34,287 research outputs found
Temperature dependence of circular DNA topological states
Circular double stranded DNA has different topological states which are
defined by their linking numbers. Equilibrium distribution of linking numbers
can be obtained by closing a linear DNA into a circle by ligase. Using Monte
Carlo simulation, we predict the temperature dependence of the linking number
distribution of small circular DNAs. Our predictions are based on flexible
defect excitations resulted from local melting or unstacking of DNA base pairs.
We found that the reduced bending rigidity alone can lead to measurable changes
of the variance of linking number distribution of short circular DNAs. If the
defect is accompanied by local unwinding, the effect becomes much more
prominent. The predictions can be easily investigated in experiments, providing
a new method to study the micromechanics of sharply bent DNAs and the thermal
stability of specific DNA sequences. Furthermore, the predictions are directly
applicable to the studies of binding of DNA distorting proteins that can
locally reduce DNA rigidity, form DNA kinks, or introduce local unwinding.Comment: 15 pages in preprint format, 4 figure
A Telescoping method for Double Summations
We present a method to prove hypergeometric double summation identities.
Given a hypergeometric term , we aim to find a difference operator and rational functions
such that .
Based on simple divisibility considerations, we show that the denominators of
and must possess certain factors which can be computed from . Using these factors as estimates, we may find the numerators of
and by guessing the upper bounds of the degrees and solving systems of
linear equations. Our method is valid for the Andrews-Paule identity, Carlitz's
identities, the Ap\'ery-Schmidt-Strehl identity, the Graham-Knuth-Patashnik
identity, and the Petkov\v{s}ek-Wilf-Zeilberger identity.Comment: 22 pages. to appear in J. Computational and Applied Mathematic
Applicability of the -Analogue of Zeilberger's Algorithm
The applicability or terminating condition for the ordinary case of
Zeilberger's algorithm was recently obtained by Abramov. For the -analogue,
the question of whether a bivariate -hypergeometric term has a -pair
remains open. Le has found a solution to this problem when the given bivariate
-hypergeometric term is a rational function in certain powers of . We
solve the problem for the general case by giving a characterization of
bivariate -hypergeometric terms for which the -analogue of Zeilberger's
algorithm terminates. Moreover, we give an algorithm to determine whether a
bivariate -hypergeometric term has a -pair.Comment: 15 page
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