A Physically-Consistent Bayesian Non-Parametric Mixture Model for Dynamical System Learning

We propose a physically-consistent Bayesian non-parametric approach for fitting Gaussian Mixture Models (GMM) on trajectory data. Physical-consistency of the GMM is ensured by imposing a prior on the component assignments biased by a novel similarity metric that leverages locality and directionality. The resulting GMM is then used to learn globally asymptotically stable Dynamical Systems (DS) via a Linear Parameter Varying (LPV) re-formulation. The proposed DS learning scheme accurately encodes challenging nonlinear motions automatically. Finally, a data-efficient incremental learning approach is introduced that encodes a DS from batches of trajectories, while preserving global stability. Our contributions are validated on 2D datasets and a variety of tasks that involve single-target complex motions with a KUKA LWR 4+ robot arm

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

DAMM: Directionality-Aware Mixture Model Parallel Sampling for Efficient Dynamical System Learning

The Linear Parameter Varying Dynamical System (LPV-DS) is a promising framework for learning stable time-invariant motion policies in robot control. By employing statistical modeling and semi-definite optimization, LPV-DS encodes complex motions via non-linear DS, ensuring the robustness and stability of the system. However, the current LPV-DS scheme faces challenges in accurately interpreting trajectory data while maintaining model efficiency and computational efficiency. To address these limitations, we propose the Directionality-aware Mixture Model (DAMM), a new statistical model that leverages Riemannian metric on $d$-dimensional sphere $\mathbb{S}^d$, and efficiently incorporates non-Euclidean directional information with position. Additionally, we introduce a hybrid Markov chain Monte Carlo method that combines the Gibbs Sampling and the Split/Merge Proposal, facilitating parallel computation and enabling faster inference for near real-time learning performance. Through extensive empirical validation, we demonstrate that the improved LPV-DS framework with DAMM is capable of producing physically-meaningful representations of the trajectory data and improved performance of the generated DS while showcasing significantly enhanced learning speed compared to its previous iterations

Quantum Theory: a Pragmatist Approach

While its applications have made quantum theory arguably the most successful theory in physics, its interpretation continues to be the subject of lively debate within the community of physicists and philosophers concerned with conceptual foundations. This situation poses a problem for a pragmatist for whom meaning derives from use. While disputes about how to use quantum theory have arisen from time to time, they have typically been quickly resolved, and consensus reached, within the relevant scientific sub-community. Yet rival accounts of the meaning of quantum theory continue to proliferate . In this article I offer a diagnosis of this situation and outline a pragmatist solution to the problem it poses, leaving further details for subsequent articles