Universal competitive spectral scaling from the critical non-Hermitian skin effect

Recently, it was discovered that certain non-Hermitian systems can exhibit qualitative different properties at different system sizes, such as being gapless at small sizes and having topological edge modes at large sizes $L$. This dramatic system size sensitivity is known as the critical non-Hermitian skin effect (cNHSE), and occurs due to the competition between two or more non-Hermitian pumping channels. In this work, we rigorously develop the notion of a size-dependent generalized Brillouin zone (GBZ) in a general multi-component cNHSE model ansatz, and found that the GBZ exhibits a universal $a+b^{1/(L+1)}$ scaling behavior. In particular, we provided analytical estimates of the scaling rate $b$ in terms of model parameters, and demonstrated their good empirical fit with two paradigmatic models, the coupled Hatano-Nelson model with offset, and the topologically coupled chain model with offset. We also provided analytic result for the critical size $L_c$, below which cNHSE scaling is frozen. The cNHSE represents the result of juxtaposing different channels for bulk-boundary correspondence breaking, and can be readily demonstrated in non-Hermitian metamaterials and circuit arrays

Table_1_Probabilistic Optimal Power Flow Calculation Method Based on Adaptive Diffusion Kernel Density Estimation.docx

To accurately evaluate the influence of the uncertainty and correlation of photovoltaic (PV) output and load on the running state of power system, a probabilistic optimal power flow (POPF) calculation method based on adaptive diffusion kernel density estimation is proposed in this paper. First, based on the distribution characteristics of PV output, the adaptive diffusion kernel density estimation model of PV output is constructed, which can transform the kernel function into a linear diffusion process to achieve self-tuning of the bandwidth of the nuclear density estimation. This model can fit the distribution of arbitrary distribution of PV power, improve the local adaptability of PV output model, and reflect the uncertainty and volatility of PV output more accurately. Therefore, it can provide more accurate input for POPF calculation. Second, the Kendall rank correlation coefficient and the least Euclidean distance are used as correlation measure and index of fitting to select the optimal Copula function, and the joint probability distribution model of PV output and load is constructed. After extracting the correlated PV output and load samples, a POPF calculation method considering the correlation of PV output and load is proposed by using genetic algorithm (GA), which takes the lowest fuel cost of power generation as the objective function. Finally, simulation studies are conducted with the measured data of a PV power plant of China and the IEEE 30-bus power system. The results show that considering the correlation between PV output and load can improve the accuracy of POPF calculation and effectively reduce the power generation cost of the power system.</p

Energy landscape with the variables of RMSD and Rg and average structure for dsRNA.

<p>A: apo-dsRNA; B: PAZ-dsRNA; C: KH-dsRNA; D: complex; E: average structure of dsRNA for apo-dsRNA; F: average structure of dsRNA for PAZ-dsRNA; G: average structure of dsRNA for KH-dsRNA; H: average structure of dsRNA for complex.</p

C5’ variation of holo and apo states for dsRNA in five systems.

<p>C5’ variation of holo and apo states for dsRNA in five systems.</p

Summary of simulation conditions.

<p>Summary of simulation conditions.</p

Distance between Phe69 of PAZ and U12 or U12U13 of dsRNA and average structure of PAZ-dsRNA and quadruqle complex.

<p>A: Distance between Phe69 of PAZ and the base of 3′ terminal of mRNA, U13 in green and U12/U13 in red, respectively. B: The detailed structure near U12/U13 and Phe 69.</p

Alignment between apo-dsRNA and the quadruple complex.

<p>The number of base pairs is marked.</p

microRNA up-regulation translation mechanism.

<p>microRNA up-regulation translation mechanism.</p

Distance between GXXG motif of KH and A14 of microRNA and structure alignment for WT and mutant KH-dsRNA.

<p>A: Distance between A14 of microRNA and I(N)GKNG motif of KH for WT and mutant KH-dsRNA. B: KH-domain based alignment of WT (blue) and mutant (red) dsRNA-KH complex. C: The detailed interaction between GXXG motif and dsRNA. I/N304–308 is shown in green stick.</p

Interaction and alignment of structure for KH-dsRNA and quadruple complex.

<p>A: Hydrogen bond, hydrophobic, and electrostatic interactions between KH domain and dsRNA for KH-dsRNA and quadruple complex, blue for complex and red for dsRNA-KH. Significant differences for interactions indicate different binding modes. B: The alignment of dsRNA-KH and quadruple complex, blue for complex and red for dsRNA-KH.</p