29,185 research outputs found
Full Counting Statistics and Field Theory
We review the relations between the full counting statistics and the field
theory of electric circuits. We demonstrate that for large conductances the
counting statistics is determined by non-trivial saddle-point of the field.
Coulomb effects in this limit are presented as quantum corrections that can
stongly renormalize the action at low energies.Comment: microreview, 15 pages, accepted to Ann. Phys. (Leipzig
A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning
We present a tutorial on Bayesian optimization, a method of finding the
maximum of expensive cost functions. Bayesian optimization employs the Bayesian
technique of setting a prior over the objective function and combining it with
evidence to get a posterior function. This permits a utility-based selection of
the next observation to make on the objective function, which must take into
account both exploration (sampling from areas of high uncertainty) and
exploitation (sampling areas likely to offer improvement over the current best
observation). We also present two detailed extensions of Bayesian optimization,
with experiments---active user modelling with preferences, and hierarchical
reinforcement learning---and a discussion of the pros and cons of Bayesian
optimization based on our experiences
Unwrapping phase fluctuations in one dimension
Correlation functions in one-dimensional complex scalar field theory provide
a toy model for phase fluctuations, sign problems, and signal-to-noise problems
in lattice field theory. Phase unwrapping techniques from signal processing are
applied to lattice field theory in order to map compact random phases to
noncompact random variables that can be numerically sampled without sign or
signal-to-noise problems. A cumulant expansion can be used to reconstruct
average correlation functions from moments of unwrapped phases, but points
where the field magnitude fluctuates close to zero lead to ambiguities in the
definition of the unwrapped phase and significant noise at higher orders in the
cumulant expansion. Phase unwrapping algorithms that average fluctuations over
physical length scales improve, but do not completely resolve, these issues in
one dimension. Similar issues are seen in other applications of phase
unwrapping, where they are found to be more tractable in higher dimensions.Comment: 14 pages, 7 figures. arXiv admin note: text overlap with
arXiv:1806.0183
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