Stable Biased Sampling

This paper presents a model in which sampling biases are evolutionary stable. We consider the sampling best response dynamics for a two-strategy population game having a unique equilibrium that is in mixed strategies. Allowing players to use differing sampling procedures, we model evolutionary competition between such procedures with a variant of the replicator dynamics that discriminates on the basis of average fitness among players with the same procedure. Using results on slow-fast systems, we find that the sampling bias in stable procedures is generically non-zero, that the size of the bias is the more extreme the closer the mixed equilibrium is to the boundary of (0,1), and that, if sample size increases, then the bias eventually decreases. Based on these observations, we argue that the presence of biases can be explained by an evolutionary second-best effect correcting for suboptimal choices induced by playing best response to small samples

Competitive function approximation for reinforcement learning

The application of reinforcement learning to problems with continuous domains requires representing the value function by means of function approximation. We identify two aspects of reinforcement learning that make the function approximation process hard: non-stationarity of the target function and biased sampling. Non-stationarity is the result of the bootstrapping nature of dynamic programming where the value function is estimated using its current approximation. Biased sampling occurs when some regions of the state space are visited too often, causing a reiterated updating with similar values which fade out the occasional updates of infrequently sampled regions. We propose a competitive approach for function approximation where many different local approximators are available at a given input and the one with expectedly best approximation is selected by means of a relevance function. The local nature of the approximators allows their fast adaptation to non-stationary changes and mitigates the biased sampling problem. The coexistence of multiple approximators updated and tried in parallel permits obtaining a good estimation much faster than would be possible with a single approximator. Experiments in different benchmark problems show that the competitive strategy provides a faster and more stable learning than non-competitive approaches.Preprin

A new family of Markov branching trees: the alpha-gamma model

We introduce a simple tree growth process that gives rise to a new two-parameter family of discrete fragmentation trees that extends Ford's alpha model to multifurcating trees and includes the trees obtained by uniform sampling from Duquesne and Le Gall's stable continuum random tree. We call these new trees the alpha-gamma trees. In this paper, we obtain their splitting rules, dislocation measures both in ranked order and in sized-biased order, and we study their limiting behaviour.Comment: 23 pages, 1 figur

A hybrid sampler for Poisson-Kingman mixture models

This paper concerns the introduction of a new Markov Chain Monte Carlo scheme for posterior sampling in Bayesian nonparametric mixture models with priors that belong to the general Poisson-Kingman class. We present a novel compact way of representing the infinite dimensional component of the model such that while explicitly representing this infinite component it has less memory and storage requirements than previous MCMC schemes. We describe comparative simulation results demonstrating the efficacy of the proposed MCMC algorithm against existing marginal and conditional MCMC samplers

Preparation and relaxation of very stable glassy states of a simulated liquid

We prepare metastable glassy states in a model glass-former made of Lennard-Jones particles by sampling biased ensembles of trajectories with low dynamical activity. These trajectories form an inactive dynamical phase whose `fast' vibrational degrees of freedom are maintained at thermal equilibrium by contact with a heat bath, while the `slow' structural degrees of freedom are located in deep valleys of the energy landscape. We examine the relaxation to equilibrium and the vibrational properties of these metastable states. The glassy states we prepare by our trajectory sampling method are very stable to thermal fluctuations and also more mechanically rigid than low-temperature equilibrated configurations.Comment: Minor revisions in light of referee comments. 5 pages, 4 fig

Isotropic-nematic interfacial tension of hard and soft rods: application of advanced grand canonical biased sampling techniques

Coexistence between the isotropic and the nematic phase in suspensions of rods is studied using grand canonical Monte Carlo simulations with a bias on the nematic order parameter. The biasing scheme makes it possible to estimate the interfacial tension gamma in systems of hard and soft rods. For hard rods with L/D=15, we obtain gamma ~ 1.4 kB T/L^2, with L the rod length, D the rod diameter, T the temperature, and kB the Boltzmann constant. This estimate is in good agreement with theoretical predictions, and the order of magnitude is consistent with experiments.Comment: 10 pages, 10 figure

Translocation and encapsulation of siRNA inside carbon nanotubes

We report spontaneous translocation of small interfering RNA (siRNA) inside carbon nanotubes (CNTs) of various diameters and chirality using all atom molecular dynamics (MD) simulations with explicit solvent. We use Umbrella sampling method to calculate the free energy landscape of the siRNA entry and translocation event. Free energy profiles shows that siRNA gains free energy while translocating inside CNT and barrier for siRNA exit from CNT ranges from 40 to 110 kcal/mol depending on CNT chirality and salt concentration. The translocation time \tau decreases with the increase of CNT diameter with a critical diameter of 24 \AA for the translocation. In contrast, double strand DNA (dsDNA) of the same sequence does not translocate inside CNT due to large free energy barrier for the translocation. This study helps in understanding the nucleic acid transport through nanopores at microscopic level and may help designing carbon nanotube based sensor for siRNA.Comment: Accepted for the Journal of Chemical Physics; 24 pages, 6 figures and 1 tabl