Randomized Dynamic Mode Decomposition

This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of deterministic algorithms, easing the computational challenges arising in the area of `big data'. The idea is to derive a small matrix from the high-dimensional data, which is then used to efficiently compute the dynamic modes and eigenvalues. The algorithm is presented in a modular probabilistic framework, and the approximation quality can be controlled via oversampling and power iterations. The effectiveness of the resulting randomized DMD algorithm is demonstrated on several benchmark examples of increasing complexity, providing an accurate and efficient approach to extract spatiotemporal coherent structures from big data in a framework that scales with the intrinsic rank of the data, rather than the ambient measurement dimension. For this work we assume that the dynamics of the problem under consideration is evolving on a low-dimensional subspace that is well characterized by a fast decaying singular value spectrum

Unsupervised decoding of long-term, naturalistic human neural recordings with automated video and audio annotations

Fully automated decoding of human activities and intentions from direct neural recordings is a tantalizing challenge in brain-computer interfacing. Most ongoing efforts have focused on training decoders on specific, stereotyped tasks in laboratory settings. Implementing brain-computer interfaces (BCIs) in natural settings requires adaptive strategies and scalable algorithms that require minimal supervision. Here we propose an unsupervised approach to decoding neural states from human brain recordings acquired in a naturalistic context. We demonstrate our approach on continuous long-term electrocorticographic (ECoG) data recorded over many days from the brain surface of subjects in a hospital room, with simultaneous audio and video recordings. We first discovered clusters in high-dimensional ECoG recordings and then annotated coherent clusters using speech and movement labels extracted automatically from audio and video recordings. To our knowledge, this represents the first time techniques from computer vision and speech processing have been used for natural ECoG decoding. Our results show that our unsupervised approach can discover distinct behaviors from ECoG data, including moving, speaking and resting. We verify the accuracy of our approach by comparing to manual annotations. Projecting the discovered cluster centers back onto the brain, this technique opens the door to automated functional brain mapping in natural settings

FlexWing-ROM: A matlab framework for data-driven reduced-order modeling of flexible wings

Flexible wings pose a considerable modeling challenge, as they involve highly coupled and nonlinear interactions between the aerodynamic and structural dynamics. In this work, we provide an open source code framework, unifying recent data-driven modeling methods that extend the dynamic mode decomposition with control (DMDc) to model the nonlinear aeroelasticity of flexible wings. Our framework consists of (1) a fully parametrized flexible wing model; (2) a fluid-structure interaction (FSI) solver that couples a detailed finite element model of the wing structure with a 3D unsteady aerodynamic panel method; and (3) three different data-driven reduced-order aeroelastic modeling methods. We demonstrate our framework on two flexible wings and provide tutorials to compare the different data-driven methods. The code is widely applicable and useful for generating accurate and efficient data-driven reduced-order models, and it provides a benchmark for future developments of aeroelastic reduced-order modeling methods

Spatio-temporal feature extraction in sensory electroneurographic signals

The recording and analysis of peripheral neural signal can provide insight for various prosthetic and bioelectronics medicine applications. However, there are few studies that investigate how informative features can be extracted from population activity electroneurographic (ENG) signals. In this study, five feature extraction frameworks were implemented on sensory ENG datasets and their classification performance was compared. The datasets were collected in acute rat experiments where multi-channel nerve cuffs recorded from the sciatic nerve in response to proprioceptive stimulation of the hindlimb. A novel feature extraction framework, which incorporates spatio-temporal focus and dynamic time warping, achieved classification accuracies above 90% while keeping a low computational cost. This framework outperformed the remaining frameworks tested in this study and has improved the discrimination accuracy of the sensory signals. Thus, this study has extended the tools available to extract features from sensory population activity ENG signals. This article is part of the theme issue ‘Advanced neurotechnologies: translating innovation for health and well-being’

Data-driven identification of parametric partial differential equations

In this work we present a data-driven method for the discovery of parametric partial differential equations (PDEs), thus allowing one to disambiguate between the underlying evolution equations and their parametric dependencies. Group sparsity is used to ensure parsimonious representations of observed dynamics in the form of a parametric PDE, while also allowing the coefficients to have arbitrary time series, or spatial dependence. This work builds on previous methods for the identification of constant coefficient PDEs, expanding the field to include a new class of equations which until now have eluded machine learning based identification methods. We show that group sequentially thresholded ridge regression outperforms group LASSO in identifying the fewest terms in the PDE along with their parametric dependency. The method is demonstrated on four canonical models with and without the introduction of noise

Optimisation of Accelerated Solvent Extraction of Antioxidant Compounds from Rosemary (Rosmarinus officinalis L.), Marjoram (Origanum majorana L.) and Oregano (Origanum vulgare L.) Using Response Surface Methodology

The present study optimised the accelerated solvent extraction (ASE) conditions (Dionex ASE® 200, USA) to maximise the antioxidant capacity of the extracts from three spices of Lamiaceae family; rosemary, oregano and marjoram. Optimised conditions with regard to extraction temperature (66–129 °C) and solvent concentration (32–88% methanol) were identified using response surface methodology (RSM). For all three spices results showed that 129 °C was the optimum temperature in order to obtain extracts with high antioxidant activity. Optimal methanol concentrations with respect to the antioxidant activity of rosemary and marjoram extracts were 56% and 57% respectively. Oregano showed a different response to the effect of methanol concentration and was optimally extracted at 33%. The antioxidant activity yields of the optimal ASE extracts were significantly (p \u3c 0.05) higher than solid/liquid extracts. The predicted models were highly significant (p \u3c 0.05) for both total phenol (TP) and ferric reducing antioxidant property (FRAP) values in all the spices with high regression coefficients (R2) ranging from 0.952 to 0.999