582 research outputs found

    Computation with Advice

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    Computation with advice is suggested as generalization of both computation with discrete advice and Type-2 Nondeterminism. Several embodiments of the generic concept are discussed, and the close connection to Weihrauch reducibility is pointed out. As a novel concept, computability with random advice is studied; which corresponds to correct solutions being guessable with positive probability. In the framework of computation with advice, it is possible to define computational complexity for certain concepts of hypercomputation. Finally, some examples are given which illuminate the interplay of uniform and non-uniform techniques in order to investigate both computability with advice and the Weihrauch lattice

    On FPL configurations with four sets of nested arches

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    The problem of counting the number of Fully Packed Loop (FPL) configurations with four sets of a,b,c,d nested arches is addressed. It is shown that it may be expressed as the problem of enumeration of tilings of a domain of the triangular lattice with a conic singularity. After reexpression in terms of non-intersecting lines, the Lindstr\"om-Gessel-Viennot theorem leads to a formula as a sum of determinants. This is made quite explicit when min(a,b,c,d)=1 or 2. We also find a compact determinant formula which generates the numbers of configurations with b=d.Comment: 22 pages, TeX, 16 figures; a new formula for a generating function adde

    Actin: its cumbersome pilgrimage through cellular compartments

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    In this article, we follow the history of one of the most abundant, most intensely studied proteins of the eukaryotic cells: actin. We report on hallmarks of its discovery, its structural and functional characterization and localization over time, and point to present days’ knowledge on its position as a member of a large family. We focus on the rather puzzling number of diverse functions as proposed for actin as a dual compartment protein. Finally, we venture on some speculations as to its origin
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