5,148 research outputs found
List Decoding Algorithm based on Voting in Groebner Bases for General One-Point AG Codes
We generalize the unique decoding algorithm for one-point AG codes over the
Miura-Kamiya Cab curves proposed by Lee, Bras-Amor\'os and O'Sullivan (2012) to
general one-point AG codes, without any assumption. We also extend their unique
decoding algorithm to list decoding, modify it so that it can be used with the
Feng-Rao improved code construction, prove equality between its error
correcting capability and half the minimum distance lower bound by Andersen and
Geil (2008) that has not been done in the original proposal except for
one-point Hermitian codes, remove the unnecessary computational steps so that
it can run faster, and analyze its computational complexity in terms of
multiplications and divisions in the finite field. As a unique decoding
algorithm, the proposed one is empirically and theoretically as fast as the BMS
algorithm for one-point Hermitian codes. As a list decoding algorithm,
extensive experiments suggest that it can be much faster for many moderate
size/usual inputs than the algorithm by Beelen and Brander (2010). It should be
noted that as a list decoding algorithm the proposed method seems to have
exponential worst-case computational complexity while the previous proposals
(Beelen and Brander, 2010; Guruswami and Sudan, 1999) have polynomial ones, and
that the proposed method is expected to be slower than the previous proposals
for very large/special inputs.Comment: Accepted for publication in J. Symbolic Computation. LaTeX2e
article.cls, 42 pages, 4 tables, no figures. Ver. 6 added an illustrative
example of the algorithm executio
From approximating to interpolatory non-stationary subdivision schemes with the same generation properties
In this paper we describe a general, computationally feasible strategy to
deduce a family of interpolatory non-stationary subdivision schemes from a
symmetric non-stationary, non-interpolatory one satisfying quite mild
assumptions. To achieve this result we extend our previous work [C.Conti,
L.Gemignani, L.Romani, Linear Algebra Appl. 431 (2009), no. 10, 1971-1987] to
full generality by removing additional assumptions on the input symbols. For
the so obtained interpolatory schemes we prove that they are capable of
reproducing the same exponential polynomial space as the one generated by the
original approximating scheme. Moreover, we specialize the computational
methods for the case of symbols obtained by shifted non-stationary affine
combinations of exponential B-splines, that are at the basis of most
non-stationary subdivision schemes. In this case we find that the associated
family of interpolatory symbols can be determined to satisfy a suitable set of
generalized interpolating conditions at the set of the zeros (with reversed
signs) of the input symbol. Finally, we discuss some computational examples by
showing that the proposed approach can yield novel smooth non-stationary
interpolatory subdivision schemes possessing very interesting reproduction
properties
Segmentation of Photovoltaic Module Cells in Electroluminescence Images
High resolution electroluminescence (EL) images captured in the infrared
spectrum allow to visually and non-destructively inspect the quality of
photovoltaic (PV) modules. Currently, however, such a visual inspection
requires trained experts to discern different kinds of defects, which is
time-consuming and expensive. Automated segmentation of cells is therefore a
key step in automating the visual inspection workflow. In this work, we propose
a robust automated segmentation method for extraction of individual solar cells
from EL images of PV modules. This enables controlled studies on large amounts
of data to understanding the effects of module degradation over time-a process
not yet fully understood. The proposed method infers in several steps a
high-level solar module representation from low-level edge features. An
important step in the algorithm is to formulate the segmentation problem in
terms of lens calibration by exploiting the plumbline constraint. We evaluate
our method on a dataset of various solar modules types containing a total of
408 solar cells with various defects. Our method robustly solves this task with
a median weighted Jaccard index of 94.47% and an score of 97.54%, both
indicating a very high similarity between automatically segmented and ground
truth solar cell masks
Final report on estimation and statistical analysis of spatially distributed random processes
Includes bibliographical references.Final report;Supported by the NSF. ECS-8312921prepared by Alan S. Willsky, Bernard C. Levy, George C. Verghese
A practical method for computing with piecewise Chebyshevian splines
A piecewise Chebyshevian spline space is good for design when it possesses a B-spline basis and this property is preserved under knot insertion. The interest in such kind of spaces is justified by the fact that, similarly as for polynomial splines, the related parametric curves exhibit the desired properties of convex hull inclusion, variation diminution and intuitive relation between the curve shape and the location of the control points. For a good-for-design space, in this paper we construct a set of functions, called transition functions, which allow for efficient computation of the B-spline basis, even in the case of nonuniform and multiple knots. Moreover, we show how the spline coefficients of the representations associated with a refined knot partition and with a raised order can conveniently be expressed by means of transition functions.
This result allows us to provide effective procedures that generalize the classical knot insertion and degree raising algorithms for polynomial splines. We further discuss how the approach can straightforwardly be generalized to deal with geometrically continuous piecewise Chebyshevian splines as well as with splines having section spaces of different dimensions. From a numerical point of view, we show that the proposed evaluation method is easier to implement and has higher accuracy than other existing algorithms
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