arXiv subjects

Zhou Fan

Publications and source records attributed to Zhou Fan.

At least 73 records · Page 4Linked to original sources

arXiv2023

Photometric calibration of the Stellar Abundance and Galactic Evolution Survey (SAGES): Nanshan One-meter Wide-field Telescope g, r, and i band imaging data

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.

astro-ph.SR↗

arXiv2023

Beyond spectroscopy. II. Stellar parameters for over twenty million stars in the northern sky from SAGES DR1 and Gaia DR3

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.

astro-ph.GA↗

arXiv2023

The Stellar Abundances and Galactic Evolution Survey (SAGES) -- -- I. General Description and the First Data Release (DR1)

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.

astro-ph.GA↗

arXiv2023

Local Group Dwarf Galaxy Detection Limit in the CSST survey

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 $μ_{250} = 32.0$ 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 $μ_{250} = 30.5$ mag/arcsec$^2$ around the Andromeda galaxy. Beyond the Local Group, the CSST survey will achieve $M_V = -5.8$, and $μ_{250}$ = 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.

astro-ph.GA↗

arXiv2023

Local convexity of the TAP free energy and AMP convergence for Z2-synchronization

We study mean-field variational Bayesian inference using the TAP approach, for Z2-synchronization as a prototypical example of a high-dimensional Bayesian model. We show that for any signal strength $λ> 1$ (the weak-recovery threshold), there exists a unique local minimizer of the TAP free energy functional near the mean of the Bayes posterior law. Furthermore, the TAP free energy in a local neighborhood of this minimizer is strongly convex. Consequently, a natural-gradient/mirror-descent algorithm achieves linear convergence to this minimizer from a local initialization, which may be obtained by a constant number of iterates of Approximate Message Passing (AMP). This provides a rigorous foundation for variational inference in high dimensions via minimization of the TAP free energy. We also analyze the finite-sample convergence of AMP, showing that AMP is asymptotically stable at the TAP minimizer for any $λ> 1$, and is linearly convergent to this minimizer from a spectral initialization for sufficiently large $λ$. Such a guarantee is stronger than results obtainable by state evolution analyses, which only describe a fixed number of AMP iterations in the infinite-sample limit. Our proofs combine the Kac-Rice formula and Sudakov-Fernique Gaussian comparison inequality to analyze the complexity of critical points that satisfy strong convexity and stability conditions within their local neighborhoods.

math.ST↗

arXiv2022

TAP equations for orthogonally invariant spin glasses at high temperature

We study the high-temperature regime of a mean-field spin glass model whose couplings matrix is orthogonally invariant in law. The magnetization of this model is conjectured to satisfy a system of TAP equations, originally derived by Parisi and Potters using a diagrammatic expansion of the Gibbs free energy. We prove that this TAP description is correct in an $L^2$ sense, in a regime of sufficiently high temperature. Our approach develops a novel geometric argument for proving the convergence of an Approximate Message Passing (AMP) algorithm to the magnetization vector, which is applicable in models without i.i.d. couplings. This convergence is shown via a conditional second moment analysis of the free energy restricted to a thin band around the output of the AMP algorithm, in a system of many "orthogonal" replicas.

math.PR↗

arXiv2022

Random linear estimation with rotationally-invariant designs: Asymptotics at high temperature

We study estimation in the linear model $y=Aβ^\star+ε$, in a Bayesian setting where $β^\star$ 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 $β^\star$. 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.

cs.IT↗

arXiv2022

Maximum likelihood for high-noise group orbit estimation and single-particle cryo-EM

Motivated by applications to single-particle cryo-electron microscopy (cryo-EM), we study several problems of function estimation in a high noise regime, where samples are observed after random rotation and possible linear projection of the function domain. We describe a stratification of the Fisher information eigenvalues according to transcendence degrees of graded pieces of the algebra of group invariants, and we relate critical points of the log-likelihood landscape to a sequence of moment optimization problems, extending previous results for a discrete rotation group without projections. We then compute the transcendence degrees and forms of these optimization problems for several examples of function estimation under $SO(2)$ and $SO(3)$ rotations, including a simplified model of cryo-EM as introduced by Bandeira, Blum-Smith, Kileel, Perry, Weed, and Wein. We affirmatively resolve conjectures that $3^\text{rd}$-order moments are sufficient to locally identify a generic signal up to its rotational orbit in these examples. For low-dimensional approximations of the electric potential maps of two small protein molecules, we empirically verify that the noise-scalings of the Fisher information eigenvalues conform with our theoretical predictions over a range of SNR, in a model of $SO(3)$ rotations without projections.

math.ST↗

arXiv2022

Differential Liquidity Provision in Uniswap v3 and Implications for Contract Design

Decentralized exchanges (DEXs) provide a means for users to trade pairs of assets on-chain without the need for a trusted third party to effectuate a trade. Amongst these, constant function market maker DEXs such as Uniswap handle the most volume of trades between ERC-20 tokens. With the introduction of Uniswap v3, liquidity providers can differentially allocate liquidity to trades that occur within specific price intervals. In this paper, we formalize the profit and loss that liquidity providers can earn when providing specific liquidity allocations to a v3 contract. We give a convex stochastic optimization problem for computing optimal liquidity allocation for a liquidity provider who holds a belief on how prices will evolve over time and use this to study the design question regarding how v3 contracts should partition the price space for permissible liquidity allocations. Our results show that making a greater diversity of price-space partitions available to a contract designer can simultaneously benefit both liquidity providers and traders.

cs.GT↗

arXiv2021

Beyond spectroscopy. I. Metallicities, distances, and age estimates for over twenty million stars from SMSS DR2 and Gaia EDR3

Accurate determinations of stellar parameters and distances for large complete samples of stars are keys for conducting detailed studies of the formation and evolution of our Galaxy. Here we present stellar atmospheric parameters ($T_{\rm eff}$, luminosity classifications, and [Fe/H]) estimates for some 24 million stars determined from the stellar colors of SMSS DR2 and Gaia EDR3, based on training datasets with available spectroscopic measurements from previous high/medium/low-resolution spectroscopic surveys. The number of stars with photometric-metallicity estimates is 4-5 times larger than that collected by the current largest spectroscopic survey to date - LAMOST - over the course of the past decade. External checks indicate that the precision of the photometric-metallicity estimates are quite high, comparable to or slightly better than that derived from spectroscopy, with typical values around 0.05-0.15dex for both dwarf and giant stars with [Fe/H]>$-$1.0, 0.10-0.20dex for giant stars with $-$2.0<[Fe/H]<$-$1.0. and 0.20-0.25dex for giant stars with [Fe/H]<$-$2.0, and include estimates for stars as metal-poor as [Fe/H]~$-$3.5, substantially lower than previous photometric techniques. Photometric-metallicity estimates are obtained for an unprecedented number of metal-poor stars, including a total of over three million metal-poor (MP; [Fe/H] <$-$1.0) stars, over half a million very metal-poor (VMP; [Fe/H]<$-$2.0) stars, and over 25,000 extremely metal-poor (EMP; [Fe/H]<$-$3.0) stars. Moreover, distances are determined for over 20 million stars in our sample. For the over 18 million sample stars with accurate Gaia parallaxes, stellar ages are estimated by comparing with theoretical isochrones. Astrometric information is provided for the stars in our catalog, along with radial velocities for ~10% of our sample stars, taken from completed/ongoing large-scale spectroscopic surveys.

astro-ph.SR↗

arXiv2021

Empirical Bayes PCA in high dimensions

When the dimension of data is comparable to or larger than the number of data samples, Principal Components Analysis (PCA) may exhibit problematic high-dimensional noise. In this work, we propose an Empirical Bayes PCA method that reduces this noise by estimating a joint prior distribution for the principal components. EB-PCA is based on the classical Kiefer-Wolfowitz nonparametric MLE for empirical Bayes estimation, distributional results derived from random matrix theory for the sample PCs, and iterative refinement using an Approximate Message Passing (AMP) algorithm. In theoretical "spiked" models, EB-PCA achieves Bayes-optimal estimation accuracy in the same settings as an oracle Bayes AMP procedure that knows the true priors. Empirically, EB-PCA significantly improves over PCA when there is strong prior structure, both in simulation and on quantitative benchmarks constructed from the 1000 Genomes Project and the International HapMap Project. An illustration is presented for analysis of gene expression data obtained by single-cell RNA-seq.

stat.ME↗

arXiv2021

Approximate Message Passing algorithms for rotationally invariant matrices

Approximate Message Passing (AMP) algorithms have seen widespread use across a variety of applications. However, the precise forms for their Onsager corrections and state evolutions depend on properties of the underlying random matrix ensemble, limiting the extent to which AMP algorithms derived for white noise may be applicable to data matrices that arise in practice. In this work, we study more general AMP algorithms for random matrices $W$ that satisfy orthogonal rotational invariance in law, where $W$ may have a spectral distribution that is different from the semicircle and Marcenko-Pastur laws characteristic of white noise. The Onsager corrections and state evolutions in these algorithms are defined by the free cumulants or rectangular free cumulants of the spectral distribution of $W$. Their forms were derived previously by Opper, Çakmak, and Winther using non-rigorous dynamic functional theory techniques, and we provide rigorous proofs. Our motivating application is a Bayes-AMP algorithm for Principal Components Analysis, when there is prior structure for the principal components (PCs) and possibly non-white noise. For sufficiently large signal strengths and any non-Gaussian prior distributions for the PCs, we show that this algorithm provably achieves higher estimation accuracy than the sample PCs.

math.PR↗

arXiv2021

Likelihood landscape and maximum likelihood estimation for the discrete orbit recovery model

We study the non-convex optimization landscape for maximum likelihood estimation in the discrete orbit recovery model with Gaussian noise. This model is motivated by applications in molecular microscopy and image processing, where each measurement of an unknown object is subject to an independent random rotation from a rotational group. Equivalently, it is a Gaussian mixture model where the mixture centers belong to a group orbit. We show that fundamental properties of the likelihood landscape depend on the signal-to-noise ratio and the group structure. At low noise, this landscape is "benign" for any discrete group, possessing no spurious local optima and only strict saddle points. At high noise, this landscape may develop spurious local optima, depending on the specific group. We discuss several positive and negative examples, and provide a general condition that ensures a globally benign landscape. For cyclic permutations of coordinates on $\mathbb{R}^d$ (multi-reference alignment), there may be spurious local optima when $d \geq 6$, and we establish a correspondence between these local optima and those of a surrogate function of the phase variables in the Fourier domain. We show that the Fisher information matrix transitions from resembling that of a single Gaussian in low noise to having a graded eigenvalue structure in high noise, which is determined by the graded algebra of invariant polynomials under the group action. In a local neighborhood of the true object, the likelihood landscape is strongly convex in a reparametrized system of variables given by a transcendence basis of this polynomial algebra. We discuss implications for optimization algorithms, including slow convergence of expectation-maximization, and possible advantages of momentum-based acceleration and variable reparametrization for first- and second-order descent methods.

math.ST↗

arXiv2020

Spectra of the Conjugate Kernel and Neural Tangent Kernel for linear-width neural networks

We study the eigenvalue distributions of the Conjugate Kernel and Neural Tangent Kernel associated to multi-layer feedforward neural networks. In an asymptotic regime where network width is increasing linearly in sample size, under random initialization of the weights, and for input samples satisfying a notion of approximate pairwise orthogonality, we show that the eigenvalue distributions of the CK and NTK converge to deterministic limits. The limit for the CK is described by iterating the Marcenko-Pastur map across the hidden layers. The limit for the NTK is equivalent to that of a linear combination of the CK matrices across layers, and may be described by recursive fixed-point equations that extend this Marcenko-Pastur map. We demonstrate the agreement of these asymptotic predictions with the observed spectra for both synthetic and CIFAR-10 training data, and we perform a small simulation to investigate the evolutions of these spectra over training.

stat.ML↗

arXiv2020

Comparisons of Different Fitting Methods for the Physical Parameters of A Star Cluster Sample of M33 with Spectroscopy and Photometry

Star clusters are good tracers for formation and evolution of galaxies. We compared different fitting methods by using spectra (or by combining photometry) to determine the physical parameters. We choose a sample of 17 star clusters in M33, which previously lacked spectroscopic observations. The low-resolution spectra were taken with the Xinglong 2.16-m reflector of NAOC. The photometry used in the fitting includes $\rm u_{SC}$ and $\rm v_{SAGE}$ bands from the SAGE survey, as well as the published $UBVRI$ and $ugriz$ photometry. We firstly derived ages and metallicities with the {\sc ULySS} (Vazdekis et al. and {\sc pegase-hr}) SSP model and the Bruzual \& Charlot (2003) (BC03) stellar population synthesis models for the full-spectrum fitting. The fitting results of both the BC03 and {\sc ULySS} models seem consistent with those of previous works as well. Then we add the SAGE $\rm u_{SC}$ and $\rm v_{SAGE}$ photometry in the spectroscopic fitting with the BC03 models. It seems the results become much better, especially for the Padova 2000+Chabrier IMF set. Finally we add more photometry data, $UBVRI$ and $ugriz$, in the fitting and we found that the results do not improve significantly. Therefore, we conclude that the photometry is useful for improving the fitting results, especially for the blue bands ($λ<4000$ Å), e.g., $\rm u_{SC}$ and $\rm v_{SAGE}$ band. At last, we discuss the "UV-excess" for the star clusters and we find five star clusters have UV-excess, based on the $GALEX$ FUV, NUV photometry.

astro-ph.GA↗

arXiv2020

Principal components in linear mixed models with general bulk

We study the principal components of covariance estimators in multivariate mixed-effects linear models. We show that, in high dimensions, the principal eigenvalues and eigenvectors may exhibit bias and aliasing effects that are not present in low-dimensional settings. We derive the first-order limits of the principal eigenvalue locations and eigenvector projections in a high-dimensional asymptotic framework, allowing for general population spectral distributions for the random effects and extending previous results from a more restrictive spiked model. Our analysis uses free probability techniques, and we develop two general tools of independent interest-- strong asymptotic freeness of GOE and deterministic matrices and a free deterministic equivalent approximation for bilinear forms of resolvents.

math.PR↗

arXiv2020

Tracy-Widom at each edge of real covariance and MANOVA estimators

We study the sample covariance matrix for real-valued data with general population covariance, as well as MANOVA-type covariance estimators in variance components models under null hypotheses of global sphericity. In the limit as matrix dimensions increase proportionally, the asymptotic spectra of such estimators may have multiple disjoint intervals of support, possibly intersecting the negative half line. We show that the distribution of the extremal eigenvalue at each regular edge of the support has a GOE Tracy-Widom limit. Our proof extends a comparison argument of Ji Oon Lee and Kevin Schnelli, replacing a continuous Green function flow by a discrete Lindeberg swapping scheme.

math.PR↗

arXiv2020

Tree-Projected Gradient Descent for Estimating Gradient-Sparse Parameters on Graphs

We study estimation of a gradient-sparse parameter vector $\boldsymbolθ^* \in \mathbb{R}^p$, having strong gradient-sparsity $s^*:=\|\nabla_G \boldsymbolθ^*\|_0$ on an underlying graph $G$. Given observations $Z_1,\ldots,Z_n$ and a smooth, convex loss function $\mathcal{L}$ for which $\boldsymbolθ^*$ minimizes the population risk $\mathbb{E}[\mathcal{L}(\boldsymbolθ;Z_1,\ldots,Z_n)]$, we propose to estimate $\boldsymbolθ^*$ by a projected gradient descent algorithm that iteratively and approximately projects gradient steps onto spaces of vectors having small gradient-sparsity over low-degree spanning trees of $G$. We show that, under suitable restricted strong convexity and smoothness assumptions for the loss, the resulting estimator achieves the squared-error risk $\frac{s^*}{n} \log (1+\frac{p}{s^*})$ up to a multiplicative constant that is independent of $G$. In contrast, previous polynomial-time algorithms have only been shown to achieve this guarantee in more specialized settings, or under additional assumptions for $G$ and/or the sparsity pattern of $\nabla_G \boldsymbolθ^*$. As applications of our general framework, we apply our results to the examples of linear models and generalized linear models with random design.

stat.ML↗