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The Einstein Probe (EP) achieved its first detection and localization of a bright X-ray flare, EP240219a, on February 19, 2024, during its commissioning phase. Subsequent targeted searches triggered by the EP240219a alert identified a faint, untriggered gamma-ray burst (GRB) in the archived data of Fermi/GBM, Swift/BAT, Insight-HXMT/HE and INTEGRAL/SPI-ACS. The EP/WXT light curve reveals a long duration of approximately 160 seconds with a slow decay, whereas the Fermi/GBM light curve shows a total duration of approximately 70 seconds. The peak in the Fermi/GBM light curve occurs slightly later with respect to the peak seen in the EP/WXT light curve. Our spectral analysis shows that a single cutoff power-law model effectively describes the joint EP/WXT-Fermi/GBM spectra in general, indicating coherent broad emission typical of GRBs. The model yielded a photon index of $\sim -1.70 \pm 0.05$ and a peak energy of $\sim 257 \pm 134$ keV. After detection of GRB 240219A, long-term observations identified several candidates in optical and radio wavelengths, none of which was confirmed as the afterglow counterpart during subsequent optical and near-infrared follow-ups. The analysis of GRB 240219A classifies it as an X-ray rich GRB with a high peak energy, presenting both challenges and opportunities for studying the physical origins of X-ray flashes (XRFs), X-ray rich GRBs (XRRs), and classical GRBs (C-GRBs). Furthermore, linking the cutoff power-law component to non-thermal synchrotron radiation suggests that the burst is driven by a Poynting flux-dominated outflow., Comment: 14 pages, 8 figures, 3 tables

We study the eigenvalue distribution and resolvent of a Kronecker-product random matrix model $A \otimes I_{n \times n}+I_{n \times n} \otimes B+\Theta \otimes \Xi \in \mathbb{C}^{n^2 \times n^2}$, where $A,B$ are independent Wigner matrices and $\Theta,\Xi$ are deterministic and diagonal. For fixed spectral arguments, we establish a quantitative approximation for the Stieltjes transform by that of an approximating free operator, and a diagonal deterministic equivalent approximation for the resolvent. We further obtain sharp estimates in operator norm for the $n \times n$ resolvent blocks, and show that off-diagonal resolvent entries fall on two differing scales of $n^{-1/2}$ and $n^{-1}$ depending on their locations in the Kronecker structure. Our study is motivated by consideration of a matrix-valued least-squares optimization problem $\min_{X \in \mathbb{R}^{n \times n}} \frac{1}{2}\|XA+BX\|_F^2+\frac{1}{2}\sum_{ij} \xi_i\theta_j x_{ij}^2$ subject to a linear constraint. For random instances of this problem defined by Wigner inputs $A,B$, our analyses imply an asymptotic characterization of the minimizer $X$ and its associated minimum objective value as $n \to \infty$.

Motivated by applications to group synchronization and quadratic assignment on random data, we study a general problem of Bayesian inference of an unknown ``signal'' belonging to a high-dimensional compact group, given noisy pairwise observations of a featurization of this signal. We establish a quantitative comparison between the signal-observation mutual information in any such problem with that in a simpler model with linear observations, using interpolation methods. For group synchronization, our result proves a replica formula for the asymptotic mutual information and Bayes-optimal mean-squared-error. Via analyses of this replica formula, we show that the conjectural phase transition threshold for computationally-efficient weak recovery of the signal is determined by a classification of the real-irreducible components of the observed group representation(s), and we fully characterize the information-theoretic limits of estimation in the example of angular/phase synchronization over $SO(2)$/$U(1)$. For quadratic assignment, we study observations given by a kernel matrix of pairwise similarities and a randomly permutated and noisy counterpart, and we show in a bounded signal-to-noise regime that the asymptotic mutual information coincides with that in a Bayesian spiked model with i.i.d. signal prior.

Utilizing high-cadence and continuous g- and r-band data over three nights acquired from the 3.6-meter Canada France Hawaii Telescope (CFHT) aimed to find short-duration microlensing events, we conduct a systematic search for variables, transients, and asteroids across a $\sim1^\circ$ field of view of the Andromeda Galaxy (M 31). We present a catalog of 5859 variable stars, yielding the most extensive compilation of short-period variable sources of M 31. We also detected 19 flares, predominantly associated with foreground M dwarfs in the Milky Way. In addition, we discovered 17 previously unknown asteroid candidates, and we subsequently reported them to the Minor Planet Center. Lastly, we report a microlensing event candidate C-ML-1 and present a preliminary analysis.

This work shows details of an evaluation of an observational system comprising a CMOS detector, 60-cm telescope, and filter complement. The system's photometric precision and differential photometric precision, and extinction coefficients were assessed through observations of Supersky flat fields, open clusters, standard stars, and exoplanets. Photometry was precision achieved at the 0.02 mag level, while differential photometry of 0.004 mag precision. Extinction was found to be agreed with previous studies conducted at Xinglong Observatory. Ultimately, the results demonstrate this observing system is capable of precision scientific observations with CCD across the optical wavelengths.

Many recent works have studied the eigenvalue spectrum of the Conjugate Kernel (CK) defined by the nonlinear feature map of a feedforward neural network. However, existing results only establish weak convergence of the empirical eigenvalue distribution, and fall short of providing precise quantitative characterizations of the ''spike'' eigenvalues and eigenvectors that often capture the low-dimensional signal structure of the learning problem. In this work, we characterize these signal eigenvalues and eigenvectors for a nonlinear version of the spiked covariance model, including the CK as a special case. Using this general result, we give a quantitative description of how spiked eigenstructure in the input data propagates through the hidden layers of a neural network with random weights. As a second application, we study a simple regime of representation learning where the weight matrix develops a rank-one signal component over training and characterize the alignment of the target function with the spike eigenvector of the CK on test data., Comment: 55 pages

The role of a market maker is to simultaneously offer to buy and sell quantities of goods, often a financial asset such as a share, at specified prices. An automated market maker (AMM) is a mechanism that offers to trade according to some predetermined schedule; the best choice of this schedule depends on the market maker's goals. The literature on the design of AMMs has mainly focused on prediction markets with the goal of information elicitation. More recent work motivated by DeFi has focused instead on the goal of profit maximization, but considering only a single type of good (traded with a numeraire), including under adverse selection (Milionis et al. 2022). Optimal market making in the presence of multiple goods, including the possibility of complex bundling behavior, is not well understood. In this paper, we show that finding an optimal market maker is dual to an optimal transport problem, with specific geometric constraints on the transport plan in the dual. We show that optimal mechanisms for multiple goods and under adverse selection can take advantage of bundling, both improved prices for bundled purchases and sales as well as sometimes accepting payment "in kind." We present conjectures of optimal mechanisms in additional settings which show further complex behavior. From a methodological perspective, we make essential use of the tools of differentiable economics to generate conjectures of optimal mechanisms, and give a proof-of-concept for the use of such tools in guiding theoretical investigations.

We present 206 unpublished optical spectra of 104 type II supernovae obtained by the Xinglong 2.16m telescope and Lijiang 2.4m telescope during the period from 2011 to 2018, spanning the phases from about 1 to 200 days after the SN explosion. The spectral line identifications, evolution of line velocities and pseudo equivalent widths, as well as correlations between some important spectral parameters are presented. Our sample displays a large range in expansion velocities. For instance, the Fe~{\sc ii} $5169$ velocities measured from spectra at $t\sim 50$ days after the explosion vary from ${\rm 2000\ km\ s^{-1}}$ to ${\rm 5500\ km\ s^{-1}}$, with an average value of ${\rm 3872 \pm 949\ km\ s^{-1}}$. Power-law functions can be used to fit the velocity evolution, with the power-law exponent quantifying the velocity decline rate. We found an anticorrelation existing between H$\beta$ velocity at mid-plateau phase and its velocity decay exponent, SNe II with higher velocities tending to have smaller velocity decay rate. Moreover, we noticed that the velocity decay rate inferred from the Balmer lines (i.e., H$\alpha$ and H$\beta$) have moderate correlations with the ratio of absorption to emission for H$\alpha$ (a/e). In our sample, two objects show possibly flash-ionized features at early phases. Besides, we noticed that multiple high-velocity components may exist on the blue side of hydrogen lines of SN 2013ab, possibly suggesting that these features arise from complex line forming region. All our spectra can be found in WISeREP and Zenodo.

Empirical Bayes provides a powerful approach to learning and adapting to latent structure in data. Theory and algorithms for empirical Bayes have a rich literature for sequence models, but are less understood in settings where latent variables and data interact through more complex designs. In this work, we study empirical Bayes estimation of an i.i.d. prior in Bayesian linear models, via the nonparametric maximum likelihood estimator (NPMLE). We introduce and study a system of gradient flow equations for optimizing the marginal log-likelihood, jointly over the prior and posterior measures in its Gibbs variational representation using a smoothed reparametrization of the regression coefficients. A diffusion-based implementation yields a Langevin dynamics MCEM algorithm, where the prior law evolves continuously over time to optimize a sequence-model log-likelihood defined by the coordinates of the current Langevin iterate. We show consistency of the NPMLE as $n, p \rightarrow \infty$ under mild conditions, including settings of random sub-Gaussian designs when $n \asymp p$. In high noise, we prove a uniform log-Sobolev inequality for the mixing of Langevin dynamics, for possibly misspecified priors and non-log-concave posteriors. We then establish polynomial-time convergence of the joint gradient flow to a near-NPMLE if the marginal negative log-likelihood is convex in a sub-level set of the initialization.

We study mean-field variational inference in a Bayesian linear model when the sample size n is comparable to the dimension p. In high dimensions, the common approach of minimizing a Kullback-Leibler divergence from the posterior distribution, or maximizing an evidence lower bound, may deviate from the true posterior mean and underestimate posterior uncertainty. We study instead minimization of the TAP free energy, showing in a high-dimensional asymptotic framework that it has a local minimizer which provides a consistent estimate of the posterior marginals and may be used for correctly calibrated posterior inference. Geometrically, we show that the landscape of the TAP free energy is strongly convex in an extensive neighborhood of this local minimizer, which under certain general conditions can be found by an Approximate Message Passing (AMP) algorithm. We then exhibit an efficient algorithm that linearly converges to the minimizer within this local neighborhood. In settings where it is conjectured that no efficient algorithm can find this local neighborhood, we prove analogous geometric properties for a local minimizer of the TAP free energy reachable by AMP, and show that posterior inference based on this minimizer remains correctly calibrated., Comment: 79 pages, 5 figures

Photometric stellar surveys now cover a large fraction of the sky, probe to fainter magnitudes than large-scale spectroscopic surveys, and are relatively free from the target-selection biases often associated with such studies. Photometric-metallicity estimates that include narrow/medium-band filters can achieve comparable accuracy and precision to existing low-resolution spectroscopic surveys such as SDSS/SEGUE and LAMOST. Here we report on an effort to identify likely members of the Galactic disk system among the very metal-poor (VMP; [Fe/H] $\leq$ --2) and extremely metal-poor (EMP; [Fe/H] $\leq$ --3) stars. Our analysis is based on an initial sample of $\sim11.5$ million stars with full space motions selected from the SkyMapper Southern Survey (SMSS) and Stellar Abundance and Galactic Evolution Survey (SAGES). After applying a number of quality cuts to obtain the best available metallicity and dynamical estimates, we analyze a total of $\sim$5.86 million stars in the combined SMSS/SAGES sample. We employ two techniques that, depending on the method, identify between 876 and 1,476 VMP stars (6.9%-11.7% of all VMP stars) and between 40 and 59 EMP stars (12.4%-18.3% of all EMP stars) that appear to be members of the Galactic disk system on highly prograde orbits (v$_{\phi} > 150$ km/s). The total number of candidate VMP/EMP disk-like stars is 1,496, the majority of which have low orbital eccentricities, ecc $\le 0.4$; many have ecc $\le 0.2$. The large fractions of VMP/EMP stars associated with the Milky Way disk system strongly suggest the presence of an early forming ``primordial" disk., Comment: It is now accepted to the ApJS

Bayesian optimization (BO) is a popular black-box function optimization method, which makes sequential decisions based on a Bayesian model, typically a Gaussian process (GP), of the function. To ensure the quality of the model, transfer learning approaches have been developed to automatically design GP priors by learning from observations on "training" functions. These training functions are typically required to have the same domain as the "test" function (black-box function to be optimized). In this paper, we introduce MPHD, a model pre-training method on heterogeneous domains, which uses a neural net mapping from domain-specific contexts to specifications of hierarchical GPs. MPHD can be seamlessly integrated with BO to transfer knowledge across heterogeneous search spaces. Our theoretical and empirical results demonstrate the validity of MPHD and its superior performance on challenging black-box function optimization tasks.

In this paper, a total of approximately 2.6 million dwarfs were constructed as standard stars, with an accuracy of about 0.01-0.02 mag for each band, by combining spectroscopic data from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope Data Release 7, photometric data from the corrected Gaia Early Data Release 3, and photometric metallicities. Using the spectroscopy based stellar color regression method (SCR method) and the photometric-based SCR method (SCR' method), we performed the relative calibration of the Nanshan One-meter Wide-field Telescope imaging data. Based on the corrected Pan-STARRS DR1 photometry, the absolute calibration was also performed. In the photometric calibration process, we analyzed the dependence of the calibration zero points on different images (observation time), different gates of the CCD detector, and different CCD positions. We found that the stellar flat and the relative gain between different gates depend on time. The amplitude of gain variation in three channels is approximately 0.5%-0.7% relative to the other channel, with a maximum value of 4%. In addition, significant spatial variations of the stellar flat fitting residual are found and corrected. Using repeated sources in the adjacent images, we checked and discovered internal consistency of about 1-2 mmag in all the filters. Using the PS1 magnitudes synthesized by Gaia DR3 BP/RP spectra by the synthetic photometry method, we found that the photometric calibration uniformity is about 1-2 mmag for all the bands, at a spatial resolution of 1.3 degree. A detailed comparison between the spectroscopy-based SCR and photometric-based SCR method magnitude offsets was performed, and we achieved an internal consistency precision of about 2 mmag or better with resolutions of 1.3 degree for all the filters. Which is mainly from the position-dependent errors of the E(B-V) used in SCR' method., Comment: 15 pages in Chinese language, 8 figures, Chinese Science Bulletin accepted and published online (https://www.sciengine.com/CSB/doi/10.1360/TB-2023-0052), see main results in Figures 6, 7 and 8

We present precise photometric estimates of stellar parameters, including effective temperature, metallicity, luminosity classification, distance, and stellar age, for nearly 26 million stars using the methodology developed in the first paper of this series, based on the stellar colors from the Stellar Abundances and Galactic Evolution Survey (SAGES) DR1 and Gaia EDR3. The optimal design of stellar-parameter sensitive $uv$ filters by SAGES has enabled us to determine photometric-metallicity estimates down to $-3.5$, similar to our previous results with the SkyMapper Southern Survey (SMSS), yielding a large sample of over five million metal-poor (MP; [Fe/H]$\le -1.0$) stars and nearly one million very metal-poor (VMP; [Fe/H]$\le -2.0$) stars. The typical precision is around $0.1$ dex for both dwarf and giant stars with [Fe/H]$>-1.0$, and 0.15-0.25/0.3-0.4 dex for dwarf/giant stars with [Fe/H]$<-1.0$. Using the precise parallax measurements and stellar colors from Gaia, effective temperature, luminosity classification, distance and stellar age are further derived for our sample stars. This huge data set in the Northern sky from SAGES, together with similar data in the Southern sky from SMSS, will greatly advance our understanding of the Milky Way, in particular its formation and evolution., Comment: 14 pages, 14 figures, 3 tables, accepted by ApJ. arXiv admin note: text overlap with arXiv:2104.14154

The Stellar Abundances and Galactic Evolution Survey (SAGES) of the northern sky is a specifically-designed multi-band photometric survey aiming to provide reliable stellar parameters with accuracy comparable to those from low-resolution optical spectra. It was carried out with the 2.3-m Bok telescope of Steward Observatory and three other telescopes. The observations in the $u_s$ and $v_s$ passband produced over 36,092 frames of images in total, covering a sky area of $\sim9960$ degree$^2$. The median survey completeness of all observing fields for the two bands are of $u_{\rm s}=20.4$ mag and $v_s=20.3$ mag, respectively, while the limiting magnitudes with signal-to-noise ratio (S/N) of 100 are $u_s\sim17$ mag and $v_s\sim18$ mag, correspondingly. We combined our catalog with the data release 1 (DR1) of the first of Panoramic Survey Telescope And Rapid Response System (Pan-STARRS1, PS1) catalog, and obtained a total of 48,553,987 sources which have at least one photometric measurement in each of the SAGES $u_s$ and $v_s$ and PS1 $grizy$ passbands, which is the DR1 of SAGES and it will be released in our paper. We compare our $gri$ point-source photometry with those of PS1 and found an RMS scatter of $\sim2$% in difference of PS1 and SAGES for the same band. We estimated an internal photometric precision of SAGES to be on the order of $\sim1$%. Astrometric precision is better than $0^{\prime\prime}.2$ based on comparison with the DR1 of Gaia mission. In this paper, we also describe the final end-user database, and provide some science applications., Comment: 49 pages, 21 figures, 5 table, accepted for publication in ApJS

We predict the dwarf galaxy detection limits for the upcoming Chinese Space Station Telescope (CSST) survey that will cover 17,500 deg$^{2}$ of the sky with a wide field of view of 1.1 deg$^2$. The point-source depth reaches 26.3 mag in the $g$ band and 25.9 mag in the $i$ band. Constructing mock survey data based on the designed photometric bands, we estimate the recovery rate of artificial dwarf galaxies from mock point-source photometric catalogues. The detection of these artificial dwarf galaxies is strongly dependent on their distance, magnitude and size, in agreement with searches in current surveys. We expect CSST to enable the detection of dwarf galaxies with $M_V = -3.0$ and $\mu_{250} = 32.0$ mag/arcsec$^2$ (surface-brightness limit for a system of half-light radius $r_{\rm h}$ = 250 pc at 400 kpc, and $M_V = -4.9$ and $\mu_{250} = 30.5$ mag/arcsec$^2$ around the Andromeda galaxy. Beyond the Local Group, the CSST survey will achieve $M_V = -5.8$, and $\mu_{250}$ = 29.7 mag/arcsec$^2$ in the distance range of 1--2 Mpc, opening up an exciting discovery space for faint field dwarf galaxies. With its optical bands, wide survey footprint, and space resolution, CSST will undoubtedly expand our knowledge of low-mass dwarf galaxies to an unprecedented volume., Comment: 11 pages, 10 figures. Accepted to MNRAS

We study estimation in the linear model $y=A\beta^\star+\epsilon$, in a Bayesian setting where $\beta^\star$ has an entrywise i.i.d. prior and the design $A$ is rotationally-invariant in law. In the large system limit as dimension and sample size increase proportionally, a set of related conjectures have been postulated for the asymptotic mutual information, Bayes-optimal mean squared error, and TAP mean-field equations that characterize the Bayes posterior mean of $\beta^\star$. In this work, we prove these conjectures for a general class of signal priors and for arbitrary rotationally-invariant designs $A$, under a "high-temperature" condition that restricts the range of eigenvalues of $A^\top A$. Our proof uses a conditional second-moment method argument, where we condition on the iterates of a version of the Vector AMP algorithm for solving the TAP mean-field equations.

Bayesian optimization (BO), while proved highly effective for many black-box function optimization tasks, requires practitioners to carefully select priors that well model their functions of interest. Rather than specifying by hand, researchers have investigated transfer learning based methods to automatically learn the priors, e.g. multi-task BO (Swersky et al., 2013), few-shot BO (Wistuba and Grabocka, 2021) and HyperBO (Wang et al., 2022). However, those prior learning methods typically assume that the input domains are the same for all tasks, weakening their ability to use observations on functions with different domains or generalize the learned priors to BO on different search spaces. In this work, we present HyperBO+: a pre-training approach for hierarchical Gaussian processes that enables the same prior to work universally for Bayesian optimization on functions with different domains. We propose a two-step pre-training method and analyze its appealing asymptotic properties and benefits to BO both theoretically and empirically. On real-world hyperparameter tuning tasks that involve multiple search spaces, we demonstrate that HyperBO+ is able to generalize to unseen search spaces and achieves lower regrets than competitive baselines., Comment: Full version of the workshop paper at 2022 NeurIPS Workshop on Gaussian Processes, Spatiotemporal Modeling, and Decision-making Systems

Approximate Message Passing (AMP) algorithms provide a valuable tool for studying mean-field approximations and dynamics in a variety of applications. Although these algorithms are often first derived for matrices having independent Gaussian entries or satisfying rotational invariance in law, their state evolution characterizations are expected to hold over larger universality classes of random matrix ensembles. We develop several new results on AMP universality. For AMP algorithms tailored to independent Gaussian entries, we show that their state evolutions hold over broadly defined generalized Wigner and white noise ensembles, including matrices with heavy-tailed entries and heterogeneous entrywise variances that may arise in data applications. For AMP algorithms tailored to rotational invariance in law, we show that their state evolutions hold over delocalized sign-and-permutation-invariant matrix ensembles that have a limit distribution over the diagonal, including sensing matrices composed of subsampled Hadamard or Fourier transforms and diagonal operators. We establish these results via a simplified moment-method proof, reducing AMP universality to the study of products of random matrices and diagonal tensors along a tensor network. As a by-product of our analyses, we show that the aforementioned matrix ensembles satisfy a notion of asymptotic freeness with respect to such tensor networks, which parallels usual definitions of freeness for traces of matrix products., Comment: 54 pages. Accepted to The Annals of Applied Probability

We study the continuous multi-reference alignment model of estimating a periodic function on the circle from noisy and circularly-rotated observations. Motivated by analogous high-dimensional problems that arise in cryo-electron microscopy, we establish minimax rates for estimating generic signals that are explicit in the dimension $K$. In a high-noise regime with noise variance $\sigma^2 \gtrsim K$, for signals with Fourier coefficients of roughly uniform magnitude, the rate scales as $\sigma^6$ and has no further dependence on the dimension. This rate is achieved by a bispectrum inversion procedure, and our analyses provide new stability bounds for bispectrum inversion that may be of independent interest. In a low-noise regime where $\sigma^2 \lesssim K/\log K$, the rate scales instead as $K\sigma^2$, and we establish this rate by a sharp analysis of the maximum likelihood estimator that marginalizes over latent rotations. A complementary lower bound that interpolates between these two regimes is obtained using Assouad's hypercube lemma. We extend these analyses also to signals whose Fourier coefficients have a slow power law decay., Comment: 56 pages