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We prove the Jacquet--Rallis fundamental lemma for spherical Hecke algebras over local function fields using multiplicative Hitchin fibrations. Our work is inspired by the proof of [Yun11] in the Lie algebra case and builds upon the general framework of multiplicative Hitchin fibrations in [Wang24].

The NOEMA formIng Cluster survEy (NICE) is a large program targeting 69 massive galaxy group candidates at $z>2$ in six deep fields. We report spectroscopic confirmation of eight groups at $1.65\leq z\leq3.61$ in COSMOS. Homogeneously selected as significant overdensities of red IRAC sources with red Herschel colors, four groups are confirmed by CO and [CI] with NOEMA 3mm observations, three are confirmed with ALMA, and one is confirmed by H$\alpha$ from Subaru/FMOS. We constructed the integrated FIR SEDs for the eight groups, obtaining total IR SFR $=260-1300~{\rm M_\odot}$~yr$^{-1}$. We adopted six methods to estimate the dark matter masses, including stellar mass to halo mass relations, overdensity with galaxy bias, and NFW profile fitting to radial stellar mass density. We found the radial stellar mass density are consistent with a NFW profile, supporting that they are collapsed structures hosted by a single dark matter halo. The best halo mass estimates are $\log(M_{\rm h}/{\rm M_\odot})=12.8-13.7$ with uncertainty of 0.3 dex. From halo mass estimates, we derive baryonic accretion rate ${\rm BAR}=(1-8)\times10^{3}\,{\rm M_{\odot}/yr}$ for this sample. We find a quasi-linear correlation between the integrated SFR/BAR and the theoretical halo mass limit for cold streams, $M_{\rm stream}/M_{\rm h}$, with ${\rm SFR/BAR}=10^{-0.46\pm0.22}\left({M_{\rm stream}/M_{\rm h}}\right)^{0.71\pm0.16}$ with a scatter of $0.40\,{\rm dex}$. Further, we compare halo masses and stellar masses with simulations, and find all structures are consistent with being progenitors of $M_{\rm h}(z=0)>10^{14}\,{\rm M_{\odot}}$ galaxy clusters, and the most massive central galaxies have stellar masses consistent with brightest cluster galaxies (BCGs) progenitors in the TNG300 simulation. The results strongly suggest these structures are forming massive galaxy clusters via baryonic and dark matter accretion., Comment: 44 pages (27pp appendix), 32 figures, 18 tables, accepted for publication in A&A

Conformal prediction (CP) enables machine learning models to output prediction sets with guaranteed coverage rate, assuming exchangeable data. Unfortunately, the exchangeability assumption is frequently violated due to distribution shifts in practice, and the challenge is often compounded by the lack of ground truth labels at test time. Focusing on classification in this paper, our goal is to improve the quality of CP-generated prediction sets using only unlabeled data from the test domain. This is achieved by two new methods called ECP and EACP, that adjust the score function in CP according to the base model's uncertainty on the unlabeled test data. Through extensive experiments on a number of large-scale datasets and neural network architectures, we show that our methods provide consistent improvement over existing baselines and nearly match the performance of supervised algorithms.

We consider arithmetic analogs of the relative Langlands program and applications of new non-reductive geometry. Firstly, we introduce mirabolic special cycles, which produce special cycles on many Hodge type Rapoport-Zink spaces via pullbacks e.g. Kudla--Rapoport cycles. Secondly, we formulate arithmetic intersection problems for these cycles and formulate a method of arithmetic induction. As a main example, we formulate arithmetic twisted Gan--Gross--Prasad conjectures on unitary Shimura varieties and prove a key twisted arithmetic fundamental lemma using mirabolic special cycles, arithmetic inductions, and Weil type relative trace formulas., Comment: 42 pages, comments welcome!

The discovery of high-mobility two-dimensional electron gas and low carrier density superconductivity in multiple SrTiO$_3$-based heterostructures has stimulated intense interest in the surface properties of SrTiO$_3$. The recent discovery of high-T$_c$ superconductivity in the monolayer FeSe/SrTiO$_3$ aroused the upsurge and underscored the atomic precision probe of the surface structure. By performing atomically resolved cryogenic scanning tunneling microscopy/spectroscopy characterization on dual-TiO$_{2}$-${\delta}$-terminated SrTiO$_3$(001) surfaces with ($\sqrt{13}$ $\times$ $\sqrt{13}$), c(4 $\times$ 2), mixed (2 $\times$ 1), and (2 $\times$ 2) reconstructions, we disclosed universally broken rotational symmetry and contrasting bias- and temperature-dependent electronic states for apical and equatorial oxygen sites. With the sequentially evolved surface reconstructions and simultaneously increasing equatorial oxygen vacancies, the surface anisotropy reduces, and the work function lowers. Intriguingly, unidirectional stripe orders appear on the c(4 $\times$ 2) surface, whereas local (4 $\times$ 4) order emerges and eventually forms long-range unidirectional c(4 $\times$ 4) charge order on the (2 $\times$ 2) surface. This work reveals robust unidirectional charge orders induced by oxygen vacancies due to strong and delicate electronic-lattice interaction under broken rotational symmetry, providing insights into understanding the complex behaviors in perovskite oxide-based heterostructures.

A key challenge in lifelong reinforcement learning (RL) is the loss of plasticity, where previous learning progress hinders an agent's adaptation to new tasks. While regularization and resetting can help, they require precise hyperparameter selection at the outset and environment-dependent adjustments. Building on the principled theory of online convex optimization, we present a parameter-free optimizer for lifelong RL, called TRAC, which requires no tuning or prior knowledge about the distribution shifts. Extensive experiments on Procgen, Atari, and Gym Control environments show that TRAC works surprisingly well-mitigating loss of plasticity and rapidly adapting to challenging distribution shifts-despite the underlying optimization problem being nonconvex and nonstationary., Comment: Code and Website: https://computationalrobotics.seas.harvard.edu/TRAC/

Physics-based models are computationally time-consuming and infeasible for real-time scenarios of urban drainage networks, and a surrogate model is needed to accelerate the online predictive modelling. Fully-connected neural networks (NNs) are potential surrogate models, but may suffer from low interpretability and efficiency in fitting complex targets. Owing to the state-of-the-art modelling power of graph neural networks (GNNs) and their match with urban drainage networks in the graph structure, this work proposes a GNN-based surrogate of the flow routing model for the hydraulic prediction problem of drainage networks, which regards recent hydraulic states as initial conditions, and future runoff and control policy as boundary conditions. To incorporate hydraulic constraints and physical relationships into drainage modelling, physics-guided mechanisms are designed on top of the surrogate model to restrict the prediction variables with flow balance and flooding occurrence constraints. According to case results in a stormwater network, the GNN-based model is more cost-effective with better hydraulic prediction accuracy than the NN-based model after equal training epochs, and the designed mechanisms further limit prediction errors with interpretable domain knowledge. As the model structure adheres to the flow routing mechanisms and hydraulic constraints in urban drainage networks, it provides an interpretable and effective solution for data-driven surrogate modelling. Simultaneously, the surrogate model accelerates the predictive modelling of urban drainage networks for real-time use compared with the physics-based model.

We study online learning in adversarial nonstationary environments. Since the future can be very different from the past, a critical challenge is to gracefully forget the history while new data comes in. To formalize this intuition, we revisit the discounted regret in online convex optimization, and propose an adaptive (i.e., instance optimal), FTRL-based algorithm that improves the widespread non-adaptive baseline -- gradient descent with a constant learning rate. From a practical perspective, this refines the classical idea of regularization in lifelong learning: we show that designing good regularizers can be guided by the principled theory of adaptive online optimization. Complementing this result, we also consider the (Gibbs and Cand\`es, 2021)-style online conformal prediction problem, where the goal is to sequentially predict the uncertainty sets of a black-box machine learning model. We show that the FTRL nature of our algorithm can simplify the conventional gradient-descent-based analysis, leading to instance-dependent performance guarantees., Comment: ICML 2024

Volumetric videos, benefiting from immersive 3D realism and interactivity, hold vast potential for various applications, while the tremendous data volume poses significant challenges for compression. Recently, NeRF has demonstrated remarkable potential in volumetric video compression thanks to its simple representation and powerful 3D modeling capabilities, where a notable work is ReRF. However, ReRF separates the modeling from compression process, resulting in suboptimal compression efficiency. In contrast, in this paper, we propose a volumetric video compression method based on dynamic NeRF in a more compact manner. Specifically, we decompose the NeRF representation into the coefficient fields and the basis fields, incrementally updating the basis fields in the temporal domain to achieve dynamic modeling. Additionally, we perform end-to-end joint optimization on the modeling and compression process to further improve the compression efficiency. Extensive experiments demonstrate that our method achieves higher compression efficiency compared to ReRF on various datasets.

Despite the success of the Adam optimizer in practice, the theoretical understanding of its algorithmic components still remains limited. In particular, most existing analyses of Adam show the convergence rate that can be simply achieved by non-adative algorithms like SGD. In this work, we provide a different perspective based on online learning that underscores the importance of Adam's algorithmic components. Inspired by Cutkosky et al. (2023), we consider the framework called online learning of updates/increments, where we choose the updates/increments of an optimizer based on an online learner. With this framework, the design of a good optimizer is reduced to the design of a good online learner. Our main observation is that Adam corresponds to a principled online learning framework called Follow-the-Regularized-Leader (FTRL). Building on this observation, we study the benefits of its algorithmic components from the online learning perspective., Comment: Accepted at ICML 2024

The Five-hundred-meter Aperture Spherical radio Telescope (FAST) has the largest aperture and a 19-beam L-band receiver, making it powerful for investigating the neutral hydrogen atomic gas (HI) in the universe. We present HiFAST (https://hifast.readthedocs.io), a dedicated, modular, and self-contained calibration and imaging pipeline for processing the HI data of FAST. The pipeline consists of frequency-dependent noise diode calibration, baseline fitting, standing wave removal using an FFT-based method, flux density calibration, stray radiation correction, and gridding to produce data cubes. These modules can be combined as needed to process the data from most FAST observation modes: tracking, drift scanning, On-The-Fly mapping, and most of their variants. With HiFAST, the RMS noises of the calibrated spectra from all 19 beams were only slightly (~ 5%) higher than the theoretical expectation. The results for the extended source M33 and the point sources are consistent with the results from Arecibo. The moment maps (0,1 and 2) of M33 agree well with the results from the Arecibo Galaxy Environment Survey (AGES) with a fractional difference of less than 10%. For a common sample of 221 sources with signal-to-noise ratio S/N >10 from the Arecibo Legacy Fast ALFA (ALFALFA) survey, the mean value of fractional difference in the integrated flux density, $S_{\mathrm{int}}$, between the two datasets is approximately 0.005 %, with a dispersion of 15.4%. Further checks on the integrated flux density of 23 sources with seven observations indicate that the variance in the flux density of the source with luminous objects ($S_\mathrm{int}$ $ > 2.5$ Jy km s$^{-1}$) is less than 5%. Our tests suggest that the FAST telescope, with the efficient, precise, and user-friendly pipeline HiFAST, will yield numerous significant scientific findings in the investigation of the HI in the universe., Comment: Accepted by SCPMA. 21 pages, 14 figures. The pipeline is accessible at https://hifast.readthedocs.io

In this article, we prove that a version of Tate conjectures for certain Deligne-Lusztig varieties implies the Kudla-Rapoport conjecture for unitary Shimura varieties with maximal parahoric level at unramified primes. Furthermore, we prove that the Kudla-Rapoport conjecture holds unconditionally for several new cases in any dimension., Comment: 93 pages

We study unconstrained Online Linear Optimization with Lipschitz losses. Motivated by the pursuit of instance optimality, we propose a new algorithm that simultaneously achieves ($i$) the AdaGrad-style second order gradient adaptivity; and ($ii$) the comparator norm adaptivity also known as "parameter freeness" in the literature. In particular, - our algorithm does not employ the impractical doubling trick, and does not require an a priori estimate of the time-uniform Lipschitz constant; - the associated regret bound has the optimal $O(\sqrt{V_T})$ dependence on the gradient variance $V_T$, without the typical logarithmic multiplicative factor; - the leading constant in the regret bound is "almost" optimal. Central to these results is a continuous time approach to online learning. We first show that the aimed simultaneous adaptivity can be achieved fairly easily in a continuous time analogue of the problem, where the environment is modeled by an arbitrary continuous semimartingale. Then, our key innovation is a new discretization argument that preserves such adaptivity in the discrete time adversarial setting. This refines a non-gradient-adaptive discretization argument from (Harvey et al., 2023), both algorithmically and analytically, which could be of independent interest., Comment: ALT 2024

The cosmic-ray ionization rate (CRIR, $\zeta_2$) is one of the key parameters controlling the formation and destruction of various molecules in molecular clouds. However, the current most commonly used CRIR tracers, such as H$_3^+$, OH$^+$, and H$_2$O$^+$, are hard to detect and require the presence of background massive stars for absorption measurements. In this work, we propose an alternative method to infer the CRIR in diffuse clouds using the abundance ratios of OH/CO and HCO$^+$/CO. We have analyzed the response of chemical abundances of CO, OH, and HCO$^+$ on various environmental parameters of the interstellar medium in diffuse clouds and found that their abundances are proportional to $\zeta_2$. Our analytic expressions give an excellent calculation of the abundance of OH for $\zeta_2$ $\leq$10$^{-15}$ s$^{-1}$, which are potentially useful for modelling chemistry in hydrodynamical simulations. The abundances of OH and HCO$^+$ were found to monotonically decrease with increasing density, while the CO abundance shows the opposite trend. With high-sensitivity absorption transitions of both CO (1--0) and (2--1) lines from ALMA, we have derived the H$_2$ number densities ($n_{\rm H_2}$) toward 4 line-of-sights (LOSs); assuming a kinetic temperature of $T_{\rm k}=50\,{\rm K}$, we find a range of (0.14$\pm$0.03--1.2$\pm$0.1)$\times$10$^2$ cm$^{-3}$}. By comparing the observed and modelled HCO$^+$/CO ratios, we find that $\zeta_2$ in our diffuse gas sample is in the { range of $1.0_{-1.0}^{+14.8}$ $\times$10$^{-16}- 2.5_{-2.4}^{+1.4}$ $\times$10$^{-15}$ s$^{-1}$. This is $\sim$2 times higher than the average value measured at higher extinction, supporting an attenuation of CRs as suggested by theoretical models., Comment: 22 pages, 9 figures, accepted by ApJ

Motivated by the challenge of nonstationarity in sequential decision making, we study Online Convex Optimization (OCO) under the coupling of two problem structures: the domain is unbounded, and the comparator sequence $u_1,\ldots,u_T$ is arbitrarily time-varying. As no algorithm can guarantee low regret simultaneously against all comparator sequences, handling this setting requires moving from minimax optimality to comparator adaptivity. That is, sensible regret bounds should depend on certain complexity measures of the comparator relative to one's prior knowledge. This paper achieves a new type of these adaptive regret bounds via a sparse coding framework. The complexity of the comparator is measured by its energy and its sparsity on a user-specified dictionary, which offers considerable versatility. Equipped with a wavelet dictionary for example, our framework improves the state-of-the-art bound (Jacobsen & Cutkosky, 2022) by adapting to both ($i$) the magnitude of the comparator average $||\bar u||=||\sum_{t=1}^Tu_t/T||$, rather than the maximum $\max_t||u_t||$; and ($ii$) the comparator variability $\sum_{t=1}^T||u_t-\bar u||$, rather than the uncentered sum $\sum_{t=1}^T||u_t||$. Furthermore, our analysis is simpler due to decoupling function approximation from regret minimization., Comment: NeurIPS 2023

Owing to the recent identification of major substructures in our Milky Way (MW), the astronomical community has started to reevaluate the importance of dissolved and existing dwarf galaxies. In this work, we investigate up to 13 elements in 43 giant stars of the Sculptor dwarf galaxy (Scl) using high-signal-to-noise-ratio near-infrared (NIR) APOGEE spectra. Thanks to the strong feature lines in the NIR, we were able to determine high-resolution O, Si, and Al abundances for a large group of sample stars for the first time in Scl. By comparing the [$\alpha$/Fe] (i.e., O, Mg, Si, Ca, and Ti) of the stars in Scl, Sagittarius, and the MW, we confirm the general trend that less massive galaxies tend to show lower [$\alpha$/Fe]. The low [Al/Fe] ($\sim -0.5$) in Scl demonstrates the value of this ratio as a discriminator with which to identify stars born in dwarf galaxies (from MW field stars). A chemical-evolution model suggests that Scl has a top-light initial mass function (IMF), with a high-mass IMF power index of $\sim -2.7$, and a minimum Type Ia supernovae delay time of $\sim 100$ Myr. Furthermore, a linear regression analysis indicates a negative radial metallicity gradient and positive radial gradients for [Mg/Fe] and [Ca/Fe], in qualitative agreement with the outside-in formation scenario., Comment: A&A accepted

We report the discovery of a new 5.78 ms-period millisecond pulsar (MSP), PSR J1740-5340B (NGC 6397B), in an eclipsing binary system discovered with the Parkes radio telescope (now also known as Murriyang), Australia, and confirmed with the MeerKAT radio telescope in South Africa. The measured orbital period, 1.97 days, is the longest among all eclipsing binaries in globular clusters (GCs) and consistent with that of the coincident X-ray source U18, previously suggested to be a 'hidden MSP'. Our XMM-Newton observations during NGC 6397B's radio quiescent epochs detected no X-ray flares. NGC 6397B is either a transitional MSP or an eclipsing binary in its initial stage of mass transfer after the companion star left the main sequence. The discovery of NGC 6397B potentially reveals a subgroup of extremely faint and heavily obscured binary pulsars, thus providing a plausible explanation to the apparent dearth of binary neutron stars in core-collapsed GCs as well as a critical constraint on the evolution of GCs.

Practical online learning tasks are often naturally defined on unconstrained domains, where optimal algorithms for general convex losses are characterized by the notion of comparator adaptivity. In this paper, we design such algorithms in the presence of switching cost - the latter penalizes the typical optimism in adaptive algorithms, leading to a delicate design trade-off. Based on a novel dual space scaling strategy discovered by a continuous-time analysis, we propose a simple algorithm that improves the existing comparator adaptive regret bound [ZCP22a] to the optimal rate. The obtained benefits are further extended to the expert setting, and the practicality of the proposed algorithm is demonstrated through a sequential investment task., Comment: NeurIPS 2022

As the latest video coding standard, versatile video coding (VVC) has shown its ability in retaining pixel quality. To excavate more compression potential for video conference scenarios under ultra-low bitrate, this paper proposes a bitrate adjustable hybrid compression scheme for face video. This hybrid scheme combines the pixel-level precise recovery capability of traditional coding with the generation capability of deep learning based on abridged information, where Pixel wise Bi-Prediction, Low-Bitrate-FOM and Lossless Keypoint Encoder collaborate to achieve PSNR up to 36.23 dB at a low bitrate of 1.47 KB/s. Without introducing any additional bitrate, our method has a clear advantage over VVC under a completely fair comparative experiment, which proves the effectiveness of our proposed scheme. Moreover, our scheme can adapt to any existing encoder / configuration to deal with different encoding requirements, and the bitrate can be dynamically adjusted according to the network condition.

The physical mechanisms for starburst or quenching in less massive ($M_* < 10^{10} M_{\odot}$) galaxies are unclear. The merger is one of the inescapable processes referred to as both starburst and quenching in massive galaxies. However, the effects of the merger on star formation in dwarf galaxies and their evolution results are still uncertain. We aim to explore how to trigger and quench star formation in dwarf galaxies by studying the metal-poor gas-rich dwarf mergers based on the multi-band observations at a spatial resolution of $\sim$ 460 pc. We use the archival data of ALMA (band 3, 8) and VLT/MUSE to map CO($J=$1-0), [CI]($^3$P$_1 - ^3$P$_0$), and H$\alpha$ emission in one of the most extreme starburst merging dwarf galaxies, Haro 11. We find the molecular gas is assembled around the central two star-forming regions. The molecular/ionized gas and stellar components show complex kinematics, indicating that the gas is probably at a combined stage of collision of clouds and feedback from star formation. The peak location and distribution of [CI](1-0) strongly resemble the CO(1-0) emission, meaning that it might trace the same molecular gas as CO in such a dwarf merger starburst galaxy. The enhancement of line ratios ($\sim 0.5$) of [CI]/CO around knot C is probably generated by the dissociation of CO molecules by cosmic rays and far-ultraviolet photons. Globally, Haro 11 and its star-forming regions share similar SFEs as the high-$z$ starburst galaxies or the clumps in nearby (U)LIRGs. Given the high SFE, sSFR, small stellar mass, low metallicity, and deficient HI gas, Haro 11 could be an analog of high-$z$ dwarf starburst and the potential progenitor of the nearby less massive elliptical galaxies. The significantly smaller turbulent pressure and viral parameter will probably trigger the intense starbursts. We also predict that it will quench at $M_* < 8.5 \times 10^9 M_{\odot}$., Comment: 14 pages, 10 figures; accepted for publication in A&A

Unconstrained Online Linear Optimization (OLO) is a practical problem setting to study the training of machine learning models. Existing works proposed a number of potential-based algorithms, but in general the design of these potential functions relies heavily on guessing. To streamline this workflow, we present a framework that generates new potential functions by solving a Partial Differential Equation (PDE). Specifically, when losses are 1-Lipschitz, our framework produces a novel algorithm with anytime regret bound $C\sqrt{T}+||u||\sqrt{2T}[\sqrt{\log(1+||u||/C)}+2]$, where $C$ is a user-specified constant and $u$ is any comparator unknown and unbounded a priori. Such a bound attains an optimal loss-regret trade-off without the impractical doubling trick. Moreover, a matching lower bound shows that the leading order term, including the constant multiplier $\sqrt{2}$, is tight. To our knowledge, the proposed algorithm is the first to achieve such optimalities., Comment: ICML 2022