Notes

Precursor-dependent structural diversity throughout luminescent carbonized polymer-bonded spots (CPDs): the nomenclature.
A complex mode-locking (entrainment) topology underlying the continuous stirred tank reactor reaction model subjected to impulsive perturbations is identified. Employing high-resolution stability diagrams, we exhibit the global structure of mode-locking oscillations and describe how they are interconnected and how their complexity unfolds with control parameters varying. The scenarios shown in the bi-parametric planes revealed that the skeleton of Arnold's tongues is organized according to the symmetric Stern-Brocot sum tree. Moreover, the mode-locking organization is controlled by an invariant torus (a pair of frequencies) initiated from Hopf bifurcations. Interestingly, the mode-locking order is unfolded in an elusive way, that is, in perfect agreement with the reciprocal of the Stern-Brocot sum tree. The findings reported here contribute to providing a description and classification of mode-locking oscillations for the impulsive system.Labyrinth chaos was discovered by Otto Rössler and René Thomas in their endeavor to identify the necessary mathematical conditions for the appearance of chaotic and hyperchaotic motion in continuous flows. Here, we celebrate their discovery by considering a single labyrinth walk system and an array of coupled labyrinth chaos systems that exhibit complex, chaotic behavior, reminiscent of chimera-like states, a peculiar synchronization phenomenon. We discuss the properties of the single labyrinth walk system and review the ability of coupled labyrinth chaos systems to exhibit chimera-like states due to the unique properties of their space-filling, chaotic trajectories, which amounts to elegant, hyperchaotic walks. Finally, we discuss further implications in relation to the labyrinth walk system by showing that even though it is volume-preserving, it is not force-conservative.Epilepsy is one of the most common neurological conditions affecting over 65 million people worldwide. Over one third of people with epilepsy are considered refractory they do not respond to drug treatments. For this significant cohort of people, surgery is a potentially transformative treatment. However, only a small minority of people with refractory epilepsy are considered suitable for surgery, and long-term seizure freedom is only achieved in half the cases. Recently, several computational approaches have been proposed to support presurgical planning. Typically, these approaches use a dynamic network model to explore the potential impact of surgical resection in silico. The network component of the model is informed by clinical imaging data and is considered static thereafter. This assumption critically overlooks the plasticity of the brain and, therefore, how continued evolution of the brain network post-surgery may impact upon the success of a resection in the longer term. In this work, we use a simplified dynamic network model, which describes transitions to seizures, to systematically explore how the network structure influences seizure propensity, both before and after virtual resections. We illustrate key results in small networks, before extending our findings to larger networks. We demonstrate how the evolution of brain networks post resection can result in a return to increased seizure propensity. Our results effectively determine the robustness of a given resection to possible network reconfigurations and so provide a potential strategy for optimizing long-term seizure freedom.In this paper, we present a presumably new approach in order to solve the time-fractional Drinfeld-Sokolov-Wilson system, which is based upon the Liouville-Caputo fractional integral (LCFI), the Caputo-Fabrizio fractional integral, and the Atangana-Baleanu fractional integral in the sense of the LCFI by using the Adomian decomposition method. We compare the approximate solutions with the exact solution (if available), and we find an excellent agreement between them. In the case of a non-integer order, we evaluate the residual error function, thereby showing that the order of the error is very small. In all of our calculations, we apply the software package, Mathematica (Version 9).A great variety of complex networks can be well represented as random graphs with some constraints for instance, a provided degree distribution, a smaller diameter, and a higher clustering coefficient. Among them, the degree distribution has attracted considerable attention from various science communities in the last few decades. In this paper, we focus mainly on a family of random graphs modeling complex networks that have an exponential degree distribution; i.e., P(k)∼ exp(αk), where k is the degree of a vertex, P(k) is a probability for choosing randomly a vertex with degree equal to k, and α is a constant. To do so, we first introduce two types of operations type-A operation and type-B operation. By both the helpful operations, we propose an available algorithm A for a seminal model to construct exactly solvable random graphs, which are able to be extended to a graph space S(p,pc,t) with probability parameters p and pc satisfying p+pc=1. Based on the graph space S(p,pc,t), we discuss several topological structure properties of interest on each member N(p,pc,t) itself and find model N(p,pc,t) to exhibit the small-world property and assortative mixing. In addition, we also report a fact that in some cases, two arbitrarily chosen members might have completely different other topological properties, such as the total number of spanning trees, although they share a degree distribution in common. Extensive experimental simulations are in strong agreement with our analytical results.Methods are presented to evaluate the entropy production rate in stochastic reactive systems. These methods are shown to be consistent with known results from nonequilibrium chemical thermodynamics. Moreover, it is proved that the time average of the entropy production rate can be decomposed into the contributions of the cycles obtained from the stoichiometric matrix in both stochastic processes and deterministic systems. These methods are applied to a complex reaction network constructed on the basis of Rössler's reinjection principle and featuring chemical chaos.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. The correspondence of the phase diagram for such nonlinear waves on the wave number plane is presented. Conteltinib price 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.
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