calculate an extensive set of characteristics for Internet AS topologies
extracted from the three data sources most frequently used by the research
community: traceroutes, BGP, and WHOIS. We discover that traceroute and BGP
topologies are similar to one another but differ substantially from the WHOIS
topology. Among the widely considered metrics, we find that the joint degree
distribution appears to fundamentally characterize Internet AS topologies as
well as narrowly define values for other important metrics. We discuss the
interplay between the specifics of the three data collection mechanisms and the
resulting topology views. In particular, we show how the data collection
peculiarities explain differences in the resulting joint degree distributions
of the respective topologies. Finally, we release to the community the input
topology datasets, along with the scripts and output of our calculations. This
supplement should enable researchers to validate their models against real data
and to make more informed selection of topology data sources for their specific
needs.Comment: This paper is a revised journal version of cs.NI/050803
Entrograms and coarse graining of dynamics on complex networks
Using an information theoretic point of view, we investigate how a dynamics
acting on a network can be coarse grained through the use of graph partitions.
Specifically, we are interested in how aggregating the state space of a Markov
process according to a partition impacts on the thus obtained lower-dimensional
dynamics. We highlight that for a dynamics on a particular graph there may be
multiple coarse grained descriptions that capture different, incomparable
features of the original process. For instance, a coarse graining induced by
one partition may be commensurate with a time-scale separation in the dynamics,
while another coarse graining may correspond to a different lower-dimensional
dynamics that preserves the Markov property of the original process. Taking
inspiration from the literature of Computational Mechanics, we find that a
convenient tool to summarise and visualise such dynamical properties of a
coarse grained model (partition) is the entrogram. The entrogram gathers
certain information-theoretic measures, which quantify how information flows
across time steps. These information theoretic quantities include the entropy
rate, as well as a measure for the memory contained in the process, i.e., how
well the dynamics can be approximated by a first order Markov process. We use
the entrogram to investigate how specific macro-scale connection patterns in
the state-space transition graph of the original dynamics result in desirable
properties of coarse grained descriptions. We thereby provide a fresh
perspective on the interplay between structure and dynamics in networks, and
the process of partitioning from an information theoretic perspective. We focus
on networks that may be approximated by both a core-periphery or a clustered
organization, and highlight that each of these coarse grained descriptions can
capture different aspects of a Markov process acting on the network.Comment: 17 pages, 6 figue
An Invitation to the Study of Brain Networks, with Some Statistical Analysis of Thresholding Techniques
We provide a brief introduction to the nascent application of network theory to mesoscale networks in the human brain. Following an overview of the typical data-gathering, processing, and analysis methods employed in this field, we describe the process for inferring a graph from neural time series. A crucial step in the construction of a graph from time series is the thresholding of graph edges to ensure that the graphs represent physiological relationships rather than artifactual noise. We discuss the most popular currently employed methodologies and then introduce one of our own, based on the theory of random matrices. Finally, we provide a comparison of our random-matrix-theory thresholding approach with two dominant approaches on a data set of 1,000 real resting-state functional magnetic resonance imaging scans
Graph Element Networks: adaptive, structured computation and memory
We explore the use of graph neural networks (GNNs) to model spatial processes
in which there is no a priori graphical structure. Similar to finite element
analysis, we assign nodes of a GNN to spatial locations and use a computational
process defined on the graph to model the relationship between an initial
function defined over a space and a resulting function in the same space. We
use GNNs as a computational substrate, and show that the locations of the nodes
in space as well as their connectivity can be optimized to focus on the most
complex parts of the space. Moreover, this representational strategy allows the
learned input-output relationship to generalize over the size of the underlying
space and run the same model at different levels of precision, trading
computation for accuracy. We demonstrate this method on a traditional PDE
problem, a physical prediction problem from robotics, and learning to predict
scene images from novel viewpoints.Comment: Accepted to ICML 201
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