Complexity growth rates for AdS black holes in massive gravity and f(R)f(R) gravity

The "complexity = action" duality states that the quantum complexity is equal to the action of the stationary AdS black holes within the Wheeler-DeWitt patch at late time approximation. We compute the action growth rates of the neutral and charged black holes in massive gravity and the neutral, charged and Kerr-Newman black holes in $f(R)$ gravity to test this conjecture. Besides, we investigate the effects of the massive graviton terms, higher derivative terms and the topology of the black hole horizon on the complexity growth rate.Comment: 11 pages, no figur

Interaction between negative and positive index medium waveguides

The coupling between negative and positive index medium waveguides is investigated theoretically in this paper. A coupled mode theory is developed for such a waveguide system and its validity is verified. Interesting phenomena in the coupled waveguides are demonstrated, which occur in the case when the negative index medium waveguide in isolation guides its mode backward. A new type of coupled mode solution that varies exponentially with the coupling length is found in the special case when the propagation constants of two individual waveguides are nearly the same. A coupler operating in this case is insensitive to the coupling length, and its coupling efficiency can reach 100% as long as the coupling length is long enough. However, when the propagation constants of the two individual waveguides differ greatly, the coupled mode solution is still a periodic function of the coupling length, but the coupled power is output backward. In addition, the modes in the composite waveguide system are also studied using the coupled mode theory, and their fundamental properties are revealed.Comment: 7 page

Study on the Rheological Properties and Constitutive Model of Shenzhen Mucky Soft Soil

In order to obtain the basic parameters of numerical analysis about the time-space effect of the deformation occurring in Shenzhen deep soft-soil foundation pit, a series of triaxial consolidated-undrained shear rheology tests on the peripheral mucky soft soil of a deep foundation pit support were performed under different confining pressures. The relations between the axial strain of the soil and time, as well as between the pore-water pressure of the soil and time, were achieved, meanwhile on the basis of analyzing the rheological properties of the soil, the relevant rheological models were built. Analysis results were proved that the rheology of Shenzhen mucky soft soil was generally viscous, elastic, and plastic, and had a low yield stress between 90 and 150 kPa. The increase in pore-water pressure made the rheological time effect of the mucky soft soil more remarkable. Thus, the drainage performance in practical engineering should be improved to its maximum possibility extent to decrease the soft-soil rheological deformation. Lastly, a six-component extended Burgers model was employed to fit the test results and the parameters of the model were determined. Findings showed that the extended Burgers model could satisfactorily simulate the various rheological stages of the mucky soft soil. The constitutive model and the determination of its parameters can be served as a foundation for the time-space effect analysis on the deformation of deep soft-soil foundation pits

Convergence Theory of Learning Over-parameterized ResNet: A Full Characterization

ResNet structure has achieved great empirical success since its debut. Recent work established the convergence of learning over-parameterized ResNet with a scaling factor $\tau=1/L$ on the residual branch where $L$ is the network depth. However, it is not clear how learning ResNet behaves for other values of $\tau$. In this paper, we fully characterize the convergence theory of gradient descent for learning over-parameterized ResNet with different values of $\tau$. Specifically, with hiding logarithmic factor and constant coefficients, we show that for $\tau\le 1/\sqrt{L}$ gradient descent is guaranteed to converge to the global minma, and especially when $\tau\le 1/L$ the convergence is irrelevant of the network depth. Conversely, we show that for $\tau>L^{-\frac{1}{2}+c}$, the forward output grows at least with rate $L^c$ in expectation and then the learning fails because of gradient explosion for large $L$. This means the bound $\tau\le 1/\sqrt{L}$ is sharp for learning ResNet with arbitrary depth. To the best of our knowledge, this is the first work that studies learning ResNet with full range of $\tau$.Comment: 31 page

Effects of Dynamic Icons on the Perceived Usability in the Travel App

With the advancements in hardware and information technology, the use of dynamic icons in travel app interfaces to convey information has become increasingly common. The goal is to provide users with a novel experience that was not available in the static interfaces of the past. However, it remains unclear whether the availability and utilization of dynamic icons actually enhance the usability of apps and if it is done with genuine consideration for users\u27 benefit. This study aims to investigate how users perceive and use dynamic icons in the context of human-computer interaction, using a travel app as the research object. We propose a user-centered subjective and objective hybrid evaluation methodology to examine the perceived usability of dynamic icons, taking into account different evaluation characteristics at various usability levels. Our results indicate no significant statistical difference between the perceived usability of dynamic icons and static icons. We employed two indicators, perceived ease and subjective priority, to evaluate the perceived usability of dynamic icons. The findings show that the perceived ease of dynamic icons is higher than that of static icons, with an increase of 3.72% (I) and 3.09% (II) in respective studies, but with a reduction of 13.19% compared to static icons in study III. We conclude that although the perceived usability of dynamic icons may not be significantly different from static icons, they exhibit higher objective usability in users\u27 decision-making behavior