23,574 research outputs found
RNA secondary structure design
We consider the inverse-folding problem for RNA secondary structures: for a
given (pseudo-knot-free) secondary structure find a sequence that has that
structure as its ground state. If such a sequence exists, the structure is
called designable. We implemented a branch-and-bound algorithm that is able to
do an exhaustive search within the sequence space, i.e., gives an exact answer
whether such a sequence exists. The bound required by the branch-and-bound
algorithm are calculated by a dynamic programming algorithm. We consider
different alphabet sizes and an ensemble of random structures, which we want to
design. We find that for two letters almost none of these structures are
designable. The designability improves for the three-letter case, but still a
significant fraction of structures is undesignable. This changes when we look
at the natural four-letter case with two pairs of complementary bases:
undesignable structures are the exception, although they still exist. Finally,
we also study the relation between designability and the algorithmic complexity
of the branch-and-bound algorithm. Within the ensemble of structures, a high
average degree of undesignability is correlated to a long time to prove that a
given structure is (un-)designable. In the four-letter case, where the
designability is high everywhere, the algorithmic complexity is highest in the
region of naturally occurring RNA.Comment: 11 pages, 10 figure
Density Matrix Renormalization Group in the Heisenberg Picture
In some cases the state of a quantum system with a large number of subsystems
can be approximated efficiently by the density matrix renormalization group,
which makes use of redundancies in the description of the state. Here we show
that the achievable efficiency can be much better when performing density
matrix renormalization group calculations in the Heisenberg picture, as only
the observable of interest but not the entire state is considered. In some
non-trivial cases, this approach can even be exact for finite bond dimensions.Comment: version to appear in PRL, acronyms in title and abstract expanded,
new improved numerical example
Ground-State and Domain-Wall Energies in the Spin-Glass Region of the 2D Random-Bond Ising Model
The statistics of the ground-state and domain-wall energies for the
two-dimensional random-bond Ising model on square lattices with independent,
identically distributed bonds of probability of and of
are studied. We are able to consider large samples of up to
spins by using sophisticated matching algorithms. We study
systems, but we also consider samples, for different aspect ratios
. We find that the scaling behavior of the ground-state energy and
its sample-to-sample fluctuations inside the spin-glass region () are characterized by simple scaling functions. In particular, the
fluctuations exhibit a cusp-like singularity at . Inside the spin-glass
region the average domain-wall energy converges to a finite nonzero value as
the sample size becomes infinite, holding fixed. Here, large finite-size
effects are visible, which can be explained for all by a single exponent
, provided higher-order corrections to scaling are included.
Finally, we confirm the validity of aspect-ratio scaling for : the
distribution of the domain-wall energies converges to a Gaussian for ,
although the domain walls of neighboring subsystems of size are
not independent.Comment: 11 pages with 15 figures, extensively revise
Renormalization algorithm with graph enhancement
We introduce a class of variational states to describe quantum many-body
systems. This class generalizes matrix product states which underly the
density-matrix renormalization group approach by combining them with weighted
graph states. States within this class may (i) possess arbitrarily long-ranged
two-point correlations, (ii) exhibit an arbitrary degree of block entanglement
entropy up to a volume law, (iii) may be taken translationally invariant, while
at the same time (iv) local properties and two-point correlations can be
computed efficiently. This new variational class of states can be thought of as
being prepared from matrix product states, followed by commuting unitaries on
arbitrary constituents, hence truly generalizing both matrix product and
weighted graph states. We use this class of states to formulate a
renormalization algorithm with graph enhancement (RAGE) and present numerical
examples demonstrating that improvements over density-matrix renormalization
group simulations can be achieved in the simulation of ground states and
quantum algorithms. Further generalizations, e.g., to higher spatial
dimensions, are outlined.Comment: 4 pages, 1 figur
Interpolation and harmonic majorants in big Hardy-Orlicz spaces
Free interpolation in Hardy spaces is caracterized by the well-known Carleson
condition. The result extends to Hardy-Orlicz spaces contained in the scale of
classical Hardy spaces , . For the Smirnov and the Nevanlinna
classes, interpolating sequences have been characterized in a recent paper in
terms of the existence of harmonic majorants (quasi-bounded in the case of the
Smirnov class). Since the Smirnov class can be regarded as the union over all
Hardy-Orlicz spaces associated with a so-called strongly convex function, it is
natural to ask how the condition changes from the Carleson condition in
classical Hardy spaces to harmonic majorants in the Smirnov class. The aim of
this paper is to narrow down this gap from the Smirnov class to ``big''
Hardy-Orlicz spaces. More precisely, we characterize interpolating sequences
for a class of Hardy-Orlicz spaces that carry an algebraic structure and that
are strictly bigger than . It turns out that the
interpolating sequences are again characterized by the existence of
quasi-bounded majorants, but now the weights of the majorants have to be in
suitable Orlicz spaces. The existence of harmonic majorants in such Orlicz
spaces will also be discussed in the general situation. We finish the paper
with an example of a separated Blaschke sequence that is interpolating for
certain Hardy-Orlicz spaces without being interpolating for slightly smaller
ones.Comment: 19 pages, 2 figure
Flows, Fragmentation, and Star Formation. I. Low-mass Stars in Taurus
The remarkably filamentary spatial distribution of young stars in the Taurus
molecular cloud has significant implications for understanding low-mass star
formation in relatively quiescent conditions. The large scale and regular
spacing of the filaments suggests that small-scale turbulence is of limited
importance, which could be consistent with driving on large scales by flows
which produced the cloud. The small spatial dispersion of stars from gaseous
filaments indicates that the low-mass stars are generally born with small
velocity dispersions relative to their natal gas, of order the sound speed or
less. The spatial distribution of the stars exhibits a mean separation of about
0.25 pc, comparable to the estimated Jeans length in the densest gaseous
filaments, and is consistent with roughly uniform density along the filaments.
The efficiency of star formation in filaments is much higher than elsewhere,
with an associated higher frequency of protostars and accreting T Tauri stars.
The protostellar cores generally are aligned with the filaments, suggesting
that they are produced by gravitational fragmentation, resulting in initially
quasi-prolate cores. Given the absence of massive stars which could strongly
dominate cloud dynamics, Taurus provides important tests of theories of
dispersed low-mass star formation and numerical simulations of molecular cloud
structure and evolution.Comment: 32 pages, 9 figures: to appear in Ap
Reduction of Two-Dimensional Dilute Ising Spin Glasses
The recently proposed reduction method is applied to the Edwards-Anderson
model on bond-diluted square lattices. This allows, in combination with a
graph-theoretical matching algorithm, to calculate numerically exact ground
states of large systems. Low-temperature domain-wall excitations are studied to
determine the stiffness exponent y_2. A value of y_2=-0.281(3) is found,
consistent with previous results obtained on undiluted lattices. This
comparison demonstrates the validity of the reduction method for bond-diluted
spin systems and provides strong support for similar studies proclaiming
accurate results for stiffness exponents in dimensions d=3,...,7.Comment: 7 pages, RevTex4, 6 ps-figures included, for related information, see
http://www.physics.emory.edu/faculty/boettcher
Spontaneous scalarization of self-gravitating magnetic fields
In this paper, we study the spontaneous scalarization of an extended, self-gravitating system which is static, cylindrically symmetric and possesses electromagnetic fields. We demonstrate that a real massive scalar field condenses on this Melvin magnetic universe solution when introducing a nonminimal coupling between the scalar field and (a) the magnetic field and (b) the curvature of the space-time, respectively. We find that in both cases, the solutions exist on a finite interval of the coupling constant and that solutions with a number of nodes k in the scalar field are present. For case (a) we observe that the intervals of existence are mutually exclusive for different k
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