1,455 research outputs found
Estimation of subgraph density in noisy networks
While it is common practice in applied network analysis to report various
standard network summary statistics, these numbers are rarely accompanied by
uncertainty quantification. Yet any error inherent in the measurements
underlying the construction of the network, or in the network construction
procedure itself, necessarily must propagate to any summary statistics
reported. Here we study the problem of estimating the density of an arbitrary
subgraph, given a noisy version of some underlying network as data. Under a
simple model of network error, we show that consistent estimation of such
densities is impossible when the rates of error are unknown and only a single
network is observed. Accordingly, we develop method-of-moment estimators of
network subgraph densities and error rates for the case where a minimal number
of network replicates are available. These estimators are shown to be
asymptotically normal as the number of vertices increases to infinity. We also
provide confidence intervals for quantifying the uncertainty in these estimates
based on the asymptotic normality. To construct the confidence intervals, a new
and non-standard bootstrap method is proposed to compute asymptotic variances,
which is infeasible otherwise. We illustrate the proposed methods in the
context of gene coexpression networks
Complex network analysis and nonlinear dynamics
This chapter aims at reviewing complex network and nonlinear dynamical
models and methods that were either developed for or applied to socioeconomic
issues, and pertinent to the theme of New Economic Geography. After an introduction
to the foundations of the field of complex networks, the present summary
introduces some applications of complex networks to economics, finance, epidemic
spreading of innovations, and regional trade and developments. The chapter also
reviews results involving applications of complex networks to other relevant
socioeconomic issue
Performance enhancement of surface codes via recursive MWPM decoding
The minimum weight perfect matching (MWPM) decoder is the standard decoding
strategy for quantum surface codes. However, it suffers a harsh decrease in
performance when subjected to biased or non-identical quantum noise. In this
work, we modify the conventional MWPM decoder so that it considers the biases,
the non-uniformities and the relationship between , and errors of
the constituent qubits of a given surface code. Our modified approach, which we
refer to as the recursive MWPM decoder, obtains an improvement in the
probability threshold under depolarizing noise. We also obtain
significant performance improvements when considering biased noise and
independent non-identically distributed (i.ni.d.) error models derived from
measurements performed on state-of-the-art quantum processors. In fact, when
subjected to i.ni.d. noise, the recursive MWPM decoder yields a performance
improvement of over the conventional MWPM strategy and, in some
cases, it even surpasses the performance obtained over the well-known
depolarizing channel
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