695 research outputs found
The stability of a graph partition: A dynamics-based framework for community detection
Recent years have seen a surge of interest in the analysis of complex
networks, facilitated by the availability of relational data and the
increasingly powerful computational resources that can be employed for their
analysis. Naturally, the study of real-world systems leads to highly complex
networks and a current challenge is to extract intelligible, simplified
descriptions from the network in terms of relevant subgraphs, which can provide
insight into the structure and function of the overall system.
Sparked by seminal work by Newman and Girvan, an interesting line of research
has been devoted to investigating modular community structure in networks,
revitalising the classic problem of graph partitioning.
However, modular or community structure in networks has notoriously evaded
rigorous definition. The most accepted notion of community is perhaps that of a
group of elements which exhibit a stronger level of interaction within
themselves than with the elements outside the community. This concept has
resulted in a plethora of computational methods and heuristics for community
detection. Nevertheless a firm theoretical understanding of most of these
methods, in terms of how they operate and what they are supposed to detect, is
still lacking to date.
Here, we will develop a dynamical perspective towards community detection
enabling us to define a measure named the stability of a graph partition. It
will be shown that a number of previously ad-hoc defined heuristics for
community detection can be seen as particular cases of our method providing us
with a dynamic reinterpretation of those measures. Our dynamics-based approach
thus serves as a unifying framework to gain a deeper understanding of different
aspects and problems associated with community detection and allows us to
propose new dynamically-inspired criteria for community structure.Comment: 3 figures; published as book chapte
Effects of Volcanic Emissions on Clouds During Kilauea Degassing Events
Aerosols influence Earths radiative balance directly by scattering and absorbing solar radiation, and indirectly by modifying cloud properties. Current scientific consensus indicates that these effects may offset as much as 50% of the warming due to greenhouse gas emissions. Over the last two decades dramatic volcanic events in Hawaii have produced localized aerosol emissions in otherwise clean environments. These are natural experiments" where the aerosol effects on clouds and climate can be partitioned from other effects like meteorology and industrial emissions. Therefore, these events provide a unique opportunity to learn about possible effects of aerosol pollution on climate through cloud modification. In this work we use the version 5 of the NASA Goddard Earth Observing System (GEOS-5) and satellite retrievals to analyze and evaluate the strength of the aerosol indirect effect on liquid and ice clouds during the 2008 and 2018 Kilauea degassing events using different emissions scenarios (0, 1, and 5 actual emissions). Our results suggested that the 2018 event was stronger and more regionally significant with respect to cloud formation process for both liquid and ice clouds, while the 2008 affected local liquid clouds only. GEOS-5 predictions reproduced spatial patterns for all parameters, however better precision could be gained by using more accurate plume parameters for height and ash concentration
Emergence of slow-switching assemblies in structured neuronal networks
Unraveling the interplay between connectivity and spatio-temporal dynamics in
neuronal networks is a key step to advance our understanding of neuronal
information processing. Here we investigate how particular features of network
connectivity underpin the propensity of neural networks to generate
slow-switching assembly (SSA) dynamics, i.e., sustained epochs of increased
firing within assemblies of neurons which transition slowly between different
assemblies throughout the network. We show that the emergence of SSA activity
is linked to spectral properties of the asymmetric synaptic weight matrix. In
particular, the leading eigenvalues that dictate the slow dynamics exhibit a
gap with respect to the bulk of the spectrum, and the associated Schur vectors
exhibit a measure of block-localization on groups of neurons, thus resulting in
coherent dynamical activity on those groups. Through simple rate models, we
gain analytical understanding of the origin and importance of the spectral gap,
and use these insights to develop new network topologies with alternative
connectivity paradigms which also display SSA activity. Specifically, SSA
dynamics involving excitatory and inhibitory neurons can be achieved by
modifying the connectivity patterns between both types of neurons. We also show
that SSA activity can occur at multiple timescales reflecting a hierarchy in
the connectivity, and demonstrate the emergence of SSA in small-world like
networks. Our work provides a step towards understanding how network structure
(uncovered through advancements in neuroanatomy and connectomics) can impact on
spatio-temporal neural activity and constrain the resulting dynamics.Comment: The first two authors contributed equally -- 18 pages, including
supplementary material, 10 Figures + 2 SI Figure
Protein multi-scale organization through graph partitioning and robustness analysis: Application to the myosin-myosin light chain interaction
Despite the recognized importance of the multi-scale spatio-temporal
organization of proteins, most computational tools can only access a limited
spectrum of time and spatial scales, thereby ignoring the effects on protein
behavior of the intricate coupling between the different scales. Starting from
a physico-chemical atomistic network of interactions that encodes the structure
of the protein, we introduce a methodology based on multi-scale graph
partitioning that can uncover partitions and levels of organization of proteins
that span the whole range of scales, revealing biological features occurring at
different levels of organization and tracking their effect across scales.
Additionally, we introduce a measure of robustness to quantify the relevance of
the partitions through the generation of biochemically-motivated surrogate
random graph models. We apply the method to four distinct conformations of
myosin tail interacting protein, a protein from the molecular motor of the
malaria parasite, and study properties that have been experimentally addressed
such as the closing mechanism, the presence of conserved clusters, and the
identification through computational mutational analysis of key residues for
binding.Comment: 13 pages, 7 Postscript figure
Encoding dynamics for multiscale community detection: Markov time sweeping for the Map equation
The detection of community structure in networks is intimately related to
finding a concise description of the network in terms of its modules. This
notion has been recently exploited by the Map equation formalism (M. Rosvall
and C.T. Bergstrom, PNAS, 105(4), pp.1118--1123, 2008) through an
information-theoretic description of the process of coding inter- and
intra-community transitions of a random walker in the network at stationarity.
However, a thorough study of the relationship between the full Markov dynamics
and the coding mechanism is still lacking. We show here that the original Map
coding scheme, which is both block-averaged and one-step, neglects the internal
structure of the communities and introduces an upper scale, the `field-of-view'
limit, in the communities it can detect. As a consequence, Map is well tuned to
detect clique-like communities but can lead to undesirable overpartitioning
when communities are far from clique-like. We show that a signature of this
behavior is a large compression gap: the Map description length is far from its
ideal limit. To address this issue, we propose a simple dynamic approach that
introduces time explicitly into the Map coding through the analysis of the
weighted adjacency matrix of the time-dependent multistep transition matrix of
the Markov process. The resulting Markov time sweeping induces a dynamical
zooming across scales that can reveal (potentially multiscale) community
structure above the field-of-view limit, with the relevant partitions indicated
by a small compression gap.Comment: 10 pages, 6 figure
Structure of complex networks: Quantifying edge-to-edge relations by failure-induced flow redistribution
The analysis of complex networks has so far revolved mainly around the role
of nodes and communities of nodes. However, the dynamics of interconnected
systems is commonly focalised on edge processes, and a dual edge-centric
perspective can often prove more natural. Here we present graph-theoretical
measures to quantify edge-to-edge relations inspired by the notion of flow
redistribution induced by edge failures. Our measures, which are related to the
pseudo-inverse of the Laplacian of the network, are global and reveal the
dynamical interplay between the edges of a network, including potentially
non-local interactions. Our framework also allows us to define the embeddedness
of an edge, a measure of how strongly an edge features in the weighted cuts of
the network. We showcase the general applicability of our edge-centric
framework through analyses of the Iberian Power grid, traffic flow in road
networks, and the C. elegans neuronal network.Comment: 24 pages, 6 figure
Identifying naturally occurring communities of primary care providers in the English National Health Service in London
Objectives - Primary Care Networks (PCNs) are a new organisational hierarchy with wide-ranging responsibilities introduced in the National Health Service (NHS) Long Term Plan. The vision is that they represent ‘natural’ communities of general practices (GP practices) working together at scale and covering a geography that make sense to practices, other healthcare providers and local communities. Our study aims to identify natural communities of GP practices based on patient registration patterns using Markov Multiscale Community Detection, an unsupervised network-based clustering technique to create catchments for these communities. Design - Retrospective observational study using Hospital Episode Statistics – patient-level administrative records of inpatient, outpatient and emergency department attendances to hospital. Setting – General practices in the 32 Clinical Commissioning Groups of Greater London Participants - All adult patients resident in and registered to a GP practices in Greater London that had one or more outpatient encounters at NHS hospital trusts between 1st April 2017 and 31st March 2018. Main outcome measures The allocation of GP practices in Greater London to PCNs based on the registrations of patients resident in each Lower Super Output Area (LSOA) of Greater London. The population size and coverage of each proposed PCN. Results - 3,428,322 unique patients attended 1,334 GPs in 4,835 LSOAs in Greater London. Our model grouped 1,291 GPs (96.8%) and 4,721 LSOAs (97.6%), into 165 mutually exclusive PCNs. The median PCN list size was 53,490, with a lower quartile of 38,079 patients and an upper quartile of 72,982 patients. A median of 70.1% of patients attended a GP within their allocated PCN, ranging from 44.6% to 91.4%. Conclusions - With PCNs expected to take a role in population health management and with community providers expected to reconfigure around them, it is vital we recognise how PCNs represent their communities. Our method may be used by policy-makers to understand the populations and geography shared between networks
Robustness of adiabatic quantum computation
We study the fault tolerance of quantum computation by adiabatic evolution, a
quantum algorithm for solving various combinatorial search problems. We
describe an inherent robustness of adiabatic computation against two kinds of
errors, unitary control errors and decoherence, and we study this robustness
using numerical simulations of the algorithm.Comment: 11 pages, 5 figures, REVTe
Lower Critical Dimension of Ising Spin Glasses
Exact ground states of two-dimensional Ising spin glasses with Gaussian and
bimodal (+- J) distributions of the disorder are calculated using a
``matching'' algorithm, which allows large system sizes of up to N=480^2 spins
to be investigated. We study domain walls induced by two rather different types
of boundary-condition changes, and, in each case, analyze the system-size
dependence of an appropriately defined ``defect energy'', which we denote by
DE. For Gaussian disorder, we find a power-law behavior DE ~ L^\theta, with
\theta=-0.266(2) and \theta=-0.282(2) for the two types of boundary condition
changes. These results are in reasonable agreement with each other, allowing
for small systematic effects. They also agree well with earlier work on smaller
sizes. The negative value indicates that two dimensions is below the lower
critical dimension d_c. For the +-J model, we obtain a different result, namely
the domain-wall energy saturates at a nonzero value for L\to \infty, so \theta
= 0, indicating that the lower critical dimension for the +-J model exactly
d_c=2.Comment: 4 pages, 4 figures, 1 table, revte
Flow graphs: interweaving dynamics and structure
The behavior of complex systems is determined not only by the topological
organization of their interconnections but also by the dynamical processes
taking place among their constituents. A faithful modeling of the dynamics is
essential because different dynamical processes may be affected very
differently by network topology. A full characterization of such systems thus
requires a formalization that encompasses both aspects simultaneously, rather
than relying only on the topological adjacency matrix. To achieve this, we
introduce the concept of flow graphs, namely weighted networks where dynamical
flows are embedded into the link weights. Flow graphs provide an integrated
representation of the structure and dynamics of the system, which can then be
analyzed with standard tools from network theory. Conversely, a structural
network feature of our choice can also be used as the basis for the
construction of a flow graph that will then encompass a dynamics biased by such
a feature. We illustrate the ideas by focusing on the mathematical properties
of generic linear processes on complex networks that can be represented as
biased random walks and also explore their dual consensus dynamics.Comment: 4 pages, 1 figur
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