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The double-spike MC TIMS dimension procedure for low-amount Los angeles isotopic examination regarding restricted natural tissue trials.
The understanding of how synchronization in directed networks is influenced by structural changes in network topology is far from complete. While the addition of an edge always promotes synchronization in a wide class of undirected networks, this addition may impede synchronization in directed networks. In this paper, we develop the augmented graph stability method, which allows for explicitly connecting the stability of synchronization to changes in network topology. The transformation of a directed network into a symmetrized-and-augmented undirected network is the central component of this new method. This transformation is executed by symmetrizing and weighting the underlying connection graph and adding new undirected edges with consideration made for the mean degree imbalance of each pair of nodes. These new edges represent "non-existent ties" in the original directed network and often control the location of critical nodes whose directed connections can be altered to manipulate the stability of synchronization in a desired way. In particular, we show that the addition of small-world shortcuts to directed networks, which makes "non-existent ties" disappear, can worsen the synchronizability, thereby revealing a destructive role of small-world connections in directed networks. An extension of our method may open the door to studying synchronization in directed multilayer networks, which cannot be effectively handled by the eigenvalue-based methods.We propose and study a simple model for the evolution of political opinion through a population. The model includes a nonlinear term that causes individuals with more extreme views to be less receptive to external influence. Such a term was suggested in 1981 by Cobb in the context of a scalar-valued diffusion equation, and recent empirical studies support this modeling assumption. Here, we use the same philosophy in a network-based model. This allows us to incorporate the pattern of pairwise social interactions present in the population. We show that the model can admit two distinct stable steady states. This bi-stability property is seen to support polarization and can also make the long-term behavior of the system extremely sensitive to the initial conditions and to the precise connectivity structure. Computational results are given to illustrate these effects.The photothermal phenomenon resulting in thermal lens formation in liquid media involves complex molecular dynamics responsible for temperature and refractive index variation. As a thermodynamic system, the entropy of the medium also changes. In this paper, the time series and phase portrait analysis of the thermal lens signal is carried out to understand the molecular dynamics. The study reveals the increase in complexity, disorder, and antipersistance nature through fractal dimension, sample entropy, and Hurst exponent, respectively. The analysis of the signal on segmentation reveals the evolution of sample entropy and the stochastic nature of the system with time. The phase portrait analysis also is in support of these observations. Thus, the study suggests that the temporal evolution of sample entropy is similar to the temperature-dependent refractive index.In this paper, a novel non-autonomous chaotic system with rich dynamical behaviors is proposed by introducing parametric excitation to a Lorenz-like system, and the effect of the initial value of the excitation system on the resulting system dynamics is then thoroughly investigated. The attractors resulting from the proposed chaotic system will enter different oscillating states or have topological change when the initial value varies. Furthermore, some novel bursting oscillations and bifurcation mechanism are revealed. Stability and bifurcation of the proposed 3D non-autonomous system are comprehensively investigated to analyze the causes of the observed dynamics through a range of analytical methods, including bifurcation diagram, Lyapunov exponent spectrum, and sequence and phase diagrams. Software simulation and hardware experimentation are conducted in this study, which verify the dynamic behaviors of the proposed chaotic system. This study will create a new perspective and dimension of perceiving non-autonomous chaotic systems and exploring their applicability in real-world engineering applications.Data mining is routinely used to organize ensembles of short temporal observations so as to reconstruct useful, low-dimensional realizations of an underlying dynamical system. In this paper, we use manifold learning to organize unstructured ensembles of observations ("trials") of a system's response surface. We have no control over where every trial starts, and during each trial, operating conditions are varied by turning "agnostic" knobs, which change system parameters in a systematic, but unknown way. As one (or more) knobs "turn," we record (possibly partial) observations of the system response. We demonstrate how such partial and disorganized observation ensembles can be integrated into coherent response surfaces whose dimension and parametrization can be systematically recovered in a data-driven fashion. The approach can be justified through the Whitney and Takens embedding theorems, allowing reconstruction of manifolds/attractors through different types of observations. We demonstrate our approach by organizing unstructured observations of response surfaces, including the reconstruction of a cusp bifurcation surface for hydrogen combustion in a continuous stirred tank reactor. Finally, we demonstrate how this observation-based reconstruction naturally leads to informative transport maps between the input parameter space and output/state variable spaces.Direct numerical simulations of a liquid metal filling the gap between two concentric spheres are presented. The flow is governed by the interplay between the rotation of the inner sphere (measured by the Reynolds number Re) and a weak externally applied axial magnetic field (measured by the Hartmann number Ha). By varying the latter, a rich variety of flow features, both in terms of spatial symmetry and temporal dependence, is obtained. Flows with two or three independent frequencies describing their time evolution are found as a result of Hopf bifurcations. AZD9668 supplier They are stable on a sufficiently large interval of Hartmann numbers where regions of multistability of two, three, and even four types of these different flows are detected. The temporal character of the solutions is analyzed by means of an accurate frequency analysis and Poincaré sections. An unstable branch of flows undergoing a period doubling cascade and frequency locking of three-frequency solutions is described as well.
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