Some chaotic and a series of stochastic neural firings are multimodal. Stochastic multimodal firing patterns are of special importance because they indicate a possible utility of noise. A number of previous studies confused the dynamics of chaotic and stochastic multimodal firing patterns. The confusion resulted partly from inappropriate interpretations of estimations of nonlinear time series measures. With deliberately chosen examples the present paper introduces strategies and methods of identification of stochastic firing patterns from chaotic ones. Aided by theoretical simulation we show that the stochastic multimodal firing patterns result from the effects of noise on neuronal systems near to a bifurcation between two simpler attractors, such as a point attractor and a limit cycle attractor or two limit cycle attractors. In contrast, the multimodal chaotic firing trains are generated by the dynamics of a specific strange attractor. Three systems were carefully chosen to elucidate these two mechanisms. An experimental neural pacemaker model and the Chay mathematical model were used to show the stochastic dynamics, while the deterministic Wang model was used to show the deterministic dynamics. The usage and interpretation of nonlinear time series measures were systematically tested by applying them to firing trains generated by the three systems. We successfully identified the distinct differences between stochastic and chaotic multimodal firing patterns and showed the dynamics underlying two categories of stochastic firing patterns. The first category results from the effects of noise on the neuronal system near a Hopf bifurcation. The second category results from the effects of noise on the period-adding bifurcation between two limit cycles. Although direct application of nonlinear measures to interspike interval series of these firing trains misleadingly implies chaotic properties, definition of eigen events based on more appropriate judgments of the underlying dynamics leads to accurate identifications of the stochastic properties.
Two-dimensional (2D) materials are promising candidates for uses in next-generation electronic and optoelectronic devices. However, only a few high-quality 2D materials have been mechanically exfoliated to date. One of the critical issues is that the exfoliability of 2D materials from their bulk precursors is unknown. To assess the exfoliability of potential 2D materials from their bulk counterparts, we derived an elasticity-based-exfoliability measure based on an exfoliation mechanics model. The proposed measure has a clear physical meaning and is universally applicable to all material systems. We used this measure to calculate the exfoliability of 10,812 crystals having a first-principles calculated elastic tensor. By setting the threshold values for easy and potential exfoliation based on already-exfoliated materials, we predicted 58 easily exfoliable bulk crystals and 90 potentially exfoliable bulk crystals for 2D materials. As evidence, a topology-based algorithm indicates that there is no interlayer bonding topology for 93% predicted exfoliable bulk crystals, and the analysis on packing ratios shows that 99% predicted exfoliable bulk crystals exhibit a relatively low packing ratio value. Moreover, literature survey shows that 34 predicted exfoliable bulk crystals have been experimentally exfoliated into 2D materials. In addition, the characteristics of these predicted 2D materials were discussed for practical use of such materials.
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