47,658 research outputs found
All about A Minimal Normal Form for DNA Expressions
Algorithms and the Foundations of Software technolog
DNA expressions : a formal notation for DNA
We describe a formal notation for DNA molecules that may contain
nicks and gaps. The resulting DNA expressions denote formal DNA molecules.
Different DNA expressions may denote the same molecule. Such DNA expressions
are called equivalent. We examine which DNA expressions are minimal,
which means that they have the shortest length among all equivalent
DNA expressions. Among others, we describe how to construct a minimal
DNA expression for a given molecule. We also present an efficient,
recursive algorithm to rewrite a given DNA expression into an equivalent,
minimal DNA expression.
For many formal DNA molecules, there exists more than one minimal
DNA expression. We define a minimal normal form, i.e., a set of properties
such that for each formal DNA molecule, there is exactly one (minimal)
DNA expression with these properties. We finally describe an efficient,
two-step algorithm to rewrite an arbitrary DNA expression into this
normal form.Algorithms and the Foundations of Software technolog
Radial distribution function of semiflexible polymers
We calculate the distribution function of the end--to--end distance of a
semiflexible polymer with large bending rigidity. This quantity is directly
observable in experiments on single semiflexible polymers (e.g., DNA, actin)
and relevant to their interpretation. It is also an important starting point
for analyzing the behavior of more complex systems such as networks and
solutions of semiflexible polymers. To estimate the validity of the obtained
analytical expressions, we also determine the distribution function numerically
using Monte Carlo simulation and find good quantitative agreement.Comment: RevTeX, 4 pages, 1 figure. Also available at
http://www.cip.physik.tu-muenchen.de/tumphy/d/T34/Mitarbeiter/frey.htm
A Proof of Entropy Minimization for Outputs in Deletion Channels via Hidden Word Statistics
From the output produced by a memoryless deletion channel from a uniformly
random input of known length , one obtains a posterior distribution on the
channel input. The difference between the Shannon entropy of this distribution
and that of the uniform prior measures the amount of information about the
channel input which is conveyed by the output of length , and it is natural
to ask for which outputs this is extremized. This question was posed in a
previous work, where it was conjectured on the basis of experimental data that
the entropy of the posterior is minimized and maximized by the constant strings
and and the alternating strings
and respectively. In the present
work we confirm the minimization conjecture in the asymptotic limit using
results from hidden word statistics. We show how the analytic-combinatorial
methods of Flajolet, Szpankowski and Vall\'ee for dealing with the hidden
pattern matching problem can be applied to resolve the case of fixed output
length and , by obtaining estimates for the entropy in
terms of the moments of the posterior distribution and establishing its
minimization via a measure of autocorrelation.Comment: 11 pages, 2 figure
Intermediate coherent-incoherent charge transport: DNA as a case study
We study an intermediate quantum coherent-incoherent charge transport
mechanism in metal-molecule-metal junctions using B\"uttiker's probe technique.
This tool allows us to include incoherent effects in a controlled manner, and
thus to study situations in which partial decoherence affects charge transfer
dynamics. Motivated by recent experiments on intermediate coherent-incoherent
charge conduction in DNA molecules [L. Xiang {\it et al.}, Nature Chem. 7,
221-226 (2015)], we focus on two representative structures: alternating
(GC) and stacked GC sequences; the latter structure is argued to
support charge delocalization within G segments, and thus an intermediate
coherent-incoherent conduction. We begin our analysis with a highly simplified
1-dimensional tight-binding model, while introducing environmental effects
through B\"uttiker's probes. This minimal model allows us to gain fundamental
understanding of transport mechanisms and derive analytic results for molecular
resistance in different limits. We then use a more detailed ladder-model
Hamiltonian to represent double-stranded DNA structures---with environmental
effects captured by B\"uttiker's probes. We find that hopping conduction
dominates in alternating sequences, while in stacked sequences charge
delocalization (visualized directly through the electronic density matrix)
supports significant resonant-ballistic charge dynamics reflected by an
even-odd effect and a weak distance dependence for resistance. Our analysis
illustrates that lessons learned from minimal models are helpful for
interpreting charge dynamics in DNA.Comment: 16 pages, 14 figure
Mutations of fake weighted projective planes
In previous work by Coates, Galkin, and the authors, the notion of mutation
between lattice polytopes was introduced. Such a mutation gives rise to a
deformation between the corresponding toric varieties. In this paper we study
one-step mutations that correspond to deformations between weighted projective
planes, giving a complete characterisation of such mutations in terms of
T-singularities. We show also that the weights involved satisfy Diophantine
equations, generalising results of Hacking-Prokhorov.Comment: 14 pages, 2 figure
Fluctuating Filaments I: Statistical Mechanics of Helices
We examine the effects of thermal fluctuations on thin elastic filaments with
non-circular cross-section and arbitrary spontaneous curvature and torsion.
Analytical expressions for orientational correlation functions and for the
persistence length of helices are derived, and it is found that this length
varies non-monotonically with the strength of thermal fluctuations. In the weak
fluctuation regime, the local helical structure is preserved and the
statistical properties are dominated by long wavelength bending and torsion
modes. As the amplitude of fluctuations is increased, the helix ``melts'' and
all memory of intrinsic helical structure is lost. Spontaneous twist of the
cross--section leads to resonant dependence of the persistence length on the
twist rate.Comment: 5 figure
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