48,065 research outputs found
A Survey of Satisfiability Modulo Theory
Satisfiability modulo theory (SMT) consists in testing the satisfiability of
first-order formulas over linear integer or real arithmetic, or other theories.
In this survey, we explain the combination of propositional satisfiability and
decision procedures for conjunctions known as DPLL(T), and the alternative
"natural domain" approaches. We also cover quantifiers, Craig interpolants,
polynomial arithmetic, and how SMT solvers are used in automated software
analysis.Comment: Computer Algebra in Scientific Computing, Sep 2016, Bucharest,
Romania. 201
Improved method for phase wraps reduction in profilometry
In order to completely eliminate, or greatly reduce the number of phase wraps
in 2D wrapped phase map, Gdeisat et al. proposed an algorithm, which uses
shifting the spectrum towards the origin. But the spectrum can be shifted only
by an integer number, meaning that the phase wraps reduction is often not
optimal. In addition, Gdeisat's method will take much time to make the Fourier
transform, inverse Fourier transform, select and shift the spectral components.
In view of the above problems, we proposed an improved method for phase wraps
elimination or reduction. First, the wrapped phase map is padded with zeros,
the carrier frequency of the projected fringe is determined by high resolution,
which can be used as the moving distance of the spectrum. And then realize
frequency shift in spatial domain. So it not only can enable the spectrum to be
shifted by a rational number when the carrier frequency is not an integer
number, but also reduce the execution time. Finally, the experimental results
demonstrated that the proposed method is feasible.Comment: 16 pages, 15 figures, 1 table. arXiv admin note: text overlap with
arXiv:1604.0723
Renormalization by Projection: On the Equivalence of the Bloch-Feshbach Formalism and Wilson's Renormalization
We employ projection operator techniques in Hilbert space to derive a
continuous sequence of effective Hamiltonians which describe the dynamics on
successively larger length scales. We show for the case of \phi^4 theory that
the masses and couplings in these effective Hamiltonians vary in accordance
with 1-loop renormalization group equations. This is evidence for an intimate
connection between Wilson's renormalization and the venerable Bloch-Feshbach
formalism.Comment: 8 pages LaTeX, no figures; revised introduction and discussion, new
titl
Singular perturbations and scaling
Scaling transformations involving a small parameter ({\em degenerate
scalings}) are frequently used for ordinary differential equations that model
(bio-) chemical reaction networks. They are motivated by quasi-steady state
(QSS) of certain chemical species, and ideally lead to slow-fast systems for
singular perturbation reductions, in the sense of Tikhonov and Fenichel. In the
present paper we discuss properties of such scaling transformations, with
regard to their applicability as well as to their determination.
Transformations of this type are admissible only when certain consistency
conditions are satisfied, and they lead to singular perturbation scenarios only
if additional conditions hold, including a further consistency condition on
initial values. Given these consistency conditions, two scenarios occur. The
first (which we call standard) is well known and corresponds to a classical
quasi-steady state (QSS) reduction. Here, scaling may actually be omitted
because there exists a singular perturbation reduction for the unscaled system,
with a coordinate subspace as critical manifold. For the second (nonstandard)
scenario scaling is crucial. Here one may obtain a singular perturbation
reduction with the slow manifold having dimension greater than expected from
the scaling. For parameter dependent systems we consider the problem to find
all possible scalings, and we show that requiring the consistency conditions
allows their determination. This lays the groundwork for algorithmic
approaches, to be taken up in future work. In the final section we consider
some applications. In particular we discuss relevant nonstandard reductions of
certain reaction-transport systems
A clever elimination strategy for efficient minimal solvers
We present a new insight into the systematic generation of minimal solvers in
computer vision, which leads to smaller and faster solvers. Many minimal
problem formulations are coupled sets of linear and polynomial equations where
image measurements enter the linear equations only. We show that it is useful
to solve such systems by first eliminating all the unknowns that do not appear
in the linear equations and then extending solutions to the rest of unknowns.
This can be generalized to fully non-linear systems by linearization via
lifting. We demonstrate that this approach leads to more efficient solvers in
three problems of partially calibrated relative camera pose computation with
unknown focal length and/or radial distortion. Our approach also generates new
interesting constraints on the fundamental matrices of partially calibrated
cameras, which were not known before.Comment: 13 pages, 7 figure
Filling in CMB map missing data using constrained Gaussian realizations
For analyzing maps of the cosmic microwave background sky, it is necessary to
mask out the region around the galactic equator where the parasitic foreground
emission is strongest as well as the brightest compact sources. Since many of
the analyses of the data, particularly those searching for non-Gaussianity of a
primordial origin, are most straightforwardly carried out on full-sky maps, it
is of great interest to develop efficient algorithms for filling in the missing
information in a plausible way. We explore practical algorithms for filling in
based on constrained Gaussian realizations. Although carrying out such
realizations is in principle straightforward, for finely pixelized maps as will
be required for the Planck analysis a direct brute force method is not
numerically tractable. We present some concrete solutions to this problem, both
on a spatially flat sky with periodic boundary conditions and on the pixelized
sphere. One approach is to solve the linear system with an appropriately
preconditioned conjugate gradient method. While this approach was successfully
implemented on a rectangular domain with periodic boundary conditions and
worked even for very wide masked regions, we found that the method failed on
the pixelized sphere for reasons that we explain here. We present an approach
that works for full-sky pixelized maps on the sphere involving a kernel-based
multi-resolution Laplace solver followed by a series of conjugate gradient
corrections near the boundary of the mask.Comment: 22 pages, 14 figures, minor changes, a few missing references adde
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