An Adaptive Interacting Wang-Landau Algorithm for Automatic Density Exploration

While statisticians are well-accustomed to performing exploratory analysis in the modeling stage of an analysis, the notion of conducting preliminary general-purpose exploratory analysis in the Monte Carlo stage (or more generally, the model-fitting stage) of an analysis is an area which we feel deserves much further attention. Towards this aim, this paper proposes a general-purpose algorithm for automatic density exploration. The proposed exploration algorithm combines and expands upon components from various adaptive Markov chain Monte Carlo methods, with the Wang-Landau algorithm at its heart. Additionally, the algorithm is run on interacting parallel chains -- a feature which both decreases computational cost as well as stabilizes the algorithm, improving its ability to explore the density. Performance is studied in several applications. Through a Bayesian variable selection example, the authors demonstrate the convergence gains obtained with interacting chains. The ability of the algorithm's adaptive proposal to induce mode-jumping is illustrated through a trimodal density and a Bayesian mixture modeling application. Lastly, through a 2D Ising model, the authors demonstrate the ability of the algorithm to overcome the high correlations encountered in spatial models.Comment: 33 pages, 20 figures (the supplementary materials are included as appendices

Trajectory Synthesis for Fisher Information Maximization

Estimation of model parameters in a dynamic system can be significantly improved with the choice of experimental trajectory. For general, nonlinear dynamic systems, finding globally "best" trajectories is typically not feasible; however, given an initial estimate of the model parameters and an initial trajectory, we present a continuous-time optimization method that produces a locally optimal trajectory for parameter estimation in the presence of measurement noise. The optimization algorithm is formulated to find system trajectories that improve a norm on the Fisher information matrix. A double-pendulum cart apparatus is used to numerically and experimentally validate this technique. In simulation, the optimized trajectory increases the minimum eigenvalue of the Fisher information matrix by three orders of magnitude compared to the initial trajectory. Experimental results show that this optimized trajectory translates to an order of magnitude improvement in the parameter estimate error in practice.Comment: 12 page

A Hybrid Active Filter Using the Backstepping Controller for Harmonic Current Compensation

This document presents a new hybrid combination of filters using passive and active elements because of the generalization in the use of non-linear loads that generate harmonics directly affecting the symmetry of energy transmission systems that influence the functioning of the electricity grid and, consequently, the deterioration of power quality. In this context, active power filters represent one of the best solutions for improving power quality and compensating harmonic currents to get a symmetrical waveform. In addition, given the importance and occupation of the transmission network, it is necessary to control the stability of the system. Traditionally, passive filters were used to improve energy quality, but they have endured problems such as resonance, fixed remuneration, etc. In order to mitigate these problems, a hybrid HAPF active power filter is proposed combining a parallel active filter and a passive filter controlled by a backstepping algorithm strategy. This control strategy is compared with two other methods, namely the classical PI control, and the fuzzy logic control in order to verify the effectiveness and the level of symmetry of the backstepping controller proposed for the HAPF. The proposed backstepping controller inspires the notion of stability in Lyapunov’s sense. This work is carried out to improve the performance of the HAPF by the backstepping command. It perfectly compensates the harmonics according to standards. The results of simulations performed under the Matlab/Simulink environment show the efficiency and robustness of the proposed backstepping controller applied on HAPF, compared to other control methods. The HAPF with the backstepping controller shows a significant decrease in the THD harmonic distortion rate

Achieving Extreme Resolution in Numerical Cosmology Using Adaptive Mesh Refinement: Resolving Primordial Star Formation

As an entry for the 2001 Gordon Bell Award in the "special" category, we describe our 3-d, hybrid, adaptive mesh refinement (AMR) code, Enzo, designed for high-resolution, multiphysics, cosmological structure formation simulations. Our parallel implementation places no limit on the depth or complexity of the adaptive grid hierarchy, allowing us to achieve unprecedented spatial and temporal dynamic range. We report on a simulation of primordial star formation which develops over 8000 subgrids at 34 levels of refinement to achieve a local refinement of a factor of 10^12 in space and time. This allows us to resolve the properties of the first stars which form in the universe assuming standard physics and a standard cosmological model. Achieving extreme resolution requires the use of 128-bit extended precision arithmetic (EPA) to accurately specify the subgrid positions. We describe our EPA AMR implementation on the IBM SP2 Blue Horizon system at the San Diego Supercomputer Center.Comment: 23 pages, 5 figures. Peer reviewed technical paper accepted to the proceedings of Supercomputing 2001. This entry was a Gordon Bell Prize finalist. For more information visit http://www.TomAbel.com/GB

Adaptive smartphone-based sensor fusion for estimating competitive rowing kinematic metrics.

Competitive rowing highly values boat position and velocity data for real-time feedback during training, racing and post-training analysis. The ubiquity of smartphones with embedded position (GPS) and motion (accelerometer) sensors motivates their possible use in these tasks. In this paper, we investigate the use of two real-time digital filters to achieve highly accurate yet reasonably priced measurements of boat speed and distance traveled. Both filters combine acceleration and location data to estimate boat distance and speed; the first using a complementary frequency response-based filter technique, the second with a Kalman filter formalism that includes adaptive, real-time estimates of effective accelerometer bias. The estimates of distance and speed from both filters were validated and compared with accurate reference data from a differential GPS system with better than 1 cm precision and a 5 Hz update rate, in experiments using two subjects (an experienced club-level rower and an elite rower) in two different boats on a 300 m course. Compared with single channel (smartphone GPS only) measures of distance and speed, the complementary filter improved the accuracy and precision of boat speed, boat distance traveled, and distance per stroke by 44%, 42%, and 73%, respectively, while the Kalman filter improved the accuracy and precision of boat speed, boat distance traveled, and distance per stroke by 48%, 22%, and 82%, respectively. Both filters demonstrate promise as general purpose methods to substantially improve estimates of important rowing performance metrics