953 research outputs found
JuliBootS: a hands-on guide to the conformal bootstrap
We introduce {\tt JuliBootS}, a package for numerical conformal bootstrap
computations coded in {\tt Julia}. The centre-piece of {\tt JuliBootS} is an
implementation of Dantzig's simplex method capable of handling arbitrary
precision linear programming problems with continuous search spaces. Current
supported features include conformal dimension bounds, OPE bounds, and
bootstrap with or without global symmetries. The code is trivially
parallelizable on one or multiple machines. We exemplify usage extensively with
several real-world applications. In passing we give a pedagogical introduction
to the numerical bootstrap methods.Comment: 29 page
A Simulation Estimator for Testing the Time Homogeneity of Credit Rating Transition
The measurement of credit quality is at the heart of the models designed to assess the reserves and capital needed to support the risks of both individual credits and portfolios of credit instruments. A popular specification for credit- rating transitions is the simple, time-homogeneous Markov model. While the Markov specification cannot really describe processes in the long run, it may be useful for adequately describing short-run changes in portfolio risk. In this specification, the entire stochastic process can be characterized in terms of estimated transition probabilities. However, the simple homogeneous Markovian transition framework is restrictive. We propose a test of the null hypotheses of time-homogeneity that can be performed on the sorts of data often reported. We apply the tests to 4 data sets, on commercial paper, sovereign debt, municipal bonds and S&P Corporates. The results indicate that commercial paper looks Markovian on a 30-day time scale for up to 6 months; sovereign debt also looks Markovian (perhaps due to a small sample size); municipals are well-modeled by the Markov specification for up to 5 years, but could probably benefit from frequent updating of the estimated transition matrix or from more sophisticated modeling, and S&P Corporate ratings are approximately Markov over 3 transitions but not 4.
Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof
New measures of multipartite entanglement are constructed based on two
definitions of multipartite information and different methods of optimizing
over extensions of the states. One is a generalization of the squashed
entanglement where one takes the mutual information of parties conditioned on
the state's extension and takes the infimum over such extensions. Additivity of
the multipartite squashed entanglement is proved for both versions of the
multipartite information which turn out to be related. The second one is based
on taking classical extensions. This scheme is generalized, which enables to
construct measures of entanglement based on the {\it mixed convex roof} of a
quantity, which in contrast to the standard convex roof method involves
optimization over all decompositions of a density matrix rather than just the
decompositions into pure states. As one of the possible applications of these
results we prove that any multipartite monotone is an upper bound on the amount
of multipartite distillable key. The findings are finally related to analogous
results in classical key agreement.Comment: improved version, 13 pages, 1 figur
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