Miracle-dz/UniFAR-FTUs huggingface dataset:
Weyl curvature evolution system for GR

Starting from the chiral first-order pure connection formulation of General Relativity, we put the field equations of GR in a strikingly simple evolution system form. The two dynamical fields are a complex symmetric tracefree 3×3 matrix Ψij , which encodes the self-dual part of the Weyl curvature tensor, as well as a spatial SO(3,C) connection Aai . The right-hand sides of the evolution equations also contain the triad for the spatial metric, and this is constructed non-linearly from the field Ψij and the curvature of the spatial connection Aai . The evolution equations for this pair are first order in both time and spatial derivatives, and so simple that they could have been guessed without a computation. They are the most natural spin two generalisations of Maxwell’s spin one equations. We also determine the modifications of the evolution system needed to enforce the ‘constraint sweeping’, so that any possible numerical violation of the constraints present becomes propagating and gets removed from the computational grid.
An Exact Mapping From ReLU Networks to Spiking Neural Networks

Deep spiking neural networks (SNNs) offer the promise of low-power artificial intelligence. However, training deep SNNs from scratch or converting deep artificial neural networks to SNNs without loss of performance has been a challenge. Here we propose an exact mapping from a network with Rectified Linear Units (ReLUs) to an SNN that fires exactly one spike per neuron. For our constructive proof, we assume that an arbitrary multi-layer ReLU network with or without convolutional layers, batch normalization and max pooling layers was trained to high performance on some training set. Furthermore, we assume that we have access to a representative example of input data used during training and to the exact parameters (weights and biases) of the trained ReLU network. The mapping from deep ReLU networks to SNNs causes zero percent drop in accuracy on CIFAR10, CIFAR100 and the ImageNet-like data sets Places365 and PASS. More generally our work shows that an arbitrary deep ReLU network can be replaced by an energy-efficient single-spike neural network without any loss of performance.
No pressure? Energy-consistent ROMs for the incompressible Navier-Stokes equations with time-dependent boundary conditions

This work presents a novel reduced-order model (ROM) for the incompressible Navier-Stokes equations with time-dependent boundary conditions. This ROM is velocity-only, i.e. the simulation of the velocity does not require the computation of the pressure, and preserves the structure of the kinetic energy evolution. The key ingredient of the novel ROM is a decomposition of the velocity into a field with homogeneous boundary conditions and a lifting function that satisfies the mass equation with the prescribed inhomogeneous boundary conditions. This decomposition is inspired by the Helmholtz-Hodge decomposition and exhibits orthogonality of the two components. This orthogonality is crucial to preserve the structure of the kinetic energy evolution. To make the evaluation of the lifting function efficient, we propose a novel method that involves an explicit approximation of the boundary conditions with POD modes, while preserving the orthogonality of the velocity decomposition and thus the structure of the kinetic energy evolution. We show that the proposed velocity-only ROM is equivalent to a velocity-pressure ROM, i.e., a ROM that simulates both velocity and pressure. This equivalence can be generalized to other existing velocity-pressure ROMs and reveals valuable insights in their behaviour. Numerical experiments on test cases with inflow-outflow boundary conditions confirm the correctness and efficiency of the new ROM, and the equivalence with the velocity-pressure formulation.
Multi-Projection Fusion and Refinement Network for Salient Object Detection in 360° Omnidirectional Image

Salient object detection (SOD) aims to determine the most visually attractive objects in an image. With the development of virtual reality (VR) technology, 360 ° omnidirectional image has been widely used, but the SOD task in 360 ° omnidirectional image is seldom studied due to its severe distortions and complex scenes. In this article, we propose a multi-projection fusion and refinement network (MPFR-Net) to detect the salient objects in 360 ° omnidirectional image. Different from the existing methods, the equirectangular projection (EP) image and four corresponding cube-unfolding (CU) images are embedded into the network simultaneously as inputs, where the CU images not only provide supplementary information for EP image but also ensure the object integrity of cube-map projection. In order to make full use of these two projection modes, a dynamic weighting fusion (DWF) module is designed to adaptively integrate the features of different projections in a complementary and dynamic manner from the perspective of inter and intrafeatures. Furthermore, in order to fully explore the way of interaction between encoder and decoder features, a filtration and refinement (FR) module is designed to suppress the redundant information of the feature itself and between the features. Experimental results on two omnidirectional datasets demonstrate that the proposed approach outperforms the state-of-the-art methods both qualitatively and quantitatively. The code and results can be found from the link of https://rmcong.github. io/proj_MPFRNet. html.
Magnetic Braking with MESA Evolutionary Models in the Single Star and Low-mass X-Ray Binary Regimes

Magnetic braking has a prominent role in driving the evolution of close low-mass binary systems and heavily influences the rotation rates of low-mass F- and later-type stars with convective envelopes. Several possible prescriptions that describe magnetic braking in the context of 1D stellar evolution models currently exist. We test four magnetic braking prescriptions against both low-mass X-ray binary orbital periods from the Milky Way and single-star rotation periods observed in open clusters. We find that the data favor a magnetic braking prescription that follows a rapid transition from fast to slow rotation rates, exhibits saturated (inefficient) magnetic braking below a critical Rossby number, and that is sufficiently strong to reproduce ultra-compact X-ray binary systems. Of the four prescriptions tested, these conditions are satisfied by a braking prescription that incorporates the effect of high-order magnetic field topology on angular momentum loss. None of the braking prescriptions tested are able to replicate the stalled spin down observed in open cluster stars aged 700–1000 Myr or so, with masses ≲0.8 M ⊙.
Principled and Efficient Transfer Learning of Deep Models via Neural Collapse

As model size continues to grow and access to labeled training data remains limited, transfer learning has become a popular approach in many scientific and engineering fields. This study explores the phenomenon of neural collapse (NC) in transfer learning for classification problems, which is characterized by the last-layer features and classifiers of deep networks having zero within-class variability in features and maximally and equally separated between-class feature means. Through the lens of NC, in this work the following findings on transfer learning are discovered: (i) preventing within-class variability collapse to a certain extent during model pre-training on source data leads to better transferability, as it preserves the intrinsic structures of the input data better; (ii) obtaining features with more NC on downstream data during fine-tuning results in better test accuracy. These results provide new insight into commonly used heuristics in model pre-training, such as loss design, data augmentation, and projection heads, and lead to more efficient and principled methods for fine-tuning large pre-trained models. Compared to full model fine-tuning, our proposed fine-tuning methods achieve comparable or even better performance while reducing fine-tuning parameters by at least 70% as well as alleviating overfitting.
TESS Observations of the Pleiades Cluster: A Nursery for δ Scuti Stars

We studied 89 A- and F-type members of the Pleiades open cluster, including five escaped members. We measured projected rotational velocities ( vsini ) for 49 stars and confirmed that stellar rotation causes a broadening of the main sequence in the color–magnitude diagram. Using time-series photometry from NASA’s TESS Mission (plus one star observed by Kepler/K2), we detected δ Scuti pulsations in 36 stars. The fraction of Pleiades stars in the middle of the instability strip that pulsate is unusually high (over 80%), and their range of effective temperatures agrees well with theoretical models. On the other hand, the characteristics of the pulsation spectra are varied and do not correlate with stellar temperature, calling into question the existence of a useful νmax relation for δ Scutis, at least for young main-sequence stars. By including δ Scuti stars observed in the Kepler field, we show that the instability strip is shifted to the red with increasing distance by interstellar reddening. Overall, this work demonstrates the power of combining observations with Gaia and TESS for studying pulsating stars in open clusters.
Dropping Anchor: Understanding the Populations of Binary Black Holes with Random and Aligned-spin Orientations

The relative spin orientations of black holes (BHs) in binaries encode their evolutionary history: BHs assembled dynamically should have isotropically distributed spins, while spins of BHs originating in the field should be aligned with the orbital angular momentum. In this article, we introduce a simple population model for these dynamical and field binaries that uses spin orientations as an anchor to disentangle these two evolutionary channels. We then analyze binary BH mergers in the Third Gravitational-Wave Transient Catalog (GWTC-3) and ask whether BHs from the isotropic-spin population possess different distributions of mass ratios, spin magnitudes, or redshifts from the preferentially aligned-spin population. We find no compelling evidence that binary BHs in GWTC-3 have different source-property distributions depending on their spin alignment, but we do find that the dynamical and field channels cannot both have mass-ratio distributions that strongly favor equal masses. We give an example of how this can be used to provide insights into the various processes that drive these BHs to merge. We also find that the current detections are insufficient in extracting differences in spin magnitude or redshift distributions of isotropic and aligned-spin populations.
Parity-detection-based Mach-Zehnder interferometry with coherent and non-Gaussian squeezed vacuum states as inputs

We theoretically explore the advantages rendered by non-Gaussian operations in phase estimation using a parity-detection-based Mach-Zehnder interferometer, with one input being a coherent state and the other being a non-Gaussian squeezed vacuum state (SVS). We consider a realistic model to perform three different non-Gaussian operations, namely photon subtraction, photon addition, and photon catalysis on a single-mode SVS. We start by deriving the Wigner function of the non-Gaussian SVSs, which is then utilized to derive the expression for the phase sensitivity. The analysis of the phase sensitivity reveals that all three different non-Gaussian operations can enhance the phase sensitivity under suitable choices of parameters. We also consider the probabilistic nature of these non-Gaussian operations, the results of which reveal the single photon addition to be the optimal operation. Further, our analysis also enables us to identify the optimal squeezing of the SVS and the transmissivity of the beam splitter involved in the implementation of the non-Gaussian operations.
Factoring integers with sublinear resources on a superconducting quantum processor

Shor's algorithm has seriously challenged information security based on public key cryptosystems. However, to break the widely used RSA-2048 scheme, one needs millions of physical qubits, which is far beyond current technical capabilities. Here, we report a universal quantum algorithm for integer factorization by combining the classical lattice reduction with a quantum approximate optimization algorithm (QAOA). The number of qubits required is O(logN/loglog N), which is sublinear in the bit length of the integer $N$, making it the most qubit-saving factorization algorithm to date. We demonstrate the algorithm experimentally by factoring integers up to 48 bits with 10 superconducting qubits, the largest integer factored on a quantum device. We estimate that a quantum circuit with 372 physical qubits and a depth of thousands is necessary to challenge RSA-2048 using our algorithm. Our study shows great promise in expediting the application of current noisy quantum computers, and paves the way to factor large integers of realistic cryptographic significance.
Rule Learning by Modularity

In this paper, we present a modular methodology that combines state-of-the-art methods in (stochastic) machine learning with traditional methods in rule learning to provide efficient and scalable algorithms for the classification of vast data sets, while remaining explainable. Apart from evaluating our approach on the common large scale data sets MNIST, Fashion-MNIST and IMDB, we present novel results on explainable classifications of dental bills. The latter case study stems from an industrial collaboration with Allianz Private Krankenversicherungs-Aktiengesellschaft which is an insurance company offering diverse services in Germany.
Generalization Bounds for Transfer Learning with Pretrained Classifiers

We study the ability of foundation models to learn representations for classiﬁcation that are transferable to new, unseen classes. Recent results in the literature show that representations learned by a single classiﬁer over many classes are competitive on few-shot learning problems with representations learned by special-purpose algorithms designed for such problems. We oﬀer an explanation for this phenomenon based on the concept of class-features variability collapse, which refers to the training dynamics of deep classiﬁcation networks where the feature embeddings of samples belonging to the same class tend to concentrate around their class means. More speciﬁcally, we examine the few-shot error of the learned feature map, which is the classiﬁcation error of the nearest class-center classiﬁer using centers learned from a small number of random samples from each class. Assuming that the classes appearing in the data are selected independently from a distribution, we show that the few-shot error generalizes from the training data to unseen test data, and we provide an upper bound on the expected few-shot error for new classes (selected from the same distribution) using the average few-shot error for the source classes. Additionally, we show that the few-shot error on the training data can be upper bounded using the degree of class-features variability collapse. This suggests that foundation models can provide feature maps that are transferable to new downstream tasks even with limited data available.
Scaling limits of nonlinear functions of random grain model, with application to Burgers' equation

We study scaling limits of nonlinear functions $G$ of random grain model $X$ on $\mathbb{R}^d $ with long-range dependence and marginal Poisson distribution. Following Kaj et al (2007) we assume that the intensity $M$ of the underlying Poisson process of grains increases together with the scaling parameter $\lambda$ as $M = \lambda^\gamma $, for some $\gamma>0$. The results are applicable to the Boolean model and exponential $G$ and rely on an expansion of $G$ in Charlier polynomials and a generalization of Mehler's formula. Application to solution of Burgers' equation with initial aggregated random grain data is discussed.
Reconstruction of charged tracks with Timepix4 ASICs

The spatial and temporal performance of a four-plane system composed of silicon sensors bump-bonded to Timepix4 ASICs is assessed with a 180 GeV/c mixed hadron beam at the CERN SPS and reported in detail. Particle tracks are reconstructed using time-space measurements from the four detector planes, two 100 μm planes perpendicular to the beam and two 300 μm sensors under an angle of 9°. The spatial hit resolution is assessed to be (15.5 ± 0.5) μm and (4.5 ± 0.3) μm for 100 μm and 300 μm thick sensors, respectively. The timestamps from the detectors are also measured with fine precision, yielding time resolutions of (452 ± 10) ps, (420 ± 10) ps, (639 ± 10) ps, (631 ± 10) ps for the two 100 μm and two 300 μm thick sensors respectively. These measurements are combined to a track time resolution of (340 ± 5) ps. The design of the detector system is described together with its data acquisition system, operational infrastructure, and dedicated software.
Angular Momentum in Quantum Physics: Theory and Application

1. Introduction 2. The kinematics of rotations 3. Standard treatment of angular momentum in quantum mechanics 4. The theory of turns adapted from Hamilton 5. The Boson Calculus applied to the theory of turns 6. Orbital angular momentum and angular functions on the sphere 7. Some applications to physical problems.
The Significance of Oral Inflammation in Elite Sports: A Narrative Review

Abstract Recently, there has been intense discussion about sports dentistry and potential interactions between oral health and athletes’ performance. This narrative review aims to provide a comprehensive overview of the available literature about oral inflammation in sports. For this purpose, it presents the most common types of oral inflammation (gingivitis, periodontitis, pericoronitis, apical periodontitis), and their prevalence in athletes. Both the impact of oral inflammation on performance and causes for oral inflammation in athletes are discussed by presenting current literature. Finally, international recommendations for dental care in sports are presented. Several studies stated a high prevalence of oral inflammation in athletes, especially of gingivitis (58–97%) and periodontitis (41%). Also, many athletes report oral pain (17–30%) and a negative impact of oral health on training (3–9%). Besides this, a systemic impact of oral inflammation is discussed: In periodontitis patients, blood parameters and physical fitness are changed. In athletes, associations between muscle injuries and poor oral health are reported. There are deficits in oral health behavior. Furthermore, systemic changes due to physical stress could influence oral tissues. Overall, complex bidirectional interactions between competitive sports and oral inflammation are possible. Regular dental examinations and prevention strategies should be implemented in sports.
Time-asymptotic behaviour of a solution of the Cauchy initial-value problem for a conservation law with non-linear divergent viscosity

We study the time-asymptotic behaviour of a solution of the Cauchy initial-value problem for a conservation law with non-linear divergent viscosity. We shall prove that when a bounded measurable initial function has limits at , a solution of the Cauchy initial-value problem converges uniformly to a system of waves consisting of travelling waves and rarefaction waves, where the phase shifts of the travelling waves are allowed to depend on time. The rate of convergence is estimated under additional conditions on the initial function.
A review of time reversal-based methods applied to fault location in power networks

Electromagnetic time reversal (EMTR)-based methods have been applied to the problem of fault location in power networks since 2012. Over the past decade, considerable theoretical investigations have led to a continuous improvement of the EMTR method in terms of fault location accuracy and efficiency. Meanwhile, different full-scale experiments, including pilot tests, were carried out, demonstrating the applicability and robustness of the EMTR method when applied to real power-system environments. This paper presents a review of the foregoing theoretical and experimental studies. Furthermore, suggestions for future studies are propounded, along with discussing various challenging research questions that still need to be addressed.
The Impact of Size Sorting on the Polarimetric Radar Variables

AbstractDifferential sedimentation of precipitation occurs because heavier hydrometeors fall faster than lighter ones. Updrafts and vertical wind shear can maintain this otherwise transient size sorting, resulting in prolonged regions of ongoing particle sorting in storms. This study quantifies the impact of size sorting on the S-band polarimetric radar variables (radar reflectivity factor at horizontal polarization ZH, differential reflectivity ZDR, specific differential phase KDP, and the copolar cross-correlation coefficient ρhv). These variables are calculated from output of two idealized bin models: a one-dimensional model of pure raindrop fallout and a two-dimensional rain shaft encountering vertical wind shear. Additionally, errors in the radar variables as simulated by single-, double-, and triple-moment bulk microphysics parameterizations are quantified for the same size sorting scenarios.Size sorting produces regions of sparsely concentrated large drops with a lack of smaller drops, causing ZDR .
Head‐up tilt does not enhance prostate tumor perfusion or oxygenation in young rats

Solid tumors contain hypoxic regions that contribute to anticancer therapy resistance. Thus, mitigating tumor hypoxia may enhance the efficacy of radiation therapy which is commonly utilized for patients with prostate cancer. Increasing perfusion pressure in the prostate with head‐up tilt (HUT) may augment prostate tumor perfusion and decrease hypoxia. The purpose of this study was to determine if an increase in the vascular hydrostatic gradient via 70° HUT increases tumor perfusion and decreases tumor hypoxia in a preclinical orthotopic model of prostate cancer. Male Copenhagen rats (n = 17) were orthotopically injected with Dunning R‐3327 (AT‐1) prostate adenocarcinoma cells to induce prostate tumors. After tumors were established, prostate tumor perfusion and hypoxia were measured in rats during level (0°) and 70° HUT positions. To compare the magnitude of the hydrostatic column to that present in humans, ultrasound was used to measure the heart to prostate distance in male human subjects to estimate the prostate vascular hydrostatic pressure with the upright posture. In young rats, no differences were detected in prostate tumor perfusion or prostate tumor hypoxia with 70° HUT versus the level position. However, from the retrospective study, young rats increased prostate vascular resistance to HUT, whereas aged rats lacked this response. Tumor vessels co‐opted from existing functional vasculature in young rats may be sufficient to negate increases in perfusion pressure with HUT seen in aged rats. Additionally, in humans, the estimated hydrostatic column at the level of the prostate is five times greater than that of the rat. Therefore, 70° HUT may elicit increases in prostate/prostate tumor blood flow in humans that is not seen in rats.