1,027 research outputs found
Multi-level interference resonances in strongly-driven three-level systems
We study multi-photon resonances in a strongly-driven three-level quantum
system, where one level is periodically swept through a pair of levels with
constant energy separation . Near the multi-photon resonance condition
, where is an integer, we find qualitatively different
behavior for even or odd. We explain this phenomenon in terms of families
of interfering trajectories of the multi-level system. Remarkably, the behavior
is insensitive to fluctuations of the energy of the driven level, and survives
deep into the strong dephasing regime. The setup can be relevant for a variety
of solid state and atomic or molecular systems. In particular, it provides a
clear mechanism to explain recent puzzling experimental observations in
strongly-driven double quantum dots.Comment: 4 pages, 3 figure
Module identification in bipartite and directed networks
Modularity is one of the most prominent properties of real-world complex
networks. Here, we address the issue of module identification in two important
classes of networks: bipartite networks and directed unipartite networks. Nodes
in bipartite networks are divided into two non-overlapping sets, and the links
must have one end node from each set. Directed unipartite networks only have
one type of nodes, but links have an origin and an end. We show that directed
unipartite networks can be conviniently represented as bipartite networks for
module identification purposes. We report a novel approach especially suited
for module detection in bipartite networks, and define a set of random networks
that enable us to validate the new approach
Benchmark graphs for testing community detection algorithms
Community structure is one of the most important features of real networks
and reveals the internal organization of the nodes. Many algorithms have been
proposed but the crucial issue of testing, i.e. the question of how good an
algorithm is, with respect to others, is still open. Standard tests include the
analysis of simple artificial graphs with a built-in community structure, that
the algorithm has to recover. However, the special graphs adopted in actual
tests have a structure that does not reflect the real properties of nodes and
communities found in real networks. Here we introduce a new class of benchmark
graphs, that account for the heterogeneity in the distributions of node degrees
and of community sizes. We use this new benchmark to test two popular methods
of community detection, modularity optimization and Potts model clustering. The
results show that the new benchmark poses a much more severe test to algorithms
than standard benchmarks, revealing limits that may not be apparent at a first
analysis.Comment: 6 pages, 8 figures. Extended version published on Physical Review E.
The code to build the new benchmark graphs can be downloaded from
http://santo.fortunato.googlepages.com/inthepress
Identifying network communities with a high resolution
Community structure is an important property of complex networks. An
automatic discovery of such structure is a fundamental task in many
disciplines, including sociology, biology, engineering, and computer science.
Recently, several community discovery algorithms have been proposed based on
the optimization of a quantity called modularity (Q). However, the problem of
modularity optimization is NP-hard, and the existing approaches often suffer
from prohibitively long running time or poor quality. Furthermore, it has been
recently pointed out that algorithms based on optimizing Q will have a
resolution limit, i.e., communities below a certain scale may not be detected.
In this research, we first propose an efficient heuristic algorithm, Qcut,
which combines spectral graph partitioning and local search to optimize Q.
Using both synthetic and real networks, we show that Qcut can find higher
modularities and is more scalable than the existing algorithms. Furthermore,
using Qcut as an essential component, we propose a recursive algorithm, HQcut,
to solve the resolution limit problem. We show that HQcut can successfully
detect communities at a much finer scale and with a higher accuracy than the
existing algorithms. Finally, we apply Qcut and HQcut to study a
protein-protein interaction network, and show that the combination of the two
algorithms can reveal interesting biological results that may be otherwise
undetectable.Comment: 14 pages, 5 figures. 1 supplemental file at
http://cic.cs.wustl.edu/qcut/supplemental.pd
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
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
Detection of Complex Networks Modularity by Dynamical Clustering
Based on cluster de-synchronization properties of phase oscillators, we
introduce an efficient method for the detection and identification of modules
in complex networks. The performance of the algorithm is tested on computer
generated and real-world networks whose modular structure is already known or
has been studied by means of other methods. The algorithm attains a high level
of precision, especially when the modular units are very mixed and hardly
detectable by the other methods, with a computational effort on
a generic graph with nodes and links.Comment: 5 pages, 2 figures. Version accepted for publication on PRE Rapid
Communications: figures changed and text adde
Majorana bound states in a coupled quantum-dot hybrid-nanowire system
Hybrid nanowires combining semiconductor and superconductor materials appear
well suited for the creation, detection, and control of Majorana bound states
(MBSs). We demonstrate the emergence of MBSs from coalescing Andreev bound
states (ABSs) in a hybrid InAs nanowire with epitaxial Al, using a quantum dot
at the end of the nanowire as a spectrometer. Electrostatic gating tuned the
nanowire density to a regime of one or a few ABSs. In an applied axial magnetic
field, a topological phase emerges in which ABSs move to zero energy and remain
there, forming MBSs. We observed hybridization of the MBS with the end-dot
bound state, which is in agreement with a numerical model. The ABS/MBS spectra
provide parameters that are useful for understanding topological
superconductivity in this system.Comment: Article and Supplementary Materia
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
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