Miracle-dz/UniFAR-FTUs huggingface dataset:
Relative Magnetic Helicity Based on a Periodic Potential Field

Magnetic helicity is conserved under ideal magnetohydrodynamics and quasi-conserved even under a resistive process. The standard definition for magnetic helicity cannot be applied directly to an open magnetic field in a volume, because it is gauge-dependent. Instead, the relative magnetic helicity is widely used. We find that the energy of a potential magnetic field in a rectangular domain with periodic lateral boundary conditions is less than that of the field with a fixed normal component on all six boundaries. To make use of this lower energy potential field in the analysis of relative magnetic helicity, we introduce a new definition for magnetic helicity for the magnetic field, which involves the periodic potential field. We apply this definition to a sequence of analytic solutions and a numerical simulation. The results show that our new gauge-invariant helicity is very close to the current-carrying part of the relative magnetic helicity of the original magnetic field. We find also that the ratio between the current-carrying helicity and the relative magnetic helicity for the original and our defined relative helicity show different behavior. It seems that the new helicity is more sensitive to the component of the field due to the electric current in the volume, which is the source for instabilities and solar eruptive phenomena.
Distributed weighted min-cut in nearly-optimal time

Minimum-weight cut (min-cut) is a basic measure of a network’s connectivity strength. While the min-cut can be computed efficiently in the sequential setting [Karger STOC’96], there was no efficient way for a distributed network to compute its own min-cut without limiting the input structure or dropping the output quality: In the standard CONGEST model, existing algorithms with nearly-optimal time (e.g. [Ghaffari, Kuhn, DISC’13; Nanongkai, Su, DISC’14]) can guarantee a solution that is (1+є)-approximation at best while the exact Õ(n0.8D0.2 + n0.9)-time algorithm [Ghaffari, Nowicki, Thorup, SODA’20] works only on simple networks (no weights and no parallel edges). Throughout, n and D denote the network’s number of vertices and hop-diameter, respectively. For the weighted case, the best bound was Õ(n) [Daga, Henzinger, Nanongkai, Saranurak, STOC’19]. In this paper, we provide an exact Õ(√n + D)-time algorithm for computing min-cut on weighted networks. Our result improves even the previous algorithm that works only on simple networks. Its time complexity matches the known lower bound up to polylogarithmic factors. At the heart of our algorithm are a routing trick and two structural lemmas regarding the structure of a minimum cut of a graph. These two structural lemmas considerably strengthen and generalize the framework of Mukhopadhyay-Nanongkai [STOC’20] and can be of independent interest.
Self-sustained large-scale motions in the asymptotic suction boundary layer

Large-scale motions, also known as superstructures, are dynamically relevant coherent structures in a wall-bounded turbulent flow, that span the entire domain in wall-normal direction and significantly contribute to the global energy and momentum transport. Recent investigations in channel and Couette flow, suggest that these large-scale motions are self-sustained, implying they are not driven by small-scale motions at the wall. Whether large-scale motions are self-sustained has however not yet been answered for open boundary layers, which are relevant for many applications. Here, using the asymptotic suction boundary layer flow at the friction Reynolds number $Re_\tau = 1\,168$ as a testbed, we show that large-scale motions are self-sustained also in boundary layers. Together with the previous investigations in confined flows, this observation provides strong evidence of the robust and general nature of coherent self-sustained processes in turbulent wall-bounded flows. The dynamics of the large-scale self-sustained process involving the growth, breakdown and regeneration of quasi-streamwise coherent streaks and vortices within the boundary layer shows temporal phase relations reminiscent of bursting as observed in buffer layer structures. The dynamics however differs from the quasi-periodic large-scale streak-vortex regeneration cycle observed in confined flows. Based on the similarity of the dynamics of large-scale motions in boundary layers and of small-scale buffer layer structures, we conjecture that the bursting behaviour is associated with the dynamical relevance of only one wall, while two confining walls lead to the quasi-periodic cycle.
Three-dimensional Simulations of Magnetar-powered Superluminous Supernovae

A rapidly spinning magnetar in a young supernova (SN) can produce a superluminous transient by converting a fraction of its rotational energy into radiation. Here, we present the first three-dimensional hydrodynamical simulations ever performed of a magnetar-powered SN in the circumstellar medium formed by the ejection of the outer layers of the star prior to the blast. We find that hydrodynamical instabilities form on two scales in the ejecta, not just one as in ordinary core-collapse SNe: in the hot bubble energized by the magnetar and in the forward shock of the SN as it plows up ambient gas. Pressure from the bubble also makes the instabilities behind the forward shock more violent and causes more mixing in the explosion than in normal SNe, with important consequences for the light curves and spectra of the event that cannot be captured by one-dimensional models. We also find that the magnetar can accelerate Ca and Si to velocities of ∼12,000 and account for their broadened emission lines in observations. Our simulations also reveal that energy from even weak magnetars can accelerate iron-group elements deep in the ejecta to 5000–7000 and explain the high-velocity Fe observed at early times in some core-collapse SNe such as SN 1987A.
Isotropy and Log-Concave Polynomials: Accelerated Sampling and High-Precision Counting of Matroid Bases

We define a notion of isotropy for discrete set distributions. If <tex>$\mu$</tex> is a distribution over subsets <tex>$\mathcal{S}$</tex> of a ground set [<tex>$n$</tex>], we say that <tex>$\mu$</tex> is in isotropic position if <tex>$\mathbb{P}_{\mathcal{S}\sim\mu}[e\in \mathcal{S}]$</tex> is the same for all <tex>$e\in[n]$</tex>. We design a new approximate sampling algorithm that leverages isotropy for the class of distributions <tex>$\mu$</tex> that have a log-concave generating polynomial; this class includes determinantal point processes, strongly Rayleigh distributions, and uniform distributions over matroid bases. We show that when <tex>$\mu$</tex> is in approximately isotropic position, the running time of our algorithm depends polynomially on the size of the set <tex>$\mathcal{S}$</tex>, and only logarithmically on <tex>$n$</tex>. When <tex>$n$</tex> is much larger than the size of <tex>$\mathcal{S}$</tex>, this is significantly faster than prior algorithms, and can even be sublinear in <tex>$n$</tex>. We then show how to transform a non-isotropic <tex>$\mu$</tex> into an equivalent approximately isotropic form with a polynomial-time pre-processing step, accelerating subsequent sampling times. The main new ingredient enabling our algorithms is a class of negative dependence inequalities that may be of independent interest. As an application of our results, we show how to approximately count bases of a matroid of rank <tex>$k$</tex> over a ground set of <tex>$n$</tex> elements to within a factor of <tex>$1+\epsilon$</tex> in time <tex>$O((n+1/\epsilon^{2}) \cdot \text{poly}(k,\log n))$</tex>. This is the first algorithm that runs in nearly linear time for fixed rank <tex>$k$</tex>, and achieves an inverse polynomially low approximation error. The full version of this paper is available at: https://arxiv.org/abs/2004.09079
Entanglement revivals as a probe of scrambling in finite quantum systems

The entanglement evolution after a quantum quench became one of the tools to distinguish integrable versus chaotic (non-integrable) quantum many-body dynamics. Following this line of thoughts, here we propose that the revivals in the entanglement entropy provide a finite-size diagnostic benchmark for the purpose. Indeed, integrable models display periodic revivals manifested in a dip in the block entanglement entropy in a finite system. On the other hand, in chaotic systems, initial correlations get dispersed in the global degrees of freedom (information scrambling) and such a dip is suppressed. We show that while for integrable systems the height of the dip of the entanglement of an interval of fixed length decays as a power law with the total system size, upon breaking integrability a much faster decay is observed, signalling strong scrambling. Our results are checked by exact numerical techniques in free-fermion and free-boson theories, and by time-dependent density matrix renormalisation group in interacting integrable and chaotic models.
A Strongly Polynomial Label-Correcting Algorithm for Linear Systems with Two Variables per Inequality

We present a strongly polynomial label-correcting algorithm for solving the feasibility of linear systems with two variables per inequality (2VPI). The algorithm is based on the Newton-Dinkelbach method for fractional combinatorial optimization. We extend and strengthen previous work of Madani (2002) that showed a weakly polynomial bound for a variant of the Newton-Dinkelbach method for solving deterministic Markov decision processes (DMDPs), a special class of 2VPI linear programs. For a 2VPI system with $n$ variables and $m$ constraints, our algorithm runs in $O(mn)$ iterations. Every iteration takes $O(m + n\log n)$ time for DMDPs, and $O(mn)$ time for general 2VPI systems. The key technical idea is a new analysis of the Newton-Dinkelbach method exploiting gauge symmetries of the algorithm. This also leads to an acceleration of the Newton-Dinkelbach method for general fractional combinatorial optimization problems. For the special case of linear fractional combinatorial optimization, our method converges in $O(m\log m)$ iterations, improving upon the previous best bound of $O(m^2\log m)$ by Wang et al. (2006).
MorphStore

In this paper, we present MorphStore, an open-source in-memory columnar analytical query engine with a novel holistic compression-enabled processing model. Basically, compression using lightweight integer compression algorithms already plays an important role in existing in-memory column-store database systems, but mainly for base data. In particular, during query processing, these systems only keep the data compressed until an operator cannot process the compressed data directly, whereupon the data is decompressed, but not recompressed. Thus, the full potential of compression during query processing is not exploited. To overcome that, we developed a novel compression-enabled processing model as presented in this paper. As we are going to show, the continuous usage of compression for all base data and all intermediates is very beneficial to reduce the overall memory footprint as well as to improve the query performance.
Halluci-Net: Scene Completion by Exploiting Object Co-occurrence Relationships

We address the new problem of complex scene completion from sparse label maps. We use a two-stage deep network based method, called `Halluci-Net', that uses object co-occurrence relationships to produce a dense and complete label map. The generated dense label map is fed into a state-of-the-art image synthesis method to obtain the final image. The proposed method is evaluated on the Cityscapes dataset and it outperforms a single-stage baseline method on various performance metrics like Frechet Inception Distance (FID), semantic segmentation accuracy, and similarity in object co-occurrences. In addition to this, we show qualitative results on a subset of ADE20K dataset containing bedroom images.
Current-induced torque originating from orbital current

The electrical manipulation of magnetization by current-induced spin torques has given access to realize a plethora of ultralow power and fast spintronic devices such as non-volatile magnetic memories, spin-torque nano-oscillators, and neuromorphic computing devices. Recent advances have led to the notion that relativistic spin-orbit coupling is an efficient source for current-induced torques, opening the field of spin-orbitronics. Despite the significant progress, however, the fundamental mechanism of magnetization manipulation, the requirement of spin currents in generating current-induced torques, has remained unchanged. Here, we demonstrate the generation of current-induced torques without the use of spin currents. By measuring the current-induced torque for naturally-oxidized-Cu/ferromagnetic-metal bilayers, we observed an exceptionally high effective spin Hall conductivity at low temperatures despite the absence of strong spin-orbit coupling. Furthermore, we found that the direction of the torque depends on the choice of the ferromagnetic layer, which counters the conventional understanding of the current-induced torque. These unconventional features are best interpreted in terms of an orbital counterpart of the spin torque, an orbital torque, which arises from the orbital Rashba effect and orbital current. These findings will shed light on the underlying physics of current-induced magnetization manipulation, potentially altering the landscape of spin-orbitronics.
Are we pretraining it right? Digging deeper into visio-linguistic pretraining

Numerous recent works have proposed pretraining generic visio-linguistic representations and then finetuning them for downstream vision and language tasks. While architecture and objective function design choices have received attention, the choice of pretraining datasets has received little attention. In this work, we question some of the default choices made in literature. For instance, we systematically study how varying similarity between the pretraining dataset domain (textual and visual) and the downstream domain affects performance. Surprisingly, we show that automatically generated data in a domain closer to the downstream task (e.g., VQA v2) is a better choice for pretraining than "natural" data but of a slightly different domain (e.g., Conceptual Captions). On the other hand, some seemingly reasonable choices of pretraining datasets were found to be entirely ineffective for some downstream tasks. This suggests that despite the numerous recent efforts, vision & language pretraining does not quite work "out of the box" yet. Overall, as a by-product of our study, we find that simple design choices in pretraining can help us achieve close to state-of-art results on downstream tasks without any architectural changes.
Performance bound of the intensity-based model for noisy phase retrieval

The aim of noisy phase retrieval is to estimate a signal $\mathbf{x}_0\in \mathbb{C}^d$ from $m$ noisy intensity measurements $b_j=\left\lvert \langle \mathbf{a}_j,\mathbf{x}_0 \rangle \right\rvert^2+\eta_j, \; j=1,\ldots,m$, where $\mathbf{a}_j \in \mathbb{C}^d$ are known measurement vectors and $\eta=(\eta_1,\ldots,\eta_m)^\top \in \mathbb{R}^m$ is a noise vector. A commonly used model for estimating $\mathbf{x}_0$ is the intensity-based model $\widehat{\mathbf{x}}:=\mbox{argmin}_{\mathbf{x} \in \mathbb{C}^d} \sum_{j=1}^m \big(\left\lvert \langle \mathbf{a}_j,\mathbf{x} \rangle \right\rvert^2-b_j \big)^2$. Although one has already developed many efficient algorithms to solve the intensity-based model, there are very few results about its estimation performance. In this paper, we focus on the estimation performance of the intensity-based model and prove that the error bound satisfies $\min_{\theta\in \mathbb{R}}\|\widehat{\mathbf{x}}-e^{i\theta}\mathbf{x}_0\|_2 \lesssim \min\Big\{\frac{\sqrt{\|\eta\|_2}}{{m}^{1/4}}, \frac{\|\eta\|_2}{\| \mathbf{x}_0\|_2 \cdot \sqrt{m}}\Big\}$ under the assumption of $m \gtrsim d$ and $\mathbf{a}_j, j=1,\ldots,m,$ being Gaussian random vectors. We also show that the error bound is sharp. For the case where $\mathbf{x}_0$ is a $s$-sparse signal, we present a similar result under the assumption of $m \gtrsim s \log (ed/s)$. To the best of our knowledge, our results are the first theoretical guarantees for the intensity-based model and its sparse version. Our proofs employ Mendelson's small ball method which can deliver an effective lower bound on a nonnegative empirical process.
A Biologically Interpretable Two-stage Deep Neural Network (BIT-DNN) For Hyperspectral Imagery Classification

Spectral-spatial based deep learning models have recently proven to be effective in hyperspectral image (HSI) classification for various earth monitoring applications such as land cover classification and agricultural monitoring. However, due to the nature of "black-box" model representation, how to explain and interpret the learning process and the model decision remains an open problem. This study proposes an interpretable deep learning model -- a biologically interpretable two-stage deep neural network (BIT-DNN), by integrating biochemical and biophysical associated information into the proposed framework, capable of achieving both high accuracy and interpretability on HSI based classification tasks. The proposed model introduces a two-stage feature learning process. In the first stage, an enhanced interpretable feature block extracts low-level spectral features associated with the biophysical and biochemical attributes of the target entities; and in the second stage, an interpretable capsule block extracts and encapsulates the high-level joint spectral-spatial features into the featured tensors representing the hierarchical structure of the biophysical and biochemical attributes of the target ground entities, which provides the model an improved performance on classification and intrinsic interpretability. We have tested and evaluated the model using two real HSI datasets for crop type recognition and crop disease recognition tasks and compared it with six state-of-the-art machine learning models. The results demonstrate that the proposed model has competitive advantages in terms of both classification accuracy and model interpretability.
Degree-targeted cascades in modular, degree-heterogeneous networks

Many large scale phenomena, such as rapid changes in public opinion and the outbreak of disease epidemics, can be fruitfully modeled as cascades of activation on networks. This provides understanding of how various connectivity patterns among agents can influence the eventual extent of a cascade. We consider cascading dynamics on modular, degree-heterogeneous networks, as such features are observed in many real-world networks, and consider specifically the impact of the seeding strategy. We derive an analytic set of equations for the system by introducing a reduced description that extends a method developed by Gleeson that lets us accurately capture different seeding strategies using only one dynamical variable per module, namely the conditional exposure probability. We establish that activating the highest-degree nodes rather than random selection is more effective at growing a cascade locally, while the ability of a cascade to fully activate other modules is determined by the extent of large-scale interconnection between modules and is independent of how seed nodes are selected.
Learning to Evaluate Perception Models Using Planner-Centric Metrics

Variants of accuracy and precision are the gold-standard by which the computer vision community measures progress of perception algorithms. One reason for the ubiquity of these metrics is that they are largely task-agnostic; we in general seek to detect zero false negatives or positives. The downside of these metrics is that, at worst, they penalize all incorrect detections equally without conditioning on the task or scene, and at best, heuristics need to be chosen to ensure that different mistakes count differently. In this paper, we propose a principled metric for 3D object detection specifically for the task of self-driving. The core idea behind our metric is to isolate the task of object detection and measure the impact the produced detections would induce on the downstream task of driving. Without hand-designing it to, we find that our metric penalizes many of the mistakes that other metrics penalize by design. In addition, our metric downweighs detections based on additional factors such as distance from a detection to the ego car and the speed of the detection in intuitive ways that other detection metrics do not. For human evaluation, we generate scenes in which standard metrics and our metric disagree and find that humans side with our metric 79% of the time. Our project page including an evaluation server can be found at https://nv-tlabs.github. io/detection-relevance.
Time Series Data Augmentation for Neural Networks by Time Warping with a Discriminative Teacher

Neural networks have become a powerful tool in pattern recognition and part of their success is due to generalization from using large datasets. However, unlike other domains, time series classification datasets are often small. In order to address this problem, we propose a novel time series data augmentation called guided warping. While many data augmentation methods are based on random transformations, guided warping exploits the element alignment properties of Dynamic Time Warping (DTW) and shapeDTW, a high-level DTW method based on shape descriptors, to deterministically warp sample patterns. In this way, the time series are mixed by warping the features of a sample pattern to match the time steps of a reference pattern. Furthermore, we introduce a discriminative teacher in order to serve as a directed reference for the guided warping. We evaluate the method on all 85 datasets in the 2015 UCR Time Series Archive with a deep convolutional neural network (CNN) and a recurrent neural network (RNN). The code with an easy to use implementation can be found at https://github.com/uchidalab/time_series_augmentation.
The Laplacian Spectrum of Large Graphs Sampled From Graphons

This paper studies the Laplacian spectrum and the average effective resistance of (large) graphs that are sampled from graphons. Broadly speaking, our main finding is that the Laplacian eigenvalues of a large dense graph can be effectively approximated by using the degree function of the corresponding graphon. More specifically, we show how to approximate the distribution of the Laplacian eigenvalues and the average effective resistance (Kirchhoff index) of the graph. For all cases, we provide explicit bounds on the approximation errors and derive the asymptotic rates at which the errors go to zero when the number of nodes goes to infinity. Our main results are proved under the conditions that the graphon is piecewise Lipschitz and bounded away from zero.
Tractable Approximate Gaussian Inference for Bayesian Neural Networks

In this paper, we propose an analytical method allowing for tractable approximate Gaussian inference (TAGI) in Bayesian neural networks. The method enables: (1) the analytical inference of the posterior mean vector and diagonal covariance matrix for weights and bias, (2) the end-to-end treatment of uncertainty from the input layer to the output, and (3) the online inference of model parameters using a single observation at a time. The method proposed has a computational complexity of O(n) with respect to the number of parameters n, and the tests performed on regression and classification benchmarks confirm that, for a same network architecture, it matches the performance of existing methods relying on gradient backpropagation.