2,358 research outputs found
Flow Logic
Flow networks have attracted a lot of research in computer science. Indeed,
many questions in numerous application areas can be reduced to questions about
flow networks. Many of these applications would benefit from a framework in
which one can formally reason about properties of flow networks that go beyond
their maximal flow. We introduce Flow Logics: modal logics that treat flow
functions as explicit first-order objects and enable the specification of rich
properties of flow networks. The syntax of our logic BFL* (Branching Flow
Logic) is similar to the syntax of the temporal logic CTL*, except that atomic
assertions may be flow propositions, like or , for
, which refer to the value of the flow in a vertex, and
that first-order quantification can be applied both to paths and to flow
functions. We present an exhaustive study of the theoretical and practical
aspects of BFL*, as well as extensions and fragments of it. Our extensions
include flow quantifications that range over non-integral flow functions or
over maximal flow functions, path quantification that ranges over paths along
which non-zero flow travels, past operators, and first-order quantification of
flow values. We focus on the model-checking problem and show that it is
PSPACE-complete, as it is for CTL*. Handling of flow quantifiers, however,
increases the complexity in terms of the network to , even
for the LFL and BFL fragments, which are the flow-counterparts of LTL and CTL.
We are still able to point to a useful fragment of BFL* for which the
model-checking problem can be solved in polynomial time. Finally, we introduce
and study the query-checking problem for BFL*, where under-specified BFL*
formulas are used for network exploration
Level sets and non Gaussian integrals of positively homogeneous functions
We investigate various properties of the sublevel set
and the integration of on this sublevel set when and are positively
homogeneous functions. For instance, the latter integral reduces to integrating
on the whole space (a non Gaussian integral) and when is
a polynomial, then the volume of the sublevel set is a convex function of the
coefficients of . In fact, whenever is nonnegative, the functional is a convex function of for a large class of functions
. We also provide a numerical approximation scheme to compute
the volume or integrate (or, equivalently to approximate the associated non
Gaussian integral). We also show that finding the sublevel set of minimum volume that contains some given subset is a
(hard) convex optimization problem for which we also propose two convergent
numerical schemes. Finally, we provide a Gaussian-like property of non Gaussian
integrals for homogeneous polynomials that are sums of squares and critical
points of a specific function
A GPU-Computing Approach to Solar Stokes Profile Inversion
We present a new computational approach to the inversion of solar
photospheric Stokes polarization profiles, under the Milne-Eddington model, for
vector magnetography. Our code, named GENESIS (GENEtic Stokes Inversion
Strategy), employs multi-threaded parallel-processing techniques to harness the
computing power of graphics processing units GPUs, along with algorithms
designed to exploit the inherent parallelism of the Stokes inversion problem.
Using a genetic algorithm (GA) engineered specifically for use with a GPU, we
produce full-disc maps of the photospheric vector magnetic field from polarized
spectral line observations recorded by the Synoptic Optical Long-term
Investigations of the Sun (SOLIS) Vector Spectromagnetograph (VSM) instrument.
We show the advantages of pairing a population-parallel genetic algorithm with
data-parallel GPU-computing techniques, and present an overview of the Stokes
inversion problem, including a description of our adaptation to the
GPU-computing paradigm. Full-disc vector magnetograms derived by this method
are shown, using SOLIS/VSM data observed on 2008 March 28 at 15:45 UT
Nonlinear force-free modeling of the solar coronal magnetic field
The coronal magnetic field is an important quantity because the magnetic
field dominates the structure of the solar corona. Unfortunately direct
measurements of coronal magnetic fields are usually not available. The
photospheric magnetic field is measured routinely with vector magnetographs.
These photospheric measurements are extrapolated into the solar corona. The
extrapolated coronal magnetic field depends on assumptions regarding the
coronal plasma, e.g. force-freeness. Force-free means that all non-magnetic
forces like pressure gradients and gravity are neglected. This approach is well
justified in the solar corona due to the low plasma beta. One has to take care,
however, about ambiguities, noise and non-magnetic forces in the photosphere,
where the magnetic field vector is measured. Here we review different numerical
methods for a nonlinear force-free coronal magnetic field extrapolation:
Grad-Rubin codes, upward integration method, MHD-relaxation, optimization and
the boundary element approach. We briefly discuss the main features of the
different methods and concentrate mainly on recently developed new codes.Comment: 33 pages, 3 figures, Review articl
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