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- Berglund, Tomas, et al.
(author)
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An obstacle-avoiding minimum variation B-spline problem
- 2003
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In: Proceedings. - Los Alamitos, Calif : IEEE Communications Society. - 0769519857 ; , s. 156-161
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Conference paper (peer-reviewed)abstract
- We study the problem of computing a planar curve, restricted to lie between two given polygonal chains, such that the integral of the square of arc-length derivative of curvature along the curve is minimized. We introduce the minimum variation B-spline problem, which is a linearly constrained optimization problem over curves, defined by B-spline functions only. An empirical investigation indicates that this problem has one unique solution among all uniform quartic B-spline functions. Furthermore, we prove that, for any B-spline function, the convexity properties of the problem are preserved subject to a scaling and translation of the knot sequence defining the B-spline.
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- Berglund, Tomas, et al.
(author)
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Epi-convergence of minimum curvature variation B-splines
- 2003
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Reports (other academic/artistic)abstract
- We study the curvature variation functional, i.e., the integral over the square of arc-length derivative of curvature, along a planar curve. With no other constraints than prescribed position, slope angle, and curvature at the endpoints of the curve, the minimizer of this functional is known as a cubic spiral. It remains a challenge to effectively compute minimizers or approximations to minimizers of this functional subject to additional constraints such as, for example, for the curve to avoid obstacles such as other curves. In this paper, we consider the set of smooth curves that can be written as graphs of three times continuously differentiable functions on an interval, and, in particular, we consider approximations using quartic uniform B- spline functions. We show that if quartic uniform B-spline minimizers of the curvature variation functional converge to a curve, as the number of B-spline basis functions tends to infinity, then this curve is in fact a minimizer of the curvature variation functional. In order to illustrate this result, we present an example of sequences of B-spline minimizers that converge to a cubic spiral.
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- Berglund, Tomas, et al.
(author)
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The problem of computing an obstacle-avoiding minimum variation B-spline
- 2003
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Reports (other academic/artistic)abstract
- We study the problem of computing a planar curve restricted to lie between two given polygonal chains such that the integral of the square of arc- length derivative of curvature along the curve is minimized. We introduce the Minimum Variation B-spline problem which is a linearly constrained optimization problem over curves defined by B-spline functions only. An empirical investigation indicates that this problem has one unique solution among all uniform quartic B-spline functions. Furthermore, we prove that, for any B-spline function, the convexity properties of the problem are preserved subject to a scaling and translation of the knot sequence defining the B-spline.
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- Borrvall, Charlotte, et al.
(author)
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Biodiversity lessens the risk of cascading extinction in model food webs
- 2000
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In: Ecology Letters. - : Wiley. - 1461-023X .- 1461-0248. ; 3:2, s. 131-136
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Journal article (peer-reviewed)abstract
- Due to the complex interactions between species in food webs, the extinction of one species could lead to a cascade of further extinctions and hence cause dramatic changes in species composition and ecosystem processes. We found that the risk of additional species extinction, following the loss of one species in model food webs, decreases with the number of species per functional group. For a given number of species per functional group, the risk of further extinctions is highest when an autotroph is removed and lowest when a top predator is removed. In addition, stability decreases when the distribution of interaction strengths in the webs is changed from equal to skew (few strong and many weak links). We also found that omnivory appears to stabilize model food webs. Our results indicate that high biodiversity may serve as an insurance against radical ecosystem changes.
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- Brage, Tomas, et al.
(author)
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Spectral lines for polarization measurements of the coronal magnetic field. III. Atomic data for SiIX
- 2000
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In: Astrophysical Journal. - : American Astronomical Society. - 0004-637X .- 1538-4357. ; 540:2, s. 1114-1118
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Journal article (peer-reviewed)abstract
- We report on large-scale ab initio multiconfiguration Dirac-Fock (MCDF) calculations for spectral lines of Si IX, with emphasis on the forbidden transitions 2p(2) P-3(J-->J'). The J = 0 --> J' = 1 transition at 3.9346 mu m holds promise as a diagnostic of coronal magnetic fields if and when future coronagraphic instruments can measure the polarized light at this wavelength.
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