10,526 research outputs found
Uniform sampling of steady states in metabolic networks: heterogeneous scales and rounding
The uniform sampling of convex polytopes is an interesting computational
problem with many applications in inference from linear constraints, but the
performances of sampling algorithms can be affected by ill-conditioning. This
is the case of inferring the feasible steady states in models of metabolic
networks, since they can show heterogeneous time scales . In this work we focus
on rounding procedures based on building an ellipsoid that closely matches the
sampling space, that can be used to define an efficient hit-and-run (HR) Markov
Chain Monte Carlo. In this way the uniformity of the sampling of the convex
space of interest is rigorously guaranteed, at odds with non markovian methods.
We analyze and compare three rounding methods in order to sample the feasible
steady states of metabolic networks of three models of growing size up to
genomic scale. The first is based on principal component analysis (PCA), the
second on linear programming (LP) and finally we employ the lovasz ellipsoid
method (LEM). Our results show that a rounding procedure is mandatory for the
application of the HR in these inference problem and suggest that a combination
of LEM or LP with a subsequent PCA perform the best. We finally compare the
distributions of the HR with that of two heuristics based on the Artificially
Centered hit-and-run (ACHR), gpSampler and optGpSampler. They show a good
agreement with the results of the HR for the small network, while on genome
scale models present inconsistencies.Comment: Replacement with major revision
A Cubic Algorithm for Computing Gaussian Volume
We present randomized algorithms for sampling the standard Gaussian
distribution restricted to a convex set and for estimating the Gaussian measure
of a convex set, in the general membership oracle model. The complexity of
integration is while the complexity of sampling is for
the first sample and for every subsequent sample. These bounds
improve on the corresponding state-of-the-art by a factor of . Our
improvement comes from several aspects: better isoperimetry, smoother
annealing, avoiding transformation to isotropic position and the use of the
"speedy walk" in the analysis.Comment: 23 page
Glassy Phase of Optimal Quantum Control
We study the problem of preparing a quantum many-body system from an initial
to a target state by optimizing the fidelity over the family of bang-bang
protocols. We present compelling numerical evidence for a universal
spin-glass-like transition controlled by the protocol time duration. The glassy
critical point is marked by a proliferation of protocols with close-to-optimal
fidelity and with a true optimum that appears exponentially difficult to
locate. Using a machine learning (ML) inspired framework based on the manifold
learning algorithm t-SNE, we are able to visualize the geometry of the
high-dimensional control landscape in an effective low-dimensional
representation. Across the transition, the control landscape features an
exponential number of clusters separated by extensive barriers, which bears a
strong resemblance with replica symmetry breaking in spin glasses and random
satisfiability problems. We further show that the quantum control landscape
maps onto a disorder-free classical Ising model with frustrated nonlocal,
multibody interactions. Our work highlights an intricate but unexpected
connection between optimal quantum control and spin glass physics, and shows
how tools from ML can be used to visualize and understand glassy optimization
landscapes.Comment: Modified figures in appendix and main text (color schemes). Corrected
references. Added figures in SI and pseudo-cod
Optimal computation of brightness integrals parametrized on the unit sphere
We compare various approaches to find the most efficient method for the
practical computation of the lightcurves (integrated brightnesses) of
irregularly shaped bodies such as asteroids at arbitrary viewing and
illumination geometries. For convex models, this reduces to the problem of the
numerical computation of an integral over a simply defined part of the unit
sphere. We introduce a fast method, based on Lebedev quadratures, which is
optimal for both lightcurve simulation and inversion in the sense that it is
the simplest and fastest widely applicable procedure for accuracy levels
corresponding to typical data noise. The method requires no tessellation of the
surface into a polyhedral approximation. At the accuracy level of 0.01 mag, it
is up to an order of magnitude faster than polyhedral sums that are usually
applied to this problem, and even faster at higher accuracies. This approach
can also be used in other similar cases that can be modelled on the unit
sphere. The method is easily implemented in lightcurve inversion by a simple
alteration of the standard algorithm/software.Comment: Astronomy and Astrophysics, in pres
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