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Information-theoretic quantities have found wide applications in understanding interactions in complex systems primarily due to their non-parametric nature and ability to capture non-linear relationships. Increasingly popular among these tools is conditional transfer entropy, also known as causation entropy. In the present work, we leverage this tool to study the interaction among car drivers for the first time. Specifically, we investigate whether a driver responds to its immediate front and its immediate rear car to the same extent and whether we can separately quantify these responses. Using empirical data, we learn about the important features related to human driving behavior. Results demonstrate the evidence that drivers respond to both front and rear cars, and the response to their immediate front car increases in the presence of jammed traffic. Our approach provides a data-driven perspective to study interactions and is expected to aid in analyzing traffic dynamics.We provide an overview of the Koopman-operator analysis for a class of partial differential equations describing relaxation of the field variable to a stable stationary state. We introduce Koopman eigenfunctionals of the system and use the notion of conjugacy to develop spectral expansion of the Koopman operator. For linear systems such as the diffusion equation, the Koopman eigenfunctionals can be expressed as linear functionals of the field variable. The notion of inertial manifolds is shown to correspond to joint zero level sets of Koopman eigenfunctionals, and the notion of isostables is defined as the level sets of the slowest decaying Koopman eigenfunctional. Linear diffusion equation, nonlinear Burgers equation, and nonlinear phase-diffusion equation are analyzed as examples.The coronavirus disease 2019 (COVID-19) outbreak, due to SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2), originated in Wuhan, China and is now a global pandemic. The unavailability of vaccines, delays in diagnosis of the disease, and lack of proper treatment resources are the leading causes of the rapid spread of COVID-19. The world is now facing a rapid loss of human lives and socioeconomic status. As a mathematical model can provide some real pictures of the disease spread, enabling better prevention measures. In this study, we propose and analyze a mathematical model to describe the COVID-19 pandemic. We have derived the threshold parameter basic reproduction number, and a detailed sensitivity analysis of this most crucial threshold parameter has been performed to determine the most sensitive indices. Finally, the model is applied to describe COVID-19 scenarios in India, the second-largest populated country in the world, and some of its vulnerable states. We also have short-term forecasting of COVID-19, and we have observed that controlling only one model parameter can significantly reduce the disease's vulnerability.The goal of this study is to investigate patterns that emerge in brain and heart signals in response to external stimulating image regimes. Data were collected from 84 subjects of ages 18-22. Subjects viewed a series of both neutrally and negatively arousing pictures during 2-min and 18-s-long segments repeated nine times. Both brain [electroencephalogram (EEG)] and heart signals [electrocardiogram (EKG)] were recorded for the duration of the study (ranging from 1.5 to 2.5 h) and analyzed using nonlinear techniques. Specifically, the fractal dimension was computed from the EEG to determine how this voltage trace is related to the image sequencing. Our results showed that subjects visually stimulated by a series of mixed images (a randomized set of neutrally or negatively arousing images) had a significantly higher fractal dimension compared to subjects visually triggered by pure images (an organized set of either all neutral or all negatively arousing images). In addition, our results showed that subjects who performed better on memory recall had a higher fractal dimension computed from the EEG. Analysis of EKG also showed greater heart rate variability in subjects who viewed a series of mixed images compared to subjects visually triggered by pure images. Overall, our results show that the healthy brain and heart are responsive to environmental stimuli that promote adaptability, flexibility, and agility.In this paper, the dynamics of transformed nonlinear waves in the (2+1)-dimensional Ito equation are studied by virtue of the analysis of characteristic line and phase shift. First, the N-soliton solution is obtained via the Hirota bilinear method, from which the breath-wave solution is derived by changing values of wave numbers into complex forms. Then, the transition condition for the breath waves is obtained analytically. We show that the breath waves can be transformed into various nonlinear wave structures including the multi-peak soliton, M-shaped soliton, quasi-anti-dark soliton, three types of quasi-periodic waves, and W-shaped soliton. CFT8634 clinical trial The correspondence of the phase diagram for such nonlinear waves on the wave number plane is presented. The gradient property of the transformed solution is discussed through the wave number ratio. We study the mechanism of wave formation by analyzing the nonlinear superposition between a solitary wave component and a periodic wave component with different phases. The locality and oscillation of transformed waves can also be explained by the superposition mechanism. Furthermore, the time-varying characteristics of high-dimensional transformed waves are investigated by analyzing the geometric properties (angle and distance) of two characteristic lines of waves, which do not exist in (1+1)-dimensional systems. Based on the high-order breath-wave solutions, the interactions between those transformed nonlinear waves are investigated, such as the completely elastic mode, semi-elastic mode, inelastic mode, and collision-free mode. We reveal that the diversity of transformed waves, time-varying property, and shape-changed collision mainly appear as a result of the difference of phase shifts of the solitary wave and periodic wave components. Such phase shifts come from the time evolution as well as the collisions. Finally, the dynamics of the double shape-changed collisions are presented.