Miracle-dz/UniFAR-FTUs huggingface dataset:
Strong Tornadoes and Flash-Flood-Producing Rainstorms During the Warm Season in the Mid-Atlantic Region

Abstract Storm-related literature spanning 45 years (1942–1986) was examined to 1) establish a climatology of strong tornadoes and intense rainstorms for the Mid-Atlantic region, and 2) identify the key environmental features that distinguish the days producing strong convective events. Ninety-three strong tornado events (F3 or greater) and 63 intense rain events (19 cm or more in 12 h or less) were found for the 45-year period and were investigated. The diurnal and monthly distributions of the tornado and rainstorm events correspond well with other known climatological studies of similar events. Analysis of the upper-level flow patterns during the events shows that the Mid-Atlantic region is affected by two distinct regimes during the warm season. Events near the East Coast most frequently have southwest flow aloft. However, for the Upper Ohio Valley, the direction of the flow aloft varies as the warm season progresses. Spring and autumn events occur mostly with southwest flow aloft, while summer events .
The Skorokhod problem with two nonlinear constraints

In this paper, we study the Skorokhod problem with two constraints, where the constraints are in a nonlinear fashion. We prove the existence and uniqueness of the solution and also provide the explicit construction for the solution. In addition, a number of properties of the solution, including continuity under uniform and J1 metrics, comparison principle and non-anticipatory property, are investigated.
Tokenization and the Noiseless Channel

Subword tokenization is a key part of most NLP pipelines.However, little is known about why some tokenizer and hyperparameter combinations lead to improved downstream model performance over others. We propose that good tokenizers lead to efficient channel usage, where the channel is the means by which some input is conveyed to the model and efficiency can be quantified in information-theoretic terms as the ratio of the Shannon entropy to the maximum entropy of the subword distribution.Nevertheless, an optimal encoding according to Shannon entropy assigns extremely long codes to low-frequency subwords and very short codes to high-frequency subwords.Defining efficiency in terms of Rényi entropy, on the other hand, penalizes distributions with either very high or very low-frequency subwords.We posit that (1) extremely high-frequency subwords are problematic because their meaning is not distinct and (2) that low-frequency subwords may not appear frequently enough for their meaning to be learned properly; encodings that induce unigram distributions with either can harm model performance.In machine translation, we find that across multiple tokenizers, the Rényi entropy has a very strong correlation with BLEU: 0.82 in comparison to just -0.30 for compressed length.
Towards a Better Theoretical Understanding of Independent Subnetwork Training

Modern advancements in large-scale machine learning would be impossible without the paradigm of data-parallel distributed computing. Since distributed computing with large-scale models imparts excessive pressure on communication channels, significant recent research has been directed toward co-designing communication compression strategies and training algorithms with the goal of reducing communication costs. While pure data parallelism allows better data scaling, it suffers from poor model scaling properties. Indeed, compute nodes are severely limited by memory constraints, preventing further increases in model size. For this reason, the latest achievements in training giant neural network models also rely on some form of model parallelism. In this work, we take a closer theoretical look at Independent Subnetwork Training (IST), which is a recently proposed and highly effective technique for solving the aforementioned problems. We identify fundamental differences between IST and alternative approaches, such as distributed methods with compressed communication, and provide a precise analysis of its optimization performance on a quadratic model.
Group-based Robustness: A General Framework for Customized Robustness in the Real World

Machine-learning models are known to be vulnerable to evasion attacks that perturb model inputs to induce misclassifications. In this work, we identify real-world scenarios where the true threat cannot be assessed accurately by existing attacks. Specifically, we find that conventional metrics measuring targeted and untargeted robustness do not appropriately reflect a model's ability to withstand attacks from one set of source classes to another set of target classes. To address the shortcomings of existing methods, we formally define a new metric, termed group-based robustness, that complements existing metrics and is better-suited for evaluating model performance in certain attack scenarios. We show empirically that group-based robustness allows us to distinguish between models' vulnerability against specific threat models in situations where traditional robustness metrics do not apply. Moreover, to measure group-based robustness efficiently and accurately, we 1) propose two loss functions and 2) identify three new attack strategies. We show empirically that with comparable success rates, finding evasive samples using our new loss functions saves computation by a factor as large as the number of targeted classes, and finding evasive samples using our new attack strategies saves time by up to 99\% compared to brute-force search methods. Finally, we propose a defense method that increases group-based robustness by up to 3.52$\times$.
OBELISC: An Open Web-Scale Filtered Dataset of Interleaved Image-Text Documents

Large multimodal models trained on natural documents, which interleave images and text, outperform models trained on image-text pairs on various multimodal benchmarks. However, the datasets used to train these models have not been released, and the collection process has not been fully specified. We introduce the OBELICS dataset, an open web-scale filtered dataset of interleaved image-text documents comprising 141 million web pages extracted from Common Crawl, 353 million associated images, and 115 billion text tokens. We describe the dataset creation process, present comprehensive filtering rules, and provide an analysis of the dataset's content. To show the viability of OBELICS, we train vision and language models of 9 and 80 billion parameters named IDEFICS, and obtain competitive performance on different multimodal benchmarks. We release our dataset, models and code.
A Res-FCN for Electromagnetic Inversion of High Contrast Scatterers at an Arbitrary Frequency Within a Wide Frequency Band

Many successful machine learning methods have been developed for microwave inversion problems. However, so far, their inversion has been performed only at the specifically trained frequencies. To make the machine-learning-based inversion method more generalizability for realistic engineering applications, this work proposes a residual fully convolutional network (Res-FCN) to perform microwave inversion of high contrast scatterers at an arbitrary frequency within a wide frequency band. The proposed Res-FCN combines the advantages of the Res-Net and the fully convolutional network (FCN). Res-FCN consists of an encoder and a decoder: the encoder is employed to extract high-dimensional features from the measured scattered field through the residual frameworks, while the decoder is employed to map from the high-dimensional features extracted by the encoder to the electrical parameter distribution in the inversion region by the up-sample layer and the residual frameworks. Five numerical examples verify that the proposed Res-FCN can achieve good performance in the 2-D microwave inversion problem for high contrast scatterers with anti-noise ability at an arbitrary frequency point within a wide frequency band.
The Space of Contact Forms Adapted to an Open Book

We construct a complete set of two consecutive obstructions against homotopies of pointed families of adapted contact forms with parameters in the n-sphere. Using these obstructions, we show that there is a manifold with an open book decomposition together with both infinitely many adapted contact forms that all induce the same Liouville form on one page but such that the underlying contact manifolds are not contactomorphic, and infinitely many non-homotopic adapted contact forms that all induce the same Liouville form on one page and such that the underlying contact manifolds are contactomorphic. Following this, we use the neighbourhood theorem for the binding of an open book decomposition that we introduce in the construction of the obstructions to construct special generalised caps of contact manifolds. This leads us to a proof that, on closed manifolds, the Reeb vector field of every contact form defining a contact structure supported by a tower of open book decompositions has a contractible orbit provided the binding in the lowest level of this tower embeds into a subcritical Stein manifold as a hypersurface of restricted contact type or is supported by an open book decomposition with trivial monodromy. Moreover, we show that the strong Weinstein conjecture holds for contact manifolds supported by an open book whose binding is planar.
On the Jacobson radical and semisimplicity of a semiring

Based on the minimal and simple representations, we introduce two Jacobson-type Hoehnke radicals, m-radical and s-radical, of a semiring $S$. Every minimal (simple) $S$-semimodule is a quotient of $S$ by a regular right congruence (maximal) $\mu$ on $S$ such that $[0]_\mu$ is a maximal $\mu$-saturated right ideal in $S$. Thus the m(s)-radical becomes an intersection of some regular congruences. Finally, every semisimple semiring is characterized as a subdirect product of primitive semirings; and every s-primitive semiring is represented as a 1-fold transitive subsemiring of the semiring of all endomorphisms on a semimodule over a division semiring.
Sparse Model Soups: A Recipe for Improved Pruning via Model Averaging

Neural networks can be significantly compressed by pruning, yielding sparse models with reduced storage and computational demands while preserving predictive performance. Model soups (Wortsman et al., 2022) enhance generalization and out-of-distribution (OOD) performance by averaging the parameters of multiple models into a single one, without increasing inference time. However, achieving both sparsity and parameter averaging is challenging as averaging arbitrary sparse models reduces the overall sparsity due to differing sparse connectivities. This work addresses these challenges by demonstrating that exploring a single retraining phase of Iterative Magnitude Pruning (IMP) with varied hyperparameter configurations such as batch ordering or weight decay yields models suitable for averaging, sharing identical sparse connectivity by design. Averaging these models significantly enhances generalization and OOD performance over their individual counterparts. Building on this, we introduce Sparse Model Soups (SMS), a novel method for merging sparse models by initiating each prune-retrain cycle with the averaged model from the previous phase. SMS preserves sparsity, exploits sparse network benefits, is modular and fully parallelizable, and substantially improves IMP's performance. We further demonstrate that SMS can be adapted to enhance state-of-the-art pruning-during-training approaches.
Lithium in Kepler Red Giants: Defining Normal and Anomalous

The orders-of-magnitude variations in the lithium abundances of evolved stars have long been a puzzle. Diluted signals, ambiguous evolutionary states, and unknown masses have made it challenging to both map the expected lithium signals and explain the anomalously lithium-rich stars. Using a set of asteroseismically characterized evolved stars, we show here that the base lithium abundance in red giant stars is mass-dependent, with higher-mass stars having higher “normal” lithium abundances, while highly lithium-enhanced stars may cluster around 0.8 or 1.8 M ☉. We confirm previous studies that have shown that lithium enhancement and rapid rotation are often coincident but find that the actual correlation between lithium abundance and rotation rate, whether surface, internal, or radial differential rotation, is weak. Our data support previous assertions that most lithium-rich giants are in the core-helium-burning phase. We also note a tentative correlation between the highest lithium abundances and unusual carbon-to-nitrogen ratios, which is suggestive of binary interactions, though we find no simple correlation between lithium richness and indicators of binarity.
L2 to Lp bounds for spectral projectors on thin intervals in Riemannian manifolds

Given a Riemannian manifold endowed with its Laplace-Beltrami operator, consider the associated spectral projector on a thin interval. As an operator from L2 to Lp, what is its operator norm? For a window of size 1, this question is fully answered by a celebrated theorem of Sogge, which applies to any manifold. For smaller windows, the global geometry of the manifold comes into play, and connections to a number of mathematical fields (such as Differential Geometry, Combinatorics, Number Theory) appear, but the problem remains mostly open. The aim of this article is to review known results, focusing on cases exhibiting symmetry and emphasizing harmonic analytic rather than microlocal methods.
Lightweight texture transfer based on texture feature preset

In the task of texture transfer, reference texture images typically exhibit highly repetitive texture features, and the texture transfer results from different content images under the same style also share remarkably similar texture patterns. Encoding such highly similar texture features often requires deep layers and a large number of channels, making it is also the main source of the entire model's parameter count and computational load, and inference time. We propose a lightweight texture transfer based on texture feature preset (TFP). TFP takes full advantage of the high repetitiveness of texture features by providing preset universal texture feature maps for a given style. These preset feature maps can be fused and decoded directly with shallow color transfer feature maps of any content to generate texture transfer results, thereby avoiding redundant texture information from being encoded repeatedly. The texture feature map we preset is encoded through noise input images with consistent distribution (standard normal distribution). This consistent input distribution can completely avoid the problem of texture transfer differentiation, and by randomly sampling different noise inputs, we can obtain different texture features and texture transfer results under the same reference style. Compared to state-of-the-art techniques, our TFP not only produces visually superior results but also reduces the model size by 3.2-3538 times and speeds up the process by 1.8-5.6 times.
Broken-symmetry magnetic phases in two-dimensional triangulene crystals

We provide a comprehensive theory of magnetic phases in two-dimensional triangulene crystals, using both Hubbard model and density functional theory (DFT) calculations. We consider centrosymmetric and non-centrosymmetric triangulene crystals. In all cases, DFT and mean-field Hubbard model predict the emergence of broken-symmetry antiferromagnetic (ferrimagnetic) phases for the centrosymmetric (non-centrosymmetric) crystals. This includes the special case of the [4,4]triangulene crystal, whose non-interacting energy bands feature a gap with flat valence and conduction bands. We show how the lack of contrast between the local density of states of these bands, recently measured via scanning tunneling spectroscopy, is a natural consequence of a broken-symmetry N\'eel state that blocks intermolecular hybridization. Using random phase approximation, we also compute the spin wave spectrum of these crystals, including the recently synthesized [4,4]triangulene crystal. The results are in excellent agreement with the predictions of a Heisenberg spin model derived from multi-configuration calculations for the unit cell. We conclude that experimental results are compatible with an antiferromagnetically ordered phase where each triangulene retains the spin predicted for the isolated species.
Propagation of a Realistic Magnetar Jet through a Binary Neutron Star Merger Medium and Implications for Short Gamma-Ray Bursts

The origin of short gamma-ray bursts is associated with outflows powered by the remnant of a binary neutron star merger. This remnant can be either a black hole or a highly magnetized, fast-spinning neutron star, also known as a magnetar. Here we present the results of two relativistic magnetohydrodynamical simulations aimed at investigating the large-scale dynamics and propagation of magnetar collimated outflows through the medium surrounding the remnant. The first simulation evolves a realistic jet by injecting external simulation data, while the second evolves an analytical model jet with similar properties for comparison. We find that both outflows remain collimated and successfully emerge through the static medium surrounding the remnant. However, they fail to attain relativistic velocities and only reach a mean maximum speed of ∼0.7c for the realistic jet and ∼0.6c for the analytical jet. We also find that the realistic jet has a much more complex structure. The lack of highly relativistic speeds, which makes these jets unsuitable as short gamma-ray burst sources, is due to numerical limitations and is not general to all possible magnetar outflows. A jet like the one we study, however, could give rise to or augment a blue kilonova component. In addition, it would make the propagation of a relativistic jet easier, should one be launched after the neutron star collapses into a black hole.
Extension of the law of the wall exploiting the concepts of strong and weak universality of velocity ﬂuctuations in a channel

This paper explores the universality of the instantaneous velocity proﬁles in a channel, which, despite the equilibrium nature of a channel ﬂow, are subjected to strong non-equilibrium eﬀects. In the analysis, we employ a one-dimensional scalar variant of the proper orthogonal decomposition (POD) and exploit the concepts of strong and weak universalities. Strong universality requires that all POD modes are universal with respect to the Reynolds number, while weak universality only requires that the ﬁrst few POD modes are universal. As POD analysis concerns information at more than one location, these universalities are more general than various similarities and universality in the literature concerning single-point ﬂow statistics, e.g., outer layer similarity or universality of the log law. We examine ﬂows at Re τ = 180, 540, 1000, and 5200. Strong universality is observed in the outer layer, and weak universality is found in both the inner layer and the outer part of the logarithmic layer. The presence of weak universality suggests the existence of an extension to the law of the wall (LoW). Here, we propose such an extension based on the results from one-dimensional POD analysis. The usefulness of the LoW extension is assessed by comparing ﬂow reconstructions according to the extended LoW and the equilibrium LoW. We show that the extended LoW provides strikingly accurate ﬂow reconstruction in the wall layer across a wide range of Reynolds numbers, capturing ﬁne-scale motions that are entirely missed by the equilibrium LoW.
CLIPAG: Towards Generator-Free Text-to-Image Generation

Perceptually Aligned Gradients (PAG) refer to an intriguing property observed in robust image classification models, wherein their input gradients align with human perception and pose semantic meanings. While this phenomenon has gained significant research attention, it was solely studied in the context of unimodal vision-only architectures. In this work, we extend the study of PAG to Vision-Language architectures, which form the foundations for diverse image-text tasks and applications. Through an adversarial robustification finetuning of CLIP, we demonstrate that robust Vision-Language models exhibit PAG in contrast to their vanilla counterparts. This work reveals the merits of CLIP with PAG (CLIPAG) in several vision-language generative tasks. Notably, we show that seamlessly integrating CLIPAG in a"plug-n-play"manner leads to substantial improvements in vision-language generative applications. Furthermore, leveraging its PAG property, CLIPAG enables text-to-image generation without any generative model, which typically requires huge generators.
Influence of incidence angle on the aerodynamic characteristics of square cylinders with rounded corners

Purpose – The purpose of this paper is to focus on the variation of wake structures and aerodynamic forces with changes in the cylinder corner radius and orientation. Design/methodology/approach – Numerical simulations were performed for flow past a square cylinder with different corner radii placed at an angle to the incoming flow. In the present study, the rounded corner ratio R/D=0 (square cylinder), 0.1, 0.2, 0.3, and 0.4 (where R is the corner radius and D is the characteristic dimension of the body) and the angle of incidence α in the range of 0°-45° were considered. Findings – The numerical model was validated by comparing the present results with results in the available literature, and they were found to be in good agreement. The critical incidence angle for the rounded corner cylinder – corresponding to the minimum mean drag coefficient (C D ), the minimum root mean square value of the lift coefficient C L,RMS), and the maximum Strouhal number – shifted to a lower incidence angle compared with t.
Representation and Numerical Approximation of American Option Prices under Heston

The following sections are included:IntroductionProblem Statement — The Heston ModelFinding the Density Function using Integral TransformsSolution for the American Call OptionNumerical Scheme for the Free SurfaceConclusionAppendixProof of Proposition 5.8 — The European Option PriceEvaluation of Common Integral Terms in the Heston ModelCalculation of the DeltasProof of Proposition 5.12Moments for the Heston ModelMethod of Lines for the Heston PDE
The $\mathrm{SO}(5)$ Deconfined Phase Transition under the Fuzzy Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum

The deconfined quantum critical point (DQCP) is an example of phase transitions beyond the Landau symmetry breaking paradigm that attracts wide interest. However, its nature has not been settled after decades of study. In this paper, we apply the recently proposed fuzzy sphere regularization to study the $\mathrm{SO}(5)$ non-linear sigma model (NL$\sigma$M) with a topological Wess-Zumino-Witten term, which serves as a dual description of the DQCP with an exact $\mathrm{SO}(5)$ symmetry. We demonstrate that the fuzzy sphere functions as a powerful microscope, magnifying and revealing a wealth of crucial information about the DQCP, ultimately paving the way towards its final answer. In particular, through exact diagonalization, we provide clear evidence that the DQCP exhibits approximate conformal symmetry. The evidence includes the existence of a conserved $\mathrm{SO}(5)$ symmetry current, a stress tensor, and integer-spaced levels between conformal primaries and their descendants. Most remarkably, we have identified 23 primaries and 76 conformal descendants. Furthermore, by examining the renormalization group flow of the lowest symmetry singlet as well as other primaries, we provide numerical evidence in favour of DQCP being pseudo-critical, with the approximate conformal symmetry plausibly emerging from nearby complex fixed points. The primary spectrum we compute also has important implications, including the conclusion that the $\mathrm{SO}(5)$ DQCP cannot describe a direct transition from the N\'eel to valence bond solid phase on the honeycomb lattice.