Miracle-dz/UniFAR-FTUs huggingface dataset:
Asymptotic preserving IMEX-DG-S schemes for linear kinetic transport equations based on Schur complement

We consider a linear kinetic transport equation under a diffusive scaling, that converges to a diffusion equation as the Knudsen number $\varepsilon\rightarrow0$. In [3, 21], to achieve the asymptotic preserving (AP) property and unconditional stability in the diffusive regime with $\varepsilon\ll 1$, numerical schemes are developed based on an additional reformulation of the even-odd or micro-macro decomposed version of the equation. The key of the reformulation is to add a weighted diffusive term on both sides of one equation in the decomposed system. The choice of the weight function, however, is problem-dependent and ad-hoc, and it can affect the performance of numerical simulations. To avoid issues related to the choice of the weight function and still obtain the AP property and unconditional stability in the diffusive regime, we propose in this paper a new family of AP schemes, termed as IMEX-DG-S schemes, directly solving the micro-macro decomposed system without any further reformulation. The main ingredients of the IMEX-DG-S schemes include globally stiffly accurate implicit-explicit (IMEX) Runge-Kutta (RK) temporal discretizations with a new IMEX strategy, discontinuous Galerkin (DG) spatial discretizations, discrete ordinate methods for the velocity space, and the application of the Schur complement to the algebraic form of the schemes to control the overall computational cost. The AP property of the schemes is shown formally. With an energy type stability analysis applied to the first order scheme, and Fourier type stability analysis applied to the first to third order schemes, we confirm the uniform stability of the methods with respect to $\varepsilon$ and the unconditional stability in the diffusive regime. A series of numerical examples are presented to demonstrate the performance of the new schemes.
DeeperGCN: All You Need to Train Deeper GCNs

Graph Convolutional Networks (GCNs) have been drawing significant attention with the power of representation learning on graphs. Unlike Convolutional Neural Networks (CNNs), which are able to take advantage of stacking very deep layers, GCNs suffer from vanishing gradient, over-smoothing and over-fitting issues when going deeper. These challenges limit the representation power of GCNs on large-scale graphs. This paper proposes DeeperGCN that is capable of successfully and reliably training very deep GCNs. We define differentiable generalized aggregation functions to unify different message aggregation operations (e.g. mean, max). We also propose a novel normalization layer namely MsgNorm and a pre-activation version of residual connections for GCNs. Extensive experiments on Open Graph Benchmark (OGB) show DeeperGCN significantly boosts performance over the state-of-the-art on the large scale graph learning tasks of node property prediction and graph property prediction. Please visit this https URL for more information.
Masses of doubly heavy tetraquarks 
TQQ′
 in a relativized quark model

In the present work, the mass spectra of doubly heavy tetraquarks $T_{QQ^\prime}$ are systematically investigated in a relativized quark model. The four-body systems including the Coulomb potential, confining potential, spin-spin interactions, and relativistic corrections are solved within the variational method. Our results suggest that the $IJ^P=01^+$ $bb \bar u \bar d$ state is 54 MeV below the relevant $\bar B \bar B$ and $\bar B \bar B^*$ thresholds, which indicates that both strong and electromagnetic decays are forbidden, and thus this state can be a stable one. Its large hidden color component and small root mean square radius demonstrate that it is a compact tetraquark rather than a loosely bound molecule or point-like diquark-antidiquark structure. Our predictions of the doubly heavy tetraquarks may provide valuable information for future experimental searches.
NeuroCard

Query optimizers rely on accurate cardinality estimates to produce good execution plans. Despite decades of research, existing cardinality estimators are inaccurate for complex queries, due to making lossy modeling assumptions and not capturing inter-table correlations. In this work, we show that it is possible to learn the correlations across all tables in a database without any independence assumptions. We present NeuroCard, a join cardinality estimator that builds a single neural density estimator over an entire database. Leveraging join sampling and modern deep autoregressive models, NeuroCard makes no inter-table or inter-column independence assumptions in its probabilistic modeling. NeuroCard achieves orders of magnitude higher accuracy than the best prior methods (a new state-of-the-art result of 8.5x maximum error on JOB-light), scales to dozens of tables, while being compact in space (several MBs) and efficient to construct or update (seconds to minutes).
Light-front holographic radiative transition form factors for light mesons

We predict the $\mathcal{V} \to \mathcal{P} \gamma$ decay widths and the $\mathcal{V} \to \mathcal{P} \gamma^{*}$ transition form factors, where $\mathcal{V}=(\rho, \omega, K^*, \phi)$ and $\mathcal{P}= (\pi,K, \eta,\eta^\prime)$, using spin-improved holographic light-front wavefunctions for the mesons. We find excellent agreement with the available data for both the decay widths and the timelike transition form factors extracted from the leptonic conversion decays $\mathcal{V} \to \mathcal{P} l^+ l^-$.
Correspondence Modules and Persistence Sheaves: A Unifying Framework for One-Parameter Persistent Homology

We develop a unifying framework for the treatment of various persistent homology architectures using the notion of correspondence modules. In this formulation, morphisms between vector spaces are given by partial linear relations, as opposed to linear mappings. In the one-dimensional case, among other things, this allows us to: (i) treat persistence modules and zigzag modules as algebraic objects of the same type; (ii) give a categorical formulation of zigzag structures over a continuous parameter; and (iii) construct barcodes associated with spaces and mappings that are richer in geometric information. A structural analysis of one-parameter persistence is carried out at the level of sections of correspondence modules that yield sheaf-like structures, termed persistence sheaves. Under some tameness hypotheses, we prove interval decomposition theorems for persistence sheaves and correspondence modules, as well as an isometry theorem for persistence diagrams obtained from interval decompositions of persistence sheaves. Applications include: (a) a Mayer-Vietoris sequence that relates the persistent homology of sublevelset filtrations and superlevelset filtrations to the levelset homology module of a real-valued function and (b) the construction of slices of 2-parameter persistence modules along negatively sloped lines.
A half-inverse problem for the singular diffusion operator with jump conditions

In this paper, half inverse spectral problem for diffusion operator with jump conditions dependent on the spectral parameter and discontinuoty coeffcient is considered. The half inverse problems is studied of determining the coeffcient and two potential functions of the boundary value problem its spectrum by Hocstadt- Lieberman and Yang-Zettl methods. We show that two potential functions on the whole interval and the parameters in the boundary and jump conditions can be determined from spectrum.
Coordinated Control of UAVs for Human-Centered Active Sensing of Wildfires

Fighting wildfires is a precarious task, imperiling the lives of engaging firefighters and those who reside in the fire’s path. Firefighters need online and dynamic observation of the firefront to anticipate a wildfire’s unknown characteristics, such as size, scale, and propagation velocity, and to plan accordingly. In this paper, we propose a distributed control framework to coordinate a team of unmanned aerial vehicles (UAVs) for a human-centered active sensing of wildfires. We develop a dual-criterion objective function based on Kalman uncertainty residual propagation and weighted multi-agent consensus protocol, which enables the UAVs to actively infer the wildfire dynamics and parameters, track and monitor the fire transition, and safely manage human firefighters on the ground using acquired information. We evaluate our approach relative to prior work, showing significant improvements by reducing the environments cumulative uncertainty residual in firefront coverage performance to support human-robot teaming for firefighting. We also demonstrate our method on physical robots in a mock firefighting exercise.
Iterative Algorithm Induced Deep-Unfolding Neural Networks: Precoding Design for Multiuser MIMO Systems

Optimization theory assisted algorithms have received great attention for precoding design in multiuser multiple-input multiple-output (MU-MIMO) systems. Although the resultant optimization algorithms are able to provide excellent performance, they generally require considerable computational complexity, which gets in the way of their practical application in real-time systems. In this work, in order to address this issue, we first propose a framework for deep-unfolding, where a general form of iterative algorithm induced deep-unfolding neural network (IAIDNN) is developed in matrix form to better solve the problems in communication systems. Then, we implement the proposed deep-unfolding framework to solve the sum-rate maximization problem for precoding design in MU-MIMO systems. An efficient IAIDNN based on the structure of the classic weighted minimum mean-square error (WMMSE) iterative algorithm is developed. Specifically, the iterative WMMSE algorithm is unfolded into a layer-wise structure, where a number of trainable parameters are introduced to replace the high-complexity operations in the forward propagation. To train the network, a generalized chain rule of the IAIDNN is proposed to depict the recurrence relation of gradients between two adjacent layers in the back propagation. Moreover, we discuss the computational complexity and generalization ability of the proposed scheme. Simulation results show that the proposed IAIDNN efficiently achieves the performance of the iterative WMMSE algorithm with reduced computational complexity.
Implications of baryon–dark matter interaction on IGM temperature and tSZ effect with magnetic field

We show that the combined effect of cosmic magnetic field and a possible non-standard interaction between baryons and dark matter has interesting consequences on the thermal Sunyaev$-$Zel${'}$dovich (tSZ) effect depending on the temperature and the ionization state of the intergalactic medium. The drag force between the baryons and dark matter due to the relative velocity between them, and their temperature difference results in heat transfer between these two species. At the same time the ambipolar diffusion and the decaying magnetic turbulence tends to heat up the baryons. This interplay of these two processes give rise to different evolution histories of the thermal and ionization state of the universe and hence influences the CMB spectrum at small scales through the tSZ effect. In this work, we have computed the evolution of the temperature, ionization fraction and the y-parameter of the CMB for different strengths of the magnetic field and the interaction cross-section. We note that an interaction cross-section of $\sigma_0=10^{-42}$ m$^{2}$ (with a magnetic field strength of $3.0$ nG) reduces the y-parameter by an order of magnitude as compared to the case with similar strength of magnetic field but where there is no such interaction between the baryons and dark matter.
Pairing of Massive Black Holes in Merger Galaxies Driven by Dynamical Friction

Motivated by observational searches for massive black hole (MBH) pairs at kiloparsec separations we develop a semianalytic model to describe their orbital evolution under the influence of stellar and gaseous dynamical friction (DF). The goal of this study is to determine how the properties of the merger remnant galaxy and the MBHs affect the likelihood and timescale for formation of a close MBH pair with separation of ≲1 pc. We compute approximately 40,000 configurations that cover a wide range of host galaxy properties and investigate their impact on the orbital evolution of unequal mass MBH pairs. We find that the percentage for MBH pairing within a Hubble time is larger than 80% in remnant galaxies with a gas fraction <20% and in galaxies hosting MBH pairs with total mass >106M⊙ and mass ratios ≥1/4. Among these, the remnant galaxies characterized by the fastest formation of close, gravitationally bound MBHs have one or more of the following properties: (1) a large stellar bulge, (2) comparable mass MBHs, and (3) a galactic gas disk rotating close to the circular speed. In such galaxies, the MBHs with the shortest inspiral times, which are likely progenitors of coalescing MBHs, are either on circular prograde orbits or on very eccentric retrograde orbits. Our model also indicates that remnant galaxies with opposite properties, which host slowly evolving MBH pairs, are the most likely hosts of dual active galactic nuclei at kiloparsec separations.
Attribute Restoration Framework for Anomaly Detection

With the recent advances in deep neural networks, anomaly detection in multimedia has received much attention in the computer vision community. While reconstruction-based methods have recently shown great promise for anomaly detection, the information equivalence among input and supervision for reconstruction tasks can not effectively force the network to learn semantic feature embeddings. We here propose to break this equivalence by erasing selected attributes from the original data and reformulate it as a restoration task, where the normal and the anomalous data are expected to be distinguishable based on restoration errors. Through forcing the network to restore the original image, the semantic feature embeddings related to the erased attributes are learned by the network. During testing phases, because anomalous data are restored with the attribute learned from the normal data, the restoration error is expected to be large. Extensive experiments have demonstrated that the proposed method significantly outperforms several state-of-the-arts on multiple benchmark datasets, especially on ImageNet, increasing the AUROC of the top-performing baseline by 10.1%. We also evaluate our method on a real-world anomaly detection dataset MVTec AD.
Recurrent Distillation based Crowd Counting

In recent years, with the progress of deep learning technologies, crowd counting has been rapidly developed. In this work, we propose a simple yet effective crowd counting framework that is able to achieve the state-of-the-art performance on various crowded scenes. In particular, we first introduce a perspective-aware density map generation method that is able to produce ground-truth density maps from point annotations to train crowd counting model to accomplish superior performance than prior density map generation techniques. Besides, leveraging our density map generation method, we propose an iterative distillation algorithm to progressively enhance our model with identical network structures, without significantly sacrificing the dimension of the output density maps. In experiments, we demonstrate that, with our simple convolutional neural network architecture strengthened by our proposed training algorithm, our model is able to outperform or be comparable with the state-of-the-art methods. Furthermore, we also evaluate our density map generation approach and distillation algorithm in ablation studies.
BI-MAML: Balanced Incremental Approach for Meta Learning

We present a novel Balanced Incremental Model Agnostic Meta Learning system (BI-MAML) for learning multiple tasks. Our method implements a meta-update rule to incrementally adapt its model to new tasks without forgetting old tasks. Such a capability is not possible in current state-of-the-art MAML approaches. These methods effectively adapt to new tasks, however, suffer from 'catastrophic forgetting' phenomena, in which new tasks that are streamed into the model degrade the performance of the model on previously learned tasks. Our system performs the meta-updates with only a few-shots and can successfully accomplish them. Our key idea for achieving this is the design of balanced learning strategy for the baseline model. The strategy sets the baseline model to perform equally well on various tasks and incorporates time efficiency. The balanced learning strategy enables BI-MAML to both outperform other state-of-the-art models in terms of classification accuracy for existing tasks and also accomplish efficient adaption to similar new tasks with less required shots. We evaluate BI-MAML by conducting comparisons on two common benchmark datasets with multiple number of image classification tasks. BI-MAML performance demonstrates advantages in both accuracy and efficiency.
Defensive approximation: securing CNNs using approximate computing

In the past few years, an increasing number of machine-learning and deep learning structures, such as Convolutional Neural Networks (CNNs), have been applied to solving a wide range of real-life problems. However, these architectures are vulnerable to adversarial attacks: inputs crafted carefully to force the system output to a wrong label. Since machine-learning is being deployed in safety-critical and security-sensitive domains, such attacks may have catastrophic security and safety consequences. In this paper, we propose for the first time to use hardware-supported approximate computing to improve the robustness of machine learning classifiers. We show that our approximate computing implementation achieves robustness across a wide range of attack scenarios. Specifically, we show that successful adversarial attacks against the exact classifier have poor transferability to the approximate implementation. The transferability is even poorer for the black-box attack scenarios, where adversarial attacks are generated using a proxy model. Surprisingly, the robustness advantages also apply to white-box attacks where the attacker has unrestricted access to the approximate classifier implementation: in this case, we show that substantially higher levels of adversarial noise are needed to produce adversarial examples. Furthermore, our approximate computing model maintains the same level in terms of classification accuracy, does not require retraining, and reduces resource utilization and energy consumption of the CNN. We conducted extensive experiments on a set of strong adversarial attacks; We empirically show that the proposed implementation increases the robustness of a LeNet-5 and an Alexnet CNNs by up to 99% and 87%, respectively for strong transferability-based attacks along with up to 50% saving in energy consumption due to the simpler nature of the approximate logic. We also show that a white-box attack requires a remarkably higher noise budget to fool the approximate classifier, causing an average of 4 dB degradation of the PSNR of the input image relative to the images that succeed in fooling the exact classifier.
Mustafin Models of Projective Varieties and Vector Bundles

Mustafin varieties are well-studied degenerations of projective spaces induced by a choice of integral points in a Bruhat–Tits building. In recent work, Annette Werner and the author initiated the study of degenerations of plane curves obtained by Mustafin varieties by means of arithmetic geometry. Moreover, we applied these techniques to construct models of vector bundles on plane curves with strongly semistable reduction. In this work, we take a Groebner basis approach to the more general problem of studying degenerations of projective varieties. Our methods include determining the behaviour of Groebner bases under substitution over unique factorisation rings. Finally, we outline applications to the $p-$adic Simpson correspondence, when the respective projective variety is a curve.
γ-ABC: Outlier-Robust Approximate Bayesian Computation Based on a Robust Divergence Estimator

Approximate Bayesian computation (ABC) is a likelihood-free inference method that has been employed in various applications. However, ABC can be sensitive to outliers if a data discrepancy measure is chosen inappropriately. In this paper, we propose to use a nearest-neighbor-based γ-divergence estimator as a data discrepancy measure. We show that our estimator possesses a suitable theoretical robustness property called the redescending property. In addition, our estimator enjoys various desirable properties such as high flexibility, asymptotic unbiasedness, almost sure convergence, and linear-time computational complexity. Through experiments, we demonstrate that our method achieves significantly higher robustness than existing discrepancy measures.
Globally Injective ReLU Networks

We study injective ReLU neural networks. Injectivity plays an important role in generative models where it facilitates inference; in inverse problems with generative priors it is a precursor to well posedness. We establish sharp conditions for injectivity of ReLU layers and networks, both fully connected and convolutional. We make no architectural assumptions beyond the ReLU activations so our results apply to a very general class of neural networks. We show through a layer-wise analysis that an expansivity factor of two is necessary for injectivity; we also show sufficiency by constructing weight matrices which guarantee injectivity. Further, we show that global injectivity with iid Gaussian matrices, a commonly used tractable model, requires considerably larger expansivity which might seem counterintuitive. We then derive the inverse Lipschitz constants and study the approximation-theoretic properties of injective neural networks. Using arguments from differential topology we prove that, under mild technical conditions, any Lipschitz map can be approximated by an injective neural network. This justifies the use of injective neural networks in problems which a priori do not require injectivity. Our results establish a theoretical basis for the study of nonlinear inverse and inference problems using neural networks.
Improved generalized raking estimators to address dependent covariate and failure‐time outcome error

Biomedical studies that use electronic health records (EHR) data for inference are often subject to bias due to measurement error. The measurement error present in EHR data is typically complex, consisting of errors of unknown functional form in covariates and the outcome, which can be dependent. To address the bias resulting from such errors, generalized raking has recently been proposed as a robust method that yields consistent estimates without the need to model the error structure. We provide rationale for why these previously proposed raking estimators can be expected to be inefficient in failure‐time outcome settings involving misclassification of the event indicator. We propose raking estimators that utilize multiple imputation, to impute either the target variables or auxiliary variables, to improve the efficiency. We also consider outcome‐dependent sampling designs and investigate their impact on the efficiency of the raking estimators, either with or without multiple imputation. We present an extensive numerical study to examine the performance of the proposed estimators across various measurement error settings. We then apply the proposed methods to our motivating setting, in which we seek to analyze HIV outcomes in an observational cohort with EHR data from the Vanderbilt Comprehensive Care Clinic.