2,934 research outputs found
Multilevel compression of random walks on networks reveals hierarchical organization in large integrated systems
To comprehend the hierarchical organization of large integrated systems, we
introduce the hierarchical map equation, which reveals multilevel structures in
networks. In this information-theoretic approach, we exploit the duality
between compression and pattern detection; by compressing a description of a
random walker as a proxy for real flow on a network, we find regularities in
the network that induce this system-wide flow. Finding the shortest multilevel
description of the random walker therefore gives us the best hierarchical
clustering of the network, the optimal number of levels and modular partition
at each level, with respect to the dynamics on the network. With a novel search
algorithm, we extract and illustrate the rich multilevel organization of
several large social and biological networks. For example, from the global air
traffic network we uncover countries and continents, and from the pattern of
scientific communication we reveal more than 100 scientific fields organized in
four major disciplines: life sciences, physical sciences, ecology and earth
sciences, and social sciences. In general, we find shallow hierarchical
structures in globally interconnected systems, such as neural networks, and
rich multilevel organizations in systems with highly separated regions, such as
road networks.Comment: 11 pages, 5 figures. For associated code, see
http://www.tp.umu.se/~rosvall/code.htm
The map equation
Many real-world networks are so large that we must simplify their structure
before we can extract useful information about the systems they represent. As
the tools for doing these simplifications proliferate within the network
literature, researchers would benefit from some guidelines about which of the
so-called community detection algorithms are most appropriate for the
structures they are studying and the questions they are asking. Here we show
that different methods highlight different aspects of a network's structure and
that the the sort of information that we seek to extract about the system must
guide us in our decision. For example, many community detection algorithms,
including the popular modularity maximization approach, infer module
assignments from an underlying model of the network formation process. However,
we are not always as interested in how a system's network structure was formed,
as we are in how a network's extant structure influences the system's behavior.
To see how structure influences current behavior, we will recognize that links
in a network induce movement across the network and result in system-wide
interdependence. In doing so, we explicitly acknowledge that most networks
carry flow. To highlight and simplify the network structure with respect to
this flow, we use the map equation. We present an intuitive derivation of this
flow-based and information-theoretic method and provide an interactive on-line
application that anyone can use to explore the mechanics of the map equation.
We also describe an algorithm and provide source code to efficiently decompose
large weighted and directed networks based on the map equation.Comment: 9 pages and 3 figures, corrected typos. For associated Flash
application, see http://www.tp.umu.se/~rosvall/livemod/mapequation
Why Full Open Access Matters
This perspective explains the mechanics of copyright and scholarly publishing and warns authors who support open-access publishing about a new pseudo open-access publishing model in which authors pay but publishers still retain commercial reuse rights
Maps of random walks on complex networks reveal community structure
To comprehend the multipartite organization of large-scale biological and
social systems, we introduce a new information theoretic approach that reveals
community structure in weighted and directed networks. The method decomposes a
network into modules by optimally compressing a description of information
flows on the network. The result is a map that both simplifies and highlights
the regularities in the structure and their relationships. We illustrate the
method by making a map of scientific communication as captured in the citation
patterns of more than 6000 journals. We discover a multicentric organization
with fields that vary dramatically in size and degree of integration into the
network of science. Along the backbone of the network -- including physics,
chemistry, molecular biology, and medicine -- information flows
bidirectionally, but the map reveals a directional pattern of citation from the
applied fields to the basic sciences.Comment: 7 pages and 4 figures plus supporting material. For associated source
code, see http://www.tp.umu.se/~rosvall
Microscopic calculation of 6Li elastic and transition form factors
Variational Monte Carlo wave functions, obtained from a realistic Hamiltonian
consisting of the Argonne v18 two-nucleon and Urbana-IX three-nucleon
interactions, are used to calculate the 6Li ground-state longitudinal and
transverse form factors as well as transition form factors to the first four
excited states. The charge and current operators include one- and two-body
components, leading terms of which are constructed consistently with the
two-nucleon interaction. The calculated form factors and radiative widths are
in good agreement with available experimental data.Comment: 9 pages, 2 figures, REVTeX, submitted to Physical Review Letters,
with updated introduction and reference
Gauge-invariant tree-level photoproduction amplitudes with form factors
We show how the gauge-invariance formulation given by Haberzettl is
implemented in practice for photoproduction amplitudes at the tree level with
form factors describing composite nucleons. We demonstrate that, in contrast to
Ohta's gauge-invariance prescription, this formalism allows electric current
contributions to be multiplied by a form factor, i.e., it does not require that
they be treated like bare currents. While different in detail, this
nevertheless lends support to previous ad hoc approaches which multiply the
Born amplitudes by an overall form factor. Numerical results for kaon
photoproduction off the nucleon are given. They show that the gauge procedure
by Haberzettl leads to much improved values as compared to Ohta's
prescription.Comment: 5 pages, RevTeX, two eps figure
An integrated vapor source with a porous silicon wick
A micro vapor source has been developed for calibrating micro gas chromatograph (ΜGC) systems. By utilizing a porous silicon wick in a micro diffusion system, vapor generation with excellent stability has been achieved. The source has shown uniform and repeatable vapor generation for n-decane with less than a 0.1% variation in 9 hours, and less than a 0.5% variation in rate over 7 days. The evolution rate follows the diffusion model as expected, although the room temperature rate is higher than theoretically predicted. Equipped with a refillable reservoir, this vapor source is suitable for extended ΜGC field deployment. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/56056/1/1449_ftp.pd
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