Predicting preterm births from electrohysterogram recordings via deep learning.

About one in ten babies is born preterm, i.e., before completing 37 weeks of gestation, which can result in permanent neurologic deficit and is a leading cause of child mortality. Although imminent preterm labor can be detected, predicting preterm births more than one week in advance remains elusive. Here, we develop a deep learning method to predict preterm births directly from electrohysterogram (EHG) measurements of pregnant mothers recorded at around 31 weeks of gestation. We developed a prediction model, which includes a recurrent neural network, to predict preterm births using short-time Fourier transforms of EHG recordings and clinical information from two public datasets. We predicted preterm births with an area under the receiver-operating characteristic curve (AUC) of 0.78 (95% confidence interval: 0.76-0.80). Moreover, we found that the spectral patterns of the measurements were more predictive than the temporal patterns, suggesting that preterm births can be predicted from short EHG recordings in an automated process. We show that preterm births can be predicted for pregnant mothers around their 31st week of gestation, prompting beneficial treatments to reduce the incidence of preterm births and improve their outcomes.

Containing epidemics in a local cluster via antidote distribution and partial quarantine.

The study of spreading phenomena in networks, in particular the spread of disease, has attracted considerable interest in the network science research community. In this paper, we show that the outbreak of an epidemic can be effectively contained and suppressed in a small subnetwork by a combination of antidote distribution and partial quarantine. We improve over existing antidote distribution schemes based on personalized PageRank in two ways. First, we replace the constraint on the topology of this subnetwork described by Chung et al. [Internet Math. 6, 237 (2009)1542-795110.1080/15427951.2009.10129184] that a large fraction of the value of the personalized PageRank vector must be contained in the local cluster, with a partial quarantine scheme. Second, we derive a different lower bound on the amount of antidote. We show that, under our antidote distribution scheme, the probability of the infection spreading to the whole network is bounded, and the infection inside the subnetwork will disappear after a period that is proportional to the logarithm of the number of initially infected nodes. We demonstrate the effectiveness of our strategy with numerical simulations of epidemics on benchmark networks. We also test our strategy on two examples of epidemics in real-world networks. Our strategy is dependent only on the rate of infection, the rate of recovery, and the topology around the initially infected nodes, and is independent of the rest of the network.

Local clustering via approximate heat kernel PageRank with subgraph sampling.

Graph clustering, a fundamental technique in network science for understanding structures in complex systems, presents inherent problems. Though studied extensively in the literature, graph clustering in large systems remains particularly challenging because massive graphs incur a prohibitively large computational load. The heat kernel PageRank provides a quantitative ranking of nodes, and a local cluster can be efficiently found by performing a sweep over the heat kernel PageRank vector. But computing an exact heat kernel PageRank vector may be expensive, and approximate algorithms are often used instead. Most approximate algorithms compute the heat kernel PageRank vector on the whole graph, and thus are dependent on global structures. In this paper, we present an algorithm for approximating the heat kernel PageRank on a local subgraph. Moreover, we show that the number of computations required by the proposed algorithm is sublinear in terms of the expected size of the local cluster of interest, and that it provides a good approximation of the heat kernel PageRank, with approximation errors bounded by a probabilistic guarantee. Numerical experiments verify that the local clustering algorithm using our approximate heat kernel PageRank achieves state-of-the-art performance.

Public policy and economic dynamics of COVID-19 spread: A mathematical modeling study.

With the COVID-19 pandemic infecting millions of people, large-scale isolation policies have been enacted across the globe. To assess the impact of isolation measures on deaths, hospitalizations, and economic output, we create a mathematical model to simulate the spread of COVID-19, incorporating effects of restrictive measures and segmenting the population based on health risk and economic vulnerability. Policymakers make isolation policy decisions based on current levels of disease spread and economic damage. For 76 weeks in a population of 330 million, we simulate a baseline scenario leaving strong isolation restrictions in place, rapidly reducing isolation restrictions for non-seniors shortly after outbreak containment, and gradually relaxing isolation restrictions for non-seniors. We use 76 weeks as an approximation of the time at which a vaccine will be available. In the baseline scenario, there are 235,724 deaths and the economy shrinks by 34.0%. With a rapid relaxation, a second outbreak takes place, with 525,558 deaths, and the economy shrinks by 32.3%. With a gradual relaxation, there are 262,917 deaths, and the economy shrinks by 29.8%. We also show that hospitalizations, deaths, and economic output are quite sensitive to disease spread by asymptomatic people. Strict restrictions on seniors with very gradual lifting of isolation for non-seniors results in a limited number of deaths and lesser economic damage. Therefore, we recommend this strategy and measures that reduce non-isolated disease spread to control the pandemic while making isolation economically viable.

Quantifying accuracy and heterogeneity in single-molecule super-resolution microscopy.

The resolution and accuracy of single-molecule localization microscopes (SMLMs) are routinely benchmarked using simulated data, calibration rulers, or comparisons to secondary imaging modalities. However, these methods cannot quantify the nanoscale accuracy of an arbitrary SMLM dataset. Here, we show that by computing localization stability under a well-chosen perturbation with accurate knowledge of the imaging system, we can robustly measure the confidence of individual localizations without ground-truth knowledge of the sample. We demonstrate that our method, termed Wasserstein-induced flux (WIF), measures the accuracy of various reconstruction algorithms directly on experimental 2D and 3D data of microtubules and amyloid fibrils. We further show that WIF confidences can be used to evaluate the mismatch between computational models and imaging data, enhance the accuracy and resolution of reconstructed structures, and discover hidden molecular heterogeneities. As a computational methodology, WIF is broadly applicable to any SMLM dataset, imaging system, and localization algorithm.

A myofibre model for the study of uterine excitation-contraction dynamics.

As the uterus remodels in preparation for delivery, the excitability and contractility of the uterine smooth muscle layer, the myometrium, increase drastically. But when remodelling proceeds abnormally it can contribute to preterm birth, slow progress of labour, and failure to initiate labour. Remodelling increases intercellular coupling and cellular excitability, which are the main targets of pharmaceutical treatments for uterine contraction disorders. However, the way in which electrical propagation and force development depend on intercellular coupling and cellular excitability is not fully understood. Using a computational myofibre model we study the dependency of electrical propagation and force development on intercellular coupling and cellular excitability. This model reveals that intercellular coupling determines the conduction velocity. Moreover, our model shows that intercellular coupling alone does not regulate force development. Further, cellular excitability controls whether conduction across the cells is blocked. Lastly, our model describes how cellular excitability regulates force development. Our results bridge cellular factors, targeted by drugs to regulate uterine contractions, and tissue level electromechanical properties, which are responsible for delivery. They are a step forward towards understanding uterine excitation-contraction dynamics and developing safer and more efficient pharmaceutical treatments for uterine contraction disorders.

Correction: Designing machine learning workflows with an application to topological data analysis.

[This corrects the article DOI: 10.1371/journal.pone.0225577.].

Optimal Transport in Reproducing Kernel Hilbert Spaces: Theory and Applications.

In this paper, we present a mathematical and computational framework for comparing and matching distributions in reproducing kernel Hilbert spaces (RKHS). This framework, called optimal transport in RKHS, is a generalization of the optimal transport problem in input spaces to (potentially) infinite-dimensional feature spaces. We provide a computable formulation of Kantorovich's optimal transport in RKHS. In particular, we explore the case in which data distributions in RKHS are Gaussian, obtaining closed-form expressions of both the estimated Wasserstein distance and optimal transport map via kernel matrices. Based on these expressions, we generalize the Bures metric on covariance matrices to infinite-dimensional settings, providing a new metric between covariance operators. Moreover, we extend the correlation alignment problem to Hilbert spaces, giving a new strategy for matching distributions in RKHS. Empirically, we apply the derived formulas under the Gaussianity assumption to image classification and domain adaptation. In both tasks, our algorithms yield state-of-the-art performances, demonstrating the effectiveness and potential of our framework.

Gait Cycle Validation and Segmentation Using Inertial Sensors.

In this paper, we develop an algorithm to automatically validate and segment a gait cycle in real time into three gait events, namely midstance, toe-off, and heel-strike, using inertial sensors. We first use the physical models of sensor data obtained from a foot-mounted inertial system to differentiate stationary and moving segments of the sensor data. Next, we develop an optimization routine called sparsity-assisted wavelet denoising (SAWD), which simultaneously combines linear time invariant filters, orthogonal multiresolution representations such as wavelets, and sparsity-based methods, to generate a sparse template of the moving segments of the gyroscope measurements in the sagittal plane for valid gait cycles. Thereafter, to validate any moving segment as a gait cycle, we compute the root-mean-square error between the generated sparse template and the sparse representation of the moving segment of the gyroscope data in the sagittal plane obtained using SAWD. Finally, we find the local minima for the stationary and moving segments of a valid gait cycle to detect the gait events. We compare our proposed method with existing methods, for a fixed threshold, using real data obtained from three groups, namely controls, participants with Parkinson disease, and geriatric participants. Our proposed method demonstrates an average F1 score of 87.78% across all groups for a fixed sampling rate, and an average F1 score of 92.44% across all Parkinson disease participants for a variable sampling rate.

Designing machine learning workflows with an application to topological data analysis.

In this paper we define the concept of the Machine Learning Morphism (MLM) as a fundamental building block to express operations performed in machine learning such as data preprocessing, feature extraction, and model training. Inspired by statistical learning, MLMs are morphisms whose parameters are minimized via a risk function. We explore operations such as composition of MLMs and when sets of MLMs form a vector space. These operations are used to build a machine learning workflow from data preprocessing to final task completion. We examine the Mapper Algorithm from Topological Data Analysis as an MLM, and build several workflows for binary classification incorporating Mapper on Hospital Readmissions and Credit Evaluation datasets. The advantage of this framework lies in the ability to easily build, organize, and compare multiple workflows, and allows joint optimization of parameters across multiple steps in an application.

Electro-Mechanical Ionic Channel Modeling for Uterine Contractions and Oxytocin Effect during Pregnancy.

Uterine contractions during normal pregnancy and preterm birth are an important physiological activity. Although the cause of preterm labor is usually unknown, preterm birth creates very serious health concerns in many cases. Therefore, understanding normal birth and predicting preterm birth can help both newborn babies and their families. In our previous work, we developed a multiscale dynamic electrophysiology model of uterine contractions. In this paper, we mainly focus on the cellular level and use electromyography (EMG) and cell force generation methods to construct a new ionic channel model and a corresponding mechanical force model. Specifically, the ionic channel model takes into consideration the knowledge of individual ionic channels, which include the electrochemical and bioelectrical characteristics of individual myocytes. We develop a new sodium channel and a new potassium channel based on the experimental data from the human myometrium and the average correlations are 0.9946 and 0.9945, respectively. The model is able to generate the single spike, plateau type and bursting type of action potentials. Moreover, we incorporate the effect of oxytocin on changing the properties of the L-type and T-type calcium channels and further influencing the output action potentials. In addition, we develop a mechanical force model based on the new ionic channel model that describes the detailed ionic dynamics. Our model produces cellular mechanical force that propagates to the tissue level. We illustrate the relationship between the cellular mechanical force and the intracellular ionic dynamics and discuss the relationship between the application of oxytocin and the output mechanical force. We also propose a simplified version of the model to enable large scale simulations using sensitivity analysis method. Our results show that the model is able to reproduce the bioelectrical and electromechanical characteristics of uterine contractions during pregnancy.

Low-Rank Approximation via Generalized Reweighted Iterative Nuclear and Frobenius Norms.

The low-rank approximation problem has recently attracted wide concern due to its excellent performance in real-world applications such as image restoration, traffic monitoring, and face recognition. Compared with the classic nuclear norm, the Schatten-p norm is stated to be a closer approximation to restrain the singular values for practical applications in the real world. However, Schatten-p norm minimization is a challenging non-convex, non-smooth, and non-Lipschitz problem. In this paper, inspired by the reweighted ℓ1 and ℓ2 norm for compressive sensing, the generalized iterative reweighted nuclear norm (GIRNN) and the generalized iterative reweighted Frobenius norm (GIRFN) algorithms are proposed to approximate Schatten-p norm minimization. By involving the proposed algorithms, the problem becomes more tractable and the closed solutions are derived from the iteratively reweighted subproblems. In addition, we prove that both proposed algorithms converge at a linear rate to a bounded optimum. Numerical experiments for the practical matrix completion (MC), robust principal component analysis (RPCA), and image decomposition problems are illustrated to validate the superior performance of both algorithms over some common state-of-the-art methods.

Minimizing Structural Bias in Single-Molecule Super-Resolution Microscopy.

Single-molecule localization microscopy (SMLM) depends on sequential detection and localization of individual molecular blinking events. Due to the stochasticity of single-molecule blinking and the desire to improve SMLM's temporal resolution, algorithms capable of analyzing frames with a high density (HD) of active molecules, or molecules whose images overlap, are a prerequisite for accurate location measurements. Thus far, HD algorithms are evaluated using scalar metrics, such as root-mean-square error, that fail to quantify the structure of errors caused by the structure of the sample. Here, we show that the spatial distribution of localization errors within super-resolved images of biological structures are vectorial in nature, leading to systematic structural biases that severely degrade image resolution. We further demonstrate that the shape of the microscope's point-spread function (PSF) fundamentally affects the characteristics of imaging artifacts. We built a Robust Statistical Estimation algorithm (RoSE) to minimize these biases for arbitrary structures and PSFs. RoSE accomplishes this minimization by estimating the likelihood of blinking events to localize molecules more accurately and eliminate false localizations. Using RoSE, we measure the distance between crossing microtubules, quantify the morphology of and separation between vesicles, and obtain robust recovery using diverse 3D PSFs with unmatched accuracy compared to state-of-the-art algorithms.

Estimating uterine source current during contractions using magnetomyography measurements.

Understanding the uterine source of the electrophysiological activity of contractions during pregnancy is of scientific interest and potential clinical applications. In this work, we propose a method to estimate uterine source currents from magnetomyography (MMG) temporal course measurements on the abdominal surface. In particular, we develop a linear forward model, based on the quasistatic Maxwell's equations and a realistic four-compartment volume conductor, relating the magnetic fields to the source currents on the uterine surface through a lead-field matrix. To compute the lead-field matrix, we use a finite element method that considers the anisotropic property of the myometrium. We estimate the source currents by minimizing a constrained least-squares problem to solve the non-uniqueness issue of the inverse problem. Because we lack the ground truth of the source current, we propose to predict the intrauterine pressure from our estimated source currents by using an absolute-value-based method and compare the result with real abdominal deflection recorded during contractile activity. We test the feasibility of the lead-field matrix by displaying the lead fields that are generated by putative source currents at different locations in the myometrium: cervix and fundus, left and right, front and back. We then illustrate our method by using three synthetic MMG data sets, which are generated using our previously developed multiscale model of uterine contractions, and three real MMG data sets, one of which has simultaneous real abdominal deflection measurements. The numerical results demonstrate the ability of our method to capture the local contractile activity of human uterus during pregnancy. Moreover, the predicted intrauterine pressure is in fair agreement with the real abdominal deflection with respect to the timing of uterine contractions.

Modeling, Detecting, and Tracking Freezing of Gait in Parkinson Disease Using Inertial Sensors.

In this paper, we develop new methods to automatically detect the onset and duration of freezing of gait (FOG) in people with Parkinson disease (PD) in real time, using inertial sensors. We first build a physical model that describes the trembling motion during the FOG events. Then, we design a generalized likelihood ratio test framework to develop a two-stage detector for determining the zero-velocity and trembling events during gait. Thereafter, to filter out falsely detected FOG events, we develop a point-process filter that combines the output of the detectors with information about the speed of the foot, provided by a foot-mounted inertial navigation system. We computed the probability of FOG by using the point-process filter to determine the onset and duration of the FOG event. Finally, we validate the performance of the proposed system design using real data obtained from people with PD who performed a set of gait tasks. We compare our FOG detection results with an existing method that only uses accelerometer data. The results indicate that our method yields 81.03% accuracy in detecting FOG events and a threefold decrease in the false-alarm rate relative to the existing method.

Publisher Correction: Community Detection in Complex Networks via Clique Conductance.

A correction to this article has been published and is linked from the HTML and PDF versions of this paper. The error has not been fixed in the paper.

Community Detection in Complex Networks via Clique Conductance.

Network science plays a central role in understanding and modeling complex systems in many areas including physics, sociology, biology, computer science, economics, politics, and neuroscience. One of the most important features of networks is community structure, i.e., clustering of nodes that are locally densely interconnected. Communities reveal the hierarchical organization of nodes, and detecting communities is of great importance in the study of complex systems. Most existing community-detection methods consider low-order connection patterns at the level of individual links. But high-order connection patterns, at the level of small subnetworks, are generally not considered. In this paper, we develop a novel community-detection method based on cliques, i.e., local complete subnetworks. The proposed method overcomes the deficiencies of previous similar community-detection methods by considering the mathematical properties of cliques. We apply the proposed method to computer-generated graphs and real-world network datasets. When applied to networks with known community structure, the proposed method detects the structure with high fidelity and sensitivity. When applied to networks with no a priori information regarding community structure, the proposed method yields insightful results revealing the organization of these complex networks. We also show that the proposed method is guaranteed to detect near-optimal clusters in the bipartition case.

Robustness of meta-analyses in finding gene × environment interactions.

Meta-analyses that synthesize statistical evidence across studies have become important analytical tools for genetic studies. Inspired by the success of genome-wide association studies of the genetic main effect, researchers are searching for gene × environment interactions. Confounders are routinely included in the genome-wide gene × environment interaction analysis as covariates; however, this does not control for any confounding effects on the results if covariate × environment interactions are present. We carried out simulation studies to evaluate the robustness to the covariate × environment confounder for meta-regression and joint meta-analysis, which are two commonly used meta-analysis methods for testing the gene × environment interaction or the genetic main effect and interaction jointly. Here we show that meta-regression is robust to the covariate × environment confounder while joint meta-analysis is subject to the confounding effect with inflated type I error rates. Given vast sample sizes employed in genome-wide gene × environment interaction studies, non-significant covariate × environment interactions at the study level could substantially elevate the type I error rate at the consortium level. When covariate × environment confounders are present, type I errors can be controlled in joint meta-analysis by including the covariate × environment terms in the analysis at the study level. Alternatively, meta-regression can be applied, which is robust to potential covariate × environment confounders.

A Hidden Markov Model for Seismocardiography.

We propose a hidden Markov model approach for processing seismocardiograms. The seismocardiogram morphology is learned using the expectation-maximization algorithm, and the state of the heart at a given time instant is estimated by the Viterbi algorithm. From the obtained Viterbi sequence, it is then straightforward to estimate instantaneous heart rate, heart rate variability measures, and cardiac time intervals (the latter requiring a small number of manual annotations). As is shown in the conducted experimental study, the presented algorithm outperforms the state-of-the-art in seismocardiogram-based heart rate and heart rate variability estimation. Moreover, the isovolumic contraction time and the left ventricular ejection time are estimated with mean absolute errors of about 5 [ms] and [Formula: see text], respectively. The proposed algorithm can be applied to any set of inertial sensors; does not require access to any additional sensor modalities; does not make any assumptions on the seismocardiogram morphology; and explicitly models sensor noise and beat-to-beat variations (both in amplitude and temporal scaling) in the seismocardiogram morphology. As such, it is well suited for low-cost implementations using off-the-shelf inertial sensors and targeting, e.g., at-home medical services.