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In this study, we present a comprehensive analysis of an unidentified point-like ultra-high-energy (UHE) $\gamma$-ray source, designated as 1LHAASO J1740+0948u, situated in the vicinity of the middle-aged pulsar PSR J1740+1000. The detection significance reached 17.1$\sigma$ (9.4$\sigma$) above 25$\,$TeV (100$\,$TeV). The source energy spectrum extended up to 300$\,$TeV, which was well fitted by a log-parabola function with $N0 = (1.93\pm0.23) \times 10^{-16} \rm{TeV^{-1}\,cm^{-2}\,s^{-2}}$, $\alpha = 2.14\pm0.27$, and $\beta = 1.20\pm0.41$ at E0 = 30$\,$TeV. The associated pulsar, PSR J1740+1000, resides at a high galactic latitude and powers a bow-shock pulsar wind nebula (BSPWN) with an extended X-ray tail. The best-fit position of the gamma-ray source appeared to be shifted by $0.2^{\circ}$ with respect to the pulsar position. As the (i) currently identified pulsar halos do not demonstrate such offsets, and (ii) centroid of the gamma-ray emission is approximately located at the extension of the X-ray tail, we speculate that the UHE $\gamma$-ray emission may originate from re-accelerated electron/positron pairs that are advected away in the bow-shock tail.

We report direct measurement of the dispersion relation of polaritons in GaAs/AlGaAs microcavity structures at room temperature, which clearly shows that the polaritons are in the strong coupling limit. The Rabi splitting of the polariton states decreases as the polariton gas increases in density, but even when the polariton gas becomes a coherent, Bose-condensate-like state, the polaritons retain a strong exciton component, as seen in the nonlinear energy shift of the light emission. This opens up the possibility of polaritonic devices at room temperature in a material system which can be grown with very high quality and uniformity.

Source functions are obtained from $p$-$p$ and $d$--$\alpha$ correlation functions by applying the Richardson-Lucy (RL) deblurring to the Koonin-Pratt (KP) equation. To prevent fitting of noise in the correlation function, total-variation (TV) regularization is employed that has been effective in ordinary image restoration. TV alone cannot ensure normalization of the source functions. To ensure the latter, we propose a maximum-entropy regularized RL algorithm (MEM-RL). We outline the MEM-RL formalism and optimization strategy for the KP equation, demonstrating its effectiveness on both simulated and experimental data, including the $p$-$p$ and $d$-$\alpha$ correlation functions., Comment: 22 pages, 6 figures

Splitting methods constitute a well-established class of numerical schemes for solving convection-diffusion-reaction problems. They have been shown to be effective in solving problems with periodic boundary conditions. However, in the case of Dirichlet boundary conditions, order reduction has been observed even with homogeneous boundary conditions. In this paper, we propose a novel splitting approach, the so-called `initial-corrected splitting method', which succeeds in overcoming order reduction. A convergence analysis is performed to demonstrate second-order convergence of this modified Strang splitting method. Furthermore, we conduct numerical experiments to illustrate the performance of the newly developed splitting approach.

Photonic computing has emerged as a promising platform for accelerating computational tasks with high degrees of parallelism, such as image processing and neural network. We present meta-DFT (discrete Fourier transform), a single layer metasurface device, designed to perform optical complex-to-complex DFT with O(N) time complexity. One critical challenge in free-space analog optical computing is to control the measurement error. Our scheme addresses this issue by focusing light on spatially separated focal points and reconstructing the complex phase, which enable error correction. We systematically evaluate the device's performance using input vectors with random complex amplitudes and phases, to demonstrate its robust accuracy. Our findings pave the way towards advancement of metasurface-based computation, offering a robust framework that is readily extensible to an arbitrary complex-valued matrix-vector multiplication (MVM)., Comment: 17 pages, 4 figures

The core-collapse supernova remnant (SNR) Cassiopeia A (Cas A) is one of the brightest galactic radio sources with an angular radius of $\sim$ 2.5 $\arcmin$. Although no extension of this source has been detected in the $\gamma$-ray band, using more than 1000 days of LHAASO data above $\sim 0.8$ TeV, we find that its spectrum is significantly softer than those obtained with Imaging Air Cherenkov Telescopes (IACTs) and its flux near $\sim 1$ TeV is about two times higher. In combination with analyses of more than 16 years of \textit{Fermi}-LAT data covering $0.1 \, \mathrm{GeV} - 1 \, \mathrm{TeV}$, we find that the spectrum above 30 GeV deviates significantly from a single power-law, and is best described by a smoothly broken power-law with a spectral index of $1.90 \pm 0.15_\mathrm{stat}$ ($3.41 \pm 0.19_\mathrm{stat}$) below (above) a break energy of $0.63 \pm 0.21_\mathrm{stat} \, \mathrm{TeV}$. Given differences in the angular resolution of LHAASO-WCDA and IACTs, TeV $\gamma$-ray emission detected with LHAASO may have a significant contribution from regions surrounding the SNR illuminated by particles accelerated earlier, which, however, are treated as background by IACTs. Detailed modelling can be used to constrain acceleration processes of TeV particles in the early stage of SNR evolution.

Moving beyond $L^p$ geometric structure, Orlicz-Wasserstein (OW) leverages a specific class of convex functions for Orlicz geometric structure. While OW remarkably helps to advance certain machine learning approaches, it has a high computational complexity due to its two-level optimization formula. Recently, Le et al. (2024) exploits graph structure to propose generalized Sobolev transport (GST), i.e., a scalable variant for OW. However, GST assumes that input measures have the same mass. Unlike optimal transport (OT), it is nontrivial to incorporate a mass constraint to extend GST for measures on a graph, possibly having different total mass. In this work, we propose to take a step back by considering the entropy partial transport (EPT) for nonnegative measures on a graph. By leveraging Caffarelli & McCann (2010)'s observations, EPT can be reformulated as a standard complete OT between two corresponding balanced measures. Consequently, we develop a novel EPT with Orlicz geometric structure, namely Orlicz-EPT, for unbalanced measures on a graph. Especially, by exploiting the dual EPT formulation and geometric structures of the graph-based Orlicz-Sobolev space, we derive a novel regularization to propose Orlicz-Sobolev transport (OST). The resulting distance can be efficiently computed by simply solving a univariate optimization problem, unlike the high-computational two-level optimization problem for Orlicz-EPT. Additionally, we derive geometric structures for the OST and draw its relations to other transport distances. We empirically show that OST is several-order faster than Orlicz-EPT. We further illustrate preliminary evidences on the advantages of OST for document classification, and several tasks in topological data analysis.

We investigate the Sobolev IPM problem for probability measures supported on a graph metric space. Sobolev IPM is an important instance of integral probability metrics (IPM), and is obtained by constraining a critic function within a unit ball defined by the Sobolev norm. In particular, it has been used to compare probability measures and is crucial for several theoretical works in machine learning. However, to our knowledge, there are no efficient algorithmic approaches to compute Sobolev IPM effectively, which hinders its practical applications. In this work, we establish a relation between Sobolev norm and weighted $L^p$-norm, and leverage it to propose a \emph{novel regularization} for Sobolev IPM. By exploiting the graph structure, we demonstrate that the regularized Sobolev IPM provides a \emph{closed-form} expression for fast computation. This advancement addresses long-standing computational challenges, and paves the way to apply Sobolev IPM for practical applications, even in large-scale settings. Additionally, the regularized Sobolev IPM is negative definite. Utilizing this property, we design positive-definite kernels upon the regularized Sobolev IPM, and provide preliminary evidences of their advantages on document classification and topological data analysis for measures on a graph.

Let $p$ be an odd prime number. In this article, we study the variation of Iwasawa invariants among $p$-congruent elliptic curves over certain $p$-adic Lie extensions. We investigate both the classical Selmer group as well as the fine Selmer group.

Recommender systems are pivotal in delivering personalised user experiences across various domains. However, capturing the heterophily patterns and the multi-dimensional nature of user-item interactions poses significant challenges. To address this, we introduce FWHDNN (Fusion-based Wavelet Hypergraph Diffusion Neural Networks), an innovative framework aimed at advancing representation learning in hypergraph-based recommendation tasks. The model incorporates three key components: (1) a cross-difference relation encoder leveraging heterophily-aware hypergraph diffusion to adapt message-passing for diverse class labels, (2) a multi-level cluster-wise encoder employing wavelet transform-based hypergraph neural network layers to capture multi-scale topological relationships, and (3) an integrated multi-modal fusion mechanism that combines structural and textual information through intermediate and late-fusion strategies. Extensive experiments on real-world datasets demonstrate that FWHDNN surpasses state-of-the-art methods in accuracy, robustness, and scalability in capturing high-order interconnections between users and items.

Maintaining consistent model performance across domains is a fundamental challenge in machine learning. While recent work has explored using LLM-generated data for fine-tuning, its impact on cross-domain generalization remains poorly understood. In this paper, we present a systematic analysis revealing that fine-tuning with LLM-generated data not only improves target task performance but also reduces out-of-domain (OOD) degradation compared to fine-tuning with ground truth data. Through analyzing the data sequence in tasks of various domains, we demonstrate that this enhanced OOD robustness stems from a reduced prevalence of high perplexity tokens in LLM-generated sequences. Following this hypothesis we showed that masking high perplexity tokens in ground truth training data also achieves similar OOD preservation comparable to using LLM-generated data. Extensive experiments across diverse model architectures and scales, including Gemma2-2B, Mistral-7B and Llama3-8B, corroborate the consistency of our findings. To the best of our knowledge, this work provides the first mechanistic explanation for the superior OOD robustness conferred by LLM-generated training data, offering valuable insights for developing more robust fine-tuning strategies.

Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achieve over 90\% accuracy on popular benchmarks like MMLU, limiting informed measurement of state-of-the-art LLM capabilities. In response, we introduce Humanity's Last Exam (HLE), a multi-modal benchmark at the frontier of human knowledge, designed to be the final closed-ended academic benchmark of its kind with broad subject coverage. HLE consists of 2,700 questions across dozens of subjects, including mathematics, humanities, and the natural sciences. HLE is developed globally by subject-matter experts and consists of multiple-choice and short-answer questions suitable for automated grading. Each question has a known solution that is unambiguous and easily verifiable, but cannot be quickly answered via internet retrieval. State-of-the-art LLMs demonstrate low accuracy and calibration on HLE, highlighting a significant gap between current LLM capabilities and the expert human frontier on closed-ended academic questions. To inform research and policymaking upon a clear understanding of model capabilities, we publicly release HLE at https://lastexam.ai., Comment: 27 pages, 6 figures

We investigate the role of foreign direct investment (FDI) in the transitional dynamics of host countries by using an optimal growth model. FDI may be beneficial for the host country because local people can work for multinational firms to get a favorable salary. However, if the host country only focuses on FDI, it may face a middle-income trap. We show that if the host country invests in research and development, its economy may have sustained growth. Moreover, in this case, FDI helps the host country only at the first stages of its development process.

Cadmium sulfide (CdS) is a well-known low-bandgap photocatalyst, but its efficiency is often hindered by rapid photo-generated carrier recombination and a limited number of active catalytic sites. To overcome these challenges, this study introduces an efficient CdS photocatalyst through a novel strategy combining metastable-to-stable phase transformation and sulfur vacancy generation. This strategy integrates hydrothermal treatment and a high-pressure process to create sulfur vacancies, which serve as active catalytic sites, within a thermodynamically stable wurtzite (hexagonal) phase known for its superior photocatalytic properties. The resulting CdS photocatalyst demonstrates exceptional performance in photoreforming for hydrogen production and the conversion of polyethylene terephthalate (PET) plastic into valuable materials. Compared to commercial CdS catalysts, this new material shows a 23-fold increase in both hydrogen production and plastic degradation without the need for co-catalysts. Quenching experiments reveal that holes and hydroxyl radicals play crucial roles in the photoreforming process of this vacancy-rich CdS. First-principles calculations via density functional theory (DFT) indicate that the hexagonal phase possesses a lower bandgap and it exhibits further bandgap narrowing with the introduction of sulfur vacancies. These findings not only present an innovative approach to CdS processing but also highlight the critical role of sulfur vacancies as effective defects for the catalytic photoreforming of microplastics.

Deep generative models are routinely used in generating samples from complex, high-dimensional distributions. Despite their apparent successes, their statistical properties are not well understood. A common assumption is that with enough training data and sufficiently large neural networks, deep generative model samples will have arbitrarily small errors in sampling from any continuous target distribution. We set up a unifying framework that debunks this belief. We demonstrate that broad classes of deep generative models, including variational autoencoders and generative adversarial networks, are not universal generators. Under the predominant case of Gaussian latent variables, these models can only generate concentrated samples that exhibit light tails. Using tools from concentration of measure and convex geometry, we give analogous results for more general log-concave and strongly log-concave latent variable distributions. We extend our results to diffusion models via a reduction argument. We use the Gromov--Levy inequality to give similar guarantees when the latent variables lie on manifolds with positive Ricci curvature. These results shed light on the limited capacity of common deep generative models to handle heavy tails. We illustrate the empirical relevance of our work with simulations and financial data.

The Einstein Probe (EP) is an interdisciplinary mission of time-domain and X-ray astronomy. Equipped with a wide-field lobster-eye X-ray focusing imager, EP will discover cosmic X-ray transients and monitor the X-ray variability of known sources in 0.5-4 keV, at a combination of detecting sensitivity and cadence that is not accessible to the previous and current wide-field monitoring missions. EP can perform quick characterisation of transients or outbursts with a Wolter-I X-ray telescope onboard. In this paper, the science objectives of the Einstein Probe mission are presented. EP is expected to enlarge the sample of previously known or predicted but rare types of transients with a wide range of timescales. Among them, fast extragalactic transients will be surveyed systematically in soft X-rays, which include {\gamma}-ray bursts and their variants, supernova shock breakouts, and the predicted X-ray transients associated with binary neutron star mergers. EP will detect X-ray tidal disruption events and outbursts from active galactic nuclei, possibly at an early phase of the flares for some. EP will monitor the variability and outbursts of X-rays from white dwarfs, neutron stars and black holes in our and neighbouring galaxies at flux levels fainter than those detectable by the current instruments, and is expected to discover new objects. A large sample of stellar X-ray flares will also be detected and characterised. In the era of multi-messenger astronomy, EP has the potential of detecting the possible X-ray counterparts of gravitational wave events, neutrino sources, and ultra-high energy {\gamma}-ray and cosmic ray sources. EP is expected to help advance the studies of extreme objects/phenomena and their underlying physical processes revealed in the dynamic X-ray universe, as well as studies in other areas of X-ray astronomy., Comment: 67 pages, 24 figures, accepted for publication in SCIENCE CHINA Physics, Mechanics & Astronomy

Models of the galaxy-halo connection are needed to understand both galaxy clusters and large scale structure. To make said models, we need a robust method that assigns galaxies to halos and matches the observed and simulated stellar-halo mass relation. We employ an empirical Subhalo Abundance Matching (SHAM) model implemented in the halos module of SkyPy which assigns blue and red galaxies based on the Peng et al. (2010) (arXiv:1003.4747v2) model containing three parameters: $M_\mu$ (halo mass where half the galaxies assigned should be quenched), $\sigma$ (transition width from star forming to quenched) and $b$ (baseline quenched fraction at low mass). We test two sets of galaxy stellar mass functions for four populations of galaxies (central/satellite, blue/red) and run parameter estimation using Approximate Bayesian Computation over each model when compared to a set of applicable literature models. For the Weigel et al. (2016) (arXiv:1604.00008v1) galaxies we find best fit values of log $M_\mu = 11.94^{+0.02}_{-0.02}$, $\sigma = 0.49^{+0.04}_{-0.04}$ and $b = 0.31^{+0.01}_{-0.01}$. For the Birrer et al. (2014) (arXiv:1401.3162v2) galaxies we find best fit values of log $M_\mu = 11.93^{+0.01}_{-0.01}$, $\sigma = 0.53^{+0.04}_{-0.04}$ and $b = 0.51^{+0.05}_{-0.04}$. Overall, we demonstrate that these constraints produce a model that is consistent with literature models for the central galaxies. Future research will focus on the normalisation of the satellite galaxies in order to better constrain the $b$ parameter., Comment: 10 pages, 9 figures

We introduce a new multimodal optimization approach called Natural Variational Annealing (NVA) that combines the strengths of three foundational concepts to simultaneously search for multiple global and local modes of black-box nonconvex objectives. First, it implements a simultaneous search by using variational posteriors, such as, mixtures of Gaussians. Second, it applies annealing to gradually trade off exploration for exploitation. Finally, it learns the variational search distribution using natural-gradient learning where updates resemble well-known and easy-to-implement algorithms. The three concepts come together in NVA giving rise to new algorithms and also allowing us to incorporate "fitness shaping", a core concept from evolutionary algorithms. We assess the quality of search on simulations and compare them to methods using gradient descent and evolution strategies. We also provide an application to a real-world inverse problem in planetary science.

Generative models are ubiquitous in modern artificial intelligence (AI) applications. Recent advances have led to a variety of generative modeling approaches that are capable of synthesizing highly realistic samples. Despite these developments, evaluating the distributional match between the synthetic samples and the target distribution in a statistically principled way remains a core challenge. We focus on evaluating image generative models, where studies often treat human evaluation as the gold standard. Commonly adopted metrics, such as the Fr\'echet Inception Distance (FID), do not sufficiently capture the differences between the learned and target distributions, because the assumption of normality ignores differences in the tails. We propose the Embedded Characteristic Score (ECS), a comprehensive metric for evaluating the distributional match between the learned and target sample distributions, and explore its connection with moments and tail behavior. We derive natural properties of ECS and show its practical use via simulations and an empirical study.

A new class of weighted spectral geometric means has recently been introduced. In this paper, we present its inequalities in terms of the L\"{o}wner order, operator norm, and trace. Moreover, we establish a log-majorization relationship between the new spectral geometric mean, and the R\'{e}nyi relative operator entropy. We also give the quantum divergence of the quantity, given by the difference of trace values between the arithmetic mean and new spectral geometric mean. Finally, we study the barycenter that minimizes the weighted sum of quantum divergences for given variables., Comment: 16 pages

The persistent existence of plastic waste causes serious problems for the environment, directly and indirectly affecting the health of organisms and humans. Photoreforming is a nature-friendly method that only uses solar energy to convert plastic waste into green hydrogen (H2) and valuable organic products. This study shows that a high-entropy oxynitride (HEON) photocatalyst, synthesized by the addition of nitrogen to a Ti-Zr-Hf-Nb-Ta-containing high-entropy oxide (HEO), exhibits a higher potential for the production of H2, formic acid and acetic acid from polyethylene terephthalate (PET) photoreforming compared to the relevant HEO. Examination of X-ray absorption near edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) by synchrotron light shows that, in addition to hybridization of 2p orbitals from oxygen and nitrogen, nitrogen atoms distort the structure and completely change the neighborhood of niobium and titanium (a main contributor to the conduction band), expands the atomic bonds of zirconium and tantalum, contracts the atomic bonds of hafnium and decreases the binding energy of titanium, niobium and tantalum. These electronic structure changes lead to a narrower bandgap and diminished electron-hole recombination, enhancing the photoreforming performance. This study introduces HEONs with distorted atomic bond structures as efficient low-bandgap and stable catalysts for transforming plastics into high-value organic chemicals and H2 by photocatalysis.

Extremely low-mass white dwarfs (ELM WDs) are helium-core white dwarfs with masses less than 0.3 $M_{\odot}$. Short-period ELM WD binaries that exhibit ellipsoidal variations may harbor heavier companions, either massive white dwarfs or millisecond pulsars (MSPs). In this study, we selected $\sim$ 12,000 ELM WDs or their candidates, and searched for ellipsoidal-like lightcurves with orbital periods shorter than one day, by using the public data from Zwicky Transient Facility. Finally 23 such systems were found, with 17 being newly discovered. We selected nine high-priority targets likely to evolve from the Roche-lobe overflow channel and estimated their companion masses from the extracted ellipsoidal variation amplitude. Among them, the four targets have companion masses exceeding 1 $M_{\odot}$. We performed a search for radio pulsations from six of these targets by using Five-hundred-meter Aperture Spherical radio Telescope. However, no convincing radio pulsed signals were found, resulting in upper limits for the radio flux at around 8 $\mu$Jy. Given the non-detection of radio pulsations from a total of 11 similar systems, the fraction of ellipsoidal ELM WDs around MSPs is estimated to be below 15$^{+6}_{-3}$%. We anticipate that multi-wavelength studies of more ellipsoidal-like ELM WDs will further constrain the fraction., Comment: 14 pages, 7 figures, accepted in ApJ

The o1 model series is trained with large-scale reinforcement learning to reason using chain of thought. These advanced reasoning capabilities provide new avenues for improving the safety and robustness of our models. In particular, our models can reason about our safety policies in context when responding to potentially unsafe prompts, through deliberative alignment. This leads to state-of-the-art performance on certain benchmarks for risks such as generating illicit advice, choosing stereotyped responses, and succumbing to known jailbreaks. Training models to incorporate a chain of thought before answering has the potential to unlock substantial benefits, while also increasing potential risks that stem from heightened intelligence. Our results underscore the need for building robust alignment methods, extensively stress-testing their efficacy, and maintaining meticulous risk management protocols. This report outlines the safety work carried out for the OpenAI o1 and OpenAI o1-mini models, including safety evaluations, external red teaming, and Preparedness Framework evaluations.

In this paper we obtain inequalities for the geometric mean of elements in the Grassmannians. These inequalities reflect the elliptic geometry of the Grassmannians as Riemannian manifolds. These include Semi-Parallelogram Law, Law of Cosines and geodesic triangle inequalities.

Today, deep neural networks are widely used since they can handle a variety of complex tasks. Their generality makes them very powerful tools in modern technology. However, deep neural networks are often overparameterized. The usage of these large models consumes a lot of computation resources. In this paper, we introduce a method called \textbf{T}ill the \textbf{L}ayers \textbf{C}ollapse (TLC), which compresses deep neural networks through the lenses of batch normalization layers. By reducing the depth of these networks, our method decreases deep neural networks' computational requirements and overall latency. We validate our method on popular models such as Swin-T, MobileNet-V2, and RoBERTa, across both image classification and natural language processing (NLP) tasks., Comment: Accepted at AAAI 2025

This summary of the second Terrestrial Very-Long-Baseline Atom Interferometry (TVLBAI) Workshop provides a comprehensive overview of our meeting held in London in April 2024, building on the initial discussions during the inaugural workshop held at CERN in March 2023. Like the summary of the first workshop, this document records a critical milestone for the international atom interferometry community. It documents our concerted efforts to evaluate progress, address emerging challenges, and refine strategic directions for future large-scale atom interferometry projects. Our commitment to collaboration is manifested by the integration of diverse expertise and the coordination of international resources, all aimed at advancing the frontiers of atom interferometry physics and technology, as set out in a Memorandum of Understanding signed by over 50 institutions., Comment: Summary of the second Terrestrial Very-Long-Baseline Atom Interferometry Workshop held at Imperial College London: https://indico.cern.ch/event/1369392/

We present new radio images of the supernova remnant (SNR) CTA 1 at 1420 and 408 MHz, and in the 21 cm line of H I observed with the Dominion Radio Astrophysical Observatory Synthesis Telescope and at 1420 MHz observed with the Effelsberg 100 m telescope. We confirm previously described continuum features and elaborate further on filamentary features identified using the high-resolution (1') maps from these new observations. We investigate the abrupt change in sign of rotation measure (RM) across the SNR, using the linear polarization observations in the four bands around 1420 MHz. Following X. H. Sun et al.'s (2011) investigation, we both confirm that the distribution of signs of the RMs for extragalactic sources in the area appears to match that of the shell, as well as combine the data from the four bands to estimate the relative depolarization and the intrinsic rotation measure of the SNR. We do not conclusively reject X. H. Sun et al.'s (2011) claim of a Faraday screen in the foreground causing the distribution of RMs that we observe; however, we do suggest an alternative explanation of a swept-up stellar wind from the progenitor star with a toroidal magnetic field. Finally, we expand on the analysis of the H I observations by applying the Rolling Hough Transform to isolate filamentary structure and better identify H I emission with the SNR. Further constraining the H I velocity channels associated with CTA 1, we use more recent Galactic rotation curves to calculate an updated kinematic distance of 1.09 +/- 0.2 kpc., Comment: 10 pages, 9 figures, 2 tables

We consider resolvent splitting algorithms for finding a zero of the sum of finitely many maximally monotone operators. The standard approach to solving this type of problem involves reformulating as a two-operator problem in the product-space and applying the Douglas-Rachford algorithm. However, existing results for linear convergence cannot be applied in the product-space formulation due to a lack of appropriate Lipschitz continuity and strong monotonicity. In this work, we investigate a different approach that does not rely on the Douglas-Rachford algorithm or the product-space directly. We establish linear convergence of the "resolvent splitting with minimal lifting" algorithm due to Malitsky and Tam for monotone inclusions with finitely many operators. Our results are then used to derive linear convergence of a primal-dual algorithm for convex minimization problems involving infimal convolutions. The theoretical results are demonstrated on numerical experiments in image denoising.

This paper investigates the performance of a subclass of exponential integrators, specifically explicit exponential Runge--Kutta methods. It is well known that third-order methods can suffer from order reduction when applied to linearized problems involving unbounded and non-commuting operators. In this work, we consider a fourth-stage third-order Runge--Kutta method, which successfully achieves the expected order of accuracy and avoids order reduction, as long as all required order conditions are satisfied. The convergence analysis is carried out under the assumption of higher regularity for the initial data. Numerical experiments are provided to validate the theoretical results., Comment: 16 pages, 2 figures

Spider pulsars constitute a distinct subset within the domain of radio millisecond pulsars, divided further into the categories of black widows and redbacks. Evident across multiple wavelengths, these pulsars manifest periodic variations and reside within binary systems. Investigating and discovering additional spider-type pulsars carries significant implications for comprehending the evolution of high-mass stars. Particularly crucial is the validation of the "Recycling" theory of millisecond pulsar genesis. In this investigation, we systematically explore spider pulsar binary systems utilizing time-domain variability data from the Zwicky Transient Facility, in conjunction with Fermi unassociated gamma-ray sources sourced from the 4FGL-DR3 catalog. We have implemented a time-domain data processing pipeline utilizing the Lomb-Scargle Periodogram algorithm, integrated with the wget data crawling technology. This approach has led to the identification of 194 ellipsoidal variables and irradiation-type binary stars. Subsequent refinement through the Gaia Hertzsprung-Russell diagram has culled a selection of 24 spider pulsar gold sample candidates. By incorporating the 4FGL 95\% confidence error ellipse, the pool was narrowed down to 19 gold sample candidates. Utilizing the Gaia color-reduced proper motion diagram further refined the selection to 9 gold sample candidates. These newly identified spider pulsar candidates will inform subsequent observational campaigns across radio, X-ray, and optical spectroscopy, thereby facilitating a deeper validation of their physical characteristics., Comment: 34 pages, 17 figures, accepted to be published in ApJ

Paramagnetic rim lesions (PRLs) are imaging biomarker of the innate immune response in MS lesions. QSM-RimNet, a state-of-the-art tool for PRLs detection on QSM, can identify PRLs but requires precise QSM lesion mask and does not provide rim segmentation. Therefore, the aims of this study are to develop QSM-RimDS algorithm to detect PRLs using the readily available FLAIR lesion mask and to provide rim segmentation for microglial quantification. QSM-RimDS, a deep-learning based tool for joint PRL rim segmentation and PRL detection has been developed. QSM-RimDS has obtained state-of-the art performance in PRL detection and therefore has the potential to be used in clinical practice as a tool to assist human readers for the time-consuming PRL detection and segmentation task. QSM-RimDS is made publicly available [https://github.com/kennyha85/QSM_RimDS], Comment: 11 pages, 6 figures

We propose utilizing background operators for mathematical reasoning in large language models (LLMs). To achieve this, we define a set of fundamental mathematical predicates as the basic building blocks. For each mathematical problem, we develop a Prolog solution that includes problem-specific predicates and intermediate predicates derived from these background operators, ensuring that each solution adheres to the defined operator set. We introduce the MATH-Prolog corpus, which is derived from the counting and probability categories of the MATH corpus. For efficient data augmentation, we apply K-fold cross-validated self-training. This method incrementally generates new Prolog solutions for each fold, incorporating those verified as correct into the training set throughout the model training process. Our experimental results demonstrate that 5-fold crossvalidated self-training effectively identifies new, accurate Prolog solutions, achieving an accuracy of 84.6% on the cross-validated set, and 84.8% on the test set during fine-tuning the Meta-Llama-3.1-8B-Instruct model. This approach successfully uncovers new solutions with fully computable inference steps for previously unseen problems. Additionally, incorporating the background mathematical predicates into the prompt enhances solution coverage.

Photoreforming is a sustainable photocatalytic process that degrades plastic waste while simultaneously producing hydrogen (H2) from water. However, this process has received limited attention due to the scarcity of effective catalysts capable of both plastic degradation and H2 production, such as titanium dioxide (TiO2). In this study, an active catalyst is developed by stabilizing the high-pressure orthorhombic phase of TiO2, known as columbite, using a high pressure torsion (HPT) method. This material effectively degrades polyethylene terephthalate (PET) plastic under light, converting it into valuable organic compounds such as formic acid, terephthalate, glycolic acid, and acetic acid. Additionally, it produces a significant amount of H2. The findings show that the high-pressure orthorhombic phase, especially in the presence of oxygen vacancies, enhances catalytic H2 production and microplastic degradation by increasing light absorption, reducing electron-hole recombination, and generating hydroxyl radicals. These results highlight the substantial potential of modified high-pressure TiO2 photocatalysts in simultaneously addressing the plastic waste crisis and the demand for H2 fuel.

Bismuth (III) oxide (Bi2O3) has been highly studied as a photocatalyst for green hydrogen production due to its low band gap, yet its efficiency requires enhancement. This study synthesizes a defective and strained black Bi2O3 by severe straining under high pressure, via a high-pressure torsion method, to improve its photocatalytic hydrogen production. The material rich in oxygen vacancies exhibits a ten-fold improvement in water splitting with excellent cycling stability. Such improvement is due to improved light absorption, narrowing band gap and reduced irradiative electron-hole recombination. Moreover, the valence band bottom energy positively increases by straining leading to a high overpotential for hydrogen production. This research highlights the potential of vacancies and lattice strain in developing dopant-free active catalysts for water splitting.

Simultaneous catalytic hydrogen (H2) production and plastic waste degradation under light, known as photoreforming, is a novel approach to green fuel production and efficient waste management. Here, we use a high-entropy oxide (HEO), a new family of catalysts with five or more principal cations in their structure, for plastic degradation and simultaneous H2 production. The HEO shows higher activity than that of P25 TiO2, a benchmark photocatalyst, for the degradation of polyethylene terephthalate (PET) plastics in water. Several valuable products are produced by photoreforming of PET bottles and microplastics including H2, terephthalate, ethylene glycol and formic acid. The high activity is attributed to the diverse existence of several cations in the HEO lattice, lattice defects, and appropriate charge carrier lifetime. These findings suggest that HEOs possess high potential as new catalysts for concurrent plastic waste conversion and clean H2 production.

The rapid advancement of large language models (LLMs) and multimodal learning has transformed digital content creation and manipulation. Traditional visual editing tools require significant expertise, limiting accessibility. Recent strides in instruction-based editing have enabled intuitive interaction with visual content, using natural language as a bridge between user intent and complex editing operations. This survey provides an overview of these techniques, focusing on how LLMs and multimodal models empower users to achieve precise visual modifications without deep technical knowledge. By synthesizing over 100 publications, we explore methods from generative adversarial networks to diffusion models, examining multimodal integration for fine-grained content control. We discuss practical applications across domains such as fashion, 3D scene manipulation, and video synthesis, highlighting increased accessibility and alignment with human intuition. Our survey compares existing literature, emphasizing LLM-empowered editing, and identifies key challenges to stimulate further research. We aim to democratize powerful visual editing across various industries, from entertainment to education. Interested readers are encouraged to access our repository at https://github.com/tamlhp/awesome-instruction-editing., Comment: Fixed a serious error in author information

Internet of Things and Deep Learning are synergetically and exponentially growing industrial fields with a massive call for their unification into a common framework called Edge AI. While on-device inference is a well-explored topic in recent research, backpropagation remains an open challenge due to its prohibitive computational and memory costs compared to the extreme resource constraints of embedded devices. Drawing on tensor decomposition research, we tackle the main bottleneck of backpropagation, namely the memory footprint of activation map storage. We investigate and compare the effects of activation compression using Singular Value Decomposition and its tensor variant, High-Order Singular Value Decomposition. The application of low-order decomposition results in considerable memory savings while preserving the features essential for learning, and also offers theoretical guarantees to convergence. Experimental results obtained on main-stream architectures and tasks demonstrate Pareto-superiority over other state-of-the-art solutions, in terms of the trade-off between generalization and memory footprint.

This paper considers a class of thrust vectoring systems, which are nonlinear, overactuated, and time-invariant. We assume that the system is composed of two subsystems and there exist singular points around which the linearized system is uncontrollable. Furthermore, we assume that the system is stabilizable through a two-level control allocation. In this particular setting, we cannot do much with the linearized system, and a direct nonlinear control approach must be used to analyze the system stability. Under adequate assumptions and a suitable nonlinear continuous control-allocation law, we can prove uniform asymptotic convergence of the points of equilibrium using Lyapunov input-to-state stability and the small gain theorem. This control allocation, however, requires the design of an allocated mapping and introduces two exogenous inputs. In particular, the closed-loop system is cascaded, and the output of one subsystem is the disturbance of the other, and vice versa. In general, it is difficult to find a closed-form solution for the allocated mapping; it needs to satisfy restrictive conditions, among which Lipschitz continuity to ensure that the disturbances eventually vanish. Additionally, this mapping is in general nontrivial and non-unique. In this paper, we propose a new kernel-based predictive control allocation to substitute the need for designing an analytic mapping, and assess if it can produce a meaningful mapping ``on-the-fly" by solving online an optimization problem. The simulations include three examples, which are the manipulation of an object through an unmanned aerial vehicle in two and three dimensions, and the control of a surface vessel actuated by two azimuthal thrusters., Comment: The preliminary results were presented in `Nguyen, Tam W., Kenji Hirata, and Kyoungseok Han. "A Nullspace-Based Predictive Control Allocation for the Control of a Quadcopter Manipulating an Object Attached to the Ground." IFAC-PapersOnLine 56.2 (2023): 6286-6291.'

The Water Cherenkov Detector Array (WCDA) is one of the components of Large High Altitude Air Shower Observatory (LHAASO) and can monitor any sources over two-thirds of the sky for up to 7 hours per day with >98\% duty cycle. In this work, we report the detection of two outbursts of the Fanaroff-Riley I radio galaxy NGC 1275 that were detected by LHAASO-WCDA between November 2022 and January 2023 with statistical significance of 5.2~$\sigma$ and 8.3~$\sigma$. The observed spectral energy distribution in the range from 500 GeV to 3 TeV is fitted by a power-law with a best-fit spectral index of $\alpha=-3.37\pm0.52$ and $-3.35\pm0.29$, respectively. The outburst flux above 0.5~TeV was ($4.55\pm 4.21)\times~10^{-11}~\rm cm^{-2}~s^{-1}$ and ($3.45\pm 1.78)\times~10^{-11}~\rm cm^{-2}~s^{-1}$, corresponding to 60\%, 45\% of Crab Nebula flux. Variation analysis reveals the variability time-scale of days at the TeV energy band. A simple test by one-zone synchrotron self-Compton model reproduces the data in the gamma-ray band well., Comment: 11 pages, 8 figures, 3 tables

In logistics, the ability to quickly compute and execute pick-and-place motions from bins is critical to increasing productivity. We present Bin-Optimized Motion Planning (BOMP), a motion planning framework that plans arm motions for a six-axis industrial robot with a long-nosed suction tool to remove boxes from deep bins. BOMP considers robot arm kinematics, actuation limits, the dimensions of a grasped box, and a varying height map of a bin environment to rapidly generate time-optimized, jerk-limited, and collision-free trajectories. The optimization is warm-started using a deep neural network trained offline in simulation with 25,000 scenes and corresponding trajectories. Experiments with 96 simulated and 15 physical environments suggest that BOMP generates collision-free trajectories that are up to 58 % faster than baseline sampling-based planners and up to 36 % faster than an industry-standard Up-Over-Down algorithm, which has an extremely low 15 % success rate in this context. BOMP also generates jerk-limited trajectories while baselines do not. Website: https://sites.google.com/berkeley.edu/bomp.

GPT-4o is an autoregressive omni model that accepts as input any combination of text, audio, image, and video, and generates any combination of text, audio, and image outputs. It's trained end-to-end across text, vision, and audio, meaning all inputs and outputs are processed by the same neural network. GPT-4o can respond to audio inputs in as little as 232 milliseconds, with an average of 320 milliseconds, which is similar to human response time in conversation. It matches GPT-4 Turbo performance on text in English and code, with significant improvement on text in non-English languages, while also being much faster and 50\% cheaper in the API. GPT-4o is especially better at vision and audio understanding compared to existing models. In line with our commitment to building AI safely and consistent with our voluntary commitments to the White House, we are sharing the GPT-4o System Card, which includes our Preparedness Framework evaluations. In this System Card, we provide a detailed look at GPT-4o's capabilities, limitations, and safety evaluations across multiple categories, focusing on speech-to-speech while also evaluating text and image capabilities, and measures we've implemented to ensure the model is safe and aligned. We also include third-party assessments on dangerous capabilities, as well as discussion of potential societal impacts of GPT-4o's text and vision capabilities.

Imaging atmospheric Cherenkov telescopes (IACTs) are used to observe very high-energy photons from the ground. Gamma rays are indirectly detected through the Cherenkov light emitted by the air showers they induce. The new generation of experiments, in particular the Cherenkov Telescope Array Observatory (CTAO), sets ambitious goals for discoveries of new gamma-ray sources and precise measurements of the already discovered ones. To achieve these goals, both hardware and data analysis must employ cutting-edge techniques. This also applies to the LST-1, the first IACT built for the CTAO, which is currently taking data on the Canary island of La Palma. This paper introduces a new event reconstruction technique for IACT data, aiming to improve the image reconstruction quality and the discrimination between the signal and the background from misidentified hadrons and electrons. The technique models the development of the extensive air shower signal, recorded as a waveform per pixel, seen by CTAO telescopes' cameras. Model parameters are subsequently passed to random forest regressors and classifiers to extract information on the primary particle. The new reconstruction was applied to simulated data and to data from observations of the Crab Nebula performed by the LST-1. The event reconstruction method presented here shows promising performance improvements. The angular and energy resolution, and the sensitivity, are improved by 10 to 20% over most of the energy range. At low energy, improvements reach up to 22%, 47%, and 50%, respectively. A future extension of the method to stereoscopic analysis for telescope arrays will be the next important step., Comment: Accepted in A&A

In this paper, we propose a distributed first-order algorithm with backtracking linesearch for solving multi-agent minimisation problems, where each agent handles a local objective involving nonsmooth and smooth components. Unlike existing methods that require global Lipschitz continuity and predefined stepsizes, our algorithm adjusts stepsizes using distributed linesearch procedures, making it suitable for problems where global constants are unavailable or difficult to compute. The proposed algorithm is designed within an abstract linesearch framework for a primal-dual proximal-gradient method to solve min-max convex-concave problems, enabling the consensus constraint to be decoupled from the optimisation task. Our theoretical analysis allows for gradients of functions to be locally Lipschitz continuous, relaxing the prevalent assumption of globally Lipschitz continuous gradients., Comment: 21 pages

The aggressiveness of prostate cancer, the most common cancer in men worldwide, is primarily assessed based on histopathological data using the Gleason scoring system. While artificial intelligence (AI) has shown promise in accurately predicting Gleason scores, these predictions often lack inherent explainability, potentially leading to distrust in human-machine interactions. To address this issue, we introduce a novel dataset of 1,015 tissue microarray core images, annotated by an international group of 54 pathologists. The annotations provide detailed localized pattern descriptions for Gleason grading in line with international guidelines. Utilizing this dataset, we develop an inherently explainable AI system based on a U-Net architecture that provides predictions leveraging pathologists' terminology. This approach circumvents post-hoc explainability methods while maintaining or exceeding the performance of methods trained directly for Gleason pattern segmentation (Dice score: 0.713 $\pm$ 0.003 trained on explanations vs. 0.691 $\pm$ 0.010 trained on Gleason patterns). By employing soft labels during training, we capture the intrinsic uncertainty in the data, yielding strong results in Gleason pattern segmentation even in the context of high interobserver variability. With the release of this dataset, we aim to encourage further research into segmentation in medical tasks with high levels of subjectivity and to advance the understanding of pathologists' reasoning processes., Comment: 58 pages, 15 figures (incl. supplementary)