2,074 research outputs found
Parametrized Stochastic Grammars for RNA Secondary Structure Prediction
We propose a two-level stochastic context-free grammar (SCFG) architecture
for parametrized stochastic modeling of a family of RNA sequences, including
their secondary structure. A stochastic model of this type can be used for
maximum a posteriori estimation of the secondary structure of any new sequence
in the family. The proposed SCFG architecture models RNA subsequences
comprising paired bases as stochastically weighted Dyck-language words, i.e.,
as weighted balanced-parenthesis expressions. The length of each run of
unpaired bases, forming a loop or a bulge, is taken to have a phase-type
distribution: that of the hitting time in a finite-state Markov chain. Without
loss of generality, each such Markov chain can be taken to have a bounded
complexity. The scheme yields an overall family SCFG with a manageable number
of parameters.Comment: 5 pages, submitted to the 2007 Information Theory and Applications
Workshop (ITA 2007
Extensions of the Classical Transformations of 3F2
It is shown that the classical quadratic and cubic transformation identities
satisfied by the hypergeometric function can be extended to include
additional parameter pairs, which differ by integers. In the extended
identities, which involve hypergeometric functions of arbitrarily high order,
the added parameters are nonlinearly constrained: in the quadratic case, they
are the negated roots of certain orthogonal polynomials of a discrete argument
(dual Hahn and Racah ones). Specializations and applications of the extended
identities are given, including an extension of Whipple's identity relating
very well poised series and balanced series, and
extensions of other summation identities.Comment: 22 pages, expanded version, to appear in Advances in Applied
Mathematic
A Theory of Magnetization Reversal in Nanowires
Magnetization reversal in a ferromagnetic nanowire which is much narrower
than the exchange length is believed to be accomplished through the thermally
activated growth of a spatially localized nucleus, which initially occupies a
small fraction of the total volume. To date, the most detailed theoretical
treatments of reversal as a field-induced but noise-activated process have
focused on the case of a very long ferromagnetic nanowire, i.e., a highly
elongated cylindrical particle, and have yielded a reversal rate per unit
length, due to an underlying assumption that the nucleus may form anywhere
along the wire. But in a bounded-length (though long) cylindrical particle with
flat ends, it is energetically favored for nucleation to begin at either end.
We indicate how to compute analytically the energy of the critical nucleus
associated with either end, i.e., the activation barrier to magnetization
reversal, which governs the reversal rate in the low-temperature (Kramers)
limit. Our treatment employs elliptic functions, and is partly analytic rather
than numerical. We also comment on the Kramers prefactor, which for this
reversal pathway does not scale linearly as the particle length increases, and
tends to a constant in the low-temperature limit.Comment: 11 pages, presented at Fluctuations and Noise 200
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