Hard X-ray emission cutoff in anomalous X-ray pulsar 4U 0142+61 detected by INTEGRAL

The anomalous X-ray pulsar 4U 0142+61 was studied by the INTEGRAL observations. The hard X-ray spectrum of 18 -- 500 keV for 4U 0142+61 was derived using near 9 years of INTEGRAL/IBIS data. We obtained the average hard X-ray spectrum of 4U 0142+61 with all available data. The spectrum of 4U 0142+61 can be fitted with a power-law with an exponential high energy cutoff. This average spectrum is well fitted with a power-law of $\Gamma\sim 0.51\pm 0.11$ plus a cutoff energy at $128.6\pm 17.2$ keV. The hard X-ray flux of the source from 20 -- 150 keV showed no significant variations (within 20$\%$) from 2003 -- 2011. The spectral profiles have some variability in nine years: photon index varied from 0.3 -- 1.5, and cutoff energies of 110 -- 250 keV. The detection of the high energy cutoff around 130 keV shows some constraints on the radiation mechanisms of magnetars and possibly probes the differences between magnetar and accretion models for these special class of neutron stars. Future HXMT observations could provide stronger constraints on the hard X-ray spectral properties of this source and other magnetar candidates.Comment: 9 pages, 5 figures, 2 tables, figures are updated, new data are added, conclusion does not change, to be published in RA

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

Adjusting inverse regression for predictors with clustered distribution

A major family of sufficient dimension reduction (SDR) methods, called inverse regression, commonly require the distribution of the predictor $X$ to have a linear $E(X|\beta^\mathsf{T}X)$ and a degenerate $\mathrm{var}(X|\beta^\mathsf{T}X)$ for the desired reduced predictor $\beta^\mathsf{T}X$. In this paper, we adjust the first and second-order inverse regression methods by modeling $E(X|\beta^\mathsf{T}X)$ and $\mathrm{var}(X|\beta^\mathsf{T}X)$ under the mixture model assumption on $X$, which allows these terms to convey more complex patterns and is most suitable when $X$ has a clustered sample distribution. The proposed SDR methods build a natural path between inverse regression and the localized SDR methods, and in particular inherit the advantages of both; that is, they are $\sqrt{n}$-consistent, efficiently implementable, directly adjustable under the high-dimensional settings, and fully recovering the desired reduced predictor. These findings are illustrated by simulation studies and a real data example at the end, which also suggest the effectiveness of the proposed methods for nonclustered data

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