Miracle-dz/UniFAR-FTUs huggingface dataset:
Non‐Linear Electrodynamics in Blandford–Znajek Energy Extraction

Non‐linear electrodynamics (NLED) is a generalization of Maxwell's electrodynamics for strong fields. It has significant implications for the study of black holes and cosmology and has been extensively studied in the literature, extending from quantum to cosmological contexts. In this work, two new ways to investigate these non‐linear theories are investigated. First, the Blandford‐Znajek mechanism is analyzed in light of this promising theoretical context, providing the general form of the extracted power up to second order in the black hole spin parameter a. It is found that, depending on the NLED model, the emitted power can be extremely increased or decreased, and that the magnetic field lines around the black hole seem to become vertical quickly. Considering only separated solutions, it is found that no monopole solutions exist and this could have interesting astrophysical consequences (not considered here). Last but not least, it is attempted to confine the NLED parameters by inducing the amplification of primordial magnetic fields (“seeds”), thus admitting non‐linear theories already during the early stages of the Universe. However, the latter approach proves to be useful for NLED research only in certain models. These (analytical) results emphasize that the behavior of non‐linear electromagnetic phenomena strongly depends on the physical context and that only a power‐law model seems to have any chance to compete with Maxwell.
New Financial Ratios Based on the Compositional Data Methodology

Due to the type of mathematical construction, the use of standard financial ratios in studies analyzing the financial health of a group of firms leads to a series of statistical problems that can invalidate the results obtained. These problems originate from the asymmetry of financial ratios. The present article justifies the use of a new methodology using Compositional Data (CoDa) to analyze the financial statements of an industry, improving analyses using conventional ratios, since the new methodology enables statistical techniques to be applied without encountering any serious drawbacks, such as skewness and outliers, and without the results depending on the arbitrary choice as to which of the accounting figures is the numerator of the ratio and which is the denominator. An example with data on the wine industry is provided. The results show that when using CoDa, outliers and skewness are much reduced, and results are invariant to numerator and denominator permutation.
HT-Net: Hierarchical Transformer based Operator Learning Model for Multiscale PDEs

Complex nonlinear interplays of multiple scales give rise to many interesting physical phenomena and pose major diﬃculties for the computer simulation of multiscale PDE models in areas such as reservoir simulation, high frequency scattering and turbulence modeling. In this paper, we introduce a hierarchical transformer (HT) scheme to eﬃciently learn the solution operator for multiscale PDEs. We construct a hierarchical architecture with scale adaptive interaction range, such that the features can be computed in a nested manner and with a controllable linear cost. Self-attentions over a hierarchy of levels can be used to encode and decode the multiscale solution space over all scale ranges. In addition, we adopt an empirical H 1 loss function to counteract the spectral bias of the neural network approximation for multiscale functions. In the numerical experiments, we demonstrate the superior performance of the HT scheme compared with state-of-the-art (SOTA) methods for representative multiscale problems.
Identities and periodic oscillations of divide-and-conquer recurrences splitting at half

We study divide-and-conquer recurrences of the form \begin{equation*} f(n) = \alpha f(\lfloor \tfrac n2\rfloor) + \beta f(\lceil \tfrac n2\rceil) + g(n) \qquad(n\ge2), \end{equation*} with $g(n)$ and $f(1)$ given, where $\alpha,\beta\ge0$ with $\alpha+\beta>0$; such recurrences appear often in analysis of computer algorithms, numeration systems, combinatorial sequences, and related areas. We show that the solution satisfies always the simple \emph{identity} \begin{equation*} f(n) = n^{\log_2(\alpha+\beta)} P(\log_2n) - Q(n) \end{equation*} under an optimum (iff) condition on $g(n)$. This form is not only an identity but also an asymptotic expansion because $Q(n)$ is of a smaller order. Explicit forms for the \emph{continuity} of the periodic function $P$ are provided, together with a few other smoothness properties. We show how our results can be easily applied to many dozens of concrete examples collected from the literature, and how they can be extended in various directions. Our method of proof is surprisingly simple and elementary, but leads to the strongest types of results for all examples to which our theory applies.
Random complexes with free involution

We introduce a new model for random simplicial complexes which with high probability generates a complex that has a simply-connected double cover. Hence we develop a model for random simplicial complexes with fundamental group Z / 2 Z . We establish results about the typical asymptotic topology of these complexes. As a consequence we give bounds for the dimension d such that Z / 2 Z -equivariant maps from the double cover to R d have zeros with high probability, thus establishing a random Borsuk–Ulam theorem. We apply this to derive a structural result for pairs of non-adjacent cliques in Erd˝os–R´enyi random graphs.
Precision $\mu^+\mu^+$ and $\mu^+e^-$ elastic scatterings

Expected precisions of measurements of the elastic scattering cross sections are estimated for $\mu^+ \mu^+$ and $\mu^+ e^-$ colliders, which are recently proposed as future realistic possibilities ($\mu$TRISTAN). Comparing with contributions from possible new physics represented by higher dimensional operators, we find that the measurements at a TeV energy $\mu^+\mu^+$ collider can probe the scale of new physics up to $O(100)$~TeV. A $\mu^+ e^-$ collider for the Higgs boson factory can also improve the electroweak precision test.
Numerical Methods for Large-Scale Optimal Transport

The optimal transport (OT) problem is a classical optimization problem having the form of linear programming. Machine learning applications put forward new computational challenges in its solution. In particular, the OT problem defines a distance between real-world objects such as images, videos, texts, etc., modeled as probability distributions. In this case, the large dimension of the corresponding optimization problem does not allow applying classical methods such as network simplex or interior-point methods. This challenge was overcome by introducing entropic regularization and using the efficient Sinkhorn's algorithm to solve the regularized problem. A flexible alternative is the accelerated primal-dual gradient method, which can use any strongly-convex regularization. We discuss these algorithms and other related problems such as approximating the Wasserstein barycenter together with efficient algorithms for its solution, including decentralized distributed algorithms.
Maximum Common Subgraph Guided Graph Retrieval: Late and Early Interaction Networks

The graph retrieval problem is to search in a large corpus of graphs for ones that are most similar to a query graph. A common consideration for scoring similarity is the maximum common subgraph (MCS) between the query and corpus graphs, usually counting the number of common edges (i.e., MCES). In some applications, it is also desirable that the common subgraph be connected, i.e., the maximum common connected subgraph (MCCS). Finding exact MCES and MCCS is intractable, but may be unnecessary if ranking corpus graphs by relevance is the goal. We design fast and trainable neural functions that approximate MCES and MCCS well. Late interaction methods compute dense representations for the query and corpus graph separately, and compare these representations using simple similarity functions at the last stage, leading to highly scalable systems. Early interaction methods combine information from both graphs right from the input stages, are usually considerably more accurate, but slower. We propose both late and early interaction neural MCES and MCCS formulations. They are both based on a continuous relaxation of a node alignment matrix between query and corpus nodes. For MCCS, we propose a novel differentiable network for estimating the size of the largest connected common subgraph. Extensive experiments with seven data sets show that our proposals are superior among late interaction models in terms of both accuracy and speed. Our early interaction models provide accuracy competitive with the state of the art, at substantially greater speeds.
Apple of Sodom: Hidden Backdoors in Superior Sentence Embeddings via Contrastive Learning

This paper ﬁnds that contrastive learning can produce superior sentence embeddings for pre-trained models but is also vulnerable to backdoor attacks. We present the ﬁrst backdoor attack framework, BadCSE , for state-of-the-art sentence embeddings under supervised and unsupervised learning settings. The attack manipulates the construction of positive and negative pairs so that the backdoored samples have a similar embedding with the target sample (targeted attack) or the negative embedding of its clean version (non-targeted attack). By injecting the backdoor in sentence embeddings, BadCSE is resistant against downstream ﬁnetuning. We evaluate BadCSE on both STS tasks and other downstream tasks. The supervised non-targeted attack obtains a performance degradation of 194 . 86%, and the targeted attack maps the backdoored samples to the target embedding with a 97 . 70% success rate while maintaining the model utility.
Hall Effect Induced by Topologically Trivial Target Skyrmions

Electrons moving through a noncoplanar magnetic texture acquire a Berry phase, which can be described as an effective magnetic field. This effect is known as the topological Hall effect and has been observed in topological spin textures. Motivated by recent experimental realizations, here we study the Hall effect in a nontopological magnetic texture known as a target skyrmion. We start from a simplified semiclassical picture and show that the Hall signal is a nonmonotonic function of both the electronic energy and target skyrmion radius. That observation carries over to the fully quantum mechanical treatment in a Landauer-B\"uttiker formalism in a mesoscopic setting. Our conclusion challenges the popular opinion in the community that the Hall effect in such structures necessarily requires a nonzero skyrmion number.
Controller-Guided Partial Label Consistency Regularization with Unlabeled Data

Partial label learning (PLL) learns from training examples each associated with multiple candidate labels, among which only one is valid. In recent years, benefiting from the strong capability of dealing with ambiguous supervision and the impetus of modern data augmentation methods, consistency regularization-based PLL methods have achieved a series of successes and become mainstream. However, as the partial annotation becomes insufficient, their performances drop significantly. In this paper, we leverage easily accessible unlabeled examples to facilitate the partial label consistency regularization. In addition to a partial supervised loss, our method performs a controller-guided consistency regularization at both the label-level and representation-level with the help of unlabeled data. To minimize the disadvantages of insufficient capabilities of the initial supervised model, we use the controller to estimate the confidence of each current prediction to guide the subsequent consistency regularization. Furthermore, we dynamically adjust the confidence thresholds so that the number of samples of each class participating in consistency regularization remains roughly equal to alleviate the problem of class-imbalance. Experiments show that our method achieves satisfactory performances in more practical situations, and its modules can be applied to existing PLL methods to enhance their capabilities.
Quantum-inspired tempering for ground state approximation using artificial neural networks

A large body of work has demonstrated that parameterized artificial neural networks (ANNs) can efficiently describe ground states of numerous interesting quantum many-body Hamiltonians. However, the standard variational algorithms used to update or train the ANN parameters can get trapped in local minima, especially for frustrated systems and even if the representation is sufficiently expressive. We propose a parallel tempering method that facilitates escape from such local minima. This methods involves training multiple ANNs independently, with each simulation governed by a Hamiltonian with a different "driver" strength, in analogy to quantum parallel tempering, and it incorporates an update step into the training that allows for the exchange of neighboring ANN configurations. We study instances from two classes of Hamiltonians to demonstrate the utility of our approach using Restricted Boltzmann Machines as our parameterized ANN. The first instance is based on a permutation-invariant Hamiltonian whose landscape stymies the standard training algorithm by drawing it increasingly to a false local minimum. The second instance is four hydrogen atoms arranged in a rectangle, which is an instance of the second quantized electronic structure Hamiltonian discretized using Gaussian basis functions. We study this problem in a minimal basis set, which exhibits false minima that can trap the standard variational algorithm despite the problem’s small size. We show that augmenting the training with quantum parallel tempering becomes useful to finding good approximations to the ground states of these problem instances.
First Millimeter Flares Detected from Epsilon Eridani with ALMA

We report the detection of three large millimeter ﬂaring events from the nearby Sun-like, (cid:15) Eridani, found in archival ALMA 12m and ACA observations at 1.33 mm taken from 2015 January 17–18 and 2016 October 24–November 23, respectively. This is the ﬁrst time that ﬂares have been detected from a Sun-like star at millimeter wavelengths. The largest ﬂare among our data was detected in the ALMA observations on 2015 January 17 from 20:09:10.4–21:02:49.3 (UTC) with a peak ﬂux density of 28 ± 7 mJy and a duration of 9 sec. The peak brightness of the largest ﬂare is 3 . 4 ± 0 . 9 × 10 14 erg s − 1 Hz − 1 , a factor of > 50 × times brighter than the star’s quiescent luminosity and > 10 × brighter than solar ﬂares observed at comparable wavelengths. We ﬁnd changes in the spectral index (F ν ∝ ν α ) at the ﬂare peak, with α = 1.81 ± 1.94 and a lower limit on the fractional linear polarization | Q/I | = 0.08 ± 0.12. This positive spectral index is more similar to millimeter solar ﬂares, diﬀering from M dwarf ﬂares also detected at millimeter wavelengths that exhibit steeply negative spectral indices.
DiffEdit: Diffusion-based semantic image editing with mask guidance

Image generation has recently seen tremendous advances, with diffusion models allowing to synthesize convincing images for a large variety of text prompts. In this article, we propose DiffEdit, a method to take advantage of text-conditioned diffusion models for the task of semantic image editing, where the goal is to edit an image based on a text query. Semantic image editing is an extension of image generation, with the additional constraint that the generated image should be as similar as possible to a given input image. Current editing methods based on diffusion models usually require to provide a mask, making the task much easier by treating it as a conditional inpainting task. In contrast, our main contribution is able to automatically generate a mask highlighting regions of the input image that need to be edited, by contrasting predictions of a diffusion model conditioned on different text prompts. Moreover, we rely on latent inference to preserve content in those regions of interest and show excellent synergies with mask-based diffusion. DiffEdit achieves state-of-the-art editing performance on ImageNet. In addition, we evaluate semantic image editing in more challenging settings, using images from the COCO dataset as well as text-based generated images.
Similarity of Neural Architectures using Adversarial Attack Transferability

In recent years, many deep neural architectures have been developed for image classification. Whether they are similar or dissimilar and what factors contribute to their (dis)similarities remains curious. To address this question, we aim to design a quantitative and scalable similarity measure between neural architectures. We propose Similarity by Attack Transferability (SAT) from the observation that adversarial attack transferability contains information related to input gradients and decision boundaries widely used to understand model behaviors. We conduct a large-scale analysis on 69 state-of-the-art ImageNet classifiers using our proposed similarity function to answer the question. Moreover, we observe neural architecture-related phenomena using model similarity that model diversity can lead to better performance on model ensembles and knowledge distillation under specific conditions. Our results provide insights into why developing diverse neural architectures with distinct components is necessary.
Pre-trained Sentence Embeddings for Implicit Discourse Relation Classification

Implicit discourse relations bind smaller linguistic units into coherent texts. Automatic sense prediction for implicit relations is hard, because it requires understanding the semantics of the linked arguments. Furthermore, annotated datasets contain relatively few labeled examples, due to the scale of the phenomenon: on average each discourse relation encompasses several dozen words. In this paper, we explore the utility of pre-trained sentence embeddings as base representations in a neural network for implicit discourse relation sense classification. We present a series of experiments using both supervised end-to-end trained models and pre-trained sentence encoding techniques - SkipThought, Sent2vec and Infersent. The pre-trained embeddings are competitive with the end-to-end model, and the approaches are complementary, with combined models yielding significant performance improvements on two of the three evaluations.
Roadmap on spatiotemporal light fields

Spatiotemporal sculpturing of light pulse with ultimately sophisticated structures represents a major goal of the everlasting pursue of ultra-fast information transmission and processing as well as ultra-intense energy concentration and extraction. It also holds the key to unlock new extraordinary fundamental physical effects. Traditionally, spatiotemporal light pulses are always treated as spatiotemporally separable wave packet as solution of the Maxwell’s equations. In the past decade, however, more generalized forms of spatiotemporally nonseparable solution started to emerge with growing importance for their striking physical effects. This roadmap intends to highlight the recent advances in the creation and control of increasingly complex spatiotemporally sculptured pulses, from spatiotemporally separable to complex nonseparable states, with diverse geometric and topological structures, presenting a bird’s eye viewpoint on the zoology of spatiotemporal light fields and the outlook of future trends and open challenges.
2022 Dynamical viscoelasticity of two-dimensional under oscillatory tensile loadings

Lipid bilayer membranes consisting of two opposite phospholipid monolayers are present in all mammalian cell types, and are largely responsible for the dual solid-ﬂuid behavior of individual cells. Despite numerous studies on the role of in-plane ﬂuidity in membrane deformation, the dynamical viscoelastic nature of lipid bilayers has not yet been fully described. We thus numerically investigate the dynamical viscoelasticity of membranes under oscillatory tensile loadings. We use hydrodynamic equations of bilayer membranes, obtained by Onsager’s variational principle, wherein the ﬂuid membrane is assumed to be an almost planar bilayer membrane. Simulations are performed for a wide range of oscillatory frequencies and membrane tensions. Our numerical results show that as frequencies increases, membrane characteristics shift from elastic dominant to viscous dominant. Furthermore, such viscous- or elastic-dominant transitions obtained with 1- µ m-wide loading proﬁle appear within the range of frequency between 40 Hz and 400 Hz, and almost independently of surface tensions. The transition will shift to lower frequency range as the width of loading proﬁle increases. These numerical results will serve as fundamental knowledge for building a precise continuum membrane model that takes multi-scale dynamics into account, and will provide insight into both passive and active cell dynamics, such as microcirculatory blood ﬂow and cancer metastasis.
Surgical Fine-Tuning Improves Adaptation to Distribution Shifts

A common approach to transfer learning under distribution shift is to fine-tune the last few layers of a pre-trained model, preserving learned features while also adapting to the new task. This paper shows that in such settings, selectively fine-tuning a subset of layers (which we term surgical fine-tuning) matches or outperforms commonly used fine-tuning approaches. Moreover, the type of distribution shift influences which subset is more effective to tune: for example, for image corruptions, fine-tuning only the first few layers works best. We validate our findings systematically across seven real-world data tasks spanning three types of distribution shifts. Theoretically, we prove that for two-layer neural networks in an idealized setting, first-layer tuning can outperform fine-tuning all layers. Intuitively, fine-tuning more parameters on a small target dataset can cause information learned during pre-training to be forgotten, and the relevant information depends on the type of shift.
Lindblad master equation approach to the topological phase transition in the disordered Su-Schrieffer-Heeger model

We use the Lindblad equation method to investigate the onset of a mobility edge and the topological phase transition in the disordered SSH chain connected to two external baths in the large bias limit. From the scaling properties of the nonequilibrium stationary current flowing across the system, we recover the localization/delocalization in the disordered chain. To probe the topological phase transition in the presence of disorder, we use the even-odd differential occupancy as a mean to discriminate topologically trivial from topologically nontrival phases in the out-of-equilibirum system. Eventually, we argue how to generalize our method to other systems undergoing a topological phase transition in the presence of disorder.