Miracle-dz/UniFAR-FTUs huggingface dataset:
Implicit Regularization for Optimal Sparse Recovery

We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under the restricted isometry assumption. For a given parametrization yielding a non-convex optimization problem, we show that prescribed choices of initialization, step size and stopping time yield a statistically and computationally optimal algorithm that achieves the minimax rate with the same cost required to read the data up to poly-logarithmic factors. Beyond minimax optimality, we show that our algorithm adapts to instance difficulty and yields a dimension-independent rate when the signal-to-noise ratio is high enough. Key to the computational efficiency of our method is an increasing step size scheme that adapts to refined estimates of the true solution. We validate our findings with numerical experiments and compare our algorithm against explicit $\ell_{1}$ penalization. Going from hard instances to easy ones, our algorithm is seen to undergo a phase transition, eventually matching least squares with an oracle knowledge of the true support.
Correlation measures and distillable entanglement in 
AdS/CFT

Recent developments have exposed close connections between quantum information and holography. In this paper, we explore the geometrical interpretations of the recently introduced $Q$-correlation and $R$-correlation, $E_Q$ and $E_R$. We find that $E_Q$ admits a natural geometric interpretation via the surface-state correspondence: it is a minimal mutual information between a surface region $A$ and a cross-section of $A$'s entanglement wedge with $B$. We note a strict trade-off between this minimal mutual information and the symmetric side-channel assisted distillable entanglement from the environment $E$ to $A$, $I^{ss}(E\rangle A)$. We also show that the $R$-correlation, $E_R$, coincides holographically with the entanglement wedge cross-section. This further elucidates the intricate relationship between entanglement, correlations, and geometry in holographic field theories.
Critical corrections to formulations of nonlinear energy dissipation of ultrasonically excited bubbles and a unifying parameter to asses and enhance bubble activity in applications

Nonlinear oscillations of bubbles can significantly increase the attenuation of the host media. Optimization of bubble related applications needs a realistic estimation of the medium attenuation and bubble activity. A correct estimation of the wave attenuation in bubbly media requires an accurate estimation of the power dissipated by nonlinear oscillations of bubbles. Pioneering work of Louisnard \cite{1} meticulously derived the nonlinear energy terms for viscous and thermal damping; however, radiation damping arising from the compressibility of the liquid was neglected. Jamshidi $\&$ Brenner \cite{2} have considered the effects of the compressibility of the liquid and showed that damping due to radiation becomes the most significant factor at pressures above the blake threshold. Despite the improvement in their formulation; however, the radiation damping term estimates non-physical values for some frequency and pressure regions including near resonance oscillations. Thus, the new terms arising from the compressibility of the liquid needs critical assessment. In this work, we provide critical corrections to the present formulations. Importance of the new corrections are highlighted by the scattering to damping ratio (STDR). We then introduce a unifying parameter to assess the efficacy of applications; this parameter is defined as the multiplication of maximum scattered pressure by STDR.
Re. I. Understanding galaxy sizes, associated luminosity densities, and the artificial division of the early-type galaxy population

Abstract For decades, the deceptive simplicity of the radius $R_{\rm e}$ , enclosing an arbitrary 50% of a galaxy’s light, has hamstrung the understanding of early-type galaxies (ETGs). Half a century ago, using these ‘effective half-light’ radii from de Vaucouleurs’ $R^{1/4}$ model, Sérsic reported that bright ETGs follow the relation $\mathfrak{M}_B\propto2.5\log R_{\rm e}$ ; and consequently, one has that $\langle\mu\rangle_{\rm e}\propto2.5\log R_{\rm e}$ and $\mu_{\rm e}\propto2.5\log R_{\rm e}$ , where $\mu_{\rm e}$ and $\langle\mu\rangle_{\rm e}$ are the effective surface brightness at $R_{\rm e}$ and the mean effective surface brightness within $R_{\rm e}$ , respectively. Sérsic additionally observed an apparent transition which led him to advocate for a division between what he called dwarf and giant ETGs; a belief frequently restated to occur at $\mathfrak{M}_B \approx -18$ mag or $n\approx 2.5$ . Here, the location of this false dichotomy in diagrams using ‘effective’ parameters is shown to change by more than 3 mag simply depending on the arbitrary percentage of light used to quantify a galaxy’s size. A range of alternative radii are explored, including where the projected intensity has dropped by a fixed percentage plus a battery of internal radii, further revealing that the transition at $\mathfrak{M}_B \approx -18$ mag is artificial and does not demark a boundary between different physical processes operating on the ETG population. The above understanding surrounding the effective radius $R_{\rm e}$ is of further importance because quantities such as dynamical mass $\sigma^2R/G$ , gravitational-binding energy $GM^2/R$ , acceleration $GM/R^2$ , and the ‘Fundamental Plane’ also depend on the arbitrary percentage of light used to define R, with implications for dark matter estimates, galaxy formation theories, compact massive galaxies, studies of peculiar velocity flows, and more. Finally, some of the vast literature which has advocated for segregating the ETG population at $\mathfrak{M}_B \approx -18$ mag ( $M\approx1$ – $2\times10^{10}\,{\rm M}_{\odot}$ ) is addressed, and it is revealed how this pervasive mindset has spilled over to influence both the classical bulge versus pseudobulge debate and recently also correlations involving supermassive black hole masses.
SciBERT: A Pretrained Language Model for Scientific Text

Obtaining large-scale annotated data for NLP tasks in the scientific domain is challenging and expensive. We release SciBERT, a pretrained language model based on BERT (Devlin et. al., 2018) to address the lack of high-quality, large-scale labeled scientific data. SciBERT leverages unsupervised pretraining on a large multi-domain corpus of scientific publications to improve performance on downstream scientific NLP tasks. We evaluate on a suite of tasks including sequence tagging, sentence classification and dependency parsing, with datasets from a variety of scientific domains. We demonstrate statistically significant improvements over BERT and achieve new state-of-the-art results on several of these tasks. The code and pretrained models are available at https://github.com/allenai/scibert/.
Amplitude analysis of the $B^+ \rightarrow \pi^+\pi^+\pi^-$ decay.

The results of an amplitude analysis of the charmless three-body decay $B^+ \rightarrow \pi^+\pi^+\pi^-$, in which $C\! P$-violation effects are taken into account, are reported. The analysis is based on a data sample corresponding to an integrated luminosity of $3 \text{fb}^{-1}$ of $pp$ collisions recorded with the LHCb detector. The most challenging aspect of the analysis is the description of the behaviour of the $\pi^+ \pi^-$ S-wave contribution, which is achieved by using three complementary approaches based on the isobar model, the K-matrix formalism, and a quasi-model-independent procedure. Additional resonant contributions for all three methods are described using a common isobar model, and include the $\rho(770)^0$, $\omega(782)$ and $\rho(1450)^0$ resonances in the $\pi^+\pi^-$ P-wave, the $f_2(1270)$ resonance in the $\pi^+\pi^-$ D-wave, and the $\rho_3(1690)^0$ resonance in the $\pi^+\pi^-$ F-wave. Significant $C\! P$-violation effects are observed in both S- and D-waves, as well as in the interference between the S- and P-waves. The results from all three approaches agree and provide new insight into the dynamics and the origin of $C\! P$-violation effects in $B^+ \rightarrow \pi^+\pi^+\pi^-$ decays.
Holomorphic Euler number of K$\ddot{a}$hler manifolds with almost nonnegative Ricci curvature

Let $M^n$ be a compact K$\ddot{a}$hler manifold with almost nonnegative Ricci curvature and nonzero first Betti number. We show that the holomorphic Euler number of $M^n$ vanishes, which gives a new obstruction for compact complex manifolds admitting K$\ddot{a}$hler metrics with almost nonnegative Ricci curvature. A crucial step in the proof is to show a vanishing theorem of Dolbeault-Morse-Novikov cohomology.
Decoupling and Matching Strategies for Compact Antenna Arrays

Antenna arrays have been used in various applications and have become an important tool to achieve high spectral efficiency in wireless communications. Its use brings to the communications system an increase in performance in terms of capacity and reliability. Recently one of the main communications architectures that makes use of antenna arrays is the Multiple-Input Multiple-Output (MIMO) technology. MIMO technology has been applied in antenna arrays composed of elements in the order of tens to hundreds. In this way, it is necessary to use the structure of compact antennas that offer all the necessary robustness to the applied project. In this context, it is important to revisit the concepts of mutual coupling and impedance matching among antenna elements in an array. This paper proposes and evaluates three strategies of joint decoupling and impedance matching networks(DMN) for antenna arrays. The first method called DMN with Lumped Elements (DMN-LE) performs the decoupling and impedance matching steps with capacitors and inductors. The second method is called the Ring Hybrid (DMN-RH). It is utilizes a microstrip line in the ring form. With this approach is achieved first the decoupling followed by impedance matching steps. The third method is called Networkless Decoupling and Matching (NDM). It brings a concept of decoupling without the presence of a network itself. A comparison of the methods is performed both analytically and via computer simulations. We conclude that the third method, networkless one, is an interesting new alternative approach.
A Lightweight and Accurate Localization Algorithm Using Multiple Inertial Measurement Units

This paper proposes a novel inertial-aided localization approach by fusing information from multiple inertial measurement units (IMUs) and exteroceptive sensors. IMU is a low-cost motion sensor which provides measurements on angular velocity and gravity compensated linear acceleration of a moving platform, and widely used in modern localization systems. To date, most existing inertial-aided localization methods exploit only one single IMU. While the single-IMU localization yields acceptable accuracy and robustness for different use cases, the overall performance can be further improved by using multiple IMUs. To this end, we propose a lightweight and accurate algorithm for fusing measurements from multiple IMUs and exteroceptive sensors, which is able to obtain noticeable performance gain without incurring additional computational cost. To achieve this, we first probabilistically map measurements from all IMUs onto a virtual IMU. This step is performed by stochastic estimation with least-square estimators and probabilistic marginalization of inter-IMU rotational accelerations. Subsequently, the propagation model for both state and error state of the virtual IMU is also derived, which enables the use of the classical filter-based or optimization-based sensor fusion algorithms for localization. Finally, results from both simulation and real-world tests are provided, which demonstrate that the proposed algorithm outperforms competing algorithms by noticeable margins.
Unified $\ell_{2\rightarrow\infty}$ Eigenspace Perturbation Theory for Symmetric Random Matrices

Modern applications in statistics, computer science and network science have seen tremendous values of finer matrix spectral perturbation theory. In this paper, we derive a generic $\ell_{2\rightarrow\infty}$ eigenspace perturbation bound for symmetric random matrices, with independent or dependent entries and fairly flexible entry distributions. In particular, we apply our generic bound to binary random matrices with independent entries or with certain dependency structures, including the unnormalized Laplacian of inhomogenous random graphs and $m$-dependent matrices. Through a detailed comparison, we found that for binary random matrices with independent entries, our $\ell_{2\rightarrow\infty}$ bound is tighter than all existing bounds that we are aware of, while our condition is weaker than all but one of them in a less common regime. We apply our perturbation bounds in three problems and improve the state of the art: concentration of the spectral norm of sparse random graphs, exact recovery of communities in stochastic block models and partial consistency of divisive hierarchical clustering. Finally we discuss the extensions of our theory to random matrices with more complex dependency structures and non-binary entries, asymmetric rectangular matrices and induced perturbation theory in other metrics.
Extremal Graphs with Local Covering Conditions

We systematically study a natural problem in extremal graph theory, to minimize the number of edges in a graph with a fixed number of vertices, subject to a certain local condition: each vertex must be in a copy of a fixed graph $H$. We completely solve this problem when $H$ is a clique, as well as more generally when $H$ is any regular graph with degree at least about half its number of vertices. We also characterize the extremal graphs when $H$ is an Erdős-Renyi random graph. The extremal structures turn out to have the same form as the conjectured extremal structures for a well-studied but elusive problem of similar flavor with local constraints: to maximize the number of copies of a fixed clique in graphs in which all degrees have a fixed upper bound.
The MUSE Ultra Deep Field (MUDF). II. Survey design and the gaseous properties of galaxy groups at 0.5 < z < 1.5

We present the goals, design, and first results of the MUSE Ultra Deep Field (MUDF) survey, a large programme using the Multi Unit Spectroscopic Explorer (MUSE) instrument at the ESO Very Large Telescope. The MUDF survey is collecting ≈150 h on-source of integral field optical spectroscopy in a 1.5 × 1.2 arcmin2 region which hosts several astrophysical structures along the line of sight, including two bright z ≈ 3.2 quasars with close separation (≈500 kpc). Following the description of the data reduction procedures, we present the analysis of the galaxy environment and gaseous properties of seven groups detected at redshifts 0.5 < z < 1.5, spanning a large dynamic range in halo mass, $\log (M_h/\rm {M_\odot }) \approx 11 - 13.5$. For four of the groups, we find associated Mg ii absorbers tracing cool gas in high-resolution spectroscopy of the two quasars, including one case of correlated absorption in both sightlines at distance ≈480 kpc. The absorption strength associated with the groups is higher than what has been reported for more isolated galaxies of comparable mass and impact parameters. We do not find evidence for widespread cool gas giving rise to strong absorption within these groups. Combining these results with the distribution of neutral and ionized gas seen in emission in lower redshift groups, we conclude that gravitational interactions in the group environment strip gas from the galaxy haloes into the intragroup medium, boosting the cross-section of cool gas and leading to the high fraction of strong Mg ii absorbers that we detect.
Simulating Metal Mixing of Both Common and Rare Enrichment Sources in a Low-mass Dwarf Galaxy

One-zone models constructed to match observed stellar abundance patterns have been used extensively to constrain the sites of nucleosynthesis with sophisticated libraries of stellar evolution and stellar yields. The metal mixing included in these models is usually highly simplified, although it is likely to be a significant driver of abundance evolution. In this work we use high-resolution hydrodynamics simulations to investigate how metals from individual enrichment events with varying source energies Eej mix throughout the multiphase interstellar medium (ISM) of a low-mass (Mgas = 2 × 106 M⊙), low-metallicity, isolated dwarf galaxy. These events correspond to the characteristic energies of both common and exotic astrophysical sites of nucleosynthesis, including asymptotic giant branch winds (Eej ∼ 1046 erg), neutron star–neutron star mergers (Eej ∼ 1049 erg), supernovae (Eej ∼ 1051 erg), and hypernovae (Eej ∼ 1052 erg). We find the mixing timescales for individual enrichment sources in our dwarf galaxy to be long (100 Myr–1 Gyr), with a clear trend of increasing homogeneity for the more energetic events. Given these timescales, we conclude that the spatial distribution and frequency of events are important drivers of abundance homogeneity on large scales; rare, low-Eej events should be characterized by particularly broad abundance distributions. The source energy Eej also correlates with the fraction of metals ejected in galactic winds, ranging anywhere from 60% at the lowest energy to 95% for hypernovae. We conclude by examining how the radial position, local ISM density, and global star formation rate influence these results.
Clinical Assessment of the Child: Does Drawing Help Children to Talk About Their Presenting Problems?

Child psychopathology is a significant mental health issue in New Zealand and overseas. When child mental health services are required, clinicians should conduct assessments that are developmentally sensitive and include the child’s point of view. Drawing is a popular and developmentally sensitive tool that is commonly used in clinical settings; research in experimental settings has confirmed that drawing increases the amount of verbal information that children report. The goal of the present research was to determine whether drawing also facilitates children’s self reports during mental health assessments. A total of 33 children, 5to 12-years of age, were asked to either draw and tell about their presenting problem or tell only. Children, who were allowed to draw and tell, provided twice as much information, as children who told only. The interviewers’ questions also varied as a function of conditions. Interviewers in the draw condition used a greater number of prompts and minimal responses. These data have important implications for clinical practice.
AnimalWeb: A Large-Scale Hierarchical Dataset of Annotated Animal Faces

Several studies show that animal needs are often expressed through their faces. Though remarkable progress has been made towards the automatic understanding of human faces, this has not been the case with animal faces. There exists significant room for algorithmic advances that could realize automatic systems for interpreting animal faces. Besides scientific value, resulting technology will foster better and cheaper animal care. We believe the underlying research progress is mainly obstructed by the lack of an adequately annotated dataset of animal faces, covering a wide spectrum of animal species. To this end, we introduce a large-scale, hierarchical annotated dataset of animal faces, featuring 22.4K faces from 350 diverse species and 21 animal orders across biological taxonomy. These faces are captured `in-the-wild' conditions and are consistently annotated with 9 landmarks on key facial features. The dataset is structured and scalable by design; its development underwent four systematic stages involving rigorous, overall effort of over 6K man-hours. We benchmark it for face alignment using the existing art under two new problem settings. Results showcase its challenging nature, unique attributes and present definite prospects for novel, adaptive, and generalized face-oriented CV algorithms. Further benchmarking the dataset across face detection and fine-grained recognition tasks demonstrates its multi-task applications and room for improvement. The dataset is available at: https://fdmaproject.wordpress. com/.
Scaling Back-propagation by Parallel Scan Algorithm

In an era when the performance of a single compute device plateaus, software must be designed to scale on a massively parallel system for better runtime performance. However, the commonly used back-propagation (BP) algorithm imposes a strong sequential dependency in the process of gradient computation. Under model parallelism, BP has a theoretical step complexity of $\Theta (n)$ which hinders its scalability in a parallel computing environment, where $n$ represents the number of compute devices into which a model is partitioned. In this work, we restructure such dependency and reformulate BP into a scan operation which is scaled by our modified version of the Blelloch scan algorithm. Our algorithm is able to achieve a theoretical step complexity of $\Theta (\log n)$. We perform an in-depth performance analysis and identify the challenges of deploying our algorithm in a practical setting, along with a variety of approaches to tackle such challenges. We demonstrate the scalability benefits of our algorithm in the use case of retraining pruned networks.
Tracing the AGN/X-ray Binary Analogy with Light Curves of Individual Changing-Look AGN

Physical models of X-ray binary outbursts can aid in understanding the origin of 'changing-look' active galactic nuclei (AGN), if we can establish that these two black hole accretion phenomena are analogous. Previously, studies of the correlation between the UV-to-X-ray spectral index alpha_OX and Eddington ratio using single-epoch observations of changing-look AGN samples have revealed possible similarities to the spectral evolution of outbursting X-ray binaries. However, direct comparisons using multi-epoch UV/X-ray light curves of individual changing-look AGN undergoing dramatic changes in Eddington ratio have been scarce. Here, we use published Swift UV/X-ray light curves of two changing-look AGN (NGC 2617 and ZTF18aajupnt) to examine the evolution of their alpha_OX values during outburst. We show that the combination of these two changing-look AGN can trace out the predicted spectral evolution from X-ray binary outbursts, including the inversion in the evolution of alpha_OX as a function of Eddington ratio. We suggest that the spectral softening that is observed to occur below a critical Eddington ratio in both AGN and X-ray binaries is due to reprocessing of Comptonized X-ray emission by the accretion disk, based on the X-ray to UV reverberation lags previously observed in NGC 2617. Our results suggest that the physical processes causing the changing-look AGN phenomenon are similar to those in X-ray binary outbursts.
Optimal Machine Intelligence Near the Edge of Chaos

It has long been suggested that living systems, in particular the brain, may operate near some critical point. How about machines? Through dynamical stability analysis on various computer vision models, we find direct evidence that optimal deep neural network performance occur near the transition point separating stable and chaotic attractors. In fact modern neural network architectures push the model closer to this edge of chaos during the training process. Our dissection into their fully connected layers reveals that they achieve the stability transition through self-adjusting an oscillation-diffusion process embedded in the weights. Further analogy to the logistic map leads us to believe that the optimality near the edge of chaos is a consequence of maximal diversity of stable states, which maximize the effective expressivity.