478 research outputs found
Nuclear spin pumping and electron spin susceptibilities
In this work we present a new formalism to evaluate the nuclear spin dynamics
driven by hyperfine interaction with non-equilibrium electron spins. To
describe the dynamics up to second order in the hyperfine coupling, it suffices
to evaluate the susceptibility and fluctuations of the electron spin. Our
approach does not rely on a separation of electronic energy scales or the
specific choice of electronic basis states, thereby overcoming practical
problems which may arise in certain limits when using a more traditional
formalism based on rate equations.Comment: 9 pages, 2 figure
Quantum Tunneling Detection of Two-photon and Two-electron Processes
We analyze the operation of a quantum tunneling detector coupled to a
coherent conductor. We demonstrate that in a certain energy range the output of
the detector is determined by two-photon processes, two-electron processes and
the interference of the two. We show how the individual contributions of these
processes can be resolved in experiments.Comment: 4 pages, 4 figure
Impact of constrained rewiring on network structure and node dynamics
In this paper, we study an adaptive spatial network. We consider a susceptible-infected-susceptible (SIS) epidemic on the network, with a link or contact rewiring process constrained by spatial proximity. In particular, we assume that susceptible nodes break links with infected nodes independently of distance and reconnect at random to susceptible nodes available within a given radius. By systematically manipulating this radius we investigate the impact of rewiring on the structure of the network and characteristics of the epidemic.We adopt a step-by-step approach whereby we first study the impact of rewiring on the network structure in the absence of an epidemic, then with nodes assigned a disease status but without disease dynamics, and finally running network and epidemic dynamics simultaneously. In the case of no labeling and no epidemic dynamics, we provide both analytic and semianalytic formulas for the value of clustering achieved in the network. Our results also show that the rewiring radius and the network’s initial structure have a pronounced effect on the endemic equilibrium, with increasingly large rewiring radiuses yielding smaller disease prevalence
Statistical Mechanics of Community Detection
Starting from a general \textit{ansatz}, we show how community detection can
be interpreted as finding the ground state of an infinite range spin glass. Our
approach applies to weighted and directed networks alike. It contains the
\textit{at hoc} introduced quality function from \cite{ReichardtPRL} and the
modularity as defined by Newman and Girvan \cite{Girvan03} as special
cases. The community structure of the network is interpreted as the spin
configuration that minimizes the energy of the spin glass with the spin states
being the community indices. We elucidate the properties of the ground state
configuration to give a concise definition of communities as cohesive subgroups
in networks that is adaptive to the specific class of network under study.
Further we show, how hierarchies and overlap in the community structure can be
detected. Computationally effective local update rules for optimization
procedures to find the ground state are given. We show how the \textit{ansatz}
may be used to discover the community around a given node without detecting all
communities in the full network and we give benchmarks for the performance of
this extension. Finally, we give expectation values for the modularity of
random graphs, which can be used in the assessment of statistical significance
of community structure
The entropy of randomized network ensembles
Randomized network ensembles are the null models of real networks and are
extensivelly used to compare a real system to a null hypothesis. In this paper
we study network ensembles with the same degree distribution, the same
degree-correlations or the same community structure of any given real network.
We characterize these randomized network ensembles by their entropy, i.e. the
normalized logarithm of the total number of networks which are part of these
ensembles.
We estimate the entropy of randomized ensembles starting from a large set of
real directed and undirected networks. We propose entropy as an indicator to
assess the role of each structural feature in a given real network.We observe
that the ensembles with fixed scale-free degree distribution have smaller
entropy than the ensembles with homogeneous degree distribution indicating a
higher level of order in scale-free networks.Comment: (6 pages,1 figure,2 tables
Complex networks: new trends for the analysis of brain connectivity
Today, the human brain can be studied as a whole. Electroencephalography,
magnetoencephalography, or functional magnetic resonance imaging techniques
provide functional connectivity patterns between different brain areas, and
during different pathological and cognitive neuro-dynamical states. In this
Tutorial we review novel complex networks approaches to unveil how brain
networks can efficiently manage local processing and global integration for the
transfer of information, while being at the same time capable of adapting to
satisfy changing neural demands.Comment: Tutorial paper to appear in the Int. J. Bif. Chao
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
Partitioning and modularity of graphs with arbitrary degree distribution
We solve the graph bi-partitioning problem in dense graphs with arbitrary
degree distribution using the replica method. We find the cut-size to scale
universally with . In contrast, earlier results studying the problem in
graphs with a Poissonian degree distribution had found a scaling with ^1/2
[Fu and Anderson, J. Phys. A: Math. Gen. 19, 1986]. The new results also
generalize to the problem of q-partitioning. They can be used to find the
expected modularity Q [Newman and Grivan, Phys. Rev. E, 69, 2004] of random
graphs and allow for the assessment of statistical significance of the output
of community detection algorithms.Comment: Revised version including new plots and improved discussion of some
mathematical detail
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