Search

In this‐30 work we propose a model selection criterion to estimate the points of independence of a random vector, producing a decomposition of the vector distribution function into independent blocks. The method, based on a general estimator of the distribution function, can be applied for discrete or continuous random vectors, and for i.i.d. data or dependent time series. We prove the consistency of the approach under general conditions on the estimator of the distribution function and we show that the consistency holds for i.i.d. data and discrete time series with mixing conditions. We also propose an efficient algorithm to approximate the estimator and show the performance of the method on simulated data. We apply the method in a real dataset to estimate the distribution of the flow over several locations on a river, observed at different time points. [ABSTRACT FROM AUTHOR]

The calculation of free energy profiles is central in understanding differential enzymatic activity, for instance, involving chemical reactions that require QM‐MM tools, ligand migration, and conformational rearrangements that can be modeled using classical potentials. The use of steered molecular dynamics (sMD) together with the Jarzynski equality is a popular approach in calculating free energy profiles. Here, we first briefly review the application of the Jarzynski equality to sMD simulations, then revisit the so‐called stiff‐spring approximation and the consequent expectation of Gaussian work distributions and, finally, reiterate the practical utility of the second‐order cumulant expansion, as it coincides with the parametric maximum‐likelihood estimator in this scenario. We illustrate this procedure using simulations of CO, both in aqueous solution and in a carbon nanotube as a model system for biologically relevant nanoheterogeneous environments. We conclude the use of the second‐order cumulant expansion permits the use of faster pulling velocities in sMD simulations, without introducing bias due to large dispersion in the non‐equilibrium work distribution. [ABSTRACT FROM AUTHOR]

The Jarzynski equality is one of the most widely celebrated and scrutinized nonequilibrium work theorems, relating free energy to the external work performed in nonequilibrium transitions. In practice, the required ensemble average of the Boltzmann weights of infinite nonequilibrium transitions is estimated as a finite sample average, resulting in the so‐called Jarzynski estimator, ΔF^J. Alternatively, the second‐order approximation of the Jarzynski equality, though seldom invoked, is exact for Gaussian distributions and gives rise to the Fluctuation‐Dissipation estimator ΔF^FD. Here we derive the parametric maximum‐likelihood estimator (MLE) of the free energy ΔF^ML considering unidirectional work distributions belonging to Gaussian or Gamma families, and compare this estimator to ΔF^J. We further consider bidirectional work distributions belonging to the same families, and compare the corresponding bidirectional ΔF^ML∗ to the Bennett acceptance ratio (ΔF^BAR) estimator. We show that, for Gaussian unidirectional work distributions, ΔF^FD is in fact the parametric MLE of the free energy, and as such, the most efficient estimator for this statistical family. We observe that ΔF^ML and ΔF^ML∗ perform better than ΔF^J and ΔF^BAR, for unidirectional and bidirectional distributions, respectively. These results illustrate that the characterization of the underlying work distribution permits an optimal use of the Jarzynski equality. © 2018 Wiley Periodicals, Inc. The Jarzynski equality is routinely used to compute equilibrium free‐energy differences from a set of non‐equilibrium work values. From a computational approach, these non‐equilibrium work values are often generated using steered Molecular Dynamics, and, under certain conditions a Gaussian distribution of nonequilibrium work values is to be anticipated. We highlight the advantage of parametric maximum‐likelihood estimators over the conventional use of the Jarzynski equality, when information about the distribution of nonequilibirum work values is available. [ABSTRACT FROM AUTHOR]

The mechanisms involved in bidirectional transport along microtubules remain largely unknown. We explored the collective action of kinesin-2 and dynein motors during transport of melanosomes in Xenopus laevis melanophores. These motors are attached to organelles through accessory proteins establishing a complex molecular linker. We determined both the stiffness of this linker and the organelles speed and observed that these parameters depended on the organelle size and cargo direction. Our results suggest that melanosome transport is driven by two dissimilar teams: whereas dynein motors compete with kinesin-2 affecting the properties of plus-end directed organelles, kinesin-2 does not seem to play a similar role during minus-end transport. [ABSTRACT FROM AUTHOR]

In a missing data setting, we have a sample in which a vector of explanatory variables ${\bf x}_i$ is observed for every subject i, while scalar responses $y_i$ are missing by happenstance on some individuals. In this work we propose robust estimators of the distribution of the responses assuming missing at random (MAR) data, under a semiparametric regression model. Our approach allows the consistent estimation of any weakly continuous functional of the response's distribution. In particular, strongly consistent estimators of any continuous location functional, such as the median, L-functionals and M-functionals, are proposed. A robust fit for the regression model combined with the robust properties of the location functional gives rise to a robust recipe for estimating the location parameter. Robustness is quantified through the breakdown point of the proposed procedure. The asymptotic distribution of the location estimators is also derived. The proofs of the theorems are presented in Supplementary Material available online. The Canadian Journal of Statistics 41: 111-132; 2013 © 2012 Statistical Society of Canada [ABSTRACT FROM AUTHOR]