Condensation of Eigen Microstate in Statistical Ensemble and Phase Transition

In a statistical ensemble with $M$ microstates, we introduce an $M \times M$ correlation matrix with the correlations between microstates as its elements. Using eigenvectors of the correlation matrix, we can define eigen microstates of the ensemble. The normalized eigenvalue by $M$ represents the weight factor in the ensemble of the corresponding eigen microstate. In the limit $M \to \infty$, weight factors go to zero in the ensemble without localization of microstate. The finite limit of weight factor when $M \to \infty$ indicates a condensation of the corresponding eigen microstate. This indicates a phase transition with new phase characterized by the condensed eigen microstate. We propose a finite-size scaling relation of weight factors near critical point, which can be used to identify the phase transition and its universality class of general complex systems. The condensation of eigen microstate and the finite-size scaling relation of weight factors have been confirmed by the Monte Carlo data of one-dimensional and two-dimensional Ising models.Comment: 9 pages, 16 figures, accepted for publication in Sci. China-Phys. Mech. Astro

Observation of vacancy-induced suppression of electronic cooling in defected graphene

Previous studies of electron-phonon interaction in impure graphene have found that static disorder can give rise to an enhancement of electronic cooling. We investigate the effect of dynamic disorder and observe over an order of magnitude suppression of electronic cooling compared with clean graphene. The effect is stronger in graphene with more vacancies, confirming its vacancy-induced nature. The dependence of the coupling constant on the phonon temperature implies its link to the dynamics of disorder. Our study highlights the effect of disorder on electron-phonon interaction in graphene. In addition, the suppression of electronic cooling holds great promise for improving the performance of graphene-based bolometer and photo-detector devices.Comment: 13 pages, 4 figure

Weighted-Sampling Audio Adversarial Example Attack

Recent studies have highlighted audio adversarial examples as a ubiquitous threat to state-of-the-art automatic speech recognition systems. Thorough studies on how to effectively generate adversarial examples are essential to prevent potential attacks. Despite many research on this, the efficiency and the robustness of existing works are not yet satisfactory. In this paper, we propose~\textit{weighted-sampling audio adversarial examples}, focusing on the numbers and the weights of distortion to reinforce the attack. Further, we apply a denoising method in the loss function to make the adversarial attack more imperceptible. Experiments show that our method is the first in the field to generate audio adversarial examples with low noise and high audio robustness at the minute time-consuming level.Comment: https://aaai.org/Papers/AAAI/2020GB/AAAI-LiuXL.9260.pd

Defining Urban Boundaries by Characteristic Scales

Defining an objective boundary for a city is a difficult problem, which remains to be solved by an effective method. Recent years, new methods for identifying urban boundary have been developed by means of spatial search techniques (e.g. CCA). However, the new algorithms are involved with another problem, that is, how to determine the characteristic radius of spatial search. This paper proposes new approaches to looking for the most advisable spatial searching radius for determining urban boundary. We found that the relationships between the spatial searching radius and the corresponding number of clusters take on an exponential function. In the exponential model, the scale parameter just represents the characteristic length that we can use to define the most objective urban boundary objectively. Two sets of China's cities are employed to test this method, and the results lend support to the judgment that the characteristic parameter can well serve for the spatial searching radius. The research may be revealing for making urban spatial analysis in methodology and implementing identification of urban boundaries in practice.Comment: 26 pages, 5 figures, 7 table

The linear dependence problem for power linear maps

AbstractLet Bl, l=1,…,k, be m×nl complex matrices and let x[l]∈Cnl,l=1,…,k, be complex vector variables. We show that the components of the map H=(B1x[1])(d1)∘⋯∘(Bkx[k])(dk) are linearly dependent over C if and only if det(B1B1∗)(d1)∘⋯∘(BkBk∗)(dk)=0, where ∘ means the Hadamard product, X∗ and X(d) denote the conjugate transpose and the dth Hadamard power of a matrix X respectively. Connections are established between the Homogenous Dependence Problem (HDP(n,d)), which arises in the study of the Jacobian Conjecture, and the dependence problem for power linear maps (PLDP(n,d)). An algorithm is given to compute counterexamples to PLDP(n,d) from those to HDP(n,d), and counterexamples to PLDP(n,3) are obtained for all n⩾67