61 research outputs found
Elastic Rod Model of a Supercoiled DNA Molecule
We study the elastic behaviour of a supercoiled DNA molecule. The simplest
model is that of a rod like chain, involving two elastic constants, the bending
and the twist rigidities. We show that this model is singular and needs a small
distance cut-off, which is a natural length scale giving the limit of validity
of the model, of the order of the double helix pitch. The rod like chain in
presence of the cutoff is able to reproduce quantitatively the experimentally
observed effects of supercoiling on the elongation-force characteristics, in
the small supercoiling regime. An exact solution of the model, using both
transfer matrix techniques and its mapping to a quantum mechanics problem,
allows to extract, from the experimental data,the value of the twist rigidity.
We also analyse the variation of the torque and the writhe to twist ratio
versus supercoiling, showing analytically the existence of a rather sharp
crossover regime which can be related to the excitation of plectonemic-like
structures. Finally we study the extension fluctuations of a stretched and
supercoiled DNA molecule, both at fixed torque and at fixed supercoiling angle,
and we compare the theoretical predictions to some preliminary experimental
data.Comment: 29 pages Revtex 5 figure
Group Testing with Random Pools: optimal two-stage algorithms
We study Probabilistic Group Testing of a set of N items each of which is
defective with probability p. We focus on the double limit of small defect
probability, p>1, taking either p->0
after or with . In both settings
the optimal number of tests which are required to identify with certainty the
defectives via a two-stage procedure, , is known to scale as
. Here we determine the sharp asymptotic value of and construct a class of two-stage algorithms over which
this optimal value is attained. This is done by choosing a proper bipartite
regular graph (of tests and variable nodes) for the first stage of the
detection. Furthermore we prove that this optimal value is also attained on
average over a random bipartite graph where all variables have the same degree,
while the tests have Poisson-distributed degrees. Finally, we improve the
existing upper and lower bound for the optimal number of tests in the case
with .Comment: 12 page
The Bethe lattice spin glass revisited
So far the problem of a spin glass on a Bethe lattice has been solved only at
the replica symmetric level, which is wrong in the spin glass phase. Because of
some technical difficulties, attempts at deriving a replica symmetry breaking
solution have been confined to some perturbative regimes, high connectivity
lattices or temperature close to the critical temperature.
Using the cavity method, we propose a general non perturbative solution of
the Bethe lattice spin glass problem at a level of approximation which is
equivalent to a one step replica symmetry breaking solution. The results
compare well with numerical simulations. The method can be used for many finite
connectivity problems appearing in combinatorial optimization.Comment: 23 pages, 6 figure
The cavity method at zero temperature
In this note we explain the use of the cavity method directly at zero
temperature, in the case of the spin glass on a Bethe lattice. The computation
is done explicitly in the formalism equivalent to 'one step replica symmetry
breaking'; we compute the energy of the global ground state, as well as the
complexity of equilibrium states at a given energy. Full results are presented
for a Bethe lattice with connectivity equal to three.Comment: 22 pages, 8 figures; Some minor correction
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