26,280 research outputs found
Generalized Directed Loop Method for Quantum Monte Carlo Simulations
Efficient quantum Monte Carlo update schemes called directed loops have
recently been proposed, which improve the efficiency of simulations of quantum
lattice models. We propose to generalize the detailed balance equations at the
local level during the loop construction by accounting for the matrix elements
of the operators associated with open world-line segments. Using linear
programming techniques to solve the generalized equations, we look for optimal
construction schemes for directed loops. This also allows for an extension of
the directed loop scheme to general lattice models, such as high-spin or
bosonic models. The resulting algorithms are bounce-free in larger regions of
parameter space than the original directed loop algorithm. The generalized
directed loop method is applied to the magnetization process of spin chains in
order to compare its efficiency to that of previous directed loop schemes. In
contrast to general expectations, we find that minimizing bounces alone does
not always lead to more efficient algorithms in terms of autocorrelations of
physical observables, because of the non-uniqueness of the bounce-free
solutions. We therefore propose different general strategies to further
minimize autocorrelations, which can be used as supplementary requirements in
any directed loop scheme. We show by calculating autocorrelation times for
different observables that such strategies indeed lead to improved efficiency;
however we find that the optimal strategy depends not only on the model
parameters but also on the observable of interest.Comment: 17 pages, 16 figures; v2 : Modified introduction and section 2,
Changed title; v3 : Added section on supplementary strategies; published
versio
Space Efficient Breadth-First and Level Traversals of Consistent Global States of Parallel Programs
Enumerating consistent global states of a computation is a fundamental
problem in parallel computing with applications to debug- ging, testing and
runtime verification of parallel programs. Breadth-first search (BFS)
enumeration is especially useful for these applications as it finds an
erroneous consistent global state with the least number of events possible. The
total number of executed events in a global state is called its rank. BFS also
allows enumeration of all global states of a given rank or within a range of
ranks. If a computation on n processes has m events per process on average,
then the traditional BFS (Cooper-Marzullo and its variants) requires
space in the worst case, whereas ou r
algorithm performs the BFS requires space. Thus, we
reduce the space complexity for BFS enumeration of consistent global states
exponentially. and give the first polynomial space algorithm for this task. In
our experimental evaluation of seven benchmarks, traditional BFS fails in many
cases by exhausting the 2 GB heap space allowed to the JVM. In contrast, our
implementation uses less than 60 MB memory and is also faster in many cases
Growth Algorithms for Lattice Heteropolymers at Low Temperatures
Two improved versions of the pruned-enriched-Rosenbluth method (PERM) are
proposed and tested on simple models of lattice heteropolymers. Both are found
to outperform not only the previous version of PERM, but also all other
stochastic algorithms which have been employed on this problem, except for the
core directed chain growth method (CG) of Beutler & Dill. In nearly all test
cases they are faster in finding low-energy states, and in many cases they
found new lowest energy states missed in previous papers. The CG method is
superior to our method in some cases, but less efficient in others. On the
other hand, the CG method uses heavily heuristics based on presumptions about
the hydrophobic core and does not give thermodynamic properties, while the
present method is a fully blind general purpose algorithm giving correct
Boltzmann-Gibbs weights, and can be applied in principle to any stochastic
sampling problem.Comment: 9 pages, 9 figures. J. Chem. Phys., in pres
Design of Sequences with Good Folding Properties in Coarse-Grained Protein Models
Background: Designing amino acid sequences that are stable in a given target
structure amounts to maximizing a conditional probability. A straightforward
approach to accomplish this is a nested Monte Carlo where the conformation
space is explored over and over again for different fixed sequences, which
requires excessive computational demand. Several approximate attempts to remedy
this situation, based on energy minimization for fixed structure or high-
expansions, have been proposed. These methods are fast but often not accurate
since folding occurs at low .
Results: We develop a multisequence Monte Carlo procedure, where both
sequence and conformation space are simultaneously probed with efficient
prescriptions for pruning sequence space. The method is explored on
hydrophobic/polar models. We first discuss short lattice chains, in order to
compare with exact data and with other methods. The method is then successfully
applied to lattice chains with up to 50 monomers, and to off-lattice 20-mers.
Conclusions: The multisequence Monte Carlo method offers a new approach to
sequence design in coarse-grained models. It is much more efficient than
previous Monte Carlo methods, and is, as it stands, applicable to a fairly wide
range of two-letter models.Comment: 23 pages, 7 figure
Phase Transitions of Single Semi-stiff Polymer Chains
We study numerically a lattice model of semiflexible homopolymers with
nearest neighbor attraction and energetic preference for straight joints
between bonded monomers. For this we use a new algorithm, the "Pruned-Enriched
Rosenbluth Method" (PERM). It is very efficient both for relatively open
configurations at high temperatures and for compact and frozen-in low-T states.
This allows us to study in detail the phase diagram as a function of
nn-attraction epsilon and stiffness x. It shows a theta-collapse line with a
transition from open coils to molten compact globules (large epsilon) and a
freezing transition toward a state with orientational global order (large
stiffness x). Qualitatively this is similar to a recently studied mean field
theory (Doniach et al. (1996), J. Chem. Phys. 105, 1601), but there are
important differences. In contrast to the mean field theory, the
theta-temperature increases with stiffness x. The freezing temperature
increases even faster, and reaches the theta-line at a finite value of x. For
even stiffer chains, the freezing transition takes place directly without the
formation of an intermediate globule state. Although being in contrast with
mean filed theory, the latter has been conjectured already by Doniach et al. on
the basis of low statistics Monte Carlo simulations. Finally, we discuss the
relevance of the present model as a very crude model for protein folding.Comment: 11 pages, Latex, 8 figure
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