Miracle-dz/UniFAR-FTUs huggingface dataset:
The Discovery of Blue-cored Dwarf Early-type Galaxies in Isolated Environments

The presence of blue-cored dwarf early-type galaxies (dE(bc)s) in high-density environments supports the scenario of the transformation of infalling late-type galaxies into quiescent dwarf early-type galaxies by environmental effects. While low-density environments lacking environmental processes could not be relevant to the formation of dE(bc)s, we discovered a large sample of rare dE(bc)s in isolated environments at z < 0.01 using the NASA–Sloan Atlas catalog. Thirty-two isolated dE(bc)s were identified by visual inspection of the Sloan Digital Sky Survey images and g − r color profiles. We found that (1) isolated dE(bc)s exhibit similar structural parameters to dE(bc)s in the Virgo cluster; (2) based on the color–magnitude relation, color gradients, and optical emission lines of dE(bc)s, isolated dE(bc)s show more vigorous, centrally concentrated star formation (SF) compared to their counterparts in the Virgo cluster; (3) at a given stellar mass, isolated dE(bc)s tend to have a larger fraction of gas mass than their Virgo counterparts. We discuss a scenario of episodic SF sustained by gas accretion, suggested by Sánchez Almeida et al., in which the star-bursting blue compact dwarf galaxy (BCD)−quiescent BCD (QBCD) cycle can be repeated during the Hubble time. We suggest that, in this cadence, isolated dE(bc)s might be QBCDs at pre- or post-BCD stages. Our results imply that dE(bc)s comprise a mixture of objects with two types of origins, nature or nurture, depending on their environment.
Almost Sure Saddle Avoidance of Stochastic Gradient Methods without the Bounded Gradient Assumption

We prove that various stochastic gradient descent methods, including the stochastic gradient descent (SGD), stochastic heavy-ball (SHB), and stochastic Nesterov's accelerated gradient (SNAG) methods, almost surely avoid any strict saddle manifold. To the best of our knowledge, this is the first time such results are obtained for SHB and SNAG methods. Moreover, our analysis expands upon previous studies on SGD by removing the need for bounded gradients of the objective function and uniformly bounded noise. Instead, we introduce a more practical local boundedness assumption for the noisy gradient, which is naturally satisfied in empirical risk minimization problems typically seen in training of neural networks.
Quadrature Mirror Filters, Low Crest Factor Arrays, Functions Achieving Optimal Uncertainty Principle Bounds, and Complete Orthonormal Sequences—A Unified Approach

Abstract Quadrature mirror filters are used throughout image and speech analysis; low crest factor arrays play an important role in many problems in antenna design and communication; uncertainty principle bounds limit resolution in time-frequency analysis and other areas; and complete orthonormal sequences are crucial in essentially all applications of mathematics to science and engineering. We present a single construction which unifies these four concepts.
Do Deep Neural Networks Capture Compositionality in Arithmetic Reasoning?

Compositionality is a pivotal property of symbolic reasoning. However, how well recent neural models capture compositionality remains underexplored in the symbolic reasoning tasks. This study empirically addresses this question by systematically examining recently published pre-trained seq2seq models with a carefully controlled dataset of multi-hop arithmetic symbolic reasoning. We introduce a skill tree on compositionality in arithmetic symbolic reasoning that defines the hierarchical levels of complexity along with three compositionality dimensions: systematicity, productivity, and substitutivity. Our experiments revealed that among the three types of composition, the models struggled most with systematicity, performing poorly even with relatively simple compositions. That difficulty was not resolved even after training the models with intermediate reasoning steps.
HALO7D. III. Chemical Abundances of Milky Way Halo Stars from Medium-resolution Spectra

The Halo Assembly in Lambda Cold Dark Matter: Observations in 7 Dimensions (HALO7D) survey measures the kinematics and chemical properties of stars in the Milky Way (MW) stellar halo to learn about the formation of our Galaxy. HALO7D consists of Keck II/DEIMOS spectroscopy and Hubble Space Telescope–measured proper motions of MW halo main-sequence turnoff stars in the four Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey fields. HALO7D consists of deep pencil beams, making it complementary to other contemporary wide-field surveys. We present the [Fe/H] and [α/Fe] abundances for 113 HALO7D stars in the Galactocentric radial range of ∼10–40 kpc along four separate pointings. Using the full 7D chemodynamical data (3D positions, 3D velocities, and abundances) of HALO7D, we measure the velocity anisotropy, β, of the halo velocity ellipsoid for each field and for different metallicity-binned subsamples. We find that two of the four fields have stars on very radial orbits, while the remaining two have stars on more isotropic orbits. Separating the stars into high-, mid-, and low-[Fe/H] bins at −2.2 and −1.1 dex for each field separately, we find differences in the anisotropies between the fields and between the bins; some fields appear dominated by radial orbits in all bins, while other fields show variation between the [Fe/H] bins. These chemodynamical differences are evidence that the HALO7D fields have different fractional contributions from the progenitors that built up the MW stellar halo. Our results highlight the additional information available on smaller spatial scales compared to results from a spherical average of the stellar halo.
Denoising Diffusion Probabilistic Models for Robust Image Super-Resolution in the Wild

Diffusion models have shown promising results on single-image super-resolution and other image- to-image translation tasks. Despite this success, they have not outperformed state-of-the-art GAN models on the more challenging blind super-resolution task, where the input images are out of distribution, with unknown degradations. This paper introduces SR3+, a diffusion-based model for blind super-resolution, establishing a new state-of-the-art. To this end, we advocate self-supervised training with a combination of composite, parameterized degradations for self-supervised training, and noise-conditioing augmentation during training and testing. With these innovations, a large-scale convolutional architecture, and large-scale datasets, SR3+ greatly outperforms SR3. It outperforms Real-ESRGAN when trained on the same data, with a DRealSR FID score of 36.82 vs. 37.22, which further improves to FID of 32.37 with larger models, and further still with larger training sets.
Global classical solution to 1D compressible Navier–Stokes equations with no vacuum at infinity

C. Miao In this paper, we are concerned with the 1D Cauchy problem of the compressible Navier–Stokes equations with the viscosity μ(ρ) = 1+ρβ(β≥0). The initial density can be arbitrarily large and keep a non‐vacuum state ρ̄>0 at far fields. We will establish the global existence of the classical solution for 0≤β < γ via a priori estimates when the initial density contains vacuum in interior interval or is away from the vacuum. We will show that the solution will not develop vacuum in any finite time if the initial density is away from the vacuum. To study the well‐posedness of the problem, it is crucial to obtain the upper bound of the density. Some new weighted estimates are applied to obtain our main results. Copyright © 2015 John Wiley & Sons, Ltd.
Speculative Decoding with Big Little Decoder

The recent emergence of Large Language Models based on the Transformer architecture has enabled dramatic advancements in the field of Natural Language Processing. However, these models have long inference latency, which limits their deployment and makes them prohibitively expensive for various real-time applications. The inference latency is further exacerbated by autoregressive generative tasks, as models need to run iteratively to generate tokens sequentially without leveraging token-level parallelization. To address this, we propose Big Little Decoder (BiLD), a framework that can improve inference efficiency and latency for a wide range of text generation applications. The BiLD framework contains two models with different sizes that collaboratively generate text. The small model runs autoregressively to generate text with a low inference cost, and the large model is only invoked occasionally to refine the small model's inaccurate predictions in a non-autoregressive manner. To coordinate the small and large models, BiLD introduces two simple yet effective policies: (1) the fallback policy that determines when to hand control over to the large model; and (2) the rollback policy that determines when the large model needs to correct the small model's inaccurate predictions. To evaluate our framework across different tasks and models, we apply BiLD to various text generation scenarios encompassing machine translation on IWSLT 2017 De-En and WMT 2014 De-En, and summarization on XSUM and CNN/DailyMail. On an NVIDIA T4 GPU, our framework achieves a speedup of up to 2.12x speedup with minimal generation quality degradation. Furthermore, our framework is fully plug-and-play and can be applied without any modifications in the training process or model architecture. Our code is open-sourced
The Geometry of Neural Nets' Parameter Spaces Under Reparametrization

Model reparametrization, which follows the change-of-variable rule of calculus, is a popular way to improve the training of neural nets. But it can also be problematic since it can induce inconsistencies in, e.g., Hessian-based flatness measures, optimization trajectories, and modes of probability densities. This complicates downstream analyses: e.g. one cannot definitively relate flatness with generalization since arbitrary reparametrization changes their relationship. In this work, we study the invariance of neural nets under reparametrization from the perspective of Riemannian geometry. From this point of view, invariance is an inherent property of any neural net if one explicitly represents the metric and uses the correct associated transformation rules. This is important since although the metric is always present, it is often implicitly assumed as identity, and thus dropped from the notation, then lost under reparametrization. We discuss implications for measuring the flatness of minima, optimization, and for probability-density maximization. Finally, we explore some interesting directions where invariance is useful.
Path-sensitive Type Analysis with Backward Analysis for Quality Assurance of Dynamic Typed Language Code

Precise and fast static type analysis for dynamically typed language is very difficult. This is mainly because the lack of static type information makes it difficult to approximate all possible values of a variable. Actually, the existing static type analysis methods are imprecise or slow. In this paper, we propose a novel method to improve the precision of static type analysis for Python code, where a backward analysis is used to obtain the path-sensitivity. By doing so, our method aims to obtain more precise static type information, which contributes to the overall improvement of static analysis. To show the effectiveness of our method, we conducted a preliminary experiment to compare our method implementation and the existing analysis tool with respect to precision and time efficiency. The result shows our method provides more precise type analysis with fewer false positives than the existing static type analysis tool. Also it shows our proposed method increases the analysis time, but it is still within the range of practical use.
Penetration of fields through a circular hole in a wall of finite thickness

Consideration is given to a uniform, static electric field on one side of a plane metallic wall of finite thickness with a circular hole. The field induces a charge distribution on the metallic surface which behaves, at large distances from the hole, as a dipole moment, with different values for the polarizability on the inside (same side as the driving field) and outside surfaces of the hole. Two integral equations are derived for the potential in the hole and variational forms are constructed for the symmetric and asymmetric polarizabilities. Trial functions with adjustable parameters lead to accurate numerical values for the inside and outside polarizabilities. A similar approach yields corresponding values for the inside and outside magnetic susceptibilities. >
CUTS: Neural Causal Discovery from Irregular Time-Series Data

Causal discovery from time-series data has been a central task in machine learning. Recently, Granger causality inference is gaining momentum due to its good explainability and high compatibility with emerging deep neural networks. However, most existing methods assume structured input data and degenerate greatly when encountering data with randomly missing entries or non-uniform sampling frequencies, which hampers their applications in real scenarios. To address this issue, here we present CUTS, a neural Granger causal discovery algorithm to jointly impute unobserved data points and build causal graphs, via plugging in two mutually boosting modules in an iterative framework: (i) Latent data prediction stage: designs a Delayed Supervision Graph Neural Network (DSGNN) to hallucinate and register unstructured data which might be of high dimension and with complex distribution; (ii) Causal graph fitting stage: builds a causal adjacency matrix with imputed data under sparse penalty. Experiments show that CUTS effectively infers causal graphs from unstructured time-series data, with significantly superior performance to existing methods. Our approach constitutes a promising step towards applying causal discovery to real applications with non-ideal observations.
Shape and multiple shape coexistence of nuclei within covariant density functional theory

Shape and multiple shape coexistence of nuclei are investigated throughout the nuclear chart by calculating the low-lying spectra and the quadrupole shape invariants for even-even nuclei with $10\leq Z\leq 104$ from the proton drip line to the neutron one within a five-dimensional collective Hamiltonian based on the covariant density functional PC-PK1. The quadrupole shape invariants are implemented to characterize the quadrupole deformations of low-lying $0^+$ states and predict nuclear mass regions of shape and multiple shape coexistence. The predicted low-lying spectra and the shape or multi-shape coexisting nuclei are overall in good agreement with the available experimental results. In addition, the present work predicts a wealth of nuclei with shape or multiple shape coexistence in the neutron-rich regions. The connection between the strong $E0$ transition strength and the occurrence of shape coexistence is analyzed systemically. It is found that nuclei with pronounced shape coexistence generally have strong $E0$ transition strengths, while the reverse may not be true. The present results can serve as useful guidelines for experimental searches and theoretical studies of shape and multiple shape coexistence, especially in neutron-rich regions.
A Provably Improved Algorithm for Crowdsourcing with Hard and Easy Tasks

Crowdsourcing is a popular method used to estimate ground-truth labels by collecting noisy labels from workers. In this work, we are motivated by crowdsourcing applications where each worker can exhibit two levels of accuracy depending on a task's type. Applying algorithms designed for the traditional Dawid-Skene model to such a scenario results in performance which is limited by the hard tasks. Therefore, we first extend the model to allow worker accuracy to vary depending on a task's unknown type. Then we propose a spectral method to partition tasks by type. After separating tasks by type, any Dawid-Skene algorithm (i.e., any algorithm designed for the Dawid-Skene model) can be applied independently to each type to infer the truth values. We theoretically prove that when crowdsourced data contain tasks with varying levels of difficulty, our algorithm infers the true labels with higher accuracy than any Dawid-Skene algorithm. Experiments show that our method is effective in practical applications.
The Quest for the Missing Dust. II. Two Orders of Magnitude of Evolution in the Dust-to-gas Ratio Resolved within Local Group Galaxies

We explore evolution in the dust-to-gas ratio with density within four well-resolved Local Group galaxies—the LMC, SMC, M31, and M33. We do this using new Herschel maps, which restore extended emission that was missed by previous Herschel reductions. Combining this sensitivity to diffuse dust emission with excellent physical resolution allows us to probe the dust-to-gas ratio across 2.5 orders of magnitude in interstellar medium (ISM) surface density. We find a significant increase in the dust-to-gas ratio with density, with the dust-to-gas ratio varying within each galaxy by up to a factor 22.4, as density changes. We explore several possible reasons for this, and our favored explanation is that it is being driven by dust grain growth in denser regions of the ISM. We find that the evolution of the dust-to-gas ratio with ISM surface density is very similar between M31 and M33, despite their large differences in mass, metallicity, and star formation rate; conversely, we find M33 and the LMC to have very different dust-to-gas evolution profiles, despite their close similarity in those properties. Our dust-to-gas ratios address previous disagreement between UV- and far-IR-based dust-to-gas estimates for the Magellanic Clouds, removing the disagreement for the LMC, and considerably reducing it for the SMC—with our new dust-to-gas measurements being factors of 2.4 and 2.0 greater than the previous far-IR estimates, respectively. We also observe that the dust-to-gas ratio appears to fall at the highest densities for the LMC, M31, and M33; this is unlikely to be an actual physical phenomenon, and we posit that it may be due to a combined effect of dark gas, and changing dust mass opacity.
UV–Optical Disk Reverberation Lags despite a Faint X-Ray Corona in the Active Galactic Nucleus Mrk 335

We present the first results from a 100-day Swift, NICER, and ground-based X-ray–UV–optical reverberation mapping campaign of the Narrow-line Seyfert 1 Mrk 335, when it was in an unprecedented low X-ray flux state. Despite dramatic suppression of the X-ray variability, we still observe UV–optical lags as expected from disk reverberation. Moreover, the UV–optical lags are consistent with archival observations when the X-ray luminosity was >10 times higher. Interestingly, both low- and high-flux states reveal UV–optical lags that are 6–11 times longer than expected from a thin disk. These long lags are often interpreted as due to contamination from the broad line region; however the u-band excess lag (containing the Balmer jump from the diffuse continuum) is less prevalent than in other active galactic nuclei. The Swift campaign showed a low X-ray-to-optical correlation (similar to previous campaigns), but NICER and ground-based monitoring continued for another 2 weeks, during which the optical rose to the highest level of the campaign, followed ∼10 days later by a sharp rise in X-rays. While the low X-ray countrate and relatively large systematic uncertainties in the NICER background make this measurement challenging, if the optical does lead X-rays in this flare, this indicates a departure from the zeroth-order reprocessing picture. If the optical flare is due to an increase in mass accretion rate, this occurs on much shorter than the viscous timescale. Alternatively, the optical could be responding to an intrinsic rise in X-rays that is initially hidden from our line of sight.
Generation of Highlights From Research Papers Using Pointer-Generator Networks and SciBERT Embeddings

Nowadays many research articles are prefaced with research highlights to summarize the main findings of the paper. Highlights not only help researchers precisely and quickly identify the contributions of a paper, they also enhance the discoverability of the article via search engines. We aim to automatically construct research highlights given certain segments of a research paper. We use a pointer-generator network with coverage mechanism and a contextual embedding layer at the input that encodes the input tokens into SciBERT embeddings. We test our model on a benchmark dataset, CSPubSum, and also present MixSub, a new multi-disciplinary corpus of papers for automatic research highlight generation. For both CSPubSum and MixSub, we have observed that the proposed model achieves the best performance compared to related variants and other models proposed in the literature. On the CSPubSum dataset, our model achieves the best performance when the input is only the abstract of a paper as opposed to other segments of the paper. It produces ROUGE-1, ROUGE-2 and ROUGE-L F1-scores of 38.26, 14.26 and 35.51, respectively, METEOR score of 32.62, and BERTScore F1 of 86.65 which outperform all other baselines. On the new MixSub dataset, where only the abstract is the input, our proposed model (when trained on the whole training corpus without distinguishing between the subject categories) achieves ROUGE-1, ROUGE-2 and ROUGE-L F1-scores of 31.78, 9.76 and 29.3, respectively, METEOR score of 24.00, and BERTScore F1 of 85.25.
Evidence of Demographic rather than Ideological Segregation in News Discussion on Reddit

We evaluate homophily and heterophily among ideological and demographic groups in a typical opinion formation context: online discussions of current news. We analyze user interactions across five years in the r/news community on Reddit, one of the most visited websites in the United States. Then, we estimate demographic and ideological attributes of these users. Thanks to a comparison with a carefully-crafted network null model, we establish which pairs of attributes foster interactions and which ones inhibit them. Individuals prefer to engage with the opposite ideological side, which contradicts the echo chamber narrative. Instead, demographic groups are homophilic, as individuals tend to interact within their own group—even in an online setting where such attributes are not directly observable. In particular, we observe age and income segregation consistently across years: users tend to avoid interactions when belonging to different groups. These results persist after controlling for the degree of interest by each demographic group in different news topics. Our findings align with the theory that affective polarization—the difficulty in socializing across political boundaries—is more connected with an increasingly divided society, rather than ideological echo chambers on social media. We publicly release our anonymized data set and all the code to reproduce our results.1