Miracle-dz/UniFAR-FTUs huggingface dataset:
SHALLOW-WATER AND DEEP-WATER LIMITS OF THE GENERALISED FINITE-DEPTH-FLUID EQUATION

We study convergence problems for the finite-depth-fluid equation (FDF) on R and T from a microscopic point of view. The FDF equation can be naturally viewed as an interpolation between the Korteweg-de Vries equation (KdV) and Benjamin-Ono equation (BO). In this paper, we prove that the solutions of FDF converge to those of KdV in the shallow-water limit (as the fluid depth goes to zero), and to those of BO in the deep-water limit (as the fluid depth reaches infinity). Our convergence results also apply to the FDF with an analytic nonlinearity f(u). In the case of FDF f(u) = u, we improve the previous results by Abdelouhab-Bona-Felland-Saut (1989); and to the best of our knowledge, the quartic case f(u) = u is the first time studied here; in the case where f(u) = u for k ≥ 5, our results improve those of Han-Wang (2008). Moreover, we provide the first convergence results on T, while all previous studies focused on R.
Topological characterization and stability of Floquet Majorana modes in Rashba nanowires

We theoretically investigate a practically realizable Floquet topological superconductor model, based on a one-dimensional Rashba nanowire and proximity induced $s$-wave superconductivity in the presence of a Zeeman field. The driven system hosts regular $0$- and anomalous $\pi$-Majorana end modes~(MEMs). By tuning the chemical potential and the frequency of the drive, we illustrate the generation of multiple MEMs in our theoretical set up. We utilize the chiral symmetry operator to topologically characterize these MEMs via a dynamical winding number constructed out of the periodized evolution operator. Interestingly, the robustness of the $0$- and $\pi$-MEMs is established in the presence of on-site time-independent random disorder potential. We employ the twisted boundary condition to define the dynamical topological invariant for this translational-symmetry broken system. The interplay between the Floquet driving and the weak disorder can stabilize the MEMs giving rise to a quantized value of the dynamical winding number for a finite range of drive parameters. This observation might be experimentally helpful in scrutinizing the topological nature of the Floquet MEMs. We showcase another driving protocol namely, a periodic kick in the chemical potential to study the generation of Floquet MEMs in our setup. Our work paves a realistic way to engineer multiple MEMs in a driven system.
TransCL: Transformer Makes Strong and Flexible Compressive Learning

Compressive learning (CL) is an emerging framework that integrates signal acquisition via compressed sensing (CS) and machine learning for inference tasks directly on a small number of measurements. It can be a promising alternative to classical image-domain methods and enjoys great advantages in memory saving and computational efficiency. However, previous attempts on CL are not only limited to a fixed CS ratio, which lacks flexibility, but also limited to MNIST/CIFAR-like datasets and do not scale to complex real-world high-resolution (HR) data or vision tasks. In this article, a novel transformer-based compressive learning framework on large-scale images with arbitrary CS ratios, dubbed TransCL, is proposed. Specifically, TransCL first utilizes the strategy of learnable block-based compressed sensing and proposes a flexible linear projection strategy to enable CL to be performed on large-scale images in an efficient block-by-block manner with arbitrary CS ratios. Then, regarding CS measurements from all blocks as a sequence, a pure transformer-based backbone is deployed to perform vision tasks with various task-oriented heads. Our sufficient analysis presents that TransCL exhibits strong resistance to interference and robust adaptability to arbitrary CS ratios. Extensive experiments for complex HR data demonstrate that the proposed TransCL can achieve state-of-the-art performance in image classification and semantic segmentation tasks. In particular, TransCL with a CS ratio of 10% can obtain almost the same performance as when operating directly on the original data and can still obtain satisfying performance even with an extremely low CS ratio of 1%. The source codes of our proposed TransCL is available at https://github.com/MC-E/TransCL/.
Highly non-Gaussian tails and primordial black holes from single-field inflation

For primordial perturbations, deviations from Gaussian statistics on the tail of the probability distribution can be associated with non-perturbative effects of inflation. In this paper, we present some particular examples in which the tail of the distribution becomes highly non-Gaussian although the statistics remains almost Gaussian in the perturbative regime. We begin with an extension of the ultra-slow-roll inflation that incorporates a transition process, where the inflaton climbs up a tiny potential step at the end of the non-attractor stage before it converges to the slow-roll attractor. Through this example, we identify the key role of the off-attractor behaviour for the upward-step transition, and then extend the analysis to another type of the transition with two slow-roll stages connected by a tiny step. We perform both the perturbative and non-perturbative analyses of primordial fluctuations generated around the step in detail, and show that the tiny but nontrivial transition may affect large perturbations in the tail of the distribution, while the perturbative non-Gaussianity remains small. Our result indicates that the non-Gaussian tails can have rich phenomenology which has been overlooked in conventional analyses. We also study the implications of this non-Gaussian tail for the formation of primordial black holes, and find that their mass fraction can be parametrically amplified by several orders of magnitudes in comparison with the case of the Gaussian distribution. Additionally, we also discuss a mechanism of primordial black holes formation for this upward step inflation model by trapping the inflaton in the bottom of the step.
Gradient-based Bi-level Optimization for Deep Learning: A Survey

Bi-level optimization, especially the gradient-based category, has been widely used in the deep learning community including hyperparameter optimization and meta-knowledge extraction. Bi-level optimization embeds one problem within another and the gradient-based category solves the outer-level task by computing the hypergradient, which is much more efficient than classical methods such as the evolutionary algorithm. In this survey, we first give a formal definition of the gradient-based bi-level optimization. Next, we delineate criteria to determine if a research problem is apt for bi-level optimization and provide a practical guide on structuring such problems into a bi-level optimization framework, a feature particularly beneficial for those new to this domain. More specifically, there are two formulations: the single-task formulation to optimize hyperparameters such as regularization parameters and the distilled data, and the multi-task formulation to extract meta-knowledge such as the model initialization. With a bi-level formulation, we then discuss four bi-level optimization solvers to update the outer variable including explicit gradient update, proxy update, implicit function update, and closed-form update. Finally, we wrap up the survey by highlighting two prospective future directions: (1) Effective Data Optimization for Science examined through the lens of task formulation. (2) Accurate Explicit Proxy Update analyzed from an optimization standpoint.
Hausdorff Dimension of the Brownian Earthworm (WXML Winter 2017 Report)

1.1. Notions of Dimension. When we refer to the “dimension” of a set, we are referring to some notion of the set’s size. In particular, we are addressing two common notions of dimension for a set A ⊂ R: • Minkowski dimension, and • Hausdorff dimension. The Minkowski dimension (sometimes called Minkwski-Bouligand dimension) is often referred to simply as box-counting dimension. As a consequence of the finite capacity of computing power, one often uses the box-counting dimension as an approximation of the Hausdorff dimension. A more thorough treatise on box-counting and Hausdorff dimension, as well as other notions of dimension, can be found in [1].
Thermal Half-Lives of Azobenzene Derivatives: Virtual Screening Based on Intersystem Crossing Using a Machine Learning Potential

Molecular photoswitches are the foundation of light-activated drugs. A key photoswitch is azobenzene, which exhibits trans–cis isomerism in response to light. The thermal half-life of the cis isomer is of crucial importance, since it controls the duration of the light-induced biological effect. Here we introduce a computational tool for predicting the thermal half-lives of azobenzene derivatives. Our automated approach uses a fast and accurate machine learning potential trained on quantum chemistry data. Building on well-established earlier evidence, we argue that thermal isomerization proceeds through rotation mediated by intersystem crossing, and incorporate this mechanism into our automated workflow. We use our approach to predict the thermal half-lives of 19,000 azobenzene derivatives. We explore trends and trade-offs between barriers and absorption wavelengths, and open-source our data and software to accelerate research in photopharmacology.
Spinon confinement in the gapped antiferromagnetic XXZ spin-1/2 chain

The inﬁnite Heisenberg XXZ spin-(1/2) chain in the gapped antiferromagnetic regime has two degenerate vacua and kink topological excitations (which are also called spinons) interpolating between these vacua as elementary excitations. Application of an arbitrary weak staggered longitudinal magnetic ﬁeld h induces a long-range attractive potential between two adjacent spinons leading to their conﬁnement into ’meson’ bound states. Exploiting the integrability of the XXZ model in the deconﬁned phase h = 0, we perform perturbative calculations of the energy spectra of the two-spinon bound states in the weak conﬁnement regime at h → +0, using the strength of the staggered magnetic ﬁeld h as a small parameter. Both transverse and longitudinal dynamical structure factors of the local spin operators are calculated as well in the two-spinon approximation in the weak conﬁnement regime to the leading order in h .
Modeling HI at the field level

We use an analytical forward model based on perturbation theory to predict the neutral hydrogen (HI) overdensity maps at low redshifts. We investigate its performance by comparing it directly at the field level to the simulated HI from the IllustrisTNG simulation TNG300-1 ($L=205\ h^{-1}$ Mpc), in both real and redshift space. We demonstrate that HI is a biased tracer of the underlying matter field and find that the cubic bias model describes the simulated HI power spectrum to within 1% up to $k=0.4 \;(0.3) \,h\,{\rm Mpc}^{-1}$ in real (redshift) space at redshifts $z=0,1$. Looking at counts in cells, we find an excellent agreement between the theory and simulations for cells as small as 5 $h^{-1}$ Mpc. These results are in line with expectations from perturbation theory and they imply that a perturbative description of the HI field is sufficiently accurate given the characteristics of upcoming 21cm intensity mapping surveys. Additionally, we study the statistical properties of the model error - the difference between the truth and the model. We show that on large scales this error is nearly Gaussian and that it has a flat power spectrum, with amplitude significantly lower than the standard noise inferred from the HI power spectrum. We explain the origin of this discrepancy, discuss its implications for the HI power spectrum Fisher matrix forecasts and argue that it motivates the HI field-level cosmological inference. On small scales in redshift space we use the difference between the model and the truth as a proxy for the Fingers-of-God effect. This allows us to estimate the nonlinear velocity dispersion of HI and show that it is smaller than for the typical spectroscopic galaxy samples at the same redshift. Finally, we provide a simple prescription based on the perturbative forward model which can be used to efficiently generate accurate HI mock data, in real and redshift space.
Aerodynamic Design Based on Topology Optimization of Turbulent Flow

: Flow topology optimization (ToOpt) based on Darcy’s source term is widely used in the field of ToOpt. It has a high degree of freedom and requires no initial configuration, making it suitable for conceptual aerodynamic design. Two problems of ToOpt are addressed in this paper to apply the ToOpt method to high-Reynolds-number turbulent flow. First, the relationship between the minimum magnitude of Darcy’s source term needed to model the solid and the characteristic variables of the flow (freestream velocity, length scale and fluid viscosity) at high Reynolds numbers is quantitively studied. A strategy for setting Darcy’s source term is then proposed. Second, the modified Launder – Sharma 𝑘 − ϵ (LSKE) model with modification terms related to Darcy’s source is developed. The ToOpt of a low-drag profile in turbulent flow is studied using the new model. The model is validated to reflect the influence of solids on turbulence even at Reynolds numbers as high as one million. Finally, a wall-distance computation method that can recognize the solid modeled by Darcy’s source term is developed and integrated into the modified shear stress transport (SST) turbulence model. The ToOpt of a rotor-like geometry, which is of great importance in aerodynamic design, is conducted using the modified SST model, proving the model’s ability to handle the ToOpt of turbomachinery.
Improving Mandarin Speech Recogntion with Block-augmented Transformer

Recently Convolution-augmented Transformer (Conformer) has shown promising results in Automatic Speech Recognition (ASR), outperforming the previous best published Transformer Transducer. In this work, we believe that the output information of each block in the encoder and decoder is not completely inclusive, in other words, their output information may be complementary. We study how to take advantage of the complementary information of each block in a parameter-efficient way, and it is expected that this may lead to more robust performance. Therefore we propose the Block-augmented Transformer for speech recognition, named Blockformer. We have implemented two block ensemble methods: the base Weighted Sum of the Blocks Output (Base-WSBO), and the Squeeze-and-Excitation module to Weighted Sum of the Blocks Output (SE-WSBO). Experiments have proved that the Blockformer significantly outperforms the state-of-the-art Conformer-based models on AISHELL-1, our model achieves a CER of 4.29\% without using a language model and 4.05\% with an external language model on the testset.
Black-box Few-shot Knowledge Distillation

Knowledge distillation (KD) is an efficient approach to transfer the knowledge from a large"teacher"network to a smaller"student"network. Traditional KD methods require lots of labeled training samples and a white-box teacher (parameters are accessible) to train a good student. However, these resources are not always available in real-world applications. The distillation process often happens at an external party side where we do not have access to much data, and the teacher does not disclose its parameters due to security and privacy concerns. To overcome these challenges, we propose a black-box few-shot KD method to train the student with few unlabeled training samples and a black-box teacher. Our main idea is to expand the training set by generating a diverse set of out-of-distribution synthetic images using MixUp and a conditional variational auto-encoder. These synthetic images along with their labels obtained from the teacher are used to train the student. We conduct extensive experiments to show that our method significantly outperforms recent SOTA few/zero-shot KD methods on image classification tasks. The code and models are available at: https://github.com/nphdang/FS-BBT
Micromagnetics of ferromagnetic/antiferromagnetic nanocomposite materials. I. Towards a mesoscopic approach

In the first of two articles, we present here a novel mesoscopic micromagnetic approach for simulating materials composed of ferromagnetic and antiferromagnetic phases. Starting with the atomistic modeling of quasi one-dimensional systems, we explicitly show how the material parameters for the mesoscopic model of an antiferromagnet can be derived. The comparison between magnetization profiles obtained in atomistic and mesoscopic calculations (using a Heusler alloy as an example) proves the validity of our method. This approach opens up the possibility to recover the details of the magnetization distribution in ferromagnetic/antiferromagnetic materials with the resolution of a few nanometers covering length scales up to several hundreds of nanometers.
Break it, Fix it: Attack and Defense for “Add-on” Access Control Solutions in Distributed Data Analytics Platforms

Distributed data analytics platforms (i.e., Apache Spark, Hadoop) enable cost-effective storage and processing by distributing data and computation to multiple nodes. Since these frameworks’ design was primarily motivated by performance and usability, most were assumed to operate in non-malicious settings. Hence, they allow users to execute arbitrary code to analyze the data. To make the situation worse, they do not support ﬁne-grained access control inherently or offer any plugin mechanism to enable it – which makes them risky to be used in multi-tier organizational settings. There have been attempts to build “add-on” solutions to enable ﬁne-grained access control for distributed data analytics platforms. In this paper, we show that by knowing the nature of the solution, an attacker can evade the access control by maliciously using the platform-provided APIs. Speciﬁcally, we crafted several attack vectors to evade such solutions. Next, we systematically analyze the threats and potentially risky APIs and propose a two-layered (i.e., proactive and reactive ) defense to protect against those attacks. Our proactive security layer utilizes state-of-the-art program analysis to detect potentially malicious user code. The reactive security layer consists of binary integrity checking, instrumentation-based runtime checks, and sandboxed execution. Finally, Using this solution, we provide a secure implementation of a new framework-agnostic ﬁne-grained attribute-based access control framework named S ECURE DL for Apache Spark. To the best of our knowledge, this is the ﬁrst work that provides secure ﬁne-grained attribute-based access control distributed data analytics platforms that allow arbitrary code execution. Performance evaluation showed that the overhead due to added security is low
Machine Learned Particle Detector Simulations

The use of machine learning algorithms is an attractive way to produce very fast detector simulations for scattering reactions that can otherwise be computationally expensive. Here we develop a factorised approach where we deal with each particle produced in a reaction individually: first determine if it was detected (acceptance) and second determine its reconstructed variables such as four momentum (reconstruction). For the acceptance we propose using a probability classification density ratio technique to determine the probability the particle was detected as a function of many variables. Neural Network and Boosted Decision Tree classifiers were tested for this purpose and we found using a combination of both, through a reweighting stage, provided the most reliable results. For reconstruction a simple method of synthetic data generation, based on nearest neighbour or decision trees was developed. Using a toy parameterised detector we demonstrate that such a method can reliably and accurately reproduce kinematic distributions from a physics reaction. The relatively simple algorithms allow for small training overheads whilst producing reliable results. Possible applications for such fast simulated data include Toy-MC studies of parameter extraction, preprocessing expensive simulations or generating templates for background distributions shapes.
Statistical inference for high-dimensional generalized estimating equations

We propose a novel inference procedure for linear combinations of high-dimensional regression coefficients in generalized estimating equations (GEE), which are widely used to analyze correlated data. Our estimator for this more general inferential target, obtained via constructing projected estimating equations, is shown to be asymptotically normally distributed under certain regularity conditions. We also introduce a data-driven cross-validation procedure to select the tuning parameter for estimating the projection direction, which is not addressed in the existing procedures. We demonstrate the robust finite-sample performance, especially in estimation bias and confidence interval coverage, of the proposed method via extensive simulations, and apply the method to a longitudinal proteomic study of COVID-19 plasma samples to investigate the proteomic signatures associated with disease severity.
Early Results from GLASS-JWST. VIII. An Extremely Magnified Blue Supergiant Star at Redshift 2.65 in the A2744 Cluster Field

We report the discovery of an extremely magnified star at redshift z = 2.65 in the James Webb Space Telescope (JWST) NIRISS pre-imaging of the A2744 galaxy-cluster field. The star’s background host galaxy lies on a fold caustic of the foreground lens, and the cluster creates a pair of images of the region close to the lensed star. We identified the bright transient in one of the merging images at a distance of ∼0. ″15 from the critical curve by subtracting the JWST F115W and F150W imaging from coadditions of archival Hubble Space Telescope (HST) F105W and F125W images and F140W and F160W images, respectively. Since the time delay between the two images should be only hours, the transient must be the microlensing event of an individual star, as opposed to a luminous stellar explosion that would persist for days to months. Analysis of individual exposures suggests that the star’s magnification is not changing rapidly during the observations. From photometry of the point source through the F115W, F150W, and F200W filters, we identify a strong Balmer break, and modeling allows us to constrain the star’s temperature to be approximately 7000–12,000 K.
Reference-based Image Super-Resolution with Deformable Attention Transformer

Reference-based image super-resolution (RefSR) aims to exploit auxiliary reference (Ref) images to super-resolve low-resolution (LR) images. Recently, RefSR has been attracting great attention as it provides an alternative way to surpass single image SR. However, addressing the RefSR problem has two critical challenges: (i) It is difficult to match the correspondence between LR and Ref images when they are significantly different; (ii) How to transfer the relevant texture from Ref images to compensate the details for LR images is very challenging. To address these issues of RefSR, this paper proposes a deformable attention Transformer, namely DATSR, with multiple scales, each of which consists of a texture feature encoder (TFE) module, a reference-based deformable attention (RDA) module and a residual feature aggregation (RFA) module. Specifically, TFE first extracts image transformation (e.g., brightness) insensitive features for LR and Ref images, RDA then can exploit multiple relevant textures to compensate more information for LR features, and RFA lastly aggregates LR features and relevant textures to get a more visually pleasant result. Extensive experiments demonstrate that our DATSR achieves state-of-the-art performance on benchmark datasets quantitatively and qualitatively.