13,556 research outputs found
Parallel Deterministic and Stochastic Global Minimization of Functions with Very Many Minima
The optimization of three problems with high dimensionality and many local minima are investigated
under five different optimization algorithms: DIRECT, simulated annealing, Spall’s SPSA algorithm, the KNITRO
package, and QNSTOP, a new algorithm developed at Indiana University
Exploring self-similarity of complex cellular networks: The edge-covering method with simulated annealing and log-periodic sampling
Song, Havlin and Makse (2005) have recently used a version of the
box-counting method, called the node-covering method, to quantify the
self-similar properties of 43 cellular networks: the minimal number of
boxes of size needed to cover all the nodes of a cellular network was
found to scale as the power law with a fractal
dimension . We propose a new box-counting method based on
edge-covering, which outperforms the node-covering approach when applied to
strictly self-similar model networks, such as the Sierpinski network. The
minimal number of boxes of size in the edge-covering method is
obtained with the simulated annealing algorithm. We take into account the
possible discrete scale symmetry of networks (artifactual and/or real), which
is visualized in terms of log-periodic oscillations in the dependence of the
logarithm of as a function of the logarithm of . In this way, we
are able to remove the bias of the estimator of the fractal dimension, existing
for finite networks. With this new methodology, we find that scales with
respect to as a power law with
for the 43 cellular networks previously analyzed by Song, Havlin and Makse
(2005). Bootstrap tests suggest that the analyzed cellular networks may have a
significant log-periodicity qualifying a discrete hierarchy with a scaling
ratio close to 2. In sum, we propose that our method of edge-covering with
simulated annealing and log-periodic sampling minimizes the significant bias in
the determination of fractal dimensions in log-log regressions.Comment: 19 elsart pages including 9 eps figure
Seeking Quantum Speedup Through Spin Glasses: The Good, the Bad, and the Ugly
There has been considerable progress in the design and construction of
quantum annealing devices. However, a conclusive detection of quantum speedup
over traditional silicon-based machines remains elusive, despite multiple
careful studies. In this work we outline strategies to design hard tunable
benchmark instances based on insights from the study of spin glasses - the
archetypal random benchmark problem for novel algorithms and optimization
devices. We propose to complement head-to-head scaling studies that compare
quantum annealing machines to state-of-the-art classical codes with an approach
that compares the performance of different algorithms and/or computing
architectures on different classes of computationally hard tunable spin-glass
instances. The advantage of such an approach lies in having to only compare the
performance hit felt by a given algorithm and/or architecture when the instance
complexity is increased. Furthermore, we propose a methodology that might not
directly translate into the detection of quantum speedup, but might elucidate
whether quantum annealing has a "`quantum advantage" over corresponding
classical algorithms like simulated annealing. Our results on a 496 qubit
D-Wave Two quantum annealing device are compared to recently-used
state-of-the-art thermal simulated annealing codes.Comment: 14 pages, 8 figures, 3 tables, way too many reference
Seeing the Unseen Network: Inferring Hidden Social Ties from Respondent-Driven Sampling
Learning about the social structure of hidden and hard-to-reach populations
--- such as drug users and sex workers --- is a major goal of epidemiological
and public health research on risk behaviors and disease prevention.
Respondent-driven sampling (RDS) is a peer-referral process widely used by many
health organizations, where research subjects recruit other subjects from their
social network. In such surveys, researchers observe who recruited whom, along
with the time of recruitment and the total number of acquaintances (network
degree) of respondents. However, due to privacy concerns, the identities of
acquaintances are not disclosed. In this work, we show how to reconstruct the
underlying network structure through which the subjects are recruited. We
formulate the dynamics of RDS as a continuous-time diffusion process over the
underlying graph and derive the likelihood for the recruitment time series
under an arbitrary recruitment time distribution. We develop an efficient
stochastic optimization algorithm called RENDER (REspoNdent-Driven nEtwork
Reconstruction) that finds the network that best explains the collected data.
We support our analytical results through an exhaustive set of experiments on
both synthetic and real data.Comment: A full version with technical proofs. Accepted by AAAI-1
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