680 research outputs found
A paradox in community detection
Recent research has shown that virtually all algorithms aimed at the
identification of communities in networks are affected by the same main
limitation: the impossibility to detect communities, even when these are
well-defined, if the average value of the difference between internal and
external node degrees does not exceed a strictly positive value, in literature
known as detectability threshold. Here, we counterintuitively show that the
value of this threshold is inversely proportional to the intrinsic quality of
communities: the detection of well-defined modules is thus more difficult than
the identification of ill-defined communities.Comment: 5 pages, 3 figure
Evaluating Local Community Methods in Networks
We present a new benchmarking procedure that is unambiguous and specific to
local community-finding methods, allowing one to compare the accuracy of
various methods. We apply this to new and existing algorithms. A simple class
of synthetic benchmark networks is also developed, capable of testing
properties specific to these local methods.Comment: 8 pages, 9 figures, code included with sourc
Fast Community Identification by Hierarchical Growth
A new method for community identification is proposed which is founded on the
analysis of successive neighborhoods, reached through hierarchical growth from
a starting vertex, and on the definition of communities as a subgraph whose
number of inner connections is larger than outer connections. In order to
determine the precision and speed of the method, it is compared with one of the
most popular community identification approaches, namely Girvan and Newman's
algorithm. Although the hierarchical growth method is not as precise as Girvan
and Newman's method, it is potentially faster than most community finding
algorithms.Comment: 6 pages, 5 figure
Transport signatures of quasiparticle poisoning in a Majorana island
We investigate effects of quasiparticle poisoning in a Majorana island with
strong tunnel coupling to normal-metal leads. In addition to the main Coulomb
blockade diamonds, "shadow" diamonds appear, shifted by 1e in gate voltage,
consistent with transport through an excited (poisoned) state of the island.
Comparison to a simple model yields an estimate of parity lifetime for the
strongly coupled island (~ 1 {\mu}s) and sets a bound for a weakly coupled
island (> 10 {\mu}s). Fluctuations in the gate-voltage spacing of Coulomb peaks
at high field, reflecting Majorana hybridization, are enhanced by the reduced
lever arm at strong coupling. In energy units, fluctuations are consistent with
previous measurements.Comment: includes supplementary materia
Local multiresolution order in community detection
Community detection algorithms attempt to find the best clusters of nodes in
an arbitrary complex network. Multi-scale ("multiresolution") community
detection extends the problem to identify the best network scale(s) for these
clusters. The latter task is generally accomplished by analyzing community
stability simultaneously for all clusters in the network. In the current work,
we extend this general approach to define local multiresolution methods, which
enable the extraction of well-defined local communities even if the global
community structure is vaguely defined in an average sense. Toward this end, we
propose measures analogous to variation of information and normalized mutual
information that are used to quantitatively identify the best resolution(s) at
the community level based on correlations between clusters in
independently-solved systems. We demonstrate our method on two constructed
networks as well as a real network and draw inferences about local community
strength. Our approach is independent of the applied community detection
algorithm save for the inherent requirement that the method be able to identify
communities across different network scales, with appropriate changes to
account for how different resolutions are evaluated or defined in a particular
community detection method. It should, in principle, easily adapt to
alternative community comparison measures.Comment: 19 pages, 11 figure
Use of cumulative incidence of novel influenza A/H1N1 in foreign travelers to estimate lower bounds on cumulative incidence in Mexico
Background: An accurate estimate of the total number of cases and severity of illness of an emerging infectious disease is
required both to define the burden of the epidemic and to determine the severity of disease. When a novel pathogen first
appears, affected individuals with severe symptoms are more likely to be diagnosed. Accordingly, the total number of cases
will be underestimated and disease severity overestimated. This problem is manifest in the current epidemic of novel
influenza A/H1N1.
Methods and Results: We used a simple approach to leverage measures of incident influenza A/H1N1 among a relatively
small and well observed group of US, UK, Spanish and Canadian travelers who had visited Mexico to estimate the incidence
among a much larger and less well surveyed population of Mexican residents. We estimate that a minimum of 113,000 to
375,000 cases of novel influenza A/H1N1 have occurred in Mexicans during the month of April, 2009. Such an estimate
serves as a lower bound because it does not account for underreporting of cases in travelers or for nonrandom mixing
between Mexican residents and visitors, which together could increase the estimates by more than an order of magnitude.
Conclusions: We find that the number of cases in Mexican residents may exceed the number of confirmed cases by two to
three orders of magnitude. While the extent of disease spread is greater than previously appreciated, our estimate suggests
that severe disease is uncommon since the total number of cases is likely to be much larger than those of confirmed cases
Modularity and community detection in bipartite networks
The modularity of a network quantifies the extent, relative to a null model
network, to which vertices cluster into community groups. We define a null
model appropriate for bipartite networks, and use it to define a bipartite
modularity. The bipartite modularity is presented in terms of a modularity
matrix B; some key properties of the eigenspectrum of B are identified and used
to describe an algorithm for identifying modules in bipartite networks. The
algorithm is based on the idea that the modules in the two parts of the network
are dependent, with each part mutually being used to induce the vertices for
the other part into the modules. We apply the algorithm to real-world network
data, showing that the algorithm successfully identifies the modular structure
of bipartite networks.Comment: RevTex 4, 11 pages, 3 figures, 1 table; modest extensions to conten
Unified Scaling Law for Earthquakes
We show that the distribution of waiting times between earthquakes occurring
in California obeys a simple unified scaling law valid from tens of seconds to
tens of years, see Eq. (1) and Fig. 4. The short time clustering, commonly
referred to as aftershocks, is nothing but the short time limit of the general
hierarchical properties of earthquakes. There is no unique operational way of
distinguishing between main shocks and aftershocks. In the unified law, the
Gutenberg-Richter b-value, the exponent -1 of the Omori law for aftershocks,
and the fractal dimension d_f of earthquakes appear as critical indices.Comment: 4 pages, 4 figure
Multiple Nuclear Polarization States in a Double Quantum Dot
We observe multiple stable states of nuclear polarization in a double quantum
dot under conditions of electron spin resonance. The stable states can be
understood within an elaborated theoretical rate equation model for the
polarization in each of the dots, in the limit of strong driving. This model
also captures unusual features of the data, such as fast switching and a
`wrong' sign of polarization. The results reported enable applications of this
polarization effect, including manipulation and control of nuclear fields.Comment: 5 pages, 4 figures, 7 pages supplementary materia
Eigenvector localization as a tool to study small communities in online social networks
We present and discuss a mathematical procedure for identification of small
"communities" or segments within large bipartite networks. The procedure is
based on spectral analysis of the matrix encoding network structure. The
principal tool here is localization of eigenvectors of the matrix, by means of
which the relevant network segments become visible. We exemplified our approach
by analyzing the data related to product reviewing on Amazon.com. We found
several segments, a kind of hybrid communities of densely interlinked reviewers
and products, which we were able to meaningfully interpret in terms of the type
and thematic categorization of reviewed items. The method provides a
complementary approach to other ways of community detection, typically aiming
at identification of large network modules
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