18,324 research outputs found
Monitoring a PGD solver for parametric power flow problems with goal-oriented error assessment
This is the peer reviewed version of the following article: [García-Blanco, R., Borzacchiello, D., Chinesta, F., and Diez, P. (2017) Monitoring a PGD solver for parametric power flow problems with goal-oriented error assessment. Int. J. Numer. Meth. Engng, 111: 529–552. doi: 10.1002/nme.5470], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5470/full. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.The parametric analysis of electric grids requires carrying out a large number of Power Flow computations. The different parameters describe loading conditions and grid properties. In this framework, the Proper Generalized Decomposition (PGD) provides a numerical solution explicitly accounting for the parametric dependence. Once the PGD solution is available, exploring the multidimensional parametric space is computationally inexpensive. The aim of this paper is to provide tools to monitor the error associated with this significant computational gain and to guarantee the quality of the PGD solution. In this case, the PGD algorithm consists in three nested loops that correspond to 1) iterating algebraic solver, 2) number of terms in the separable greedy expansion and 3) the alternated directions for each term. In the proposed approach, the three loops are controlled by stopping criteria based on residual goal-oriented error estimates. This allows one for using only the computational resources necessary to achieve the accuracy prescribed by the end- user. The paper discusses how to compute the goal-oriented error estimates. This requires linearizing the error equation and the Quantity of Interest to derive an efficient error representation based on an adjoint problem. The efficiency of the proposed approach is demonstrated on benchmark problems.Peer ReviewedPostprint (author's final draft
A rigorous and efficient asymptotic test for power-law cross-correlation
Podobnik and Stanley recently proposed a novel framework, Detrended
Cross-Correlation Analysis, for the analysis of power-law cross-correlation
between two time-series, a phenomenon which occurs widely in physical,
geophysical, financial and numerous additional applications. While highly
promising in these important application domains, to date no rigorous or
efficient statistical test has been proposed which uses the information
provided by DCCA across time-scales for the presence of this power-law
cross-correlation. In this paper we fill this gap by proposing a method based
on DCCA for testing the hypothesis of power-law cross-correlation; the method
synthesizes the information generated by DCCA across time-scales and returns
conservative but practically relevant p-values for the null hypothesis of zero
correlation, which may be efficiently calculated in software. Thus our
proposals generate confidence estimates for a DCCA analysis in a fully
probabilistic fashion
On Preparing Entangled Pairs of Polarization Qubits in the Frequency Non-Degenerate Regime
The problems associated with practical implementation of the scheme proposed
for preparation of arbitrary states of polarization ququarts based on biphotons
are discussed. The influence of frequency dispersion effects are considered,
and the necessity of group velocities dispersion compensation in the frequency
non-degenerate case even for continuous pumping is demonstrated. A method for
this compensation is proposed and implemented experimentally. Physical
restrictions on the quality of prepared two-photon states are revealed.Comment: 9 pages, 6 figure
Learning Bayesian Networks with the bnlearn R Package
bnlearn is an R package which includes several algorithms for learning the
structure of Bayesian networks with either discrete or continuous variables.
Both constraint-based and score-based algorithms are implemented, and can use
the functionality provided by the snow package to improve their performance via
parallel computing. Several network scores and conditional independence
algorithms are available for both the learning algorithms and independent use.
Advanced plotting options are provided by the Rgraphviz package.Comment: 22 pages, 4 picture
Inferring Latent States and Refining Force Estimates via Hierarchical Dirichlet Process Modeling in Single Particle Tracking Experiments
Optical microscopy provides rich spatio-temporal information characterizing
in vivo molecular motion. However, effective forces and other parameters used
to summarize molecular motion change over time in live cells due to latent
state changes, e.g., changes induced by dynamic micro-environments,
photobleaching, and other heterogeneity inherent in biological processes. This
study focuses on techniques for analyzing Single Particle Tracking (SPT) data
experiencing abrupt state changes. We demonstrate the approach on GFP tagged
chromatids experiencing metaphase in yeast cells and probe the effective forces
resulting from dynamic interactions that reflect the sum of a number of
physical phenomena. State changes are induced by factors such as microtubule
dynamics exerting force through the centromere, thermal polymer fluctuations,
etc. Simulations are used to demonstrate the relevance of the approach in more
general SPT data analyses. Refined force estimates are obtained by adopting and
modifying a nonparametric Bayesian modeling technique, the Hierarchical
Dirichlet Process Switching Linear Dynamical System (HDP-SLDS), for SPT
applications. The HDP-SLDS method shows promise in systematically identifying
dynamical regime changes induced by unobserved state changes when the number of
underlying states is unknown in advance (a common problem in SPT applications).
We expand on the relevance of the HDP-SLDS approach, review the relevant
background of Hierarchical Dirichlet Processes, show how to map discrete time
HDP-SLDS models to classic SPT models, and discuss limitations of the approach.
In addition, we demonstrate new computational techniques for tuning
hyperparameters and for checking the statistical consistency of model
assumptions directly against individual experimental trajectories; the
techniques circumvent the need for "ground-truth" and subjective information.Comment: 25 pages, 6 figures. Differs only typographically from PLoS One
publication available freely as an open-access article at
http://journals.plos.org/plosone/article?id=10.1371/journal.pone.013763
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