Designing tie knots by random walks
Article Abstract:
The development of a mathematical model of tie knots has made it possible to establish a map between tie knots and persistent random walks on a triangular lattice. Knots are classified according to size and shape, with knot sequences being represented as random walks on a triangular lattice. The size of the knot, and the primary parameter by which it is classified, is the number of moves in the knot sequence. The shape of the knot is determined by the number of right, left and centre moves in the tie sequence.
Publication Name: Nature
Subject: Zoology and wildlife conservation
ISSN: 0028-0836
Year: 1999
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p19ARF links the tumour suppressor p53 to Ras
Article Abstract:
Healthy cells have mechanisms that sense oncogenic signals, thus triggering anti-tummorigenic responses. Expression of the Ras oncogene in normal cells leads to cell-cycle arrest involving the activation of p53, the tumour-suppressor protein. It is shown that p19ARF in the mouse is necessary to activate p53 in response to oncogenic Ras. p19ARF does not activate p53 by DNA damage. The results dissociate p53 activation into two pathways.
Publication Name: Nature
Subject: Zoology and wildlife conservation
ISSN: 0028-0836
Year: 1998
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Four-thirds power law for knots and links
Article Abstract:
Mathematical analysis shows that a rope can be tied a maximum number of times. Nine knot conformations are illustrated, including the linear conformation of a twist knot, the packed Hopf tori and the figure-eight knot. Vector relationships in knot ties are calculated.
Publication Name: Nature
Subject: Zoology and wildlife conservation
ISSN: 0028-0836
Year: 1998
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