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We introduce galmoss, a python-based, torch-powered tool for two-dimensional fitting of galaxy profiles. By seamlessly enabling GPU parallelization, galmoss meets the high computational demands of large-scale galaxy surveys, placing galaxy profile fitting in the LSST-era. It incorporates widely used profiles such as the S\'ersic, Exponential disk, Ferrer, King, Gaussian, and Moffat profiles, and allows for the easy integration of more complex models. Tested on 8,289 galaxies from the Sloan Digital Sky Survey (SDSS) g-band with a single NVIDIA A100 GPU, galmoss completed classical S\'ersic profile fitting in about 10 minutes. Benchmark tests show that galmoss achieves computational speeds that are 6 $\times$ faster than those of default implementations., Comment: 12 pages, 8 figures, Accepted for publication in A&C

We present a novel approach for the dimensionality reduction of galaxy images by leveraging a combination of variational auto-encoders (VAE) and domain adaptation (DA). We demonstrate the effectiveness of this approach using a sample of low redshift galaxies with detailed morphological type labels from the Galaxy-Zoo DECaLS project. We show that 40-dimensional latent variables can effectively reproduce most morphological features in galaxy images. To further validate the effectiveness of our approach, we utilised a classical random forest (RF) classifier on the 40-dimensional latent variables to make detailed morphology feature classifications. This approach performs similarly to a direct neural network application on galaxy images. We further enhance our model by tuning the VAE network via DA using galaxies in the overlapping footprint of DECaLS and BASS+MzLS, enabling the unbiased application of our model to galaxy images in both surveys. We observed that DA led to even better morphological feature extraction and classification performance. Overall, this combination of VAE and DA can be applied to achieve image dimensionality reduction, defect image identification, and morphology classification in large optical surveys., Comment: Accepted by MNRAS 2023 October 12. 10 pages, 8 figures

In this paper, we investigate the problem of optimal strategies of dividend and reinsurance under the Cram\'{e}r-Lundberg risk model embedded with the thinning-dependence structure which was firstly introduced by Wang and Yuen (2005), subject to the optimality criteria of maximizing the expected accumulated discounted dividends paid until ruin. To enhance the practical relevance of the optimal dividend and reinsurance problem, non-cheap reinsurance is considered and transaction costs and taxes are imposed on dividends, which converts our optimization problem into a mixed classical-impulse control problem. For the purpose of better mathematical tractability and neat, explicit solutions of our control problem, instead of the Cram\'er-Lundberg framework we study its approximated diffusion model with two thinly dependent classes of insurance businesses. Using a method of quasi-variational inequalities, we show that the optimal reinsurance follows a two-dimensional excess-of-loss reinsurance strategy, and, the optimal dividend strategy turns out to be an impulse dividend strategy with an upper and a lower barrier, i.e., every thing above the lower barrier is paid as dividends each time the surplus is above the upper barrier, otherwise no dividends are paid. Closed-form expression for the value function associated with the optimal dividend and reinsurance strategy is also given. In addition, some numerical examples are presented to illustrate the optimality results.

Dark state as a consequence of interference between different quantum states has great importance in the fields of chip-scale atomic clock and quantum information. For the $\Lambda$-type three-level system, this dark state is generally regarded as being dissipation-free because it is a superposition of two lowest states without dipole transition between them. However, previous studies are based on the rotating-wave approximation (RWA) by neglecting the counter-rotating terms in the system-environment interaction. In this work, we study non-Markovian quantum dynamics of the dark state in a $\Lambda$-type three-level system coupled to two bosonic baths and reveal the effect of counter-rotating terms on the dark state. In contrast to the dark state within the RWA, leakage of the dark state occurs even at zero temperature, as a result of these counter-rotating terms. Also, we present a method to restore the quantum coherence of the dark state by applying a leakage elimination operator to the system.