A primal-dual interior-point relaxation method with adaptively updating barrier for nonlinear programs

Based on solving an equivalent parametric equality constrained mini-max problem of the classic logarithmic-barrier subproblem, we present a novel primal-dual interior-point relaxation method for nonlinear programs. In the proposed method, the barrier parameter is updated in every step as done in interior-point methods for linear programs, which is prominently different from the existing interior-point methods and the relaxation methods for nonlinear programs. Since our update for the barrier parameter is autonomous and adaptive, the method has potential of avoiding the possible difficulties caused by the unappropriate initial selection of the barrier parameter and speeding up the convergence to the solution. Moreover, it can circumvent the jamming difficulty of global convergence caused by the interior-point restriction for nonlinear programs and improve the ill conditioning of the existing primal-dual interiorpoint methods as the barrier parameter is small. Under suitable assumptions, our method is proved to be globally convergent and locally quadratically convergent. The preliminary numerical results on a well-posed problem for which many line-search interior-point methods fail to find the minimizer and a set of test problems from the CUTE collection show that our method is efficient.Comment: submitted to SIOPT on April 14, 202

Draft genome sequence of the Tibetan antelope

The Tibetan antelope (Pantholops hodgsonii) is endemic to the extremely inhospitable high-altitude environment of the Qinghai-Tibetan Plateau, a region that has a low partial pressure of oxygen and high ultraviolet radiation. Here we generate a draft genome of this artiodactyl and use it to detect the potential genetic bases of highland adaptation. Compared with other plain-dwelling mammals, the genome of the Tibetan antelope shows signals of adaptive evolution and gene-family expansion in genes associated with energy metabolism and oxygen transmission. Both the highland American pika, and the Tibetan antelope have signals of positive selection for genes involved in DNA repair and the production of ATPase. Genes associated with hypoxia seem to have experienced convergent evolution. Thus, our study suggests that common genetic mechanisms might have been utilized to enable high-altitude adaptation

Observation of GRB 221009A early afterglow in X/γ\gamma-ray energy band

The early afterglow of a Gamma-ray burst (GRB) can provide critical information on the jet and progenitor of the GRB. The extreme brightness of GRB 221009A allows us to probe its early afterglow in unprecedented detail. In this letter, we report comprehensive observation results of the early afterglow of GRB 221009A (from $T_0$+660 s to $T_0$+1860 s, where $T_0$ is the \textit{Insight}-HXMT/HE trigger time) in X/$\gamma$-ray energy band (from 20 keV to 20 MeV) by \textit{Insight}-HXMT/HE, GECAM-C and \textit{Fermi}/GBM. We find that the spectrum of the early afterglow in 20 keV-20 MeV could be well described by a cutoff power-law with an extra power-law which dominates the low and high energy bands respectively. The cutoff power-law $E_{\rm peak}$ is $\sim$ 30 keV and the power-law photon index is $\sim$ 1.8 throughout the early afterglow phase. By fitting the light curves in different energy bands, we find that a significant achromatic break (from keV to TeV) is required at $T_0$ + 1246$^{+27}_{-26}$ s (i.e. 1021 s since the afterglow starting time $T_{\rm AG}$=$T_0$+225 s), providing compelling evidence of a jet break. Interestingly, both the pre-break and post-break decay slopes vary with energy, and these two slopes become closer in the lower energy band, making the break less identifiable. Intriguingly, the spectrum of the early afterglow experienced a slight hardening before the break and a softening after the break. These results provide new insights into the understanding of this remarkable GRB.Comment: Accepted for publication in ApJ Letters on 19-Jan-2024, 11 pages, 7 figures and 2 table

Combining Image Recognition and Simulation To Reproduce the Adsorption/Desorption Behaviors of Shale Gas

Shale gas stored in deep shale is in a supercritical state. Therefore, it is necessary to study the adsorption and desorption properties of supercritical shale gas. To accurately determine the state of methane (CH4) in the pores of deep shale, the fractal characteristics of several shale samples drilled at a depth of 2650 m are analyzed using scanning electron microscopy (SEM) and image analysis. We find nanopores with different fractal features in the shale. The effects of adsorption energy and substrate strain on adsorption capacity are clarified. The virial coefficients of CH4 are obtained by molecular dynamics (MD) simulations and are consistent with the experiment. The adsorption and desorption of CH4 in different fractal nanopores are modeled using grand canonical Monte Carlo (GCMC) simulations at different temperatures and pressures (from capillary condensation to supercritical state). Additionally, the gas-in-place (GIP), excess adsorption, and absolute adsorption isotherms are obtained. We find the crossover of excess adsorption isotherms, which was observed in the experiment, and the absolute adsorption amount increases with the increase in pressure in the case of ultrahigh pressure (>40 MPa). Moreover, we obtain an ultrahigh-pressure dual-site Langmuir equation, and it can accurately describe observed adsorption isotherms from low pressure to ultrahigh pressure. Our study visually reproduces the adsorption/desorption behaviors of CH4 under in situ conditions in deep shale and reveals their microscopic mechanism

A Novel Approach for Solving Semidefinite Programs

A novel linearizing alternating direction augmented Lagrangian approach is proposed for effectively solving semidefinite programs (SDP). For every iteration, by fixing the other variables, the proposed approach alternatively optimizes the dual variables and the dual slack variables; then the primal variables, that is, Lagrange multipliers, are updated. In addition, the proposed approach renews all the variables in closed forms without solving any system of linear equations. Global convergence of the proposed approach is proved under mild conditions, and two numerical problems are given to demonstrate the effectiveness of the presented approach