Human motion data expansion from arbitrary sparse sensors with shallow recurrent decoders.

Advances in deep learning and sparse sensing have emerged as powerful tools for monitoring human motion in natural environments. We develop a deep learning architecture, constructed from a shallow recurrent decoder network, that expands human motion data by mapping a limited (sparse) number of sensors to a comprehensive (dense) configuration, thereby inferring the motion of unmonitored body segments. Even with a single sensor, we reconstruct the comprehensive set of time series measurements, which are important for tracking and informing movement-related health and performance outcomes. Notably, this mapping leverages sensor time histories to inform the transformation from sparse to dense sensor configurations. We apply this mapping architecture to a variety of datasets, including controlled movement tasks, gait pattern exploration, and free-moving environments. Additionally, this mapping can be subject-specific (based on an individual's unique data for deployment at home and in the community) or group-based (where data from a large group are used to learn a general movement model and predict outcomes for unknown subjects). By expanding our datasets to unmeasured or unavailable quantities, this work can impact clinical trials, robotic/device control, and human performance by improving the accuracy and availability of digital biomarker estimates.

Promising directions of machine learning for partial differential equations.

Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multiscale physics in a compact and symbolic representation. Here, we examine several promising avenues of PDE research that are being advanced by machine learning, including (1) discovering new governing PDEs and coarse-grained approximations for complex natural and engineered systems, (2) learning effective coordinate systems and reduced-order models to make PDEs more amenable to analysis, and (3) representing solution operators and improving traditional numerical algorithms. In each of these fields, we summarize key advances, ongoing challenges, and opportunities for further development.

Mobile Sensor Path Planning for Kalman Filter Spatiotemporal Estimation.

The estimation of spatiotemporal data from limited sensor measurements is a required task across many scientific disciplines. In this paper, we consider the use of mobile sensors for estimating spatiotemporal data via Kalman filtering. The sensor selection problem, which aims to optimize the placement of sensors, leverages innovations in greedy algorithms and low-rank subspace projection to provide model-free, data-driven estimates. Alternatively, Kalman filter estimation balances model-based information and sparsely observed measurements to collectively make better estimation with limited sensors. It is especially important with mobile sensors to utilize historical measurements. We show that mobile sensing along dynamic trajectories can achieve the equivalent performance of a larger number of stationary sensors, with performance gains related to three distinct timescales: (i) the timescale of the spatiotemporal dynamics, (ii) the velocity of the sensors, and (iii) the rate of sampling. Taken together, these timescales strongly influence how well-conditioned the estimation task is. We draw connections between the Kalman filter performance and the observability of the state space model and propose a greedy path planning algorithm based on minimizing the condition number of the observability matrix. This approach has better scalability and computational efficiency compared to previous works. Through a series of examples of increasing complexity, we show that mobile sensing along our paths improves Kalman filter performance in terms of better limiting estimation and faster convergence. Moreover, it is particularly effective for spatiotemporal data that contain spatially localized structures, whose features are captured along dynamic trajectories.

Non-Stationary Dynamic Mode Decomposition.

Many physical processes display complex high-dimensional time-varying behavior, from global weather patterns to brain activity. An outstanding challenge is to express high dimensional data in terms of a dynamical model that reveals their spatiotemporal structure. Dynamic Mode Decomposition is a means to achieve this goal, allowing the identification of key spatiotemporal modes through the diagonalization of a finite dimensional approximation of the Koopman operator. However, these methods apply best to time-translationally invariant or stationary data, while in many typical cases, dynamics vary across time and conditions. To capture this temporal evolution, we developed a method, Non-Stationary Dynamic Mode Decomposition, that generalizes Dynamic Mode Decomposition by fitting global modulations of drifting spatiotemporal modes. This method accurately predicts the temporal evolution of modes in simulations and recovers previously known results from simpler methods. To demonstrate its properties, the method is applied to multi-channel recordings from an awake behaving non-human primate performing a cognitive task.

Podocyte Senescence and Aging.

As the population in many industrial countries is aging, the risk, incidence, and prevalence of CKD increases. In the kidney, advancing age results in a progressive decrease in nephron number and an increase in glomerulosclerosis. In this review, we focus on the effect of aging on glomerular podocytes, the post-mitotic epithelial cells critical for the normal integrity and function of the glomerular filtration barrier. The podocytes undergo senescence and transition to a senescence-associated secretory phenotype typified by the production and secretion of inflammatory cytokines that can influence neighboring glomerular cells by paracrine signaling. In addition to senescence, the aging podocyte phenotype is characterized by ultrastructural and functional changes; hypertrophy; cellular, oxidative, and endoplasmic reticulum stress; reduced autophagy; and increased expression of aging genes. This results in a reduced podocyte health span and a shortened life span. Importantly, these changes in the pathways/processes characteristic of healthy podocyte aging are also often similar to pathways in the disease-induced injured podocyte. Finally, the better understanding of podocyte aging and senescence opens therapeutic options to slow the rate of podocyte aging and promote kidney health.

Pilot-wave dynamics: Using dynamic mode decomposition to characterize bifurcations, routes to chaos, and emergent statistics.

We develop a data-driven characterization of the pilot-wave hydrodynamic system in which a bouncing droplet self-propels along the surface of a vibrating bath. We consider drop motion in a confined one-dimensional geometry and apply the dynamic mode decomposition (DMD) in order to characterize the evolution of the wave field as the bath's vibrational acceleration is increased progressively. Dynamic mode decomposition provides a regression framework for adaptively learning a best-fit linear dynamics model over snapshots of spatiotemporal data. Thus, DMD reduces the complex nonlinear interactions between pilot waves and droplet to a low-dimensional linear superposition of DMD modes characterizing the wave field. In particular, it provides a low-dimensional characterization of the bifurcation structure of the pilot-wave physics, wherein the excitation and recruitment of additional modes in the linear superposition models the bifurcation sequence. This DMD characterization yields a fresh perspective on the bouncing-droplet problem that forges valuable new links with the mathematical machinery of quantum mechanics. Specifically, the analysis shows that as the vibrational acceleration is increased, the pilot-wave field undergoes a series of Hopf bifurcations that ultimately lead to a chaotic wave field. The established relation between the mean pilot-wave field and the droplet statistics allows us to characterize the evolution of the emergent statistics with increased vibrational forcing from the evolution of the pilot-wave field. We thus develop a numerical framework with the same basic structure as quantum mechanics, specifically a wave theory that predicts particle statistics.

Constructing and interpreting a large-scale variant effect map for an ultrarare disease gene: Comprehensive prediction of the functional impact of PSAT1 genotypes.

Reduced activity of the enzymes encoded by PHGDH, PSAT1, and PSPH causes a set of ultrarare, autosomal recessive diseases known as serine biosynthesis defects. These diseases present in a broad phenotypic spectrum: at the severe end is Neu-Laxova syndrome, in the intermediate range are infantile serine biosynthesis defects with severe neurological manifestations and growth deficiency, and at the mild end is childhood disease with intellectual disability. However, L-serine supplementation, especially if started early, can ameliorate and in some cases even prevent symptoms. Therefore, knowledge of pathogenic variants can improve clinical outcomes. Here, we use a yeast-based assay to individually measure the functional impact of 1,914 SNV-accessible amino acid substitutions in PSAT. Results of our assay agree well with clinical interpretations and protein structure-function relationships, supporting the inclusion of our data as functional evidence as part of the ACMG variant interpretation guidelines. We use existing ClinVar variants, disease alleles reported in the literature and variants present as homozygotes in the primAD database to define assay ranges that could aid clinical variant interpretation for up to 98% of the tested variants. In addition to measuring the functional impact of individual variants in yeast haploid cells, we also assay pairwise combinations of PSAT1 alleles that recapitulate human genotypes, including compound heterozygotes, in yeast diploids. Results from our diploid assay successfully distinguish the genotypes of affected individuals from those of healthy carriers and agree well with disease severity. Finally, we present a linear model that uses individual allele measurements to predict the biallelic function of ~1.8 million allele combinations corresponding to potential human genotypes. Taken together, our work provides an example of how large-scale functional assays in model systems can be powerfully applied to the study of ultrarare diseases.

Data-Driven Placement of PM2.5 Air Quality Sensors in the United States: An Approach to Target Urban Environmental Injustice.

In the United States, citizens and policymakers heavily rely upon Environmental Protection Agency mandated regulatory networks to monitor air pollution; increasingly they also depend on low-cost sensor networks to supplement spatial gaps in regulatory monitor networks coverage. Although these regulatory and low-cost networks in tandem provide enhanced spatiotemporal coverage in urban areas, low-cost sensors are located often in higher income, predominantly White areas. Such disparity in coverage may exacerbate existing inequalities and impact the ability of different communities to respond to the threat of air pollution. Here we present a study using cost-constrained multiresolution dynamic mode decomposition (mrDMDcc) to identify the optimal and equitable placement of fine particulate matter (PM2.5) sensors in four U.S. cities with histories of racial or income segregation: St. Louis, Houston, Boston, and Buffalo. This novel approach incorporates the variation of PM2.5 on timescales ranging from 1 day to over a decade to capture air pollution variability. We also introduce a cost function into the sensor placement optimization that represents the balance between our objectives of capturing PM2.5 extremes and increasing pollution monitoring in low-income and nonwhite areas. We find that the mrDMDcc algorithm places a greater number of sensors in historically low-income and nonwhite neighborhoods with known environmental pollution problems compared to networks using PM2.5 information alone. Our work provides a roadmap for the creation of equitable sensor networks in U.S. cities and offers a guide for democratizing air pollution data through increasing spatial coverage of low-cost sensors in less privileged communities.

The experimental multi-arm pendulum on a cart: A benchmark system for chaos, learning, and control.

The single, double, and triple pendulum has served as an illustrative experimental benchmark system for scientists to study dynamical behavior for more than four centuries. The pendulum system exhibits a wide range of interesting behaviors, from simple harmonic motion in the single pendulum to chaotic dynamics in multi-arm pendulums. Under forcing, even the single pendulum may exhibit chaos, providing a simple example of a damped-driven system. All multi-armed pendulums are characterized by the existence of index-one saddle points, which mediate the transport of trajectories in the system, providing a simple mechanical analog of various complex transport phenomena, from biolocomotion to transport within the solar system. Further, pendulum systems have long been used to design and test both linear and nonlinear control strategies, with the addition of more arms making the problem more challenging. In this work, we provide extensive designs for the construction and operation of a high-performance, multi-link pendulum on a cart system. Although many experimental setups have been built to study the behavior of pendulum systems, such an extensive documentation on the design, construction, and operation is missing from the literature. The resulting experimental system is highly flexible, enabling a wide range of benchmark problems in dynamical systems modeling, system identification and learning, and control. To promote reproducible research, we have made our entire system open-source, including 3D CAD drawings, basic tutorial code, and data. Moreover, we discuss the possibility of extending our system capability to be operated remotely, enabling researchers all around the world to use it, thus increasing access.

Non-Stationary Dynamic Mode Decomposition.

Many physical processes display complex high-dimensional time-varying behavior, from global weather patterns to brain activity. An outstanding challenge is to express high dimensional data in terms of a dynamical model that reveals their spatiotemporal structure. Dynamic Mode Decomposition is a means to achieve this goal, allowing the identification of key spatiotemporal modes through the diagonalization of a finite dimensional approximation of the Koopman operator. However, DMD methods apply best to time-translationally invariant or stationary data, while in many typical cases, dynamics vary across time and conditions. To capture this temporal evolution, we developed a method, Non-Stationary Dynamic Mode Decomposition (NS-DMD), that generalizes DMD by fitting global modulations of drifting spatiotemporal modes. This method accurately predicts the temporal evolution of modes in simulations and recovers previously known results from simpler methods. To demonstrate its properties, the method is applied to multi-channel recordings from an awake behaving non-human primate performing a cognitive task.

A machine learning approach to quantify individual gait responses to ankle exoskeletons.

Predicting an individual's response to an exoskeleton and understanding what data are needed to characterize responses remains challenging. Specifically, we lack a theoretical framework capable of quantifying heterogeneous responses to exoskeleton interventions. We leverage a neural network-based discrepancy modeling framework to quantify complex changes in gait in response to passive ankle exoskeletons in nondisabled adults. Discrepancy modeling aims to resolve dynamical inconsistencies between model predictions and real-world measurements. Neural networks identified models of (i) Nominal gait, (ii) Exoskeleton (Exo) gait, and (iii) the Discrepancy (i.e., response) between them. If an Augmented (Nominal+Discrepancy) model captured exoskeleton responses, its predictions should account for comparable amounts of variance in Exo gait data as the Exo model. Discrepancy modeling successfully quantified individuals' exoskeleton responses without requiring knowledge about physiological structure or motor control: a model of Nominal gait augmented with a Discrepancy model of response accounted for significantly more variance in Exo gait (median R2 for kinematics (0.928-0.963) and electromyography (0.665-0.788), (p<0.042)) than the Nominal model (median R2 for kinematics (0.863-0.939) and electromyography (0.516-0.664)). However, additional measurement modalities and/or improved resolution are needed to characterize Exo gait, as the discrepancy may not comprehensively capture response due to unexplained variance in Exo gait (median R2 for kinematics (0.954-0.977) and electromyography (0.724-0.815)). These techniques can be used to accelerate the discovery of individual-specific mechanisms driving exoskeleton responses, thus enabling personalized rehabilitation.

Prediction of Shock-Refractory Ventricular Fibrillation During Resuscitation of Out-of-Hospital Cardiac Arrest.

BACKGROUND: Out-of-hospital cardiac arrest due to shock-refractory ventricular fibrillation (VF) is associated with relatively poor survival. The ability to predict refractory VF (requiring ≥3 shocks) in advance of repeated shock failure could enable preemptive targeted interventions aimed at improving outcome, such as earlier administration of antiarrhythmics, reconsideration of epinephrine use or dosage, changes in shock delivery strategy, or expedited invasive treatments. METHODS: We conducted a cohort study of VF out-of-hospital cardiac arrest to develop an ECG-based algorithm to predict patients with refractory VF. Patients with available defibrillator recordings were randomized 80%/20% into training/test groups. A random forest classifier applied to 3-s ECG segments immediately before and 1 minute after the initial shock during cardiopulmonary resuscitation was used to predict the need for ≥3 shocks based on singular value decompositions of ECG wavelet transforms. Performance was quantified by area under the receiver operating characteristic curve. RESULTS: Of 1376 patients with VF out-of-hospital cardiac arrest, 311 (23%) were female, 864 (63%) experienced refractory VF, and 591 (43%) achieved functional neurological survival. Total shock count was associated with decreasing likelihood of functional neurological survival, with a relative risk of 0.95 (95% CI, 0.93-0.97) for each successive shock (P<0.001). In the 275 test patients, the area under the receiver operating characteristic curve for predicting refractory VF was 0.85 (95% CI, 0.79-0.89), with specificity of 91%, sensitivity of 63%, and a positive likelihood ratio of 6.7. CONCLUSIONS: A machine learning algorithm using ECGs surrounding the initial shock predicts patients likely to experience refractory VF, and could enable rescuers to preemptively target interventions to potentially improve resuscitation outcome.

The functional impact of 1,570 individual amino acid substitutions in human OTC.

Deleterious mutations in the X-linked gene encoding ornithine transcarbamylase (OTC) cause the most common urea cycle disorder, OTC deficiency. This rare but highly actionable disease can present with severe neonatal onset in males or with later onset in either sex. Individuals with neonatal onset appear normal at birth but rapidly develop hyperammonemia, which can progress to cerebral edema, coma, and death, outcomes ameliorated by rapid diagnosis and treatment. Here, we develop a high-throughput functional assay for human OTC and individually measure the impact of 1,570 variants, 84% of all SNV-accessible missense mutations. Comparison to existing clinical significance calls, demonstrated that our assay distinguishes known benign from pathogenic variants and variants with neonatal onset from late-onset disease presentation. This functional stratification allowed us to identify score ranges corresponding to clinically relevant levels of impairment of OTC activity. Examining the results of our assay in the context of protein structure further allowed us to identify a 13 amino acid domain, the SMG loop, whose function appears to be required in human cells but not in yeast. Finally, inclusion of our data as PS3 evidence under the current ACMG guidelines, in a pilot reclassification of 34 variants with complete loss of activity, would change the classification of 22 from variants of unknown significance to clinically actionable likely pathogenic variants. These results illustrate how large-scale functional assays are especially powerful when applied to rare genetic diseases.

Instantaneous amplitude: Association of ventricular fibrillation waveform measures at time of shock with outcome in out-of-hospital cardiac arrest.

BACKGROUND: Prompt defibrillation is key to successful resuscitation from ventricular fibrillation out-of-hospital cardiac arrest (VF-OHCA). Preliminary evidence suggests that the timing of shock relative to the amplitude of the VF ECG waveform may affect the likelihood of resuscitation. We investigated whether the VF waveform amplitude at the time of shock (instantaneous amplitude) predicts outcome independent of other validated waveform measures. METHODS: We conducted a retrospective study of VF-OHCA patients ≥18 old. We evaluated three VF waveform measures for each shock: instantaneous amplitude at the time of shock, and maximum amplitude and amplitude spectrum area (AMSA) over a 3-s window preceding the shock. Linear mixed-effects modeling was used to determine whether instantaneous amplitude was associated with shock-specific return of organized rhythm (ROR) or return of spontaneous circulation (ROSC) independent of maximum amplitude or AMSA. RESULTS: The 566 eligible patients received 1513 shocks, resulting in ROR of 62.0% (938/1513) and ROSC of 22.3% (337/1513). In unadjusted regression, an interquartile increase in instantaneous amplitude was associated with ROR (Odds ratio [OR] [95% confidence interval] = 1.27 [1.11-1.45]) and ROSC (OR = 1.27 [1.14-1.42]). However, instantaneous amplitude was not associated with ROR (OR = 1.13 [0.97-1.30]) after accounting for maximum amplitude, nor with ROR (OR = 1.00 [0.87-1.15]) or ROSC (OR = 1.05 [0.93-1.18]) after accounting for AMSA. By contrast, AMSA and maximum amplitude remained independently associated with ROR and ROSC. CONCLUSIONS: We did not observe an independent association between instantaneous amplitude and shock-specific outcomes. Efforts to time shock to the maximal amplitude of the VF waveform are unlikely to affect resuscitation outcome.

A machine learning approach to quantify individual gait responses to ankle exoskeletons.

We currently lack a theoretical framework capable of characterizing heterogeneous responses to exoskeleton interventions. Predicting an individual's response to an exoskeleton and understanding what data are needed to characterize responses has been a persistent challenge. In this study, we leverage a neural network-based discrepancy modeling framework to quantify complex changes in gait in response to passive ankle exoskeletons in nondisabled adults. Discrepancy modeling aims to resolve dynamical inconsistencies between model predictions and real-world measurements. Neural networks identified models of (i) Nominal gait, (ii) Exoskeleton ( Exo ) gait, and (iii) the Discrepancy ( i.e. , response) between them. If an Augmented (Nominal+Discrepancy) model captured exoskeleton responses, its predictions should account for comparable amounts of variance in Exo gait data as the Exo model. Discrepancy modeling successfully quantified individuals' exoskeleton responses without requiring knowledge about physiological structure or motor control: a model of Nominal gait augmented with a Discrepancy model of response accounted for significantly more variance in Exo gait (median R 2 for kinematics (0.928 - 0.963) and electromyography (0.665 - 0.788), ( p < 0.042)) than the Nominal model (median R 2 for kinematics (0.863 - 0.939) and electromyography (0.516 - 0.664)). However, additional measurement modalities and/or improved resolution are needed to characterize Exo gait, as the discrepancy may not comprehensively capture response due to unexplained variance in Exo gait (median R 2 for kinematics (0.954 - 0.977) and electromyography (0.724 - 0.815)). These techniques can be used to accelerate the discovery of individual-specific mechanisms driving exoskeleton responses, thus enabling personalized rehabilitation.

Predicting the functional effect of compound heterozygous genotypes from large scale variant effect maps.

Background: Pathogenic variants in PHGDH, PSAT1 , and PSPH cause a set of rare, autosomal recessive diseases known as serine biosynthesis defects. Serine biosynthesis defects present in a broad phenotypic spectrum that includes, at the severe end, Neu-Laxova syndrome, a lethal multiple congenital anomaly disease, intermediately in the form of infantile serine biosynthesis defects with severe neurological manifestations and growth deficiency, and at the mild end, as childhood disease with intellectual disability. However, because L-serine supplementation, especially if started early, can ameliorate and in some cases even prevent symptoms, knowledge of pathogenic variants is highly actionable. Methods: Recently, our laboratory established a yeast-based assay for human PSAT1 function. We have now applied it at scale to assay the functional impact of 1,914 SNV-accessible amino acid substitutions. In addition to assaying the functional impact of individual variants in yeast haploid cells, we can assay pairwise combinations of PSAT1 alleles that recapitulate human genotypes, including compound heterozygotes, in yeast diploids. Results: Results of our assays of individual variants (in haploid yeast cells) agree well with clinical interpretations and protein structure-function relationships, supporting the use of our data as functional evidence under the ACMG interpretation guidelines. Results from our diploid assay successfully distinguish patient genotypes from those of healthy carriers and agree well with disease severity. Finally, we present a linear model that uses individual allele measurements (in haploid yeast cells) to accurately predict the biallelic function (in diploid yeast cells) of ~ 1.8 million allele combinations corresponding to potential human genotypes. Conclusions: Taken together, our work provides an example of how large-scale functional assays in model systems can be powerfully applied to the study of a rare disease.

Arousal as a universal embedding for spatiotemporal brain dynamics.

Neural activity in awake organisms shows widespread and spatiotemporally diverse correlations with behavioral and physiological measurements. We propose that this covariation reflects in part the dynamics of a unified, arousal-related process that regulates brain-wide physiology on the timescale of seconds. Taken together with theoretical foundations in dynamical systems, this interpretation leads us to a surprising prediction: that a single, scalar measurement of arousal (e.g., pupil diameter) should suffice to reconstruct the continuous evolution of multimodal, spatiotemporal measurements of large-scale brain physiology. To test this hypothesis, we perform multimodal, cortex-wide optical imaging and behavioral monitoring in awake mice. We demonstrate that spatiotemporal measurements of neuronal calcium, metabolism, and blood-oxygen can be accurately and parsimoniously modeled from a low-dimensional state-space reconstructed from the time history of pupil diameter. Extending this framework to behavioral and electrophysiological measurements from the Allen Brain Observatory, we demonstrate the ability to integrate diverse experimental data into a unified generative model via mappings from an intrinsic arousal manifold. Our results support the hypothesis that spontaneous, spatially structured fluctuations in brain-wide physiology-widely interpreted to reflect regionally-specific neural communication-are in large part reflections of an arousal-related process. This enriched view of arousal dynamics has broad implications for interpreting observations of brain, body, and behavior as measured across modalities, contexts, and scales.

Mode-locking in quadratically nonlinear waveguide arrays.

A two-dimensional theoretical model is constructed to describe optical mode-locking (ML) in quadratically nonlinear waveguide arrays (QWGAs). Steady-state solutions of the considered model are obtained by a modified pseudo-spectral renormalization algorithm, and the mode-locking dynamics of the model are investigated through direct simulation of the nonlinear evolution and a linear stability analysis of the solutions. It is shown that stable mode-locking of elliptic steady-state solutions in quadratically nonlinear waveguide arrays are possible for a wide range of parameters, suggesting that quadratically nonlinear materials are well suited for producing stable mode-locked states for a wide range of applications.

Pruning deep neural networks generates a sparse, bio-inspired nonlinear controller for insect flight.

Insect flight is a strongly nonlinear and actuated dynamical system. As such, strategies for understanding its control have typically relied on either model-based methods or linearizations thereof. Here we develop a framework that combines model predictive control on an established flight dynamics model and deep neural networks (DNN) to create an efficient method for solving the inverse problem of flight control. We turn to natural systems for inspiration since they inherently demonstrate network pruning with the consequence of yielding more efficient networks for a specific set of tasks. This bio-inspired approach allows us to leverage network pruning to optimally sparsify a DNN architecture in order to perform flight tasks with as few neural connections as possible, however, there are limits to sparsification. Specifically, as the number of connections falls below a critical threshold, flight performance drops considerably. We develop sparsification paradigms and explore their limits for control tasks. Monte Carlo simulations also quantify the statistical distribution of network weights during pruning given initial random weights of the DNNs. We demonstrate that on average, the network can be pruned to retain a small amount of original network weights and still perform comparably to its fully-connected counterpart. The relative number of remaining weights, however, is highly dependent on the initial architecture and size of the network. Overall, this work shows that sparsely connected DNNs are capable of predicting the forces required to follow flight trajectories. Additionally, sparsification has sharp performance limits.