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  • 1
    Electronic Resource
    Electronic Resource
    Mapping the genome one molecule at a time : optical mapping (1995)
    [s.l.] : Nature Publishing Group
    Nature 378 (1995), S. 516-517 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] DESPITE rapid progress in the human genome project effort, there is little doubt that new conceptual approaches are needed before whole genome-based analyses become routine. This is largely true because current molecular biological approaches were developed primarily for characterization of single ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/378516a0
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  • 2
    Electronic Resource
    Electronic Resource
    Quantitative Steinitz's theorems with applications to multifingered grasping (1992)
    Springer
    Discrete & computational geometry 7 (1992), S. 295-318 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We prove the following quantitative form of a classical theorem of Steintiz: Letm be sufficiently large. If the convex hull of a subsetS of Euclideand-space contains a unit ball centered on the origin, then there is a subset ofS with at mostm points whose convex hull contains a solid ball also centered on the origin and havingresidual radius $$1 - 3d\left( {\frac{{2d^2 }}{m}} \right)^{2/(d - 1)} .$$ The casem=2d was first considered by Bárányet al. [1]. We also show an upper bound on the achievable radius: the residual radius must be less than $$1 - \frac{1}{{17}}\left( {\frac{{2d^2 }}{m}} \right)^{2/(d - 1)} .$$ These results have applications in the problem of computing the so-calledclosure grasps by anm-fingered robot hand. The above quantitative form of Steinitz's theorem gives a notion ofefficiency for closure grasps. The theorem also gives rise to some new problems in computational geometry. We present some efficient algorithms for these problems, especially in the two-dimensional case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02187843
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  • 3
    Electronic Resource
    Electronic Resource
    A solution to Kronecker's problem (1994)
    Springer
    Applicable algebra in engineering, communication and computing 5 (1994), S. 343-370 
    Details
    ISSN: 1432-0622
    Keywords: Ascending chain condition ; E-bases ; Gröbner bases ; Ideal membership problem ; Rapidly growing functions ; Ring of polynomials over the integers ; S-polynomials ; syzygies ; Wainer hierarchy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics , Technology
    Notes: Abstract Consider ℤ[x 1,...,x n], the multivariate polynomial ring over integers involvingn variables. For a fixedn, we show that the ideal membership problem as well as the associated representation problem for ℤ[x 1,...,x n] are primitive recursive. The precise complexity bounds are easily expressible by functions in the Wainer hierarchy. Thus, we solve a fundamental algorithmic question in the theory of multivariate polynomials over the integers. As a direct consequence, we also obtain a solution to certain foundational problem intrinsic to Kronecker's programme for constructive mathematics and provide an effective version of Hilbert's basis theorem. Our original interest in this area was aroused by Edwards' historical account of theKronecker's problem in the context of Kronecker's version of constructive mathematics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01188747
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