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Besides, a comparison is made between the present model and the existing equation based on the Tsallis entropy. The study concludes that the inclusion of the POME-based prior significantly improves the velocity profile. Overall, the proposed work shows the potential of the Tsallis relative entropy in the context of application to open the channel flow velocity.The propagation of light pulses in dual-core nonlinear optical fibers is studied using a model proposed by Sakaguchi and Malomed. The system consists of a supercritical complex Ginzburg-Landau equation coupled to a linear equation. Our analysis includes single standing and walking solitons as well as walking trains of 3, 5, 6, and 12 solitons. Zunsemetinib datasheet For the characterization of the different scenarios, we used ensemble-averaged square displacement of the soliton trajectories and time-averaged power spectrum of the background waves. Power law spectra, indicative of turbulence, were found to be associated with random walks. The number of solitons (or their separations) can trigger anomalous random walks or totally suppress the background waves.The first aim of this paper is to establish the well-posedness for a type of Caputo fractional stochastic differential equations, and we obtain the global existence and uniqueness of solutions under some conditions consistent with the classic (integer order) stochastic differential equations. The second aim is that we consider the continuity of solutions on the fractional order of those equations.A novel generalization of the Winfree model of globally coupled phase oscillators, representing phase reduction under finite coupling, is studied analytically. We consider interactions through a non-infinitesimal (or finite) phase-response curve (PRC), in contrast to the infinitesimal PRC of the original model. For a family of non-infinitesimal PRCs, the global dynamics is captured by one complex-valued ordinary differential equation resorting to the Ott-Antonsen ansatz. The phase diagrams are thereupon obtained for four illustrative cases of non-infinitesimal PRC. Bistability between collective synchronization and full desynchronization is observed in all cases.Over the past decade, the blockchain technology and its bitcoin cryptocurrency have received considerable attention. Bitcoin has experienced significant price swings in daily and long-term valuations. In this paper, we propose a partial differential equation (PDE) model on the bitcoin transaction network for forecasting the bitcoin price movement. Through analysis of bitcoin subgraphs or chainlets, the PDE model captures the influence of transaction patterns on the bitcoin price over time and combines the effect of all chainlet clusters. In addition, Google Trends index is incorporated to the PDE model to reflect the effect of the bitcoin market sentiment. The experiment results demonstrate that the PDE model is capable of forecasting the bitcoin price movement. The paper is the first attempt to apply a PDE model to the bitcoin transaction network for forecasting.Understanding the geography of society represents a challenge for social and economic sciences. The recent availability of data from social media enables the observation of societies at a global scale. In this paper, we study the geographical structure of the Twitter communication network at the global scale. We find a complex structure where self-organized patches with clear cultural, historical, and administrative boundaries are manifested and first-world economies centralize information flows. These patches unveil world regions that are socially closer to each other with direct implications for processes of collective learning and identity creation.The role of sequence complexity in 23 051 somatic missense mutations including 73 well-known mutation hotspots across 22 major cancers was studied in human TP53 proteins. A role for sequence complexity in TP53 protein mutations is suggested since (i) the mutation rate significantly increases in low amino acid pair bias complexity; (ii) probability distribution complexity increases following single point substitution mutations and strikingly increases after mutation at the mutation hotspots including six detectable hotspot mutations (R175, G245, R248, R249, R273, and R282); and (iii) the degree of increase in distribution complexity is significantly correlated with the frequency of missense mutations (r = -0.5758, P  less then  0.0001) across 20 major types of solid tumors. These results are consistent with the hypothesis that amino acid pair bias and distribution probability may be used as novel measures for protein sequence complexity, and the degree of complexity is related to its susceptibility to mutation, as such, it may be used as a predictor for modeling protein mutations in human cancers.A novel hybrid dynamical system comprising a continuous and a discrete state is introduced and shown to exhibit chaotic dynamics. The system includes an unstable first-order filter subject to asynchronous switching of a set point according to a feedback rule. Regular samples of the continuous state yield a one-dimensional return map that is a tent function. An exact analytic solution is derived using a nonlinear transformation of a previously solved chaotic oscillator. Conjugacy to a symbolic dynamics is shown, and a practical realization of the system in an electronic circuit is demonstrated.We consider the numerical solution of a third-order Falkner-Skan-like boundary value problem arising in boundary layer theory. The problem is defined on a semi-infinite interval [0,∞) with a condition given at ∞. We first transform the problem into a second-order boundary value problem defined on a finite interval [γ,1]. To solve the resulting boundary value problem, we developed an iterative finite-difference scheme based on Newton's quasilinearization. At every step, the linearized differential equation is approximated using the finite-difference method. Numerical results will be presented to demonstrate the efficiency of the method and will be compared with other results presented in the literature.