56,821 research outputs found
Quasiconvex Programming
We define quasiconvex programming, a form of generalized linear programming
in which one seeks the point minimizing the pointwise maximum of a collection
of quasiconvex functions. We survey algorithms for solving quasiconvex programs
either numerically or via generalizations of the dual simplex method from
linear programming, and describe varied applications of this geometric
optimization technique in meshing, scientific computation, information
visualization, automated algorithm analysis, and robust statistics.Comment: 33 pages, 14 figure
Existence and uniqueness theorems for massless fields on a class of spacetimes with closed timelike curves
We study the massless scalar field on asymptotically flat spacetimes with
closed timelike curves (CTC's), in which all future-directed CTC's traverse one
end of a handle (wormhole) and emerge from the other end at an earlier time.
For a class of static geometries of this type, and for smooth initial data with
all derivatives in on {\cI}^{-}, we prove existence of smooth solutions
which are regular at null and spatial infinity (have finite energy and finite
-norm) and have the given initial data on \cI^-. A restricted uniqueness
theorem is obtained, applying to solutions that fall off in time at any fixed
spatial position. For a complementary class of spacetimes in which CTC's are
confined to a compact region, we show that when solutions exist they are unique
in regions exterior to the CTC's. (We believe that more stringent uniqueness
theorems hold, and that the present limitations are our own.) An extension of
these results to Maxwell fields and massless spinor fields is sketched.
Finally, we discuss a conjecture that the Cauchy problem for free fields is
well defined in the presence of CTC's whenever the problem is well-posed in the
geometric-optics limit. We provide some evidence in support of this conjecture,
and we present counterexamples that show that neither existence nor uniqueness
is guaranteed under weaker conditions. In particular, both existence and
uniqueness can fail in smooth, asymptotically flat spacetimes with a compact
nonchronal region.Comment: 47 pages, Revtex, 7 figures (available upon request
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Advances in Kriging-Based Autonomous X-Ray Scattering Experiments.
Autonomous experimentation is an emerging paradigm for scientific discovery, wherein measurement instruments are augmented with decision-making algorithms, allowing them to autonomously explore parameter spaces of interest. We have recently demonstrated a generalized approach to autonomous experimental control, based on generating a surrogate model to interpolate experimental data, and a corresponding uncertainty model, which are computed using a Gaussian process regression known as ordinary Kriging (OK). We demonstrated the successful application of this method to exploring materials science problems using x-ray scattering measurements at a synchrotron beamline. Here, we report several improvements to this methodology that overcome limitations of traditional Kriging methods. The variogram underlying OK is global and thus insensitive to local data variation. We augment the Kriging variance with model-based measures, for instance providing local sensitivity by including the gradient of the surrogate model. As with most statistical regression methods, OK minimizes the number of measurements required to achieve a particular model quality. However, in practice this may not be the most stringent experimental constraint; e.g. the goal may instead be to minimize experiment duration or material usage. We define an adaptive cost function, allowing the autonomous method to balance information gain against measured experimental cost. We provide synthetic and experimental demonstrations, validating that this improved algorithm yields more efficient autonomous data collection
A Multi-Code Analysis Toolkit for Astrophysical Simulation Data
The analysis of complex multiphysics astrophysical simulations presents a
unique and rapidly growing set of challenges: reproducibility, parallelization,
and vast increases in data size and complexity chief among them. In order to
meet these challenges, and in order to open up new avenues for collaboration
between users of multiple simulation platforms, we present yt (available at
http://yt.enzotools.org/), an open source, community-developed astrophysical
analysis and visualization toolkit. Analysis and visualization with yt are
oriented around physically relevant quantities rather than quantities native to
astrophysical simulation codes. While originally designed for handling Enzo's
structure adaptive mesh refinement (AMR) data, yt has been extended to work
with several different simulation methods and simulation codes including Orion,
RAMSES, and FLASH. We report on its methods for reading, handling, and
visualizing data, including projections, multivariate volume rendering,
multi-dimensional histograms, halo finding, light cone generation and
topologically-connected isocontour identification. Furthermore, we discuss the
underlying algorithms yt uses for processing and visualizing data, and its
mechanisms for parallelization of analysis tasks.Comment: 18 pages, 6 figures, emulateapj format. Resubmitted to Astrophysical
Journal Supplement Series with revisions from referee. yt can be found at
http://yt.enzotools.org
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