arXiv subjects

Robert S. Martin

Publications and source records attributed to Robert S. Martin.

3 recordsLinked to original sources

arXiv2025

Contraction and Synchronization in Reservoir Systems

This paper explores the conditions under which global contraction manifests in the leaky continuous time reservoirs, thus guaranteeing generalized synchronization. Results on continuous time reservoirs make use of the logarithmic norm of the connectivity matrix. Further analysis yields some simple guidelines on how to better construct the connectivity matrix in these systems. Additionally, we outline how the universal approximation property of discrete time reservoirs is readily satisfied by virtue of the activation function being contracting, and how continuous time reservoirs may inherit a limited form of universal approximation due to their overlap with neural ordinary differential equations. The ability of the reservoir computing framework to universally approximate topological conjugates, along with their fast training, make them a compelling data-driven, black-box surrogate of dynamical systems, and a potential candidate for a component of digital twins.

nlin.CD↗

arXiv2023

Another Look at the Linear Probability Model and Nonlinear Index Models

We reassess the use of linear models to approximate response probabilities of binary outcomes, focusing on average partial effects (APE). We confirm that linear projection parameters coincide with APEs in certain scenarios. Through simulations, we identify other cases where OLS does or does not approximate APEs and find that having large fraction of fitted values in [0, 1] is neither necessary nor sufficient. We also show nonlinear least squares estimation of the ramp model is consistent and asymptotically normal and is equivalent to using OLS on an iteratively trimmed sample to reduce bias. Our findings offer practical guidance for empirical research.

econ.EM↗

arXiv2022

An Unstructured Mesh Approach to Nonlinear Noise Reduction for Coupled Systems

To address noise inherent in electronic data acquisition systems and real world sources, Araki et al. [Physica D: Nonlinear Phenomena, 417 (2021) 132819] demonstrated a grid based nonlinear technique to remove noise from a chaotic signal, leveraging a clean high-fidelity signal from the same dynamical system and ensemble averaging in multidimensional phase space. This method achieved denoising of a time-series data with 100% added noise but suffered in regions of low data density. To improve this grid-based method, here an unstructured mesh based on triangulations and Voronoi diagrams is used to accomplish the same task. The unstructured mesh more uniformly distributes data samples over mesh cells to improve the accuracy of the reconstructed signal. By empirically balancing bias and variance errors in selecting the number of unstructured cells as a function of the number of available samples, the method achieves asymptotic statistical convergence with known test data and reduces synthetic noise on experimental signals from Hall Effect Thrusters (HETs) with greater success than the original grid-based strategy.

physics.comp-ph↗