24,198 research outputs found
First passage time for random walks in heterogeneous networks
The first passage time (FPT) for random walks is a key indicator of how fast
information diffuses in a given system. Despite the role of FPT as a
fundamental feature in transport phenomena, its behavior, particularly in
heterogeneous networks, is not yet fully understood. Here, we study, both
analytically and numerically, the scaling behavior of the FPT distribution to a
given target node, averaged over all starting nodes. We find that random walks
arrive quickly at a local hub, and therefore, the FPT distribution shows a
crossover with respect to time from fast decay behavior (induced from the
attractive effect to the hub) to slow decay behavior (caused by the exploring
of the entire system). Moreover, the mean FPT is independent of the degree of
the target node in the case of compact exploration. These theoretical results
justify the necessity of using a random jump protocol (empirically used in
search engines) and provide guidelines for designing an effective network to
make information quickly accessible.Comment: 5 pages, 3 figure
Efficient Schemes for Reducing Imperfect Collective Decoherences
We propose schemes that are efficient when each pair of qubits undergoes some
imperfect collective decoherence with different baths. In the proposed scheme,
each pair of qubits is first encoded in a decoherence-free subspace composed of
two qubits. Leakage out of the encoding space generated by the imperfection is
reduced by the quantum Zeno effect. Phase errors in the encoded bits generated
by the imperfection are reduced by concatenation of the decoherence-free
subspace with either a three-qubit quantum error correcting code that corrects
only phase errors or a two-qubit quantum error detecting code that detects only
phase errors, connected with the quantum Zeno effect again.Comment: no correction, 3 pages, RevTe
Compressibility of graphene
We develop a theory for the compressibility and quantum capacitance of
disordered monolayer and bilayer graphene including the full hyperbolic band
structure and band gap in the latter case. We include the effects of disorder
in our theory, which are of particular importance at the carrier densities near
the Dirac point. We account for this disorder statistically using two different
averaging procedures: first via averaging over the density of carriers
directly, and then via averaging in the density of states to produce an
effective density of carriers. We also compare the results of these two models
with experimental data, and to do this we introduce a model for inter-layer
screening which predicts the size of the band gap between the low-energy
conduction and valence bands for arbitary gate potentials applied to both
layers of bilayer graphene. We find that both models for disorder give
qualitatively correct results for gapless systems, but when there is a band gap
at charge neutrality, the density of states averaging is incorrect and
disagrees with the experimental data.Comment: 10 pages, 7 figures, RevTe
Using Bayesian variable selection methods to choose style factors in global stock return models
This paper applies Bayesian variable selection methods from the statistics literature to
give guidance in the decision to include/omit factors in a global (linear factor) stock
return model. Once one has accounted for country and sector, it is possible to see which
style or styles best explains current asset returns. This study does not find compelling
evidence for global styles as useful explanatory factors, once country and sector have
been accounted for
Spectral dimensions of hierarchical scale-free networks with shortcuts
The spectral dimension has been widely used to understand transport
properties on regular and fractal lattices. Nevertheless, it has been little
studied for complex networks such as scale-free and small world networks. Here
we study the spectral dimension and the return-to-origin probability of random
walks on hierarchical scale-free networks, which can be either fractals or
non-fractals depending on the weight of shortcuts. Applying the renormalization
group (RG) approach to the Gaussian model, we obtain the spectral dimension
exactly. While the spectral dimension varies between and for the
fractal case, it remains at , independent of the variation of network
structure for the non-fractal case. The crossover behavior between the two
cases is studied through the RG flow analysis. The analytic results are
confirmed by simulation results and their implications for the architecture of
complex systems are discussed.Comment: 10 pages, 3 figure
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