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We propose a set of goodness-of-fit tests for the semiparametric accelerated failure time (AFT) model, including an omnibus test, a link function test, and a functional form test. This set of tests is derived from a multi-parameter cumulative sum process shown to follow asymptotically a zero-mean Gaussian process. Its evaluation is based on the asymptotically equivalent perturbed version, which enables both graphical and numerical evaluations of the assumed AFT model. Empirical p-values are obtained using the Kolmogorov-type supremum test, which provides a reliable approach for estimating the significance of both proposed un-standardized and standardized test statistics. The proposed procedure is illustrated using the induced smoothed rank-based estimator but is directly applicable to other popular estimators such as non-smooth rank-based estimator or least-squares estimator.Our proposed methods are rigorously evaluated using extensive simulation experiments that demonstrate their effectiveness in maintaining a Type I error rate and detecting departures from the assumed AFT model in practical sample sizes and censoring rates. Furthermore, the proposed approach is applied to the analysis of the Primary Biliary Cirrhosis data, a widely studied dataset in survival analysis, providing further evidence of the practical usefulness of the proposed methods in real-world scenarios. To make the proposed methods more accessible to researchers, we have implemented them in the R package afttest, which is publicly available on the Comprehensive R Archieve Network.

For warm and hot dense plasma (WHDP), the ionization potential depression (IPD) is a key physical parameter in determining its ionization balance, therefore a reliable and universal IPD model is highly required to understand its microscopic material properties and resolve those existing discrepancies between the theoretical and experimental results. However, the weak temperature dependence of the nowadays IPD models prohibits their application through much of the WHDP regime, especially for the non-LTE dense plasma produced by short-pulse laser. In this work, we propose a universal non-LTE IPD model with the contribution of the inelastic atomic processes, and found that three-body recombination and collision ionization processes become important in determining the electron distribution and further affect the IPD in warm and dense plasma. The proposed IPD model is applied to treat the IPD experiments available in warm and hot dense plasmas and excellent agreements are obtained in comparison with those latest experiments of the IPD for Al plasmas with wide-range conditions of 70-700 eV temperature and 0.2-3 times of solid density, as well as a typical non-LTE system of hollow Al ions. We demonstrate that the present IPD model has a significant temperature dependence due to the consideration of the inelastic atomic processes. With the low computational cost and wide range applicability of WHDP, the proposed model is expected to provide a promising tool to study the ionization balance and the atomic processes as well as the related radiation and particle transports properties of a wide range of WHDP.

We propose a scheme of using two fixed frequency resonator couplers to tune the coupling strength between two Xmon qubits. The induced indirect qubit-qubit interactions by two resonators could offset with each other, and the direct coupling between two qubits are not necessarily for switching off. The small direct qubit-quibt coupling could effectively suppress the frequency interval between switching off and switching on, and globally suppress the second and third-order static ZZ couplings. The frequencies differences between resonator couplers and qubits readout resonators are very large, this might be helpful for suppressing the qubits readout errors. The cross-kerr resonant processes between a qubit and two resonators might induce pole and affect the crosstalks between qubits. The double resonator couplers could unfreeze the restrictions on capacitances and coupling strengths in the superconducting circuit, and it can also reduce the flux noises and globally suppress the crosstalks., Comment: 19 page, 8 figures Accepted by Physical Review A

An edge colouring of $K_n$ with $k$ colours is a Gallai $k$-colouring if it does not contain any rainbow triangle. Gy\'arf\'as, P\'alv\"olgyi, Patk\'os and Wales proved that there exists a number $g(k)$ such that $n\geq g(k)$ if and only if for any colour distribution sequence $(e_1,\cdots,e_k)$ with $\sum_{i=1}^ke_i=\binom{n}{2}$, there exist a Gallai $k$-colouring of $K_n$ with $e_i$ edges having colour $i$. They also showed that $\Omega(k)=g(k)=O(k^2)$ and posed the problem of determining the exact order of magnitude of $g(k)$. Feffer, Fu and Yan improved both bounds significantly by proving $\Omega(k^{1.5}/\log k)=g(k)=O(k^{1.5})$. We resolve this problem by showing $g(k)=\Theta(k^{1.5}/(\log k)^{0.5})$., Comment: This result is absorbed into my new paper arXiv:2309.05606 (coauthored with Zhuo Wu), which also studies the generalised version of this problem

Compared with random sampling, low-discrepancy sampling is more effective in covering the search space. However, the existing research cannot definitely state whether the impact of a low-discrepancy sample on particle swarm optimization (PSO) is positive or negative. Using Niderreiter's theorem, this study completes an error analysis of PSO, which reveals that the error bound of PSO at each iteration depends on the dispersion of the sample set in an expanded dimensional space. Based on this error analysis, an acceleration technique for PSO-type algorithms is proposed with low-discrepancy sampling in the expanded dimensional space. The acceleration technique can generate a low-discrepancy sample set with a smaller dispersion, compared with a random sampling, in the expanded dimensional space; it also reduces the error at each iteration, and hence improves the convergence speed. The acceleration technique is combined with the standard PSO and the comprehensive learning particle swarm optimization, and the performance of the improved algorithm is compared with the original algorithm. The experimental results show that the two improved algorithms have significantly faster convergence speed under the same accuracy requirement., Comment: 29 pages, 0 figures

GRB 221009A is the brightest gamma-ray burst ever detected since the discovery of this kind of energetic explosions. However, an accurate measurement of the prompt emission properties of this burst is very challenging due to its exceptional brightness. With joint observations of \textit{Insight}-HXMT and GECAM-C, we made an unprecedentedly accurate measurement of the emission during the first $\sim$1800 s of GRB 221009A, including its precursor, main emission (ME, which dominates the burst in flux), flaring emission and early afterglow, in the hard X-ray to soft gamma-ray band from $\sim$ 10 keV to $\sim$ 6 MeV. Based on the GECAM-C unsaturated data of the ME, we measure a record-breaking isotropic equivalent energy ($E_{\rm iso}$) of $\bf \sim 1.5 \times 10^{55}$ erg, which is about eight times the total rest-mass energy of the Sun. The early afterglow data require a significant jet break between 650 s and 1100 s, most likely at $\sim950$ s from the afterglow starting time $T_{AG}$, which corresponds to a jet opening angle of $\sim {0.7^\circ} \ (\eta_\gamma n)^{1/8}$, where $n$ is the ambient medium density in units of $\rm cm^{-3}$ and $\eta_\gamma$ is the ratio between $\gamma$-ray energy and afterglow kinetic energy. The beaming-corrected total $\gamma$-ray energy $E_{\gamma}$ is $\sim 1.15 \times10^{51} \ (\eta_\gamma n)^{1/4}$ erg, which is typical for long GRBs. These results suggest that this GRB may have a special central engine, which could launch and collimate a very narrowly beamed jet with an ordinary energy budget, leading to exceptionally luminous gamma-ray radiation per unit solid angle. Alternatively, more GRBs might have such a narrow and bright beam, which are missed by an unfavorable viewing angle or have been detected without distance measurement., Comment: Submitted to National Science Review. This paper is under press embargo, contact the corresponding author for details