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We establish a priori interior curvature estimates for the special Lagrangian curvature equations in both the critical phase and convex case. Additionally, we prove a priori interior gradient estimates for any constant phases., Comment: All comments are welcome!

China Space Station Telescope (CSST) has the capability to conduct slitless spectroscopic survey simultaneously with photometric survey. The spectroscopic survey will measure slitless spectra, potentially providing more accurate estimations of galaxy properties, particularly redshift, compared to broadband photometry. However, due to low-resolution and signal-to-noise ratio of slitless spectra, measurement of these properties is significantly challenging. In this study, we employ a Bayesian neural network (BNN) to assess the accuracy of redshift estimations from slitless spectra anticipated to be observed by CSST. The slitless spectra are simulated based on real data from the early data release of the Dark Energy Spectroscopic Instrument (DESI-EDR) and the 16th data release of the Baryon Oscillaton Spectroscopic Survey (BOSS-DR16), combining the 9th data release of the DESI Legacy Survey (DESI LS DR9). The BNN provides redshifts estimates along with corresponding uncertainties, achieving an accuracy of $\sigma_{\rm NMAD} = 0.00063$, outlier percentage $\eta=0.92\%$ and weighted mean uncertainty $\bar{E} = 0.00228$. These results successfully meet the requirement for cosmological studies using slitless spectra from CSST., Comment: 12 pages, 12 figures, submitted to ApJ, comments are welcome

Accurate photometric redshift (photo-$z$) estimation requires support from multi-band observational data. However, in the actual process of astronomical observations and data processing, some sources may have missing observational data in certain bands for various reasons. This could greatly affect the accuracy and reliability of photo-$z$ estimation for these sources, and even render some estimation methods unusable. The same situation may exist for the upcoming Chinese Space Station Telescope (CSST). In this study, we employ a deep learning method called Generative Adversarial Imputation Networks (GAIN) to impute the missing photometric data in CSST, aiming to reduce the impact of data missing on photo-$z$ estimation and improve estimation accuracy. Our results demonstrate that using the GAIN technique can effectively fill in the missing photometric data in CSST. Particularly, when the data missing rate is below 30\%, the imputation of photometric data exhibits high accuracy, with higher accuracy in the $g$, $r$, $i$, $z$, and $y$ bands compared to the $NUV$ and $u$ bands. After filling in the missing values, the quality of photo-$z$ estimation obtained by the widely used Easy and Accurate Zphot from Yale (EAZY) software is notably enhanced. Evaluation metrics for assessing the quality of photo-$z$ estimation, including the catastrophic outlier fraction ($f_{out}$), the normalized median absolute deviation ($\rm {\sigma_{NMAD}}$), and the bias of photometric redshift ($bias$), all show some degree of improvement. Our research will help maximize the utilization of observational data and provide a new method for handling sample missing values for applications that require complete photometry data to produce results.

Accurate estimation of photometric redshifts (photo-$z$) is crucial in studies of both galaxy evolution and cosmology using current and future large sky surveys. In this study, we employ Random Forest (RF), a machine learning algorithm, to estimate photo-$z$ and investigate the systematic uncertainties affecting the results. Using galaxy flux and color as input features, we construct a mapping between input features and redshift by using a training set of simulated data, generated from the Hubble Space Telescope Advanced Camera for Surveys (HST-ACS) and COSMOS catalogue, with the expected instrumental effects of the planned China Space Station Telescope (CSST). To improve the accuracy and confidence of predictions, we incorporate inverse variance weighting and perturb the catalog using input feature errors. Our results show that weighted RF can achieve a photo-$z$ accuracy of $\rm \sigma_{NMAD}=0.025$ and an outlier fraction of $\rm \eta=2.045\%$, significantly better than the values of $\rm \sigma_{NMAD}=0.043$ and $\rm \eta=6.45\%$ obtained by the widely used Easy and Accurate Zphot from Yale (EAZY) software which uses template-fitting method. Furthermore, we have calculated the importance of each input feature for different redshift ranges and found that the most important input features reflect the approximate position of the break features in galaxy spectra, demonstrating the algorithm's ability to extract physical information from data. Additionally, we have established confidence indices and error bars for each prediction value based on the shape of the redshift probability distribution function, suggesting that screening sources with high confidence can further reduce the outlier fraction.

We obtain a prior $C^{1,1}$ estimates for some Hessian (quotient) equations with positive Lipschitz right hand sides, through studying a twisted special Lagrangian equation. The results imply the interior $C^{2,\alpha}$ regularity for $C^0$ viscosity solutions to $\sigma_2=f^2(x)$ in dimension 3, with positive Lipschitz $f(x)$.

We establish a prior interior $C^{1,1}$ estimates for convex solutions and supercritical phase solutions to the Lagrangian mean curvature equation with sharp Lipschitz phase. Counter-examples exist when the phase is H\"{o}lder continuous but not Lipschitz. As an application we obtain interior $C^{2,\alpha}$ regularity for $C^0$ viscosity solutions on the first phase interval $((n-2)\frac\pi2,n\frac\pi2)$.

The emergence of Neural Radiance Fields (NeRF) has promoted the development of synthesized high-fidelity views of the intricate real world. However, it is still a very demanding task to repaint the content in NeRF. In this paper, we propose a novel framework that can take RGB images as input and alter the 3D content in neural scenes. Our work leverages existing diffusion models to guide changes in the designated 3D content. Specifically, we semantically select the target object and a pre-trained diffusion model will guide the NeRF model to generate new 3D objects, which can improve the editability, diversity, and application range of NeRF. Experiment results show that our algorithm is effective for editing 3D objects in NeRF under different text prompts, including editing appearance, shape, and more. We validate our method on both real-world datasets and synthetic-world datasets for these editing tasks. Please visit https://starstesla.github.io/repaintnerf for a better view of our results., Comment: IJCAI 2023 Accepted (Main Track)

Cross-correlating the data of neutral hydrogen (HI) 21cm intensity mapping with galaxy surveys is an effective method to extract astrophysical and cosmological information. In this work, we investigate the cross-correlation of MeerKAT single-dish mode HI intensity mapping and China Space Station Telescope (CSST) spectroscopic galaxy surveys. We simulate a survey area of $\sim 300$ $\mathrm{deg}^2$ of MeerKAT and CSST surveys at $z=0.5$ using Multi-Dark N-body simulation. The PCA algorithm is applied to remove the foregrounds of HI intensity mapping, and signal compensation is considered to solve the signal loss problem in the HI-galaxy cross power spectrum caused by the foreground removal process. We find that from CSST galaxy auto and MeerKAT-CSST cross power spectra, the constraint accuracy of the parameter product $\Omega_{\rm HI}b_{\rm HI}r_{{\rm HI},g}$ can reach to $\sim1\%$, which is about one order of magnitude higher than the current results. After performing the full MeerKAT HI intensity mapping survey with 5000 deg$^2$ survey area, the accuracy can be enhanced to $<0.3\%$. This implies that the MeerKAT-CSST cross-correlation can be a powerful tool to probe the cosmic HI property and the evolution of galaxies and the Universe., Comment: 18 pages, 11 figures, 3 tables. Accepted for publication in RAA, revised to match the published version

Line intensity mapping (LIM) is a promising probe to study star formation, the large-scale structure of the Universe, and the epoch of reionization (EoR). Since carbon monoxide (CO) is the second most abundant molecule in the Universe except for molecular hydrogen ${\rm H}_2$, it is suitable as a tracer for LIM surveys. However, just like other LIM surveys, CO intensity mapping also suffers strong foreground contamination that needs to be eliminated for extracting valuable astrophysical and cosmological information. In this work, we take $^{12}$CO($\it J$=1-0) emission line as an example to investigate whether deep learning method can effectively recover the signal by removing the foregrounds. The CO(1-0) intensity maps are generated by N-body simulations considering CO luminosity and halo mass relation, and we discuss two cases with median and low CO signals by comparing different relations. We add foregrounds generated from real observations, including thermal dust, spinning dust, free-free, synchrotron emission and CMB anisotropy. The beam with sidelobe effect is also considered. Our deep learning model is built upon ResUNet, which combines image generation algorithm UNet with the state-of-the-art architecture of deep learning, ResNet. The principal component analysis (PCA) method is employed to preprocess data before feeding it to the ResUNet. We find that, in the case of low instrumental noise, our UNet can efficiently reconstruct the CO signal map with correct line power spectrum by removing the foregrounds and recovering PCA signal loss and beam effects. Our method also can be applied to other intensity mappings like neutral hydrogen 21cm surveys., Comment: 12 pages, 12 figures, 2 tables. Accepted for publication in MNRAS

Galaxy photometric redshift (photo-$z$) is crucial in cosmological studies, such as weak gravitational lensing and galaxy angular clustering measurements. In this work, we try to extract photo-$z$ information and construct its probability distribution function (PDF) using the Bayesian neural networks (BNN) from both galaxy flux and image data expected to be obtained by the China Space Station Telescope (CSST). The mock galaxy images are generated from the Advanced Camera for Surveys of Hubble Space Telescope ($HST$-ACS) and COSMOS catalog, in which the CSST instrumental effects are carefully considered. And the galaxy flux data are measured from galaxy images using aperture photometry. We construct Bayesian multilayer perceptron (B-MLP) and Bayesian convolutional neural network (B-CNN) to predict photo-$z$ along with the PDFs from fluxes and images, respectively. We combine the B-MLP and B-CNN together, and construct a hybrid network and employ the transfer learning techniques to investigate the improvement of including both flux and image data. For galaxy samples with SNR$>$10 in $g$ or $i$ band, we find the accuracy and outlier fraction of photo-$z$ can achieve $\sigma_{\rm NMAD}=0.022$ and $\eta=2.35\%$ for the B-MLP using flux data only, and $\sigma_{\rm NMAD}=0.022$ and $\eta=1.32\%$ for the B-CNN using image data only. The Bayesian hybrid network can achieve $\sigma_{\rm NMAD}=0.021$ and $\eta=1.23\%$, and utilizing transfer learning technique can improve results to $\sigma_{\rm NMAD}=0.019$ and $\eta=1.17\%$, which can provide the most confident predictions with the lowest average uncertainty., Comment: 22 pages, 12 figures, 3 tables, accepted for publication in RAA

The accuracy of galaxy photometric redshift (photo-$z$) can significantly affect the analysis of weak gravitational lensing measurements, especially for future high-precision surveys. In this work, we try to extract photo-$z$ information from both galaxy flux and image data expected to be obtained by China Space Station Telescope (CSST) using neural networks. We generate mock galaxy images based on the observational images from the Advanced Camera for Surveys of Hubble Space Telescope (HST-ACS) and COSMOS catalogs, considering the CSST instrumental effects. Galaxy flux data are then measured directly from these images by aperture photometry. The Multi-Layer Perceptron (MLP) and Convolutional Neural Network (CNN) are constructed to predict photo-$z$ from fluxes and images, respectively. We also propose to use an efficient hybrid network, which combines MLP and CNN, by employing transfer learning techniques to investigate the improvement of the result with both flux and image data included. We find that the photo-$z$ accuracy and outlier fraction can achieve $\sigma_{\rm NMAD} = 0.023$ and $\eta = 1.43\%$ for the MLP using flux data only, and $\sigma_{\rm NMAD} = 0.025$ and $\eta = 1.21\%$ for the CNN using image data only. The result can be further improved in high efficiency as $\sigma_{\rm NMAD} = 0.020$ and $\eta = 0.90\%$ for the hybrid transfer network. These approaches result in similar galaxy median and mean redshifts ~0.8 and 0.9, respectively, for the redshift range from 0 to 4. This indicates that our networks can effectively and properly extract photo-$z$ information from the CSST galaxy flux and image data., Comment: 11 pages, 8 figures, 2 tables. Accepted for publication in MNRAS

The estimation of spectroscopic and photometric redshifts (spec-z and photo-z) is crucial for future cosmological surveys. It can directly affect several powerful measurements of the Universe, e.g. weak lensing and galaxy clustering. In this work, we explore the accuracies of spec-z and photo-z that can be obtained in the China Space Station Optical Surveys (CSS-OS), which is a next-generation space survey, using neural networks. The 1-dimensional Convolutional Neural Networks (1-d CNN) and Multi-Layer Perceptron (MLP, one of the simplest forms of Artificial Neural Network) are employed to derive the spec-z and photo-z, respectively. The mock spectral and photometric data used for training and testing the networks are generated based on the COSMOS catalog. The networks have been trained with noisy data by creating Gaussian random realizations to reduce the statistical effects, resulting in similar redshift accuracy for both high-SNR (signal to noise ratio) and low-SNR data. The probability distribution functions (PDFs) of the predicted redshifts are also derived via Gaussian random realizations of the testing data, and then the best-fit redshifts and 1-sigma errors also can be obtained. We find that our networks can provide excellent redshift estimates with accuracies ~0.001 and 0.01 on spec-z and photo-z, respectively. Compared to existing photo-z codes, our MLP has similar accuracy but is more efficient in the training process. The fractions of catastrophic redshifts or outliers can be dramatically suppressed comparing to the ordinary template-fitting method. This indicates that the neural network method is feasible and powerful for spec-z and photo-z estimations in future cosmological surveys., Comment: 14 pages, 13 figures, 2 tables. Accepted for publication in ApJ