Learning to discover: expressive Gaussian mixture models for multi-dimensional simulation and parameter inference in the physical sciences

We show that density models describing multiple observables with (i) hard boundaries and (ii) dependence on external parameters may be created using an auto-regressive Gaussian mixture model. The model is designed to capture how observable spectra are deformed by hypothesis variations, and is made more expressive by projecting data onto a configurable latent space. It may be used as a statistical model for scientific discovery in interpreting experimental observations, for example when constraining the parameters of a physical model or tuning simulation parameters according to calibration data. The model may also be sampled for use within a Monte Carlo simulation chain, or used to estimate likelihood ratios for event classification. The method is demonstrated on simulated high-energy particle physics data considering the anomalous electroweak production of a $Z$ boson in association with a dijet system at the Large Hadron Collider, and the accuracy of inference is tested using a realistic toy example. The developed methods are domain agnostic; they may be used within any field to perform simulation or inference where a dataset consisting of many real-valued observables has conditional dependence on external parameters.

Impacts of COVID-19 on Electric Vehicle Charging Behavior: Data Analytics, Visualization, and Clustering

COVID-19 pandemic has infected millions and led to a catastrophic loss of lives globally. It has also significantly disrupted the movement of people, businesses, and industries. Additionally, electric vehicle (EV) users have faced challenges in charging their vehicles in public charging locations where there is a risk of COVID-19 exposure. However, a case study of EV charging behavior and its impacts during the SARS-CoV-2 is not addressed in the existing literature. This paper investigates the impacts of COVID-19 on EV charging behavior by analyzing the charging activity during the pandemic using a dataset from a public charging facility in the USA. Data visualization of charging behavior alongside significant timelines of the pandemic was utilized for analysis. Moreover, a cluster analysis using k-means, hierarchical clustering, and Gaussian mixture models was performed to identify common groups of charging behavior based on the vehicle arrival and departure times. Although the number of vehicles using the charging station was reduced significantly due to lockdown restrictions, the charging activity started to pick up again since May 2021 due to an increase in vaccination and easing of public restrictions. However, the charging activity currently still remains around half of the activity pre-pandemic. A noticeable decline in charging session length and an increase in energy consumption can be observed as well. Clustering algorithms identified three groups of charging behavior during the pandemic and their analysis and performance comparison using internal validation measures were also presented.

Patient and Clinical Factors at Admission Affect the Levels of Neutralizing Antibodies Six Months after Recovering from COVID-19

The rate of decline in the levels of neutralizing antibodies (NAbs) greatly varies among patients who recover from Coronavirus disease 2019 (COVID-19). However, little is known about factors associated with this phenomenon. The objective of this study is to investigate early factors at admission that can influence long-term NAb levels in patients who recovered from COVID-19. A total of 306 individuals who recovered from COVID-19 at the Tongji Hospital, Wuhan, China, were included in this study. The patients were classified into two groups with high (NAbhigh, n = 153) and low (NAblow, n = 153) levels of NAb, respectively based on the median NAb levels six months after discharge. The majority (300/306, 98.0%) of the COVID-19 convalescents had detected NAbs. The median NAb concentration was 63.1 (34.7, 108.9) AU/mL. Compared with the NAblow group, a larger proportion of the NAbhigh group received corticosteroids (38.8% vs. 22.4%, p = 0.002) and IVIG therapy (26.5% vs. 16.3%, p = 0.033), and presented with diabetes comorbidity (25.2% vs. 12.2%, p = 0.004); high blood urea (median (IQR): 4.8 (3.7, 6.1) vs. 3.9 (3.5, 5.4) mmol/L; p = 0.017); CRP (31.6 (4.0, 93.7) vs. 16.3 (2.7, 51.4) mg/L; p = 0.027); PCT (0.08 (0.05, 0.17) vs. 0.05 (0.03, 0.09) ng/mL; p = 0.001); SF (838.5 (378.2, 1533.4) vs. 478.5 (222.0, 1133.4) μg/L; p = 0.035); and fibrinogen (5.1 (3.8, 6.4) vs. 4.5 (3.5, 5.7) g/L; p = 0.014) levels, but low SpO2 levels (96.0 (92.0, 98.0) vs. 97.0 (94.0, 98.0)%; p = 0.009). The predictive model based on Gaussian mixture models, displayed an average accuracy of 0.7117 in one of the 8191 formulas, and ROC analysis showed an AUC value of 0.715 (0.657–0.772), and specificity and sensitivity were 72.5% and 67.3%, respectively. In conclusion, we found that several factors at admission can contribute to the high level of NAbs in patients after discharge, and constructed a predictive model for long-term NAb levels, which can provide guidance for clinical treatment and monitoring.

A Flexible Top-Down Data-Driven Stochastic Model for Synthetic Load Profiles Generation

The study of the behavior of smart distribution systems under increasingly dynamic operating conditions requires realistic and time-varying load profiles to run comprehensive and accurate simulations of power flow analysis, system state estimation and optimal control strategies. However, due to the limited availability of experimental data, synthetic load profiles with flexible duration and time resolution are often needed to this purpose. In this paper, a top-down stochastic model is proposed to generate an arbitrary amount of synthetic load profiles associated with different kinds of users exhibiting a common average daily pattern. The groups of users are identified through a preliminary Ward’s hierarchical clustering. For each cluster and each season of the year, a time-inhomogeneous Markov chain is built, and its parameters are estimated by using the available data. The states of the chain correspond to equiprobable intervals, which are then mapped to a time-varying power consumption range, depending on the statistical distribution of the load profiles at different times of the day. Such distributions are regarded as Gaussian Mixture Models (GMM). Compared with other top-down approaches reported in the scientific literature, the joint use of GMM models and time-inhomogeneous Markov chains is rather novel. Furthermore, it is flexible enough to be used in different contexts and with different temporal resolution, while keeping the number of states and the computational burden reasonable. The good agreement between synthetic and original load profiles in terms of both time series similarity and consistency of the respective probability density functions was validated by using three different data sets with different characteristics. In most cases, the median values of synthetic profiles’ mean and standard deviation differ from those of the original reference distributions by no more than ±10% both within a typical day of each season and within the population of a given cluster, although with some significant outliers.

A Riemannian Newton trust-region method for fitting Gaussian mixture models

Gaussian Mixture Models are a powerful tool in Data Science and Statistics that are mainly used for clustering and density approximation. The task of estimating the model parameters is in practice often solved by the expectation maximization (EM) algorithm which has its benefits in its simplicity and low per-iteration costs. However, the EM converges slowly if there is a large share of hidden information or overlapping clusters. Recent advances in Manifold Optimization for Gaussian Mixture Models have gained increasing interest. We introduce an explicit formula for the Riemannian Hessian for Gaussian Mixture Models. On top, we propose a new Riemannian Newton Trust-Region method which outperforms current approaches both in terms of runtime and number of iterations. We apply our method on clustering problems and density approximation tasks. Our method is very powerful for data with a large share of hidden information compared to existing methods.

Stress Level Detection and Evaluation from Phonation and PPG Signals Recorded in an Open-Air MRI Device

This paper deals with two modalities for stress detection and evaluation—vowel phonation speech signal and photo-plethysmography (PPG) signal. The main measurement is carried out in four phases representing different stress conditions for the tested person. The first and last phases are realized in laboratory conditions. The PPG and phonation signals are recorded inside the magnetic resonance imaging scanner working with a weak magnetic field up to 0.2 T in a silent state and/or with a running scan sequence during the middle two phases. From the recorded phonation signal, different speech features are determined for statistical analysis and evaluation by the Gaussian mixture models (GMM) classifier. A database of affective sounds and two databases of emotional speech were used for GMM creation and training. The second part of the developed method gives comparison of results obtained from the statistical description of the sensed PPG wave together with the determined heart rate and Oliva–Roztocil index values. The fusion of results obtained from both modalities gives the final stress level. The performed experiments confirm our working assumption that a fusion of both types of analysis is usable for this task—the final stress level values give better results than the speech or PPG signals alone.

Real-time unstructured road detection based on CNN and Gibbs energy function

Road detection algorithms with high robustness as well as timeliness are the basis for developing intelligent assisted driving systems. To improve the robustness as well as the timeliness of unstructured road detection, a new algorithm is proposed in this paper. First, for the first frame in the video, the homography matrix H is estimated based on the improved random sample consensus (RANSAC) algorithm for different regions in the image, and the features of H are automatically extracted using convolutional neural network (CNN), which in turn enables road detection. Secondly, in order to improve the rate of subsequent similar frame detection, the color as well as texture features of the road are extracted from the detection results of the first frame, and the corresponding Gaussian mixture models (GMMs) are constructed based on Orchard-Bouman, and then the Gibbs energy function is used to achieve road detection in subsequent frames. Finally, the above algorithm is verified in a real unstructured road scene, and the experimental results show that the algorithm is 98.4% accurate and can process 58 frames per second with 1024×960 pixels.