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The development of large language models (LLMs) has significantly enhanced the capabilities of multimodal LLMs (MLLMs) as general assistants. However, lack of user-specific knowledge still restricts their application in human's daily life. In this paper, we introduce the Retrieval Augmented Personalization (RAP) framework for MLLMs' personalization. Starting from a general MLLM, we turn it into a personalized assistant in three steps. (a) Remember: We design a key-value database to store user-related information, e.g., user's name, avatar and other attributes. (b) Retrieve: When the user initiates a conversation, RAP will retrieve relevant information from the database using a multimodal retriever. (c) Generate: The input query and retrieved concepts' information are fed into MLLMs to generate personalized, knowledge-augmented responses. Unlike previous methods, RAP allows real-time concept editing via updating the external database. To further improve generation quality and alignment with user-specific information, we design a pipeline for data collection and create a specialized dataset for personalized training of MLLMs. Based on the dataset, we train a series of MLLMs as personalized multimodal assistants. By pretraining on large-scale dataset, RAP-MLLMs can generalize to infinite visual concepts without additional finetuning. Our models demonstrate outstanding flexibility and generation quality across a variety of tasks, such as personalized image captioning, question answering and visual recognition. The code, data and models are available at https://github.com/Hoar012/RAP-MLLM.

Challenges in managing linguistic diversity and integrating various musical modalities are faced by current music information retrieval systems. These limitations reduce their effectiveness in a global, multimodal music environment. To address these issues, we introduce CLaMP 2, a system compatible with 101 languages that supports both ABC notation (a text-based musical notation format) and MIDI (Musical Instrument Digital Interface) for music information retrieval. CLaMP 2, pre-trained on 1.5 million ABC-MIDI-text triplets, includes a multilingual text encoder and a multimodal music encoder aligned via contrastive learning. By leveraging large language models, we obtain refined and consistent multilingual descriptions at scale, significantly reducing textual noise and balancing language distribution. Our experiments show that CLaMP 2 achieves state-of-the-art results in both multilingual semantic search and music classification across modalities, thus establishing a new standard for inclusive and global music information retrieval., Comment: 17 pages, 10 figures, 4 tables

Recent research on fine-tuning vision-language models has demonstrated impressive performance in various downstream tasks. However, the challenge of obtaining accurately labeled data in real-world applications poses a significant obstacle during the fine-tuning process. To address this challenge, this paper presents a Denoising Fine-Tuning framework, called DeFT, for adapting vision-language models. DeFT utilizes the robust alignment of textual and visual features pre-trained on millions of auxiliary image-text pairs to sieve out noisy labels. The proposed framework establishes a noisy label detector by learning positive and negative textual prompts for each class. The positive prompt seeks to reveal distinctive features of the class, while the negative prompt serves as a learnable threshold for separating clean and noisy samples. We employ parameter-efficient fine-tuning for the adaptation of a pre-trained visual encoder to promote its alignment with the learned textual prompts. As a general framework, DeFT can seamlessly fine-tune many pre-trained models to downstream tasks by utilizing carefully selected clean samples. Experimental results on seven synthetic and real-world noisy datasets validate the effectiveness of DeFT in both noisy label detection and image classification., Comment: Accepted at NeurIPS 2024

Virtual Screening is an essential technique in the early phases of drug discovery, aimed at identifying promising drug candidates from vast molecular libraries. Recently, ligand-based virtual screening has garnered significant attention due to its efficacy in conducting extensive database screenings without relying on specific protein-binding site information. Obtaining binding affinity data for complexes is highly expensive, resulting in a limited amount of available data that covers a relatively small chemical space. Moreover, these datasets contain a significant amount of inconsistent noise. It is challenging to identify an inductive bias that consistently maintains the integrity of molecular activity during data augmentation. To tackle these challenges, we propose S-MolSearch, the first framework to our knowledge, that leverages molecular 3D information and affinity information in semi-supervised contrastive learning for ligand-based virtual screening. Drawing on the principles of inverse optimal transport, S-MolSearch efficiently processes both labeled and unlabeled data, training molecular structural encoders while generating soft labels for the unlabeled data. This design allows S-MolSearch to adaptively utilize unlabeled data within the learning process. Empirically, S-MolSearch demonstrates superior performance on widely-used benchmarks LIT-PCBA and DUD-E. It surpasses both structure-based and ligand-based virtual screening methods for enrichment factors across 0.5%, 1% and 5%.

Vision-language models (VLMs) like CLIP have demonstrated impressive zero-shot ability in image classification tasks by aligning text and images but suffer inferior performance compared with task-specific expert models. On the contrary, expert models excel in their specialized domains but lack zero-shot ability for new tasks. How to obtain both the high performance of expert models and zero-shot ability is an important research direction. In this paper, we attempt to demonstrate that by constructing a model hub and aligning models with their functionalities using model labels, new tasks can be solved in a zero-shot manner by effectively selecting and reusing models in the hub. We introduce a novel paradigm, Model Label Learning (MLL), which bridges the gap between models and their functionalities through a Semantic Directed Acyclic Graph (SDAG) and leverages an algorithm, Classification Head Combination Optimization (CHCO), to select capable models for new tasks. Compared with the foundation model paradigm, it is less costly and more scalable, i.e., the zero-shot ability grows with the sizes of the model hub. Experiments on seven real-world datasets validate the effectiveness and efficiency of MLL, demonstrating that expert models can be effectively reused for zero-shot tasks. Our code will be released publicly.

We introduce a novel level crossing in the mass mixing between two QCD axions, one canonical QCD axion and one $Z_{\mathcal N}$ QCD axion. The level crossing can take place at the QCD phase transition critical temperature or slightly before it, depending on the ratio of the axion decay constants $\sim1.69$. The cosmological evolution of the mass eigenvalues in these two cases is similar, however, the transition of axion energy density is completely different. Finally, we estimate the relic density of the QCD axion dark matter. This level crossing may also have some cosmological implications., Comment: 6 pages, 4 figures

In this paper, we study the tensor products of irreducible highest weight modules with irreducible loop modules over the affine-Virasoro algebra with aid of the ``shifting technique" established for the Virasoro algebra in [H. Chen, X. Guo, K. Zhao, Tensor product weight modules over the Virasoro algebra, J. Lond. Math. Soc. 88(2013), 829-844.]. All such tensor product modules are indecomposable modules with infinite-dimensional weight spaces. Moreover, we obtain the necessary and sufficient conditions for such tensor product modules to be irreducible. Therefore, we obtain a class of new irreducible weight modules over the affine-Virasoro algebra. Finally, the necessary and sufficient conditions for any two such tensor product modules to be isomorphic are also determined., Comment: 23 pages

The interplay between quantum and thermal fluctuations can induce rich phenomena at finite temperatures in strongly correlated fermion systems. Here we report a {\it numerically exact} auxiliary-field quantum Monte Carlo (AFQMC) study for the finite-temperature properties of three-dimensional repulsive Hubbard model at half filling. We concentrate on the complete temperature-interaction strength phase diagram of the model, which contains the low-temperature antiferromagnetic (AFM) long-range ordered phase and metal-insulator crossover (MIC) in the paramagnetic phase. Enabling access to unprecedented system sizes up to $20^3$, we achieve highly accurate results of the N\'{e}el transition temperature for representative values of on-site interaction $U$ via finite-size analysis of AFM structure factor. To quantitatively characterize the MIC above the N\'{e}el transition, we have developed fully new techniques allowing to compute the thermal entropy versus $U$ at fixed temperature and to directly calculate the $U$-derivative of double occupancy in AFQMC simulations. Then combining variously thermodynamic and dynamical observables, we establish an efficient scheme to precisely determine the boundaries for the MIC by cross-checking different observables. We also demonstrate the temperature dependence of many commonly used observables. Away from half filling, we explore the behavior of the sign problem and AFM spin correlation versus hole doping, and demonstrate the persistance of N\'{e}el AFM ordered phase to finite doping with limited results., Comment: 30 pages + 24 figures

This report presents a solution for the zero-shot referring expression comprehension task. Visual-language multimodal base models (such as CLIP, SAM) have gained significant attention in recent years as a cornerstone of mainstream research. One of the key applications of multimodal base models lies in their ability to generalize to zero-shot downstream tasks. Unlike traditional referring expression comprehension, zero-shot referring expression comprehension aims to apply pre-trained visual-language models directly to the task without specific training. Recent studies have enhanced the zero-shot performance of multimodal base models in referring expression comprehension tasks by introducing visual prompts. To address the zero-shot referring expression comprehension challenge, we introduced a combination of visual prompts and considered the influence of textual prompts, employing joint prediction tailored to the data characteristics. Ultimately, our approach achieved accuracy rates of 84.825 on the A leaderboard and 71.460 on the B leaderboard, securing the first position.

In the domain of symbolic music research, the progress of developing scalable systems has been notably hindered by the scarcity of available training data and the demand for models tailored to specific tasks. To address these issues, we propose MelodyT5, a novel unified framework that leverages an encoder-decoder architecture tailored for symbolic music processing in ABC notation. This framework challenges the conventional task-specific approach, considering various symbolic music tasks as score-to-score transformations. Consequently, it integrates seven melody-centric tasks, from generation to harmonization and segmentation, within a single model. Pre-trained on MelodyHub, a newly curated collection featuring over 261K unique melodies encoded in ABC notation and encompassing more than one million task instances, MelodyT5 demonstrates superior performance in symbolic music processing via multi-task transfer learning. Our findings highlight the efficacy of multi-task transfer learning in symbolic music processing, particularly for data-scarce tasks, challenging the prevailing task-specific paradigms and offering a comprehensive dataset and framework for future explorations in this domain., Comment: 9 pages, 2 figures, 3 tables, accepted by ISMIR 2024

Pre-trained vision-language models like CLIP have shown powerful zero-shot inference ability via image-text matching and prove to be strong few-shot learners in various downstream tasks. However, in real-world scenarios, adapting CLIP to downstream tasks may encounter the following challenges: 1) data may exhibit long-tailed data distributions and might not have abundant samples for all the classes; 2) There might be emerging tasks with new classes that contain no samples at all. To overcome them, we propose a novel framework to achieve efficient and long-tailed generalization, which can be termed as Candle. During the training process, we propose compensating logit-adjusted loss to encourage large margins of prototypes and alleviate imbalance both within the base classes and between the base and new classes. For efficient adaptation, we treat the CLIP model as a black box and leverage the extracted features to obtain visual and textual prototypes for prediction. To make full use of multi-modal information, we also propose cross-modal attention to enrich the features from both modalities. For effective generalization, we introduce virtual prototypes for new classes to make up for their lack of training images. Candle achieves state-of-the-art performance over extensive experiments on 11 diverse datasets while substantially reducing the training time, demonstrating the superiority of our approach. The source code is available at https://github.com/shijxcs/Candle., Comment: Accepted by KDD 2024

In offline Imitation Learning (IL), one of the main challenges is the \textit{covariate shift} between the expert observations and the actual distribution encountered by the agent, because it is difficult to determine what action an agent should take when outside the state distribution of the expert demonstrations. Recently, the model-free solutions introduce the supplementary data and identify the latent expert-similar samples to augment the reliable samples during learning. Model-based solutions build forward dynamic models with conservatism quantification and then generate additional trajectories in the neighborhood of expert demonstrations. However, without reward supervision, these methods are often over-conservative in the out-of-expert-support regions, because only in states close to expert-observed states can there be a preferred action enabling policy optimization. To encourage more exploration on expert-unobserved states, we propose a novel model-based framework, called offline Imitation Learning with Self-paced Reverse Augmentation (SRA). Specifically, we build a reverse dynamic model from the offline demonstrations, which can efficiently generate trajectories leading to the expert-observed states in a self-paced style. Then, we use the subsequent reinforcement learning method to learn from the augmented trajectories and transit from expert-unobserved states to expert-observed states. This framework not only explores the expert-unobserved states but also guides maximizing long-term returns on these states, ultimately enabling generalization beyond the expert data. Empirical results show that our proposal could effectively mitigate the covariate shift and achieve the state-of-the-art performance on the offline imitation learning benchmarks. Project website: \url{https://www.lamda.nju.edu.cn/shaojj/KDD24_SRA/}., Comment: Accepted by KDD2024

Sterile neutrinos that couple to the Standard Model via the neutrino magnetic dipole portals have been extensively studied at various experiments. In this work, we scrutinize these interactions for sterile neutrinos in the mass range of $\unit[0.1]{}-\unit[50]{MeV}$ through the nuclear and electron recoils at various neutrino scattering experiments. For the $e$-flavor specific dipole portal, we demonstrate that Dresden-II can provide leading constraints for $m_N \lesssim \unit[0.5]{MeV}$, setting aside currently unresolved theoretical uncertainties. For the $\mu$-flavor case, we show that the COHERENT experiment can probe a unique parameter region for $m_N$ in the range of $\unit[10]{}-\unit[40]{MeV}$ with the full dataset collected by the CsI[Na] scintillation detector, including both the energy and timing structure of the neutrino beam. We also present limits on the parameter regions of the $\tau$-flavor dipole portal using measurements of the solar neutrino flux from dark matter direct detection experiments., Comment: 8 pages, 2 figures

Large language models (LLMs) have demonstrated impressive performance on reasoning tasks, which can be further improved through few-shot prompting techniques. However, the current evaluation primarily focuses on carefully constructed benchmarks and neglects the consideration of real-world reasoning problems that present missing and contradictory conditions, known as ill-defined problems. Our observations suggest that existing few-shot prompting techniques are ineffective in such scenarios, often providing overconfident answers or hallucination. To further study this problem, we develop a benchmark called Problems with Missing and Contradictory conditions (PMC) and introduce two novel metrics to evaluate the performance of few-shot prompting methods in these scenarios. Our analysis using the PMC benchmark reveals a trade-off dilemma between the performance of mathematical reasoning for well-defined problems and the ability to recognize ill-defined problems. To address the challenges posed by PMC, we propose a novel few-shot prompting method called SMT-LIB Prompting (SLP), which utilizes the SMT-LIB language to model the problems instead of solving them directly. Subsequently, a double-check solving strategy checks the satisfiability and uniqueness of the solution and provides final feedback. Extensive experiments demonstrate the superiority of our SLP approach compared to existing few-shot prompting methods when dealing with problems with missing and contradictory conditions. We will open-source our benchmark and code to facilitate future research., Comment: Preprint. arXiv admin note: text overlap with arXiv:2304.09797

Large language models (LLMs), including both proprietary and open-source models, have showcased remarkable capabilities in addressing a wide range of downstream tasks. Nonetheless, when it comes to practical Chinese legal tasks, these models fail to meet the actual requirements. Proprietary models do not ensure data privacy for sensitive legal cases, while open-source models demonstrate unsatisfactory performance due to their lack of legal knowledge. To address this problem, we introduce LawGPT, the first open-source model specifically designed for Chinese legal applications. LawGPT comprises two key components: legal-oriented pre-training and legal supervised fine-tuning. Specifically, we employ large-scale Chinese legal documents for legal-oriented pre-training to incorporate legal domain knowledge. To further improve the model's performance on downstream legal tasks, we create a knowledge-driven instruction dataset for legal supervised fine-tuning. Our experimental results demonstrate that LawGPT outperforms the open-source LLaMA 7B model. Our code and resources are publicly available at https://github.com/pengxiao-song/LaWGPT and have received 5.7K stars on GitHub., Comment: Technical Report

Markarian 421 is a well-known nearby BL Lac blazar at the redshift $z=0.031$. Many previous works were investigated to constrain the axion-photon coupling from its TeV gamma-ray observations, showing the upper limit on the coupling constant $g_{a\gamma} \lesssim 2.0\times 10^{-11} \rm \, GeV^{-1}$ for the axion mass $[5.0\times10^{-10} \, {\rm eV} \lesssim m_a \lesssim 5.0\times10^{-7} \, {\rm eV}]$. While in this work, we obtain a more stringent upper limit on the axion-photon coupling from the 1038 days gamma-ray observations of the blazar Markarian 421. The long-term gamma-ray spectra are measured by the collaborations Large Area Telescope on board NASA's Fermi Gamma-ray Space Telescope (Fermi-LAT) and High Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory from 2015 June to 2018 July. We show the best-fit spectral energy distributions (SEDs) of Markarian 421 under the null and axion hypotheses. Then we set the axion-photon limit in the $\{m_a, \, g_{a\gamma}\}$ plane. The 99% $\rm C.L.$ upper limit set by Markarian 421 is $g_{a\gamma} \lesssim 4.0\times 10^{-12} \rm \, GeV^{-1}$ for the axion mass $[1.0\times10^{-9} \, {\rm eV} \lesssim m_a \lesssim 1.0\times10^{-8} \, {\rm eV}]$. It is the most stringent upper limit in this axion mass region., Comment: 11 pages, 4 figures. Published in PLB

Vision-language models (VLMs), such as CLIP, have demonstrated impressive zero-shot capabilities for various downstream tasks. Their performance can be further enhanced through few-shot prompt tuning methods. However, current studies evaluate the performance of learned prompts separately on base and new classes. This evaluation lacks practicality for real-world applications since downstream tasks cannot determine whether the data belongs to base or new classes in advance. In this paper, we explore a problem setting called Open-world Prompt Tuning (OPT), which involves tuning prompts on base classes and evaluating on a combination of base and new classes. By introducing Decomposed Prompt Tuning framework (DePT), we theoretically demonstrate that OPT can be solved by incorporating out-of-distribution detection into prompt tuning, thereby enhancing the base-to-new discriminability. Based on DePT, we present a novel prompt tuning approach, namely, Decomposed Context Optimization (DeCoOp), which introduces new-class detectors and sub-classifiers to further enhance the base-class and new-class discriminability. Experimental results on 11 benchmark datasets validate the effectiveness of DePT and demonstrate that DeCoOp outperforms current state-of-the-art methods, providing a significant 2% average accuracy improvement., Comment: Accepted by ICML 2024. Code is available at: https://wnjxyk.github.io/DeCoOp

In this paper, we touch on the problem of markerless multi-modal human motion capture especially for string performance capture which involves inherently subtle hand-string contacts and intricate movements. To fulfill this goal, we first collect a dataset, named String Performance Dataset (SPD), featuring cello and violin performances. The dataset includes videos captured from up to 23 different views, audio signals, and detailed 3D motion annotations of the body, hands, instrument, and bow. Moreover, to acquire the detailed motion annotations, we propose an audio-guided multi-modal motion capture framework that explicitly incorporates hand-string contacts detected from the audio signals for solving detailed hand poses. This framework serves as a baseline for string performance capture in a completely markerless manner without imposing any external devices on performers, eliminating the potential of introducing distortion in such delicate movements. We argue that the movements of performers, particularly the sound-producing gestures, contain subtle information often elusive to visual methods but can be inferred and retrieved from audio cues. Consequently, we refine the vision-based motion capture results through our innovative audio-guided approach, simultaneously clarifying the contact relationship between the performer and the instrument, as deduced from the audio. We validate the proposed framework and conduct ablation studies to demonstrate its efficacy. Our results outperform current state-of-the-art vision-based algorithms, underscoring the feasibility of augmenting visual motion capture with audio modality. To the best of our knowledge, SPD is the first dataset for musical instrument performance, covering fine-grained hand motion details in a multi-modal, large-scale collection., Comment: SIGGRAPH2024

In this work we discuss the neutrino mass dependent nuclear matrix element (NME) of the neutrinoless double beta decay process and derive the limit on the parameter space of the minimal Type-I seesaw model from the current available experimental data as well as the future sensitivities from the next-generation experiments. Both the explicit many-body calculations and naive extrapolations of the mass dependent NME are employed in the current work. The uncertainties of the theoretical nuclear structure models are taken into account. By combining the latest experimental data from $^{76}$Ge-based experiments, GERDA and MAJORANA, the $^{130}$Te-based experiment, CUORE and the $^{136}$Xe-based experiments, KamLAND-Zen and EXO-200, the bounds on the parameter space of the minimal Type-I seesaw model are obtained and compared with the limits from other experimental probes. Sensitivities for future experiments utilizing $^{76}$Ge-based (LEGEND-1000), $^{82}$Se-based (SuperNEMO), $^{130}$Te based (SNO+II) and $^{136}$Xe-based (nEXO), with a ten-year exposure, are also derived., Comment: 36 pages, 14 figures, the version to be published in JHEP

We present the subspace-constrained Tyler's estimator (STE) designed for recovering a low-dimensional subspace within a dataset that may be highly corrupted with outliers. STE is a fusion of the Tyler's M-estimator (TME) and a variant of the fast median subspace. Our theoretical analysis suggests that, under a common inlier-outlier model, STE can effectively recover the underlying subspace, even when it contains a smaller fraction of inliers relative to other methods in the field of robust subspace recovery. We apply STE in the context of Structure from Motion (SfM) in two ways: for robust estimation of the fundamental matrix and for the removal of outlying cameras, enhancing the robustness of the SfM pipeline. Numerical experiments confirm the state-of-the-art performance of our method in these applications. This research makes significant contributions to the field of robust subspace recovery, particularly in the context of computer vision and 3D reconstruction., Comment: 23 pages, accepted by CVPR 24

The Hubbard model at temperature above the N\'{e}el transition, despite of being a paramagnet, can exhibit rich physics due to the interplay of Fermi surface, on-site interaction $U$ and thermal fluctuations. Nevertheless, the understanding of the crossover physics remains only at a qualitative level, because of the intrinsically smooth behavior. Employing an improved variant of the {\it numerically exact} auxiliary-field quantum Monte Carlo algorithm equipped with numerical analytic continuation, we obtain a broad variety of static and dynamical properties of the three-dimensional (3D) Hubbard model at half filling, quantitatively determine the crossover boundaries, and observe that the metal-insulator crossover state, in which antiferromagnetic spin correlations appear strongest, exists over an extended regime in between the metallic state for small $U$ and the Mott insulator for large $U$. In particular, the Widom line, corresponding to the most rapid suppression of double occupancy as $U$ increases, is found to fully reside in the metallic Fermi liquid regime, in contrast to the conventional intuition that it is a representative feature for entering the Mott insulator. Beside providing a reliable methology for numerical study of crossover physics, our work can serve as a timely and important guideline for the most recent optical lattice experiments., Comment: 7 pages + 4 figures

Atmospheric neutrinos contribute significantly to irreducible backgrounds through their neutral-current (NC) interactions with $^{12}$C nuclei in liquid-scintillator detectors, impacting diffuse supernova neutrino background, nucleon decay, and reactor neutrinos. This paper extends our prior work by systematically studying the NC backgrounds towards the MeV region of reactor neutrinos. We employ contemporary neutrino generator models from GENIE and NuWro for calculations, with a focus on predicting NC background in experimental searches for inverse-beta-decay signals below 100 MeV visible energy. We estimate the systematic uncertainty to our estimation of the NC background using various data-driven neutrino generator models, addressing factors such as the initial neutrino-nucleon NC interaction, the nuclear model, the final-state interaction model, the nucleus deexcitation, and the secondary interaction on final-state particles., Comment: 26 pages, 10 figures

This work analyzes the subspace-constrained Tyler's estimator (STE) designed for recovering a low-dimensional subspace within a dataset that may be highly corrupted with outliers. It assumes a weak inlier-outlier model and allows the fraction of inliers to be smaller than a fraction that leads to computational hardness of the robust subspace recovery problem. It shows that in this setting, if the initialization of STE, which is an iterative algorithm, satisfies a certain condition, then STE can effectively recover the underlying subspace. It further shows that under the generalized haystack model, STE initialized by the Tyler's M-estimator (TME), can recover the subspace when the fraction of iniliers is too small for TME to handle.

We explore the new physics phenomena of gravidynamics governed by the inhomogeneous spin gauge symmetry based on the gravitational quantum field theory. Such a gravidynamics enables us to derive the generalized Einstein equation and an equation beyond it. To simplify the analyses, we linearize the dynamic equations of gravitational interaction by keeping terms up to the leading order in the dual gravigauge field. We then apply the linearized dynamic equations into two particular gravitational phenomena. First, we consider the linearized equations in the absence of source fields, which is shown to have five physical propagating polarizations as gravitational waves, i.e., two tensor modes, two vector modes, and one scalar, instead of two tensor polarizations in the general relativity. Second, we examine the Newtonian limit in which the gravitational fields and the matter source distribution are weak and static. By deriving the associated Poisson equation, we obtain the exact relation of the fundamental interaction coupling in the gravidynamics with the experimentally measured Newtonian constant. We also make use of nonrelativistic objects and relativistic photons to probe the Newtonian field configurations. In particular, the experiments from the gravitational deflection of light rays and the Shapiro time delay can place stringent constraints on the linearized gravidynamics in the gravitational quantum field theory., Comment: 7 pages, 1 figure

Cosmic-ray (CR) positrons are relatively rare due to its secondary origin and thus sensitive to exotic contributions. Primordial black holes (PBHs) with masses above $\sim 5\times10^{14}\,\mathrm{g}$ can be stable sources of CR positrons due to Hawking radiation. We show that the CR positron flux measured by AMS-02 can place stringent constraints on the energy fraction of PBHs relative to that of dark matter $f_{\text{PBH}}$. Making use of the state-of-the-art models for CR propagation in both the Galaxy and heliosphere, we obtain conservative upper limit of $f_{\text{PBH}}\lesssim3\times 10^{-4}$ at $M_{\mathrm{PBH}}\simeq2\times 10^{16}$ g, which improves the previous constraints obtained from the Voyager CR all-electron data by around an order of magnitude.

We introduce a novel sufficient dimension-reduction (SDR) method which is robust against outliers using $\alpha$-distance covariance (dCov) in dimension-reduction problems. Under very mild conditions on the predictors, the central subspace is effectively estimated and model-free advantage without estimating link function based on the projection on the Stiefel manifold. We establish the convergence property of the proposed estimation under some regularity conditions. We compare the performance of our method with existing SDR methods by simulation and real data analysis and show that our algorithm improves the computational efficiency and effectiveness.

In this note, we investigate Jacobian conjecture through investigation of automorphisms of polynomial rings in characteristic $p$. Making use of the technique of inverse limits, we show that under Jacobian condition for a given homomorphism $\varphi$ of the polynomial ring $\mathbf{k}[x_1,\ldots,x_n]$, if $\varphi$ preserves the maximal ideals, then $\varphi$ is an automorphism., Comment: 8 pages, to appcar in JAA

In addressing the challenge of interpretability and generalizability of artificial music intelligence, this paper introduces a novel symbolic representation that amalgamates both explicit and implicit musical information across diverse traditions and granularities. Utilizing a hierarchical and-or graph representation, the model employs nodes and edges to encapsulate a broad spectrum of musical elements, including structures, textures, rhythms, and harmonies. This hierarchical approach expands the representability across various scales of music. This representation serves as the foundation for an energy-based model, uniquely tailored to learn musical concepts through a flexible algorithm framework relying on the minimax entropy principle. Utilizing an adapted Metropolis-Hastings sampling technique, the model enables fine-grained control over music generation. A comprehensive empirical evaluation, contrasting this novel approach with existing methodologies, manifests considerable advancements in interpretability and controllability. This study marks a substantial contribution to the fields of music analysis, composition, and computational musicology.

Sparse Bayesian Learning (SBL) models are extensively used in signal processing and machine learning for promoting sparsity through hierarchical priors. The hyperparameters in SBL models are crucial for the model's performance, but they are often difficult to estimate due to the non-convexity and the high-dimensionality of the associated objective function. This paper presents a comprehensive framework for hyperparameter estimation in SBL models, encompassing well-known algorithms such as the expectation-maximization (EM), MacKay, and convex bounding (CB) algorithms. These algorithms are cohesively interpreted within an alternating minimization and linearization (AML) paradigm, distinguished by their unique linearized surrogate functions. Additionally, a novel algorithm within the AML framework is introduced, showing enhanced efficiency, especially under low signal noise ratios. This is further improved by a new alternating minimization and quadratic approximation (AMQ) paradigm, which includes a proximal regularization term. The paper substantiates these advancements with thorough convergence analysis and numerical experiments, demonstrating the algorithm's effectiveness in various noise conditions and signal-to-noise ratios.

We present the limits on photon to axionlike particle (ALP) coupling from the 10-year period observations of the TeV BL Lacertae blazar 1ES 1215+303 (with redshift $z=0.130$). The contemporaneous gamma-ray spectra are measured by the collaborations Fermi-LAT and VERITAS with five flux phases from 2008 to 2017, including four low states and one flare. Using these flux phases, we show the spectral energy distributions (SEDs) under the null/ALP hypotheses and set the combined limit on ALP. The 95% $\rm C.L.$ combined limit set by 1ES 1215+303 with the 10-year gamma-ray data is roughly at the photon-ALP coupling constant $g_{a\gamma} \gtrsim 1.5\times 10^{-11} \rm \, GeV^{-1}$ for the ALP mass $5.0\times10^{-10} \, {\rm eV} \lesssim m_a \lesssim 1.0\times10^{-7} \, {\rm eV}$., Comment: 6 pages, 4 figures. Published in PLB