AMITE: A Novel Polynomial Expansion for Analyzing Neural Network Nonlinearities.

Polynomial expansions are important in the analysis of neural network nonlinearities. They have been applied thereto addressing well-known difficulties in verification, explainability, and security. Existing approaches span classical Taylor and Chebyshev methods, asymptotics, and many numerical approaches. We find that, while these have useful properties individually, such as exact error formulas, adjustable domain, and robustness to undefined derivatives, there are no approaches that provide a consistent method, yielding an expansion with all these properties. To address this, we develop an analytically modified integral transform expansion (AMITE), a novel expansion via integral transforms modified using derived criteria for convergence. We show the general expansion and then demonstrate an application for two popular activation functions: hyperbolic tangent and rectified linear units. Compared with existing expansions (i.e., Chebyshev, Taylor, and numerical) employed to this end, AMITE is the first to provide six previously mutually exclusive desired expansion properties, such as exact formulas for the coefficients and exact expansion errors. We demonstrate the effectiveness of AMITE in two case studies. First, a multivariate polynomial form is efficiently extracted from a single hidden layer black-box multilayer perceptron (MLP) to facilitate equivalence testing from noisy stimulus-response pairs. Second, a variety of feedforward neural network (FFNN) architectures having between three and seven layers are range bounded using Taylor models improved by the AMITE polynomials and error formulas. AMITE presents a new dimension of expansion methods suitable for the analysis/approximation of nonlinearities in neural networks, opening new directions and opportunities for the theoretical analysis and systematic testing of neural networks.

Nonlinear dynamic epidemiological analysis of effects of vaccination and dynamic transmission on COVID-19.

This paper is concerned with nonlinear modeling and analysis of the COVID-19 pandemic. We are especially interested in two current topics: effect of vaccination and the universally observed oscillations in infections. We use a nonlinear Susceptible, Infected, & Immune model incorporating a dynamic transmission rate and vaccination policy. The US data provides a starting point for analyzing stability, bifurcations and dynamics in general. Further parametric analysis reveals a saddle-node bifurcation under imperfect vaccination leading to the occurrence of sustained epidemic equilibria. This work points to the tremendous value of systematic nonlinear dynamic analysis in pandemic modeling and demonstrates the dramatic influence of vaccination, and frequency, phase, and amplitude of transmission rate on the persistent dynamic behavior of the disease.

Post-resonance backward whirl analysis in cracked overhung rotors.

Overhung rotors usually exhibit recurrent transitions through critical whirl rotational speeds during startup and coast down operations, which significantly differ from their steady-state whirl responses. The presence of angular acceleration results in a linear-time-varying (LTV) system, which, although technically linear, still presents complexities often evinced by a nonlinear system. In general, backward whirl zones can either precede the critical forward whirl speed (termed as pre-resonance backward whirl, Pr-BW), or immediately follow the critical forward whirl speed (termed as post-resonance backward whirl, Po-BW). The Po-BW in the whirl response of a cracked overhung rotor with a breathing crack is studied here as distinct from that of geometrically symmetric configurations of other rotor systems. The equations of motion from the finite element (FE) model of an overhung rotor system with a breathing crack are numerically integrated to obtain the whirl response. The transient whirl responses with different bearing conditions are thoroughly investigated for excitation of Po-BW. The Po-BW zones of rotational speeds are determined via the wavelet transform method and full spectrum analysis (FSA) and applied to signals with added noise. The results of this work confirm the excitation of the Po-BW in cracked overhung rotors and confirm the robustness of the employed methods.

MLWAVE: A novel algorithm to classify primary versus secondary asphyxia-associated ventricular fibrillation.

INTRODUCTION/HYPOTHESIS: The outcome of cardiopulmonary resuscitation (CPR) depends on timely recognition of the underlying cause of cardiac arrest. Ventricular fibrillation (VF) waveform analysis to differentiate primary VF from secondary asphyxia-associated VF may allow tailoring of therapies to improve cardiac arrest outcomes. Therefore, the primary goal of this investigation was to develop a novel technique utilizing wavelet synchrosqueezed transform (WSST) and decision-tree classifier that was specifically adapted to discriminate between these two incidents of VF. METHODS: Secondary analytical investigation of electrocardiography (ECG) data obtained from swine models of either primary VF (n=18) or secondary asphyxia-associated VF (7min of asphyxia prior to VF induction; n=12). In the primary analysis, WSST technique was applied to the first 35s of the VF ECG signal to identify the most differentiating characteristics of the signal for use as features to develop a machine learning algorithm to classify the arrest as either primary VF vs. secondary asphyxia-associated VF. The performance of this new interactive Machine Learning algorithm with Wavelet Energy features of ECG (MLWAVE) was assessed using both classification accuracy and area under the receiver operating characteristic curve (AUCROC). To evaluate the validity of the new technique, the amplitude spectrum area (AMSA)-based technique, a well-established defibrillation classification method, was also applied to the same ECG signals. The classification accuracy and AUCROC were then compared between the two techniques. RESULTS: For the primary analysis evaluating the first 35s of the VF waveform, the MLWAVE technique classified the type of VF with high accuracy (28/28 [100%], AUCROC: 1.00). The MLWAVE technique performed better than the AMSA technique across all comparisons, but given the small sample sizes, differences were not statistically significant (accuracy: 100% vs. 85.7%; p=0.24; AUCROC: 1.00 vs. 0.82; p=0.24). CONCLUSION: This analytical investigation illustrates the advantages of the MLWAVE signal processing method which was associated with 100% accuracy in classifying the type of VF waveform: primary vs. asphyxia-associated. Such classification could lead to personalized tailoring of resuscitation (e.g., immediate defibrillation vs. continued CPR and treatment of reversible cardiac arrest causes before defibrillation) to improve outcomes for cardiac arrest.

A Novel Embedded Feature Selection and Dimensionality Reduction Method for an SVM Type Classifier to Predict Periventricular Leukomalacia (PVL) in Neonates.

This paper is concerned with the prediction of the occurrence of periventricular leukomalacia (PVL) in neonates after heart surgery. Our prior work shows that the Support Vector Machine (SVM) classifier can be a powerful tool in predicting clinical outcomes of such complicated and uncommon diseases, even when the number of data samples is low. In the presented work, we first illustrate and discuss the shortcomings of the traditional automatic machine learning (aML) approach. Consequently, we describe our methodology for addressing these shortcomings, while utilizing the designed interactive ML (iML) algorithm. Finally, we conclude with a discussion of the developed method and the results obtained. In sum, by adding an additional (Genetic Algorithm) optimization step in the SVM learning framework, we were able to (a) reduce the dimensionality of an SVM model from 248 to 53 features, (b) increase generalization that was confirmed by a 100% accuracy assessed on an unseen testing set, and (c) improve the overall SVM model's performance from 65% to 100% testing accuracy, utilizing the proposed iML method.

Nonlinear dynamic analysis of an epidemiological model for COVID-19 including public behavior and government action.

This paper is concerned with nonlinear modeling and analysis of the COVID-19 pandemic currently ravaging the planet. There are two objectives: to arrive at an appropriate model that captures the collected data faithfully and to use that as a basis to explore the nonlinear behavior. We use a nonlinear susceptible, exposed, infectious and removed transmission model with added behavioral and government policy dynamics. We develop a genetic algorithm technique to identify key model parameters employing COVID-19 data from South Korea. Stability, bifurcations and dynamic behavior are analyzed. Parametric analysis reveals conditions for sustained epidemic equilibria to occur. This work points to the value of nonlinear dynamic analysis in pandemic modeling and demonstrates the dramatic influence of social and government behavior on disease dynamics.

A Framework for Modeling Flood Depth Using a Hybrid of Hydraulics and Machine Learning.

Solving river engineering problems typically requires river flow characterization, including the prediction of flow depth, flow velocity, and flood extent. Hydraulic models use governing equations of the flow in motion (conservation of mass and momentum principles) to predict the flow characteristics. However, solving such equations can be substantially expensive, depending upon their spatial extension. Moreover, modeling two- or three-dimensional river flows with high-resolution topographic data for large-scale regions (national or continental scale) is next to impossible. Such simulations are required for comprehensive river modeling, where a system of connected rivers is to be simulated simultaneously. Machine Learning (ML) approaches have shown promise for different water resources problems, and they have demonstrated an ability to learn from current data to predict new scenarios, which can enhance the understanding of the systems. The aim of this paper is to present an efficient flood simulation framework that can be applied to large-scale simulations. The framework outlines a novel, quick, efficient and versatile model to identify flooded areas and the flood depth, using a hybrid of hydraulic model and ML measures. To accomplish that, a two-dimensional hydraulic model (iRIC), calibrated by measured water surface elevation data, was used to train two ML models to predict river depth over the domain for an arbitrary discharge. The first ML model included a random forest (RF) classification model, which was used to identify wet or dry nodes over the domain. The second was a multilayer perceptron (MLP) model that was developed and trained by the iRIC simulation results, in order to estimate river depth in wet nodes. For the test data the overall accuracy of 98.5 percent was achieved for the RF classification. The regression coefficient for the MLP model for depth was 0.88. The framework outlined in this paper can be used to couple hydraulics and ML models to reduce the computation time, resources and expenses of large-scale, real-time simulations, specifically for two- or three-dimensional hydraulic modeling, where traditional hydraulic models are infeasible or prohibitively expensive.

A Novel Nonlinear Mathematical Model of Thoracic Wall Mechanics During Cardiopulmonary Resuscitation Based on a Porcine Model of Cardiac Arrest.

Cardiopulmonary resuscitation (CPR) is used widely to rescue cardiac arrest patients, yet some physiological aspects of the procedure remain poorly understood. We conducted this study to characterize the dynamic mechanical properties of the thorax during CPR in a swine model. This is an important step toward determining optimal CPR chest compression mechanics with the goals of improving the fidelity of CPR simulation manikins and ideally chest compression delivery in real-life resuscitations. This paper presents a novel nonlinear model of the thorax that captures the complex behavior of the chest during CPR. The proposed model consists of nonlinear elasticity and damping properties along with frequency dependent hysteresis. An optimization technique was used to estimate the model coefficients for force-compression using data collected from experiments conducted on swine. To track clinically relevant, time-dependent changes of the chest's properties, the data was divided into two time periods, from 1 to 10 min (early) and greater than 10 min (late) after starting CPR. The results showed excellent agreement between the actual and the estimated forces, and energy dissipation due to viscous damping in the late stages of CPR was higher when compared to the earlier stages. These findings provide insight into improving chest compression mechanics during CPR, and may provide the basis for developing CPR simulation manikins that more accurately represent the complex real world changes that occur in the chest during CPR.

Automatic Detection of Endotracheal Intubation During the Anesthesia Procedure.

This paper is concerned with the mathematical modeling and detection of endotracheal (ET) intubation in children under general anesthesia during surgery. In major pediatric surgeries, the airway is often secured with an endotracheal tube (ETT) followed by initiation of mechanical ventilation. Clinicians utilize auscultation of breath sounds and capnography to verify correct ETT placement. However, anesthesia providers often delay timely charting of ET intubation. This latency in event documentation results in decreased efficacy of clinical decision support systems. In order to target this problem, we collected real inpatient data and designed an algorithm to accurately detect the intubation time within the clinically valid range; the results show that we are able to achieve high accuracy in more than 96% of the cases. Automatic detection of ET intubation time would thus enhance better real-time data capture to support future improvement in clinical decision support systems.

Advanced analytics for outcome prediction in intensive care units.

In this paper we present a new expert knowledge based clinical decision support system for prediction of intensive care units outcome based on the physiological measurements collected during the first 48 hours of the patient's admission to the ICU. The developed CDSS algorithm is composed of several stages. First, we categorize the collected data based on the physiological organ that they represent. We then extract clinically relevant features from each data category and then rank these features based on their mutual information with the outcome. Then, we design an artificial neural network to serve as a classifier to detect patients at high risk of critical deterioration. We use the eight-fold cross validation method to test the developed CDSS classifier. The results from the classification show that the newly designed CDSS outperforms the widely used acuity scoring systems, SOFA and SAPS-III. The F-score classification result of our developed algorithms is 42% while the F-score results for SOFA and SAPS-III are 26% and 29% respectively.

Application of Mathematical Modeling for Simulation and Analysis of Hypoplastic Left Heart Syndrome (HLHS) in Pre- and Postsurgery Conditions.

This paper is concerned with the mathematical modeling of a severe and common congenital defect called hypoplastic left heart syndrome (HLHS). Surgical approaches are utilized for palliating this heart condition; however, a brain white matter injury called periventricular leukomalacia (PVL) occurs with high prevalence at or around the time of surgery, the exact cause of which is not known presently. Our main goal in this paper is to study the hemodynamic conditions under which HLHS physiology may lead to the occurrence of PVL. A lumped parameter model of the HLHS circulation has been developed integrating diffusion modeling of oxygen and carbon dioxide concentrations in order to study hemodynamic variables such as pressure, flow, and blood gas concentration. Results presented include calculations of blood pressures and flow rates in different parts of the circulation. Simulations also show changes in the ratio of pulmonary to systemic blood flow rates when the sizes of the patent ductus arteriosus and atrial septal defect are varied. These changes lead to unbalanced blood circulations and, when combined with low oxygen and carbon dioxide concentrations in arteries, result in poor oxygen delivery to the brain. We stipulate that PVL occurs as a consequence.

Prediction of periventricular leukomalacia occurrence in neonates after heart surgery.

This paper is concerned with predicting the occurrence of periventricular leukomalacia (PVL) using vital and blood gas data which are collected over a period of 12 h after the neonatal cardiac surgery. A data mining approach has been employed to generate a set of rules for classification of subjects as healthy or PVL affected. In view of the fact that blood gas and vital data have different sampling rates, in this study we have divided the data into two categories: 1) high resolution (vital), and 2) low resolution (blood gas), and designed a separate classifier based on each data category. The developed algorithm is composed of several stages; first, a feature pool has been extracted from each data category and the extracted features have been ranked based on the data reliability and their mutual information content with the output. An optimal feature subset with the highest discriminative capability has been formed using simultaneous maximization of the class separability measure and mutual information of a set. Two separate decision trees (DTs) have been developed for the classification purpose and more importantly to discover hidden relationships that exist among the data to help us better understand PVL pathophysiology. The DT result shows that high amplitude 20 min variations and low sample entropy in the vital data and the defined out of range index as well as maximum rate of change in blood gas data are important factors for PVL prediction. Low sample entropy represents lack of variability in hemodynamic measurement, and constant blood pressure with small fluctuations is an important indicator of PVL occurrence. Finally, using the different time frames of data collection, we show that the first 6 h of data contain sufficient information for PVL occurrence prediction.

Discovering hidden relationships in physiological signals for prediction of Periventricular Leukomalacia.

This paper is concerned with predicting the occurrence of Periventricular Leukomalacia (PVL) using vital data which are collected over a period of twelve hours after neonatal cardiac surgery. The vital data contain heart rate (HR), mean arterial pressure (MAP), right atrium pressure (RAP), and oxygen saturation (SpO2). Various features are extracted from the data and are then ranked so that an optimal subset of features that have the highest discriminative capabilities can be selected. A decision tree (DT) is then developed for the vital data in order to identify the most important vital measurements. The DT result shows that high amplitude 20 minutes variations and low sample entropy in the data is an important factor for prediction of PVL. Low sample entropy represents lack of variability in hemodynamic measurement, and constant blood pressure with small fluctuations is an important indicator of PVL occurrence. Finally, using the different time frames of the collected data, we show that the first six hours of data contain sufficient information for PVL occurrence prediction.

Model based optimization of the cardiopulmonary resuscitation (CPR) procedure.

This paper is concerned with the optimization of the cardiopulmonary resuscitation (CPR) procedure, which plays a critical rule in saving the life of patients suffering from cardiac arrest. In this paper, we define the performance index for optimization using the oxygen delivery. A model developed earlier is used to calculate the oxygen delivery through CPR. The free parameters of this model which depend on the rescuer performance are ventilation time, compression speed, tidal volume, and fraction of oxygen in the inspired air. Two different optimization problems are carried out. First, a global optimization is implemented to discover the best values of the free parameters which maximize the oxygen delivery. In addition to this, a sequential optimization scheme is explored which uses a two step optimization in each CPR sequence to maximize the oxygen delivery. Results show that the sequential optimization procedure will enhance the performance of the CPR significantly.

Application of decision tree in the prediction of periventricular leukomalacia (PVL) occurrence in neonates after heart surgery.

This paper is concerned with the prediction of the occurrence of periventricular leukomalacia (PVL) that occurs in neonates after heart surgery. The data which is collected over a period of 12 hours after cardiac surgery contains vital measurements as well as blood gas measurements with different resolutions. Vital data measured using near-inferred spectroscopy (NIRS) at the sampling rate of 0.25 Hz and blood gas measurement up to 12 times with irregular time intervals for 35 patients collected at Children's Hospital of Philadelphia (CHOP) are used for this study. Features derived from the data include statistical moments (mean, variance, skewness and kurtosis), trend and minimum and maximum values of the vital data and rate of change, time weighted mean and a custom defined out of range index (ORI) for the blood gas data. A decision tree is developed for the vital data in order to identify the most important vital measurements. In addition, a decision tree is developed for blood gas data to find important factors for the prediction of PVL occurrence. Results show that in the blood gas data, maximum rate of change of concentration of bicarbonate ions in blood (HCO(3)) and minimum rate of change of partial pressure of dissolved CO(2) in the blood (PaCO(2)) are the two most important factors for prediction of the PVL. Also important are the kurtosis of heart rate and hemoglobin values.

Melnikov's criteria, parametric control of chaos, and stationary chaos occurrence in systems with asymmetric potential subjected to multiscale type excitation.

We consider the problems of chaos and parametric control in nonlinear systems under an asymmetric potential subjected to a multiscale type excitation. The lower bound line for horseshoes chaos is analyzed using the Melnikov's criterion for a transition to permanent or transient nonperiodic motions, complement by the fractal or regular shape of the basin of attraction. Numerical simulations based on the basins of attraction, bifurcation diagrams, Poincaré sections, Lyapunov exponents, and phase portraits are used to show how stationary dissipative chaos occurs in the system. Our attention is focussed on the effects of the asymmetric potential term and the driven frequency. It is shown that the threshold amplitude ∣γ(c)∣ of the excitation decreases for small values of the driven frequency ω and increases for large values of ω. This threshold value decreases with the asymmetric parameter α and becomes constant for sufficiently large values of α. γ(c) has its maximum value for asymmetric load in comparison with the symmetric load. Finally, we apply the Melnikov theorem to the controlled system to explore the gain control parameter dependencies.

A cycle-averaged model of hypoplastic left heart syndrome (HLHS).

This paper is concerned with computational modeling of a severe congenital defect called Hypoplastic left heart syndrome (HLHS) that is the most common cardiac malformation with the highest likelihood of deaths in newborns. A lumped parameter model of the HLHS circulation has been developed to study the hemodynamic variables in the various sections of the cardio-pulmonary circulation system. We applied a short-term, cycle-averaging operation to the differential equations of the HLHS model to obtain the cycle-averaged model. Study has been carried out to analyze the variation of blood flow rate in different parts due to parameter changes. Results show that the developed model, could bring a good insight into understanding of the HLHS disease.

Receptors for prostaglandin E(2) that regulate cellular immune responses in the mouse.

Production of prostaglandin E(2) (PGE(2)) is enhanced during inflammation, and this lipid mediator can dramatically modulate immune responses. There are four receptors for PGE(2) (EP1-EP4) with unique patterns of expression and different coupling to intracellular signaling pathways. To identify the EP receptors that regulate cellular immune responses, we used mouse lines in which the genes encoding each of the four EP receptors were disrupted by gene targeting. Using the mixed lymphocyte response (MLR) as a model cellular immune response, we confirmed that PGE(2) has potent antiproliferative effects on wild-type responder cells. The absence of either the EP1 or EP3 receptors did not alter the inhibitory response to PGE(2) in the MLR. In contrast, when responder cells lacked the EP2 receptor, PGE(2) had little effect on proliferation. Modest resistance to PGE(2) was also observed in EP4-/- responder cells. Reconstitution experiments suggest that EP2 receptors primarily inhibit the MLR through direct actions on T cells. Furthermore, PGE(2) modulates macrophage function by activating the EP4 receptor and thereby inhibiting cytokine release. Thus, PGE(2) regulates cellular immune responses through distinct EP receptors on different immune cell populations: EP2 receptors directly inhibit T cell proliferation while EP2 and EP4 receptors regulate antigen presenting cells functions.

A role for fractalkine and its receptor (CX3CR1) in cardiac allograft rejection.

The hallmark of acute allograft rejection is infiltration of the inflamed graft by circulating leukocytes. We studied the role of fractalkine (FKN) and its receptor, CX(3)CR1, in allograft rejection. FKN expression was negligible in nonrejecting cardiac isografts but was significantly enhanced in rejecting allografts. At early time points, FKN expression was particularly prominent on vascular tissues and endothelium. As rejection progressed, FKN expression was further increased, with prominent anti-FKN staining seen around vessels and on cardiac myocytes. To determine the capacity of FKN on endothelial cells to promote leukocyte adhesion, we performed adhesion assays with PBMC and monolayers of TNF-alpha-activated murine endothelial cells under low-shear conditions. Treatment with either anti-FKN or anti-CX(3)CR1-blocking Ab significantly inhibited PBMC binding, indicating that a large proportion of leukocyte binding to murine endothelium occurs via the FKN and CX(3)CR1 adhesion receptors. To determine the functional significance of FKN in rejection, we treated cardiac allograft recipients with daily injections of anti-CX(3)CR1 Ab. Treatment with the anti-CX(3)CR1 Ab significantly prolonged allograft survival from 7 +/- 1 to 49 +/- 30 days (p < 0.0008). These studies identify a critical role for FKN in the pathogenesis of acute rejection and suggest that FKN may be a useful therapeutic target in rejection.