Data-driven Identification of Parametric Governing Equations of Dynamical Systems Using the Signed Cumulative Distribution Transform.

This paper presents a novel data-driven approach to identify partial differential equation (PDE) parameters of a dynamical system. Specifically, we adopt a mathematical "transport" model for the solution of the dynamical system at specific spatial locations that allows us to accurately estimate the model parameters, including those associated with structural damage. This is accomplished by means of a newly-developed mathematical transform, the signed cumulative distribution transform (SCDT), which is shown to convert the general nonlinear parameter estimation problem into a simple linear regression. This approach has the additional practical advantage of requiring no a priori knowledge of the source of the excitation (or, alternatively, the initial conditions). By using training data, we devise a coarse regression procedure to recover different PDE parameters from the PDE solution measured at a single location. Numerical experiments show that the proposed regression procedure is capable of detecting and estimating PDE parameters with superior accuracy compared to a number of recently developed machine learning methods. Furthermore, a damage identification experiment conducted on a publicly available dataset provides strong evidence of the proposed method's effectiveness in structural health monitoring (SHM) applications. The Python implementation of the proposed system identification technique is integrated as a part of the software package PyTransKit [1].

An evidence-based approach to assessing the effectiveness of training regimen on athlete performance: Youth soccer as a case study.

Athletic performance data are modeled in an effort to better understand the relationship between both hours spent training and a measurement of "commitment" to that training, and improvements in performance. Both increased training time and greater commitment were predicted to produce larger increases in performance improvement, and commitment was predicted to be the more important determinant of improvement. The performance of 108 soccer players (ages 9-18) was quantified over a 10-week training program. Hours spent training ranged from 16 to 90 during the course of the study, while commitment scores ranged from 0.55 to 2.00, based on a scale from 0.00 to 2.40. A model selection approach was used to discriminate among models specifying relationships between training hours and improvement, and commitment and improvement. Despite considerable variability in the data, results provided strong evidence for an increase in performance improvement with both training hours and commitment score. The best models for hours and commitment were directly compared by computing an evidence ratio of 5799, indicating much stronger evidence favoring the model based on commitment. Results of analyses such as these go beyond anecdotal experience in an effort to establish a formal evidentiary basis for athletic training programs.

Transport-based pattern recognition versus deep neural networks in underwater OAM communications.

Comparisons between machine learning and optimal transport-based approaches in classifying images are made in underwater orbital angular momentum (OAM) communications. A model is derived that justifies optimal transport for use in attenuated water environments. OAM pattern demultiplexing is performed using optimal transport and deep neural networks and compared to each other. Additionally, some of the complications introduced by signal attenuation are highlighted. The Radon cumulative distribution transform (R-CDT) is applied to OAM patterns to transform them to a linear subspace. The original OAM images and the R-CDT transformed patterns are used in several classification algorithms, and results are compared. The selected classification algorithms are the nearest subspace algorithm, a shallow convolutional neural network (CNN), and a deep neural network. It is shown that the R-CDT transformed images are more accurate than the original OAM images in pattern classification. Also, the nearest subspace algorithm performs better than the selected CNNs in OAM pattern classification in underwater environments.

Radon Cumulative Distribution Transform Subspace Modeling for Image Classification.

We present a new supervised image classification method applicable to a broad class of image deformation models. The method makes use of the previously described Radon Cumulative Distribution Transform (R-CDT) for image data, whose mathematical properties are exploited to express the image data in a form that is more suitable for machine learning. While certain operations such as translation, scaling, and higher-order transformations are challenging to model in native image space, we show the R-CDT can capture some of these variations and thus render the associated image classification problems easier to solve. The method - utilizing a nearest-subspace algorithm in the R-CDT space - is simple to implement, non-iterative, has no hyper-parameters to tune, is computationally efficient, label efficient, and provides competitive accuracies to state-of-the-art neural networks for many types of classification problems. In addition to the test accuracy performances, we show improvements (with respect to neural network-based methods) in terms of computational efficiency (it can be implemented without the use of GPUs), number of training samples needed for training, as well as out-of-distribution generalization. The Python code for reproducing our results is available at [1].

Parametric Signal Estimation Using the Cumulative Distribution Transform.

We present a new method for estimating signal model parameters using the Cumulative Distribution Transform (CDT). Our approach minimizes the Wasserstein distance between measured and model signals. We derive some useful properties of the CDT and show that the resulting estimation problem, while nonlinear in the original signal domain, becomes a linear least squares problem in the transform domain. Furthermore, we discuss the properties of the estimator in the presence of noise and present a novel approach for mitigating the impact of the noise on the estimates. The proposed estimation approach is evaluated by applying it to a source localization problem and comparing its performance against traditional approaches.

Linear transfer function estimation using the photodiode impulse response.

In this Letter, we implement a model-based auto-regressive estimator of the frequency response for a high-speed photodiode (PD). A transfer function is developed, and the associated coefficients representing the PD model and frequency response are solved for using a two-stage least-squares approach. The model is implemented for a modified uni-traveling carrier PD and experimentally compared to measured impulse response data.

De-multiplexing vortex modes in optical communications using transport-based pattern recognition.

Free space optical communications utilizing orbital angular momentum beams have recently emerged as a new technique for communications with potential for increased channel capacity. Turbulence due to changes in the index of refraction emanating from temperature, humidity, and air flow patterns, however, add nonlinear effects to the received patterns, thus making the demultiplexing task more difficult. Deep learning techniques have been previously been applied to solve the demultiplexing problem as an image classification task. Here we make use of a newly developed theory suggesting a link between image turbulence and photon transport through the continuity equation to describe a method that utilizes a "shallow" learning method instead. The decoding technique is tested and compared against previous approaches using deep convolutional neural networks. Results show that the new method can obtain similar classification accuracies (bit error ratio) at a small fraction (1/90) of the computational cost, thus enabling higher bit rates.

"Store-operated" cAMP signaling contributes to Ca2+-activated Cl- secretion in T84 colonic cells.

Apical cAMP-dependent CFTR Cl(-) channels are essential for efficient vectorial movement of ions and fluid into the lumen of the colon. It is well known that Ca(2+)-mobilizing agonists also stimulate colonic anion secretion. However, CFTR is apparently not activated directly by Ca(2+), and the existence of apical Ca(2+)-dependent Cl(-) channels in the native colonic epithelium is controversial, leaving the identity of the Ca(2+)-activated component unresolved. We recently showed that decreasing free Ca(2+) concentration ([Ca(2+)]) within the endoplasmic reticulum (ER) lumen elicits a rise in intracellular cAMP. This process, which we termed "store-operated cAMP signaling" (SOcAMPS), requires the luminal ER Ca(2+) sensor STIM1 and does not depend on changes in cytosolic Ca(2+). Here we assessed the degree to which SOcAMPS participates in Ca(2+)-activated Cl(-) transport as measured by transepithelial short-circuit current (Isc) in polarized T84 monolayers in parallel with imaging of cAMP and PKA activity using fluorescence resonance energy transfer (FRET)-based reporters in single cells. In Ca(2+)-free conditions, the Ca(2+)-releasing agonist carbachol and Ca(2+) ionophore increased Isc, cAMP, and PKA activity. These responses persisted in cells loaded with the Ca(2+) chelator BAPTA-AM. The effect on Isc was enhanced in the presence of the phosphodiesterase (PDE) inhibitor 3-isobutyl-1-methylxanthine (IBMX), inhibited by the CFTR inhibitor CFTRinh-172 and the PKA inhibitor H-89, and unaffected by Ba(2+) or flufenamic acid. We propose that a discrete component of the "Ca(2+)-dependent" secretory activity in the colon derives from cAMP generated through SOcAMPS. This alternative mode of cAMP production could contribute to the actions of diverse xenobiotic agents that disrupt ER Ca(2+) homeostasis, leading to diarrhea.

Estimating detection and identification probabilities in maritime target acquisition.

This work describes several approaches to the estimation of target detection and identification probabilities as a function of target range. A Bayesian approach to estimation is adopted, whereby the posterior probability distributions associated with these probabilities are analytically derived. The parameter posteriors are then used to develop credible intervals quantifying the degree of uncertainty in the parameter estimates. In our first approach we simply show how these credible intervals evolve as a function of range. A second approach, also following the Bayesian philosophy, attempts to directly estimate the parameterized performance curves. This second approach makes efficient use of the available data and yields a distribution of probability versus range curves. Finally, we demonstrate both approaches using experimental data collected from wide field-of-view imagers focused on maritime targets.

Bragg grating-based fibre optic sensors in structural health monitoring.

This work first considers a review of the dominant current methods for fibre Bragg grating wavelength interrogation. These methods include WDM interferometry, tunable filter (both Fabry-Perot and acousto-optic) demultiplexing, CCD/prism technique and a newer hybrid method utilizing Fabry-Perot and interferometric techniques. Two applications using these techniques are described: hull loads monitoring on an all-composite fast patrol boat and bolt pre-load loss monitoring in a composite beam in conjunction with a state-space modelling data analysis technique.