arXiv subjects

Hui Zhu

Publications and source records attributed to Hui Zhu.

At least 37 records · Page 2Linked to original sources

arXiv2025

The number of primes not in a numerical semigroup

For two coprime positive integers $a$ and $b$,let $π^* (a, b)$ be the number of primes that cannot be represented as $au+bv$, where $u$ and $v$ are nonnegative integers. It is clear that $π^* (a, b)\le π(ab-a-b)$, where $π(x)$ denotes the number of primes not exceeding $x$. In this paper, we prove that $π^* (a, b)\ge 0.04π(ab-a-b)$ and pose following conjecture: $π^* (a, b)\ge \frac 12 π(ab-a-b)$. This conjecture is confirmed for $1\le a\le 10$.

math.NT↗

arXiv2025

Primes of the form $ax+by$

For two coprime positive integers $a,b$, let $T(a,b)=\{ ax+by : x,y\in \mathbb{Z}_{\ge 0} \} $ and let $s(a,b)=ab-a-b$. It is well known that all integers which are greater than $s(a,b)$ are in $T(a,b)$. Let $π(a, b)$ be the number of primes in $T(a,b)$ which are less than or equal to $s(a,b)$. It is easy to see that $π(2, 3)=0$ and $π(2, b)=1$ for all odd integers $b\ge 5$. In this paper, we prove that if $b>a\ge 3$ with $\gcd (a, b)=1$, then $π(a, b)>0.005 s(a,b)/\log s(a,b)$. We conjecture that $\frac{13}{66}π(s(a,b))\le π(a, b)\le \frac 12π(s(a,b))$ for all $b>a\ge 3$ with $\gcd (a, b)=1$.

math.NT↗

arXiv2025

Automatic Calibration for Membership Inference Attack on Large Language Models

Membership Inference Attacks (MIAs) have recently been employed to determine whether a specific text was part of the pre-training data of Large Language Models (LLMs). However, existing methods often misinfer non-members as members, leading to a high false positive rate, or depend on additional reference models for probability calibration, which limits their practicality. To overcome these challenges, we introduce a novel framework called Automatic Calibration Membership Inference Attack (ACMIA), which utilizes a tunable temperature to calibrate output probabilities effectively. This approach is inspired by our theoretical insights into maximum likelihood estimation during the pre-training of LLMs. We introduce ACMIA in three configurations designed to accommodate different levels of model access and increase the probability gap between members and non-members, improving the reliability and robustness of membership inference. Extensive experiments on various open-source LLMs demonstrate that our proposed attack is highly effective, robust, and generalizable, surpassing state-of-the-art baselines across three widely used benchmarks. Our code is available at: \href{https://github.com/Salehzz/ACMIA}{\textcolor{blue}{Github}}.

cs.LG↗

arXiv2025

BiPVL-Seg: Bidirectional Progressive Vision-Language Fusion with Global-Local Alignment for Medical Image Segmentation

Medical image segmentation typically relies solely on visual data, overlooking the rich textual information clinicians use for diagnosis. Vision-language models attempt to bridge this gap, but existing approaches often process visual and textual features independently, resulting in weak cross-modal alignment. Simple fusion techniques fail due to the inherent differences between spatial visual features and sequential text embeddings. Additionally, medical terminology deviates from general language, limiting the effectiveness of off-the-shelf text encoders and further hindering vision-language alignment. We propose BiPVL-Seg, an end-to-end framework that integrates vision-language fusion and embedding alignment through architectural and training innovations, where both components reinforce each other to enhance medical image segmentation. BiPVL-Seg introduces bidirectional progressive fusion in the architecture, which facilitates stage-wise information exchange between vision and text encoders. Additionally, it incorporates global-local contrastive alignment, a training objective that enhances the text encoder's comprehension by aligning text and vision embeddings at both class and concept levels. Extensive experiments on diverse medical imaging benchmarks across CT and MR modalities demonstrate BiPVL-Seg's superior performance when compared with state-of-the-art methods in complex multi-class segmentation. Source code is available in this GitHub repository.

cs.CV↗

arXiv2025

Cross-Skeleton Interaction Graph Aggregation Network for Representation Learning of Mouse Social Behaviour

Automated social behaviour analysis of mice has become an increasingly popular research area in behavioural neuroscience. Recently, pose information (i.e., locations of keypoints or skeleton) has been used to interpret social behaviours of mice. Nevertheless, effective encoding and decoding of social interaction information underlying the keypoints of mice has been rarely investigated in the existing methods. In particular, it is challenging to model complex social interactions between mice due to highly deformable body shapes and ambiguous movement patterns. To deal with the interaction modelling problem, we here propose a Cross-Skeleton Interaction Graph Aggregation Network (CS-IGANet) to learn abundant dynamics of freely interacting mice, where a Cross-Skeleton Node-level Interaction module (CS-NLI) is used to model multi-level interactions (i.e., intra-, inter- and cross-skeleton interactions). Furthermore, we design a novel Interaction-Aware Transformer (IAT) to dynamically learn the graph-level representation of social behaviours and update the node-level representation, guided by our proposed interaction-aware self-attention mechanism. Finally, to enhance the representation ability of our model, an auxiliary self-supervised learning task is proposed for measuring the similarity between cross-skeleton nodes. Experimental results on the standard CRMI13-Skeleton and our PDMB-Skeleton datasets show that our proposed model outperforms several other state-of-the-art approaches.

cs.CV↗

arXiv2024

Switchable deep beamformer for high-quality and real-time passive acoustic mapping

Passive acoustic mapping (PAM) is a promising tool for monitoring acoustic cavitation activities in the applications of ultrasound therapy. Data-adaptive beamformers for PAM have better image quality compared to the time exposure acoustics (TEA) algorithms. However, the computational cost of data-adaptive beamformers is considerably expensive. In this work, we develop a deep beamformer based on a generative adversarial network, which can switch between different transducer arrays and reconstruct high-quality PAM images directly from radio frequency ultrasound signals with low computational cost. The deep beamformer was trained on the dataset consisting of simulated and experimental cavitation signals of single and multiple microbubble clouds measured by different (linear and phased) arrays covering 1-15 MHz. We compared the performance of the deep beamformer to TEA and three different data-adaptive beamformers using the simulated and experimental test dataset. Compared with TEA, the deep beamformer reduced the energy spread area by 18.9%-65.0% and improved the image signal-to-noise ratio by 9.3-22.9 dB in average for the different arrays in our data. Compared to the data-adaptive beamformers, the deep beamformer reduced the computational cost by three orders of magnitude achieving 10.5 ms image reconstruction speed in our data, while the image quality was as good as that of the data-adaptive beamformers. These results demonstrated the potential of the deep beamformer for high-resolution monitoring of microbubble cavitation activities for ultrasound therapy.

cs.AI↗

arXiv2024

High-Quality Passive Acoustic Mapping with the Cross-Correlated Angular Spectrum Method

While passive acoustic mapping (PAM) has been advanced for monitoring acoustic cavitation activity in focused ultrasound (FUS) therapy, achieving both real-time and high-quality imaging capabilities is still challenging. The angular spectrum (AS) method presents the most efficient algorithm for PAM, but it suffers from artifacts and low resolution due to the diffraction pattern of the imaging array. Data-adaptive beamformers suppress artifacts well, but their overwhelming computational complexity, more than two orders of magnitude higher than the classical time exposure acoustic (TEA) method, hinders their application in real-time. In this work, we introduce the cross-correlated AS method to address the challenge. This method is based on cross-correlating the AS back-propagated wave fields, in the frequency domain, measured by different apodized sub-apertures of the transducer array to provide the normalized correlation coefficient (NCC) matrix for artifacts suppression. We observed that the spatial pattern of NCC matrix is variable which can be utilized by the triple apodization with cross-correlation (TAX) with AS scheme, namely the AS-TAX method, for optimal artifacts suppression outcomes. Both the phantom and mouse tumor experiments showed that: 1) the AS-TAX method has comparable image quality as the data-adaptive beamformers, reducing the energy spread area by 34.8-66.6% and improving image signal-to-noise ratio by 10.7-14.5 dB compared to TEA; 2) it reduces the computational complexity by two orders of magnitude compared to TEA allowing millisecond-level image reconstruction speed with a parallel implementation; 3) it can well map microbubble cavitation activity of different status (stable or inertial). The AS-TAX method represents a real-time approach to monitor cavitation-based FUS therapy with high image quality.

physics.med-ph↗

arXiv2024

MulModSeg: Enhancing Unpaired Multi-Modal Medical Image Segmentation with Modality-Conditioned Text Embedding and Alternating Training

In the diverse field of medical imaging, automatic segmentation has numerous applications and must handle a wide variety of input domains, such as different types of Computed Tomography (CT) scans and Magnetic Resonance (MR) images. This heterogeneity challenges automatic segmentation algorithms to maintain consistent performance across different modalities due to the requirement for spatially aligned and paired images. Typically, segmentation models are trained using a single modality, which limits their ability to generalize to other types of input data without employing transfer learning techniques. Additionally, leveraging complementary information from different modalities to enhance segmentation precision often necessitates substantial modifications to popular encoder-decoder designs, such as introducing multiple branched encoding or decoding paths for each modality. In this work, we propose a simple Multi-Modal Segmentation (MulModSeg) strategy to enhance medical image segmentation across multiple modalities, specifically CT and MR. It incorporates two key designs: a modality-conditioned text embedding framework via a frozen text encoder that adds modality awareness to existing segmentation frameworks without significant structural modifications or computational overhead, and an alternating training procedure that facilitates the integration of essential features from unpaired CT and MR inputs. Through extensive experiments with both Fully Convolutional Network and Transformer-based backbones, MulModSeg consistently outperforms previous methods in segmenting abdominal multi-organ and cardiac substructures for both CT and MR modalities. The code is available in this {\href{https://github.com/ChengyinLee/MulModSeg_2024}{link}}.

eess.IV↗

arXiv2024

Progressive Multi-Level Alignments for Semi-Supervised Domain Adaptation SAR Target Recognition Using Simulated Data

Recently, an intriguing research trend for automatic target recognition (ATR) from synthetic aperture radar (SAR) imagery has arisen: using simulated data to train ATR models is a feasible solution to the issue of inadequate measured data. To close the domain gap that exists between the real and simulated data, the unsupervised domain adaptation (UDA) techniques are frequently exploited to construct ATR models. However, for UDA, the target domain lacks labeled data to direct the model training, posing a great challenge to ATR performance. To address the above problem, a semi-supervised domain adaptation (SSDA) framework has been proposed adopting progressive multi-level alignments for simulated data-aided SAR ATR. First, a progressive wavelet transform data augmentation (PWTDA) is presented by analyzing the discrepancies of wavelet decomposition sub-bands of two domain images, obtaining the domain-level alignment. Specifically, the domain gap is narrowed by mixing the wavelet transform high-frequency sub-band components. Second, we develop an asymptotic instance-prototype alignment (AIPA) strategy to push the source domain instances close to the corresponding target prototypes, aiming to achieve category-level alignment. Moreover, the consistency alignment is implemented by excavating the strong-weak augmentation consistency of both individual samples and the multi-sample relationship, enhancing the generalization capability of the model. Extensive experiments on the Synthetic and Measured Paired Labeled Experiment (SAMPLE) dataset, indicate that our approach obtains recognition accuracies of 99.63% and 98.91% in two common experimental settings with only one labeled sample per class of the target domain, outperforming the most advanced SSDA techniques.

cs.CV↗

arXiv2024

ISPO: An Integrated Ontology of Symptom Phenotypes for Semantic Integration of Traditional Chinese Medical Data

Symptom phenotypes are one of the key types of manifestations for diagnosis and treatment of various disease conditions. However, the diversity of symptom terminologies is one of the major obstacles hindering the analysis and knowledge sharing of various types of symptom-related medical data particularly in the fields of Traditional Chinese Medicine (TCM). Objective: This study aimed to construct an Integrated Ontology of symptom phenotypes (ISPO) to support the data mining of Chinese EMRs and real-world study in TCM field. Methods: To construct an integrated ontology of symptom phenotypes (ISPO), we manually annotated classical TCM textbooks and large-scale Chinese electronic medical records (EMRs) to collect symptom terms with support from a medical text annotation system. Furthermore, to facilitate the semantic interoperability between different terminologies, we incorporated public available biomedical vocabularies by manual mapping between Chinese terms and English terms with cross-references to source vocabularies. In addition, we evaluated the ISPO using independent clinical EMRs to provide a high-usable medical ontology for clinical data analysis. Results: By integrating 78,696 inpatient cases of EMRs, 5 biomedical vocabularies, 21 TCM books and dictionaries, ISPO provides 3,147 concepts, 23,475 terms, and 55,552 definition or contextual texts. Adhering to the taxonomical structure of the related anatomical systems of symptom phenotypes, ISPO provides 12 top-level categories and 79 middle-level sub-categories. The validation of data analysis showed the ISPO has a coverage rate of 95.35%, 98.53% and 92.66% for symptom terms with occurrence rates of 0.5% in additional three independent curated clinical datasets, which can demonstrate the significant value of ISPO in mapping clinical terms to ontologies.

cs.CL↗

arXiv2024

Field Line Curvature Scattering in the Dayside Off-Equatorial Minima Regions

Magnetic field line curvature (FLC) scattering is an effective mechanism for collisionless particle scattering. In the terrestrial magnetosphere, the FLC scattering plays an essential role in shaping the outer boundary of protons radiation belt, the rapid decay of ring current, and the formation of proton isotropic boundary (IB). However, previous studies have yet to adequately investigate the influence of FLC scattering on charged particles in the Earth's dayside magnetosphere, particularly in the off-equatorial magnetic minima regions. This study employs T89 magnetic field model to investigate the impacts of FLC scattering on ring current protons in the dayside magnetosphere, with a specific focus on the off-equatorial minimum regions. We analyze the spatial distributions of single and dual magnetic minima regions, adiabatic parameter, and pitch angle diffusion coefficients due to FLC scattering as functions of $Kp$. The results show that the effects of FLC scattering are significant not only on the dusk and dawn sides but also in the off-equatorial minima regions on the noon. Additionally, we investigate the role of dipole tilt angle in the hemispheric asymmetry of FLC scattering effects. The dipole tilt angle controls the overall displacement of the dayside magnetosphere, resulting in different FLC scattering effects in the two hemispheres. Our study holds significance for understanding the FLC scattering effects in the off-equatorial region of Earth's dayside magnetosphere and for constructing a more accurate dynamic model of particles.

physics.space-ph↗

arXiv2024

On universality for the kinetic wave equation

On compact Riemannian manifolds with chaotic geometries, specifically those exhibiting the random wave model conjectured by Berry, we derive heuristically a homogeneous kinetic wave equation that is universal for all such manifolds.

math.AP↗

arXiv2024

Inhomogeneous turbulence for the Wick nonlinear Schrödinger equation

We introduce a simplified model for wave turbulence theory -- the Wick NLS, of which the main feature is the absence of all self-interactions in the correlation expansions of its solutions. For this model, we derive several wave kinetic equations that govern the effective statistical behavior of its solutions in various regimes. In the homogeneous setting, where the initial correlation is translation invariant, we obtain a wave kinetic equation similar to the one predicted by the formal theory. In the inhomogeneous setting, we obtain a wave kinetic equation that describes the statistical behavior of the wavepackets of the solutions, accounting for both the transport of wavepackets and collisions among them. Another wave kinetic equation, which seems new in the literature, also appears in a certain scaling regime of this setting and provides a more refined collision picture.

math.AP↗

arXiv2023

Magneto hydrodynamic simulations of the supernova remnant G1.9+0.3

The youngest Galactic supernova remnant G1.9+0.3 shows a discrete feature between its radio and X-ray morphologies. The observed radio morphology features a single maximum in the north, while the X-ray observation shows two opposite 'ears' on the east and west sides. Using 3D magneto hydrodynamical simulations, we investigate the formation of the discrete feature of the remnant. We have tested different parameters for better simulation and reproduced similar discrete features under an environment with density gradient and an environment with clump, which provides a possible explanation of the observation.

astro-ph.HE↗

arXiv2022

A Study of Radio Knots within Supernova Remnant Cassiopeia A

The study on the dynamic evolution of young supernova remnants (SNRs) is an important way to understand the density structure of the progenitor's circumstellar medium. We have reported the acceleration or deceleration, proper motion and brightness changes of 260 compact radio features in the second youngest known SNR Cas A at 5\,GHz based on the VLA data of five epochs from 1987 to 2004. The radio expansion center locates at $α(1950)=23^{\rm h}21^{\rm m}9^{\rm s}_{\cdot}7 \pm 0^{\rm s}_{\cdot}29, δ(1950)=+58^{\circ}32^{\prime}25^{\prime\prime}_{\cdot}2 \pm 2^{\prime\prime}_{\cdot}2$. Three-quarters of the compact knots are decelerating, this suggests that there are significant density fluctuations in the stellar winds of the remnant's progenitor. We have verified that the acceleration or deceleration of compact knots are not related with the distribution of brightness. The brightening, fading, disappearing or new appearing of compact radio features in Cas A suggests that the magnetic field in the remnant is changing rapidly.

astro-ph.GA↗

arXiv2022

FAS-UNet: A Novel FAS-driven Unet to Learn Variational Image Segmentation

Solving variational image segmentation problems with hidden physics is often expensive and requires different algorithms and manually tunes model parameter. The deep learning methods based on the U-Net structure have obtained outstanding performances in many different medical image segmentation tasks, but designing such networks requires a lot of parameters and training data, not always available for practical problems. In this paper, inspired by traditional multi-phase convexity Mumford-Shah variational model and full approximation scheme (FAS) solving the nonlinear systems, we propose a novel variational-model-informed network (denoted as FAS-Unet) that exploits the model and algorithm priors to extract the multi-scale features. The proposed model-informed network integrates image data and mathematical models, and implements them through learning a few convolution kernels. Based on the variational theory and FAS algorithm, we first design a feature extraction sub-network (FAS-Solution module) to solve the model-driven nonlinear systems, where a skip-connection is employed to fuse the multi-scale features. Secondly, we further design a convolution block to fuse the extracted features from the previous stage, resulting in the final segmentation possibility. Experimental results on three different medical image segmentation tasks show that the proposed FAS-Unet is very competitive with other state-of-the-art methods in qualitative, quantitative and model complexity evaluations. Moreover, it may also be possible to train specialized network architectures that automatically satisfy some of the mathematical and physical laws in other image problems for better accuracy, faster training and improved generalization.The code is available at \url{https://github.com/zhuhui100/FASUNet}.

cs.CV↗

arXiv2022

Propagation of singularities for gravity-capillary water waves

We obtain two results of propagation for solutions to the gravity-capillary water wave system. First we show how oscillations and the spatial decay propagate at infinity; then we show a microlocal smoothing effect under the non-trapping condition of the initial free surface. These results extends the works of Craig, Kappeler and Strauss, Wunsch and Nakamura to quasilinear dispersive equations. We also prove the existence of gravity-capillary water waves in weighted Sobolev spaces. Such solutions have asymptotically Euclidean free surfaces. To obtain these results, we generalize the paradifferential calculus of Bony to weighted Sobolev spaces and develop a semiclassical paradifferential calculus. We also introduce a new family of wavefront sets -- the quasi-homogeneous wavefront sets, which is a generalization, at least in the Euclidean geometry, the wavefront sets of Hörmander, the scattering wavefront sets of Melrose, the quadratic scattering wavefront sets of Wunsch and the homogeneous wavefront sets of Nakamura.

math.AP↗

arXiv2022

Distributed processing of continuous range queries over moving objects

Monitoring range queries over moving objects is essential to extensive location-based services. The challenge faced with these location-based services is having to process numerous concurrent range queries over a large volume of moving objects. However, the existing range query processing algorithms are almost centralized based on one single machine, which are hard to address the challenge due to the limited memory and computing resources. To address this issue, we propose a distributed search solution for processing concurrent range queries over moving objects in this work. Firstly, a Distributed Dynamic Index (DDI) that consists of a global grid index and local dynamic M-ary tree indexes was proposed to maintain the moving objects and support the search algorithm. Next, a Distributed Range Query Algorithm (DRQA) was designed based on DDI, which introduces an incremental search strategy to monitor the range queries as objects evolve; during the process, it further designs a computation sharing paradigm for processing multiple concurrent queries by making full use of their common computation to decrease the search cost. Finally, three object datasets with different distributions were simulated on a New York road network and three baseline methods were introduced to more sufficiently evaluate the performance of our proposal. Compared with state-of-the-art method, the initial query cost of the DRQA algorithm reduces by $22.7\%$ and the incremental query cost drops by 15.2%, which certifies the superiority of our method over existing approaches.

cs.DB↗