25,337 research outputs found
Rare-Event Sampling: Occupation-Based Performance Measures for Parallel Tempering and Infinite Swapping Monte Carlo Methods
In the present paper we identify a rigorous property of a number of
tempering-based Monte Carlo sampling methods, including parallel tempering as
well as partial and infinite swapping. Based on this property we develop a
variety of performance measures for such rare-event sampling methods that are
broadly applicable, informative, and straightforward to implement. We
illustrate the use of these performance measures with a series of applications
involving the equilibrium properties of simple Lennard-Jones clusters,
applications for which the performance levels of partial and infinite swapping
approaches are found to be higher than those of conventional parallel
tempering.Comment: 18 figure
Path Similarity Analysis: a Method for Quantifying Macromolecular Pathways
Diverse classes of proteins function through large-scale conformational
changes; sophisticated enhanced sampling methods have been proposed to generate
these macromolecular transition paths. As such paths are curves in a
high-dimensional space, they have been difficult to compare quantitatively, a
prerequisite to, for instance, assess the quality of different sampling
algorithms. The Path Similarity Analysis (PSA) approach alleviates these
difficulties by utilizing the full information in 3N-dimensional trajectories
in configuration space. PSA employs the Hausdorff or Fr\'echet path
metrics---adopted from computational geometry---enabling us to quantify path
(dis)similarity, while the new concept of a Hausdorff-pair map permits the
extraction of atomic-scale determinants responsible for path differences.
Combined with clustering techniques, PSA facilitates the comparison of many
paths, including collections of transition ensembles. We use the closed-to-open
transition of the enzyme adenylate kinase (AdK)---a commonly used testbed for
the assessment enhanced sampling algorithms---to examine multiple microsecond
equilibrium molecular dynamics (MD) transitions of AdK in its substrate-free
form alongside transition ensembles from the MD-based dynamic importance
sampling (DIMS-MD) and targeted MD (TMD) methods, and a geometrical targeting
algorithm (FRODA). A Hausdorff pairs analysis of these ensembles revealed, for
instance, that differences in DIMS-MD and FRODA paths were mediated by a set of
conserved salt bridges whose charge-charge interactions are fully modeled in
DIMS-MD but not in FRODA. We also demonstrate how existing trajectory analysis
methods relying on pre-defined collective variables, such as native contacts or
geometric quantities, can be used synergistically with PSA, as well as the
application of PSA to more complex systems such as membrane transporter
proteins.Comment: 9 figures, 3 tables in the main manuscript; supplementary information
includes 7 texts (S1 Text - S7 Text) and 11 figures (S1 Fig - S11 Fig) (also
available from journal site
icet - A Python library for constructing and sampling alloy cluster expansions
Alloy cluster expansions (CEs) provide an accurate and computationally
efficient mapping of the potential energy surface of multi-component systems
that enables comprehensive sampling of the many-dimensional configuration
space. Here, we introduce \textsc{icet}, a flexible, extensible, and
computationally efficient software package for the construction and sampling of
CEs. \textsc{icet} is largely written in Python for easy integration in
comprehensive workflows, including first-principles calculations for the
generation of reference data and machine learning libraries for training and
validation. The package enables training using a variety of linear regression
algorithms with and without regularization, Bayesian regression, feature
selection, and cross-validation. It also provides complementary functionality
for structure enumeration and mapping as well as data management and analysis.
Potential applications are illustrated by two examples, including the
computation of the phase diagram of a prototypical metallic alloy and the
analysis of chemical ordering in an inorganic semiconductor.Comment: 10 page
The partition function zeroes of quantum critical points
The LeeâYang theorem for the zeroes of the partition function is not strictly applicable to quantum systems because the zeroes are defined in units of the fugacity ehÎÏ, and the Euclidean-time lattice spacing ÎÏ can be divergent in the infrared (IR). We recently presented analytic arguments describing how a new space-Euclidean time zeroes expansion can be defined, which reproduces Lee and Yang's scaling but avoids the unresolved branch points associated with the breaking of nonlocal symmetries such as Parity. We now present a first numerical analysis for this new zeroes approach for a quantum spin chain system. We use our scheme to quantify the renormalization group flow of the physical lattice couplings to the IR fixed point of this system. We argue that the generic Finite-Size Scaling (FSS) function of our scheme is identically the entanglement entropy of the lattice partition function and, therefore, that we are able to directly extract the central charge, c, of the quantum spin chain system using conformal predictions for the scaling of the entanglement entropy
Efficient approximate unitary t-designs from partially invertible universal sets and their application to quantum speedup
At its core a -design is a method for sampling from a set of unitaries in
a way which mimics sampling randomly from the Haar measure on the unitary
group, with applications across quantum information processing and physics. We
construct new families of quantum circuits on -qubits giving rise to
-approximate unitary -designs efficiently in
depth. These quantum circuits are based on a relaxation of technical
requirements in previous constructions. In particular, the construction of
circuits which give efficient approximate -designs by Brandao, Harrow, and
Horodecki (F.G.S.L Brandao, A.W Harrow, and M. Horodecki, Commun. Math. Phys.
(2016).) required choosing gates from ensembles which contained inverses for
all elements, and that the entries of the unitaries are algebraic. We reduce
these requirements, to sets that contain elements without inverses in the set,
and non-algebraic entries, which we dub partially invertible universal sets. We
then adapt this circuit construction to the framework of measurement based
quantum computation(MBQC) and give new explicit examples of -qubit graph
states with fixed assignments of measurements (graph gadgets) giving rise to
unitary -designs based on partially invertible universal sets, in a natural
way. We further show that these graph gadgets demonstrate a quantum speedup, up
to standard complexity theoretic conjectures. We provide numerical and
analytical evidence that almost any assignment of fixed measurement angles on
an -qubit cluster state give efficient -designs and demonstrate a quantum
speedup.Comment: 25 pages,7 figures. Comments are welcome. Some typos corrected in
newest version. new References added.Proofs unchanged. Results unchange
A Comparative Analysis of Ensemble Classifiers: Case Studies in Genomics
The combination of multiple classifiers using ensemble methods is
increasingly important for making progress in a variety of difficult prediction
problems. We present a comparative analysis of several ensemble methods through
two case studies in genomics, namely the prediction of genetic interactions and
protein functions, to demonstrate their efficacy on real-world datasets and
draw useful conclusions about their behavior. These methods include simple
aggregation, meta-learning, cluster-based meta-learning, and ensemble selection
using heterogeneous classifiers trained on resampled data to improve the
diversity of their predictions. We present a detailed analysis of these methods
across 4 genomics datasets and find the best of these methods offer
statistically significant improvements over the state of the art in their
respective domains. In addition, we establish a novel connection between
ensemble selection and meta-learning, demonstrating how both of these disparate
methods establish a balance between ensemble diversity and performance.Comment: 10 pages, 3 figures, 8 tables, to appear in Proceedings of the 2013
International Conference on Data Minin
Generalized-ensemble simulations and cluster algorithms
The importance-sampling Monte Carlo algorithm appears to be the universally
optimal solution to the problem of sampling the state space of statistical
mechanical systems according to the relative importance of configurations for
the partition function or thermal averages of interest. While this is true in
terms of its simplicity and universal applicability, the resulting approach
suffers from the presence of temporal correlations of successive samples
naturally implied by the Markov chain underlying the importance-sampling
simulation. In many situations, these autocorrelations are moderate and can be
easily accounted for by an appropriately adapted analysis of simulation data.
They turn out to be a major hurdle, however, in the vicinity of phase
transitions or for systems with complex free-energy landscapes. The critical
slowing down close to continuous transitions is most efficiently reduced by the
application of cluster algorithms, where they are available. For first-order
transitions and disordered systems, on the other hand, macroscopic energy
barriers need to be overcome to prevent dynamic ergodicity breaking. In this
situation, generalized-ensemble techniques such as the multicanonical
simulation method can effect impressive speedups, allowing to sample the full
free-energy landscape. The Potts model features continuous as well as
first-order phase transitions and is thus a prototypic example for studying
phase transitions and new algorithmic approaches. I discuss the possibilities
of bringing together cluster and generalized-ensemble methods to combine the
benefits of both techniques. The resulting algorithm allows for the efficient
estimation of the random-cluster partition function encoding the information of
all Potts models, even with a non-integer number of states, for all
temperatures in a single simulation run per system size.Comment: 15 pages, 6 figures, proceedings of the 2009 Workshop of the Center
of Simulational Physics, Athens, G
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