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Low-Energy Electron Injury to Condensed-Phase Genetic and it is Ingredients.
How the giant component of a network disappears under attacking nodes or links addresses a key aspect of network robustness, which can be framed into percolation problems. Various strategies to select the node to be deactivated have been studied in the literature, for instance, a simple random failure or high-degree adaptive (HDA) percolation. BetaLapachone Recently, a new attack strategy based on a quantity called collective-influence (CI) has been proposed from the perspective of optimal percolation. By successively deactivating the node having the largest CI-centrality value, it was shown to be able to dismantle a network more quickly and abruptly than many of the existing methods. In this paper, we focus on the critical behaviors of the percolation processes following degree-based attack and CI-based attack on random networks. Through extensive Monte Carlo simulations assisted by numerical solutions, we estimate various critical exponents of the HDA percolation and those of the CI percolations. Our results show that these attack-type percolation processes, despite displaying apparently more abrupt collapse, nevertheless exhibit standard mean-field critical behaviors at the percolation transition point. We further discover an extensive degeneracy in top-centrality nodes in both processes, which may provide a hint for understanding the observed results.We consider the interacting processes between two diseases on multiplex networks, where each node can be infected by two interacting diseases with general interacting schemes. A discrete-time individual-based probability model is rigorously derived. By the bifurcation analysis of the equilibrium, we analyze the outbreak condition of one disease. The theoretical predictions are in good agreement with discrete-time stochastic simulations on scale-free networks. Furthermore, we discuss the influence of network overlap and dynamical parameters on the epidemic dynamical behaviors. The simulation results show that the network overlap has almost no effect on both epidemic threshold and prevalence. We also find that the epidemic threshold of one disease does not depend on all system parameters. Our method offers an analytical framework for the spreading dynamics of multiple processes in multiplex networks.The ongoing novel coronavirus epidemic was announced a pandemic by the World Health Organization on March 11, 2020, and the Government of India declared a nationwide lockdown on March 25, 2020 to prevent community transmission of the coronavirus disease (COVID)-19. Due to the absence of specific antivirals or vaccine, mathematical modeling plays an important role in better understanding the disease dynamics and in designing strategies to control the rapidly spreading infectious disease. In our study, we developed a new compartmental model that explains the transmission dynamics of COVID-19. We calibrated our proposed model with daily COVID-19 data for four Indian states, namely, Jharkhand, Gujarat, Andhra Pradesh, and Chandigarh. We study the qualitative properties of the model, including feasible equilibria and their stability with respect to the basic reproduction number R0. The disease-free equilibrium becomes stable and the endemic equilibrium becomes unstable when the recovery rate of infected individuals increases, but if the disease transmission rate remains higher, then the endemic equilibrium always remains stable. For the estimated model parameters, R0>1 for all four states, which suggests the significant outbreak of COVID-19. Short-time prediction shows the increasing trend of daily and cumulative cases of COVID-19 for the four states of India.The present study derives the two-dimensional distribution of streamwise flow velocity in open channels using the Tsallis relative entropy, where the probability density function (PDF) based on the principle of maximum entropy (POME) is selected as the prior PDF. Here, we incorporate the moment constraints based on the normalization constraint, hydrodynamic transport of mass, and momentum through a cross section of an open channel for the formulation of the velocity profile. The minimization of the Tsallis relative entropy produces a nonlinear differential equation for velocity, which is solved using a non-perturbation approach along with the Padé approximation technique. We define two new parameters in terms of the Lagrange multipliers and the entropy index for assessing the velocity profile, which are calculated by solving a system of nonlinear equations using an optimization method. For different test cases of the flow in open channels, we consider a selected set of laboratory and river data for validating the proposed model. 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. 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.The control effects on the convection dynamics in a viscoelastic fluid-saturated porous medium heated from below and cooled from above are studied. A truncated Galerkin expansion was applied to balance equations to obtain a four-dimensional generalized Lorenz system. The dynamical behavior is mainly characterized by the Lyapunov exponents, bifurcation, and isospike diagrams. The results show that within a range of moderate and high Rayleigh numbers, proportional controller gain is found to enhance the stabilization and destabilization effects on the thermal convection. Furthermore, due to the effect of viscoelasticity, the system exhibits remarkable topological structures of regular regions embedded in chaotic domains.
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