Miracle-dz/UniFAR-FTUs huggingface dataset:
A principled approach for generating adversarial images under non-smooth dissimilarity metrics

Deep neural networks perform well on real world data but are prone to adversarial perturbations: small changes in the input easily lead to misclassification. In this work, we propose an attack methodology not only for cases where the perturbations are measured by $\ell_p$ norms, but in fact any adversarial dissimilarity metric with a closed proximal form. This includes, but is not limited to, $\ell_1, \ell_2$, and $\ell_\infty$ perturbations; the $\ell_0$ counting "norm" (i.e. true sparseness); and the total variation seminorm, which is a (non-$\ell_p$) convolutional dissimilarity measuring local pixel changes. Our approach is a natural extension of a recent adversarial attack method, and eliminates the differentiability requirement of the metric. We demonstrate our algorithm, ProxLogBarrier, on the MNIST, CIFAR10, and ImageNet-1k datasets. We consider undefended and defended models, and show that our algorithm easily transfers to various datasets. We observe that ProxLogBarrier outperforms a host of modern adversarial attacks specialized for the $\ell_0$ case. Moreover, by altering images in the total variation seminorm, we shed light on a new class of perturbations that exploit neighboring pixel information.
Low-Rank Pairwise Alignment Bilinear Network For Few-Shot Fine-Grained Image Classification

Deep neural networks have demonstrated advanced abilities on various visual classification tasks, which heavily rely on the large-scale training samples with annotated ground-truth. However, it is unrealistic always to require such annotation in real-world applications. Recently, Few-Shot learning (FS), as an attempt to address the shortage of training samples, has made significant progress in generic classification tasks. Nonetheless, it is still challenging for current FS models to distinguish the subtle differences between fine-grained categories given limited training data. To filling the classification gap, in this paper, we address the Few-Shot Fine-Grained (FSFG) classification problem, which focuses on tackling the fine-grained classification under the challenging few-shot learning setting. A novel low-rank pairwise bilinear pooling operation is proposed to capture the nuanced differences between the support and query images for learning an effective distance metric. Moreover, a feature alignment layer is designed to match the support image features with query ones before the comparison. We name the proposed model Low-Rank Pairwise Alignment Bilinear Network (LRPABN), which is trained in an end-to-end fashion. Comprehensive experimental results on four widely used fine-grained classification data sets demonstrate that our LRPABN model achieves the superior performances compared to state-of-the-art methods.
The 8-rank of the narrow class group and the negative Pell equation

Abstract Using a recent breakthrough of Smith [18], we improve the results of Fouvry and Klüners [4, 5] on the solubility of the negative Pell equation. Let $\mathcal {D}$ denote the set of positive squarefree integers having no prime factors congruent to $3$ modulo $4$ . Stevenhagen [19] conjectured that the density of d in $\mathcal {D}$ such that the negative Pell equation $x^2-dy^2=-1$ is solvable with $x, y \in \mathbb {Z}$ is $58.1\%$ , to the nearest tenth of a percent. By studying the distribution of the $8$ -rank of narrow class groups $\operatorname {\mathrm {Cl}}^+(d)$ of $\mathbb {Q}(\sqrt {d})$ , we prove that the infimum of this density is at least $53.8\%$ .
Elucidating plasma dynamics in Hasegawa–Wakatani turbulence by information geometry

The impact of adiabatic electrons on drift-wave turbulence, modelled by the Hasegawa-Wakatani equations, is studied using information length. Information length is a novel theoretical method for measuring distances between statistical states represented by different probability distribution functions (PDFs) along the path of a system. Specifically, the time-dependent PDFs of turbulent fluctuations for a given adiabatic index $A$ is computed. The changes in fluctuation statistics are then quantified in time by using information length. The numerical results provide time traces exhibiting intermittent plasma dynamics, and such behaviour is identified by a rapid change in the information length. The effects of $A$ are discussed.
Pairwise Multi-marginal Optimal Transport via Universal Poisson Coupling

We investigate the problem of pairwise multi-marginal optimal transport, that is, given a collection of probability distributions $P_{1},\ldots,P_{m}$ on a Polish space, to find a coupling $X_{1},\ldots,X_{m}$, $X_{i}\sim P_{i}$, such that $\mathbf{E}[c(X_{i},X_{j})]\le r\inf_{X\sim P_{i},\,Y\sim P_{j}}\mathbf{E}[c(X,Y)]$ for any $i,j$, where $c$ is a cost function and $r\ge1$. In other words, every pair $(X_{i},X_{j})$ has an expected cost at most a factor of $r$ from its lowest possible value. This can be regarded as a multi-agent matching problem with a fairness requirement. For the cost function $c(x,y)=\Vert x-y\Vert_{2}^{q}$ over $\mathbb{R}^{n}$, where $q>0$, we show that a finite $r$ is attainable when either $n=1$ or $q 1$. It is unknown whether such $r$ exists when $n\ge2$ and $q=1$. Also, we show that $r$ grows at least as fast as $\Omega(n^{\mathbf{1}\{q=1\}+q/2})$ when $n\to\infty$. The case of the discrete metric cost $c(x,y)=\mathbf{1}\{x\neq y\}$, and more general metric and ultrametric costs are also investigated.
Extended ionized-gas structures in Seyfert 2 galaxy Mrk 78

Search for and study of extended emission-line regions (EELRs) related to AGN in early-type galaxies is interesting to probe the history of nuclear ionization activity and also to understand the process of external gas accretion. In this work, we present observations of the EELR in Mrk 78 obtained at the 6-m Russian telescope using the long-slit and 3D spectroscopy methods. We show that ionized-gas clouds at the 12-16 kpc projected distances from the nucleus are ionized by the AGN radiation. Also we have checked if the galaxy appearing in the optical images in the immediate neighbourhood of Mrk 78 near the external clouds is a dwarf companion or a part of a tidal structure. However, the spectrum of this galaxy, SDSS J074240.37+651021.4, obtained at the 6-m telescope corresponds to the distant background galaxy.
Minimum-Latency FEC Design With Delayed Feedback: Mathematical Modeling and Efficient Algorithms

In this paper, we consider the packet-level forward error correction (FEC) code design, without feedback or with delayed feedback, for achieving the minimum <italic>end-to-end latency</italic>, i.e., the latency between the time that packet is generated at the source and its <italic>in-order delivery</italic> to the application layer of the destination. We first show that the minimum-latency FEC design problem can be modeled as a partially observable Markov decision process (POMDP), and hence the optimal code construction can be obtained by solving the corresponding POMDP. However, solving the POMDP optimally is in general difficult unless its state and action space is very small. To this end, we propose an efficient heuristic algorithm, namely the majority vote policy, for obtaining a high quality approximate solution. We also derive the tight lower and upper bounds of the optimal state values of this POMDP, based on which a more sophisticated <inline-formula> <tex-math notation="LaTeX">$D$ </tex-math></inline-formula>-step search algorithm can be implemented for obtaining near-optimal solutions. The simulation results show that the proposed code designs via solving the POMDP, either with the majority vote policy or the <inline-formula> <tex-math notation="LaTeX">$D$ </tex-math></inline-formula>-step search algorithm, strictly outperform the existing schemes, for both cases, without or with only delayed feedback.
Image-Guided Depth Sampling and Reconstruction

Depth acquisition, based on active illumination, is essential for autonomous and robotic navigation. LiDARs (Light Detection And Ranging) with mechanical, fixed, sampling templates are commonly used in today's autonomous vehicles. An emerging technology, based on solid-state depth sensors, with no mechanical parts, allows fast, adaptive, programmable scans. In this paper, we investigate the topic of adaptive, image-driven, sampling and reconstruction strategies. First, we formulate a piece-wise linear depth model with several tolerance parameters and estimate its validity for indoor and outdoor scenes. Our model and experiments predict that, in the optimal case, about 20-60 piece-wise linear structures can approximate well a depth map. This translates to a depth-to-image sampling ratio of about 1/1200. We propose a simple, generic, sampling and reconstruction algorithm, based on super-pixels. We reach a sampling rate which is still far from the optimal case. However, our sampling improves grid and random sampling, consistently, for a wide variety of reconstruction methods. Moreover, our proposed reconstruction achieves state-of-the-art results, compared to image-guided depth completion algorithms, reducing the required sampling rate by a factor of 3-4. A single-pixel depth camera built in our lab illustrates the concept.
Stellar mass–halo mass relation for the brightest central galaxies of X-ray clusters since z ∼ 0.65

We present the brightest cluster galaxies (BCGs) catalog for SPectroscoic IDentification of eROSITA Sources (SPIDERS) DR14 cluster program value-added catalog. We list the 416 BCGs identified as part of this process, along with their stellar mass, star formation rates (SFRs), and morphological properties. We identified the BCGs based on the available spectroscopic data from SPIDERS and photometric data from SDSS. We computed stellar masses and SFRs of the BCGs on the basis of SDSS, WISE, and GALEX photometry using spectral energy distribution fitting. Morphological properties for all BCGs were derived by Sersic profile fitting using the software package SIGMA in different optical bands (g,r,i). We combined this catalog with the BCGs of galaxy groups and clusters extracted from the deeper AEGIS, CDFS, COSMOS, XMM-CFHTLS, and XMM-XXL surveys to study the stellar mass–halo mass relation using the largest sample of X-ray groups and clusters known to date. This result suggests that the mass growth of the central galaxy is controlled by the hierarchical mass growth of the host halo. We find a strong correlation between the stellar mass of BCGs and the mass of their host halos. This relation shows no evolution since z ∼ 0.65. We measure a mean scatter of 0.21 and 0.25 for the stellar mass of BCGs in a given halo mass at low (0.1 < z < 0.3) and high (0.3 < z < 0.65) redshifts, respectively. We further demonstrate that the BCG mass is covariant with the richness of the host halos in the very X-ray luminous systems. We also find evidence that part of the scatter between X-ray luminosity and richness can be reduced by considering stellar mass as an additional variable.
The Use of Binary Choice Forests to Model and Estimate Discrete Choice Models

We show the equivalence of discrete choice models and the class of binary choice forests, which are random forest based on binary choice trees. This suggests that standard machine learning techniques based on random forest can serve to estimate discrete choice model with an interpretable output. This is confirmed by our data driven result that states that random forest can accurately predict the choice probability of any discrete choice model. Our framework has unique advantages: it can capture behavioral patterns such as irrationality or sequential searches; it handles nonstandard formats of training data that result from aggregation; it can measure product importance based on how frequently a random customer would make decisions depending on the presence of the product; it can also incorporate price information. Our numerical results show that binary choice forest can outperform the best parametric models with much better computational times.
GDRQ: Group-based Distribution Reshaping for Quantization

Low-bit quantization is challenging to maintain high performance with limited model capacity (e.g., 4-bit for both weights and activations). Naturally, the distribution of both weights and activations in deep neural network are Gaussian-like. Nevertheless, due to the limited bitwidth of low-bit model, uniform-like distributed weights and activations have been proved to be more friendly to quantization while preserving accuracy~\cite{Han2015Learning}. Motivated by this, we propose Scale-Clip, a Distribution Reshaping technique that can reshape weights or activations into a uniform-like distribution in a dynamic manner. Furthermore, to increase the model capability for a low-bit model, a novel Group-based Quantization algorithm is proposed to split the filters into several groups. Different groups can learn different quantization parameters, which can be elegantly merged in to batch normalization layer without extra computational cost in the inference stage. Finally, we integrate Scale-Clip technique with Group-based Quantization algorithm and propose the Group-based Distribution Reshaping Quantization (GDQR) framework to further improve the quantization performance. Experiments on various networks (e.g. VGGNet and ResNet) and vision tasks (e.g. classification, detection and segmentation) demonstrate that our framework achieves good performance.
Symmetry in stationary and uniformly rotating solutions of active scalar equations

In this paper, we study the radial symmetry properties of stationary and uniformly-rotating solutions of the 2D Euler and gSQG equations, both in the smooth setting and the patch setting. For the 2D Euler equation, we show that any smooth stationary solution with compactly supported and nonnegative vorticity must be radial, without any assumptions on the connectedness of the support or the level sets. In the patch setting, for the 2D Euler equation we show that every uniformly-rotating patch $D$ with angular velocity $\Omega \leq 0$ or $\Omega\geq \frac{1}{2}$ must be radial, where both bounds are sharp. For the gSQG equation we obtain a similar symmetry result for $\Omega\leq 0$ or $\Omega\geq \Omega_\alpha$ (with the bounds being sharp), under the additional assumption that the patch is simply-connected. These results settle several open questions in [T. Hmidi, J. Evol. Equ. , 15(4): 801-816, 2015] and [F. de la Hoz, Z. Hassainia, T. Hmidi, and J. Mateu, Anal. PDE, 9(7):1609-1670, 2016] on uniformly-rotating patches. Along the way, we close a question on overdetermined problems for the fractional Laplacian [R. Choksi, R. Neumayer, and I. Topaloglu, Arxiv preprint arXiv:1810.08304, 2018, Remark 1.4], which may be of independent interest. The main new ideas come from a calculus of variations point of view.
A multiwavelength study of a massive, active galaxy at z ∼ 2: coupling the kinematics of the ionized and molecular gas

We report a multiwavelength study of the massive ($M_{\star } \gtrsim 10^{11} \rm {M}_{\odot }$), z ∼ 2 star-forming galaxy GMASS 0953, which hosts an obscured AGN. We combined near-infrared observations of the GNIRS, SINFONI and KMOS spectrographs to study the kinematics of the [O iii] λ5007 and H α emission lines. Our analysis shows that GMASS 0953 may host an ionized disc extending up to 13 kpc, which rotates at a velocity of $V_{\rm {ion}} = 203^{+17}_{-20}$ km s−1 at the outermost radius. Evidence of rotation on a smaller scale (R ∼ 1 kpc) arises from the CO(J = 6–5) line. The central velocity $V_{\rm {CO}} = 320^{+ 92}_{-53}$ km s−1 traced by the molecular gas is higher than Vion, suggesting that the galaxy harbours a multiphase disc with a rotation curve that peaks in the very central regions. The galaxy appears well located on the z = 0 baryonic Tully–Fisher relation. We also discuss the possibility that the [O iii] λ5007 and H α velocity gradients are due to a galactic-scale wind. Besides, we found evidence of an AGN-driven outflow traced by a broad blueshifted wing affecting the [O iii] λ5007 line, which presents a velocity offset Δv = −535 ± 152 km s−1 from the systemic velocity. Because of the short depletion time-scale (τdep ∼ 108 yr) due to gas ejection and gas consumption by star formation activity, GMASS 0953 may likely evolve into a passive galaxy. However, the role of the AGN in depleting the gas reservoir of the galaxy is quite unclear because of the uncertainties affecting the outflow rate.
Tracing Hercules in Galactic azimuth with Gaia DR2

The second data release of the Gaia mission has revealed, in stellar velocity and action space, multiple ridges, the exact origin of which is still debated. Recently, we demonstrated that a large Galactic bar with pattern speed 39 km s−1 kpc−1 creates most of the observed ridges. Among these ridges, the Hercules moving group would then be associated with orbits trapped at the co-rotation resonance of the bar. Here we show that a distinctive prediction of such a model is that the angular momentum of Hercules at the Sun’s radius must significantly decrease with increasing Galactocentric azimuth (i.e. when getting closer to the major axis of the bar). We show that this dependence of the angular momentum of trapped orbits on the azimuth on the other hand does not happen close to the outer Lindblad resonance of a faster bar, unless the orbital distribution is still far from phase-mixed, namely for a bar perturbation younger than ∼2 Gyr. Using Gaia DR2 and Bayesian distances from the StarHorse code, and tracing the average Galactocentric radial velocity as a function of angular momentum and azimuth, we show that the Hercules angular momentum changes significantly with azimuth as expected for the co-rotation resonance of a dynamically old large bar.
Second order regularity for elliptic and parabolic equations involving $p$-Laplacian via a fundamental inequality

Denote by $\Delta$ the Laplacian and by $\Delta_\infty $ the $\infty$-Laplacian. A fundamental inequality is proved for the algebraic structure of $\Delta v\Delta_\infty v$: for every $v\in C^\infty$, $$\left| { |D^2vDv|^2} - {\Delta v \Delta_\infty v } -\frac12[|D^2v|^2-(\Delta v)^2]|Dv|^2\right| \le \frac{n-2}2 [|D^2v|^2{|Dv|^2}- |D^2vDv|^2 ]. $$ Based on this, we prove the following results: 1. For any $p$-harmonic functions $u$, $p\in(1,2)\cup(2,\infty)$, we have $$|Du|^{\frac{p-\gamma}2}Du\in W^{1,2}_{\rm loc},$$ with $\gamma 2$. 2. When $n\ge 2$ and $p\in(1,2)\cup(2,3+\frac2{n-2})$, the viscosity solutions to parabolic normalized $p $-Laplace equation have the $W_{\rm loc}^{2,q}$-regularity in the spatial variable and the $W_{\rm loc}^{1,q}$-regularity in the time variable for some $q>2$. Especially, when $n=2$ an open question in [17] is completely answered. 3. When $n\ge 1 $ and $p\in(1,2)\cup(2,3)$, the weak/viscosity solutions to parabolic $p $-Laplace equation have the $W_{\rm loc}^{2,2}$-regularity in the spatial variable and the $W_{\rm loc}^{1,2}$-regularity in the time variable. The range of $p$ (including $p=2$ from the classical result) here is sharp for the $W_{\rm loc}^{2,2}$-regularity.
Knowledge Isomorphism between Neural Networks

This paper aims to analyze knowledge isomorphism between pre-trained deep neural networks. We propose a generic deﬁnition for knowledge isomorphism between neural networks at different fuzziness levels, and design a task-agnostic and model-agnostic method to disentangle and quantify isomorphic features from intermediate layers of a neural network. As a generic tool, our method can be broadly used for different applications. In preliminary experiments, we have used knowledge isomorphism as a tool to diagnose feature representations of neural networks. Knowledge isomorphism provides new insights to explain the success of existing deep-learning techniques, such as knowledge distillation and network compression. More crucially, it has been shown that knowledge isomorphism can also be used to reﬁne pre-trained networks and boost performance
Nucleon resonances in 
γp→ωp
 reaction

The most recent high-precision data on spin observables $\Sigma$, $T$, $P'$, $E$, $F$ and $H$ reported by the CLAS Collaboration together with the previous data on differential cross sections and spin-density-matrix elements reported by the CLAS, A2, GRAAL, SAPHIR and CBELSA/TAPS Collaborations for the reaction $\gamma p \to \omega p$ are analyzed within an effective Lagrangian approach. The reaction amplitude is constructed by considering the $t$-channel $\pi$ and $\eta$ exchanges, the $s$-channel nucleon and nucleon resonances exchanges, the $u$-channel nucleon exchange and the generalized contact current. The latter accounts effectively for the interaction current and ensures that the full photoproduction amplitude is gauge invariant. It is shown that all the available CLAS data can be satisfactorily described by considering the $N(1520)3/2^-$, $N(1700)3/2^-$, $N(1720)3/2^+$, $N(1860)5/2^+$, $N(1875)3/2^-$, $N(1895)1/2^-$ and $N(2060)5/2^-$ resonances in the $s$-channel. The parameters of these resonances are extracted and compared with those quoted by PDG.
Distributed Adaptive Coverage Control of Differential Drive Robotic Sensors

This paper is concerned with the deployment of multiple mobile robots in order to autonomously cover a region Q. The region to be covered is described using a density function which may not be apriori known. In this paper, we pose the coverage problem as an optimization problem over some space of functions on Q. In particular, we look at L 2 -distance based coverage algorithm and derive adaptive control laws for the same. We also propose a modified adaptive control law incorporating consensus for better parameter convergence. We implement the algorithms on real differential drive robots with both simulated density function as well as density function implemented using light sources. We also compare the L 2 -distance based method with the locational optimization method using experiments.
Regression-adjusted average treatment effect estimates in stratified and sequentially randomized experiments

Stratified and sequentially randomized experiments are widely used in fields such as agriculture, industry, medical science, economics, and finance. Baseline covariates are often collected for each unit in the experiments. Many researchers use linear regression to analyse the experimental results for improving efficiency of treatment effect estimation by adjusting the minor imbalances of covariates in the treatment and control group. Our work studies the asymptotic properties of regression adjustment in stratified and sequentially randomized experiments, under the randomization-based inference framework. We allow both the number of strata and their sizes to be arbitrary, provided the total number of experimental units tends to infinity and each stratum has at least two treated and two control units. Under slightly stronger but interpretable conditions, we re-establish the finite population central limit theory for a stratified random sample. Based on this theorem, we prove in our main results that, with certain other mild conditions, both the stratified difference-in-means and the regression-adjusted average treatment effect estimator are consistent and asymptotically normal. The asymptotic variance of the latter is no greater and is typically lesser than that of the former when the proportion of treated units is asymptotically the same across strata or the number of stratum is bounded. The magnitude of improvement depends on the extent to which the within-strata variation of the potential outcomes can be explained by the covariates. We also provide conservative variance estimators to construct large-sample confidence intervals for the average treatment effect, which are consistent if and only if the stratum-specific treatment effect is constant. Our theoretical results are confirmed by a simulation study and we conclude with an empirical illustration.