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Zijin Li

Publications and source records attributed to Zijin Li.

At least 19 recordsLinked to original sources

A wall-law approximation for Jeffery-Hamel flows in rough wedges

We study the two-dimensional stationary Navier-Stokes equations in an unbounded wedge with small rough perturbations of its angular boundaries. The Jeffery-Hamel flow in the corresponding straight wedge is taken as the effective background flow. Under a suitable small-flux condition, we prove the existence of weak solutions and establish an $H^1$-type energy error estimate of order $O(\epsilon^2)$. For sufficiently small wedge angles, we further derive weighted estimates and improve the squared $L^2$-error to $O(\epsilon^3)$.

math.AP

UniVerse: Benchmarking and Enhancing LALMs on Culturally Inclusive Low-Resource Music Understanding

Recent advances in large audio-language models (LALMs) have significantly improved performance in tasks such as music captioning, genre classification, and sound event detection. However, limited attention has been paid to improving their adaptability across diverse musical traditions, particularly folk music rooted in distinct cultural contexts. Folk-music traditions are typically resource-scarce, unevenly represented across regions, and poorly documented. Even when such samples appear in large-scale pre-training, LALMs often fail to capture their structural and stylistic characteristics, partly due to the absence of dedicated evaluation protocols and training solutions. To address these limitations, we introduce UniVerse, a reproducible solution for low-resource music understanding. Specifically, we propose UniVerseBench, a benchmark of 5,042 Q&A pairs across more than 38 cultural and linguistic entities, constructed via an expert-guided yet highly automated pipeline. In parallel, we construct a fully automated, model-generated multi-turn dialogue training dataset UniVerseSet. By training LALMs on UniVerseSet, we systematically adapt and investigate representative multimodal imbalance learning strategies across both dense and Mixture-of-Experts (MoE) architectures. Experimental results indicate that fully automated data curation combined with imbalance-aware training yields non-trivial improvements, but models still struggle to capture fine-grained acoustic features, indicating a gap between surface-level alignment and deep musical comprehension.

cs.SD

On the axisymmetric Navier-Stokes flow passing a cone with the total-slip boundary condition

(A) It is known that among the currently unresolved cases of the axially symmetric Navier-Stokes equations (ASNS), the most relatively tractable one is where the fluid passes the exterior of a cone. In this paper, we investigate this case with Navier total-slip boundary condition. We show that there exists an absolute constant $C_* > 0$ such that if \[ \sup_{x\in D}r|v_{0,\theta}|\leq C_* \quad\text{and}\quad \int_{D} r v_{0,\theta}(x) \mathrm{d} x = 0, \] then there exists a unique global bounded strong solution with finite energy. Note that, for the initial velocity, there is neither a size restriction on other components, nor a parity assumption. There are four key ingredients in the proof. (1) Three new good unknowns are introduced, and a self-closed energy estimate for them is derived. (2) An elliptic estimate for pressure is established to control boundary terms arising from the boundary condition. (3) A De Giorgi iteration scheme is applied to establish the boundedness of $rv_\theta$. (4) A new anisotropic Hardy's inequality is derived for weighted mean-zero functions to overcome the lack of parity of $\boldsymbol{v}$. (B) Based on (A), we introduce and prove the so-called controlled regularity for the above problem, i.e. for suitable initial data without any smallness assumption, there exists an external force supported away from the axis of symmetry such that the corresponding problem admits a global strong solution. This seems to add a little weight to the regularity scenario for ASNS, since the force is supported away from the axis which is the only place regularity may break down. We also prove that if there exists a solution that blows up in finite time, an unstable blow-up solution must exist.

math.AP

The Renaissance of Expert Systems: Optical Recognition of Printed Chinese Jianpu Musical Scores with Lyrics

Large-scale optical music recognition (OMR) research has focused mainly on Western staff notation, leaving Chinese Jianpu (numbered notation) and its rich lyric resources underexplored. We present a modular expert-system pipeline that converts printed Jianpu scores with lyrics into machine-readable MusicXML and MIDI, without requiring massive annotated training data. Our approach adopts a top-down expert-system design, leveraging traditional computer-vision techniques (e.g., phrase correlation, skeleton analysis) to capitalize on prior knowledge, while integrating unsupervised deep-learning modules for image feature embeddings. This hybrid strategy strikes a balance between interpretability and accuracy. Evaluated on The Anthology of Chinese Folk Songs, our system massively digitizes (i) a melody-only collection of more than 5,000 songs (> 300,000 notes) and (ii) a curated subset with lyrics comprising over 1,400 songs (> 100,000 notes). The system achieves high-precision recognition on both melody (note-wise F1 = 0.951) and aligned lyrics (character-wise F1 = 0.931).

cs.CV

An Interpretable Multi-Plane Fusion Framework With Kolmogorov-Arnold Network Guided Attention Enhancement for Alzheimer's Disease Diagnosis

Alzheimer's disease (AD) is a progressive neurodegenerative disorder that severely impairs cognitive function and quality of life. Timely intervention in AD relies heavily on early and precise diagnosis, which remains challenging due to the complex and subtle structural changes in the brain. Most existing deep learning methods focus only on a single plane of structural magnetic resonance imaging (sMRI) and struggle to accurately capture the complex and nonlinear relationships among pathological regions of the brain, thus limiting their ability to precisely identify atrophic features. To overcome these limitations, we propose an innovative framework, MPF-KANSC, which integrates multi-plane fusion (MPF) for combining features from the coronal, sagittal, and axial planes, and a Kolmogorov-Arnold Network-guided spatial-channel attention mechanism (KANSC) to more effectively learn and represent sMRI atrophy features. Specifically, the proposed model enables parallel feature extraction from multiple anatomical planes, thus capturing more comprehensive structural information. The KANSC attention mechanism further leverages a more flexible and accurate nonlinear function approximation technique, facilitating precise identification and localization of disease-related abnormalities. Experiments on the ADNI dataset confirm that the proposed MPF-KANSC achieves superior performance in AD diagnosis. Moreover, our findings provide new evidence of right-lateralized asymmetry in subcortical structural changes during AD progression, highlighting the model's promising interpretability.

cs.CV

SFNet: A Spatial-Frequency Domain Deep Learning Network for Efficient Alzheimer's Disease Diagnosis

Alzheimer's disease (AD) is a progressive neurodegenerative disorder that predominantly affects the elderly population and currently has no cure. Magnetic Resonance Imaging (MRI), as a non-invasive imaging technique, is essential for the early diagnosis of AD. MRI inherently contains both spatial and frequency information, as raw signals are acquired in the frequency domain and reconstructed into spatial images via the Fourier transform. However, most existing AD diagnostic models extract features from a single domain, limiting their capacity to fully capture the complex neuroimaging characteristics of the disease. While some studies have combined spatial and frequency information, they are mostly confined to 2D MRI, leaving the potential of dual-domain analysis in 3D MRI unexplored. To overcome this limitation, we propose Spatio-Frequency Network (SFNet), the first end-to-end deep learning framework that simultaneously leverages spatial and frequency domain information to enhance 3D MRI-based AD diagnosis. SFNet integrates an enhanced dense convolutional network to extract local spatial features and a global frequency module to capture global frequency-domain representations. Additionally, a novel multi-scale attention module is proposed to further refine spatial feature extraction. Experiments on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset demonstrate that SFNet outperforms existing baselines and reduces computational overhead in classifying cognitively normal (CN) and AD, achieving an accuracy of 95.1%.

eess.IV

A Gradient-based Causal Discovery Framework with Applications to Complex Industrial Processes

With the advancement of deep learning technologies, various neural network-based Granger causality models have been proposed. Although these models have demonstrated notable improvements, several limitations remain. Most existing approaches adopt the component-wise architecture, necessitating the construction of a separate model for each time series, which results in substantial computational costs. In addition, imposing the sparsity-inducing penalty on the first-layer weights of the neural network to extract causal relationships weakens the model's ability to capture complex interactions. To address these limitations, we propose Gradient Regularization-based Neural Granger Causality (GRNGC), which requires only one time series prediction model and applies $L_{1}$ regularization to the gradient between model's input and output to infer Granger causality. Moreover, GRNGC is not tied to a specific time series forecasting model and can be implemented with diverse architectures such as KAN, MLP, and LSTM, offering enhanced flexibility. Numerical simulations on DREAM, Lorenz-96, fMRI BOLD, and CausalTime show that GRNGC outperforms existing baselines and significantly reduces computational overhead. Meanwhile, experiments on real-world DNA, Yeast, HeLa, and bladder urothelial carcinoma datasets further validate the model's effectiveness in reconstructing gene regulatory networks.

cs.LG

Existence and non-uniqueness of classical solutions to the axially symmetric stationary Navier-Stokes equations in an exterior cylinder

In this paper, we show existence and non-uniqueness on the axially symmetric stationary Navier-Stokes equations in an exterior periodic cylinder. On the boundary of the cylinder, the horizontally swirl velocity is subject to the perturbation of a rotation, the horizontally radial velocity is subject to the perturbation of an interior sink, while the vertical velocity is the perturbation of zero. At infinity, the flow stays at rest. We construct a solution to such problem, whose principal part admits a critical decay for the horizontal components and a supercritical decay for the vertical component of the velocity. This existence result is related to the 2D Stokes paradox and an open problem raised by V. I. Yudovich in [Eleven great problems of mathematical hydrodynamics, Mosc. Math. J. 3 (2003), no. 2, 711--737], where Problem 2 states that: Show (spatially) global existence theorems for stationary and periodic flows. Moreover, if the horizontally radial-sink velocity is relatively large ($\nu<-2$ in our setting), then the solution to this problem is non-unique.

math.AP

Kolmogorov-Arnold Networks for Time Series Granger Causality Inference

We propose the Granger causality inference Kolmogorov-Arnold Networks (KANGCI), a novel architecture that extends the recently proposed Kolmogorov-Arnold Networks (KAN) to the domain of causal inference. By extracting base weights from KAN layers and incorporating the sparsity-inducing penalty and ridge regularization, KANGCI effectively infers the Granger causality from time series. Additionally, we propose an algorithm based on time-reversed Granger causality that automatically selects causal relationships with better inference performance from the original or time-reversed time series or integrates the results to mitigate spurious connectivities. Comprehensive experiments conducted on Lorenz-96, Gene regulatory networks, fMRI BOLD signals, VAR, and real-world EEG datasets demonstrate that the proposed model achieves competitive performance to state-of-the-art methods in inferring Granger causality from nonlinear, high-dimensional, and limited-sample time series.

cs.LG

Existence of the planar stationary flow in the presence of interior sources and sinks in an exterior domain

In the paper, we consider the solvability of the two-dimensional Navier-Stokes equations in an exterior unit disk. On the boundary of the disk, the tangential velocity is subject to the perturbation of a rotation, and the normal velocity is subject to the perturbation of an interior sources or sinks. At infinity, the flow stays at rest. We will construct a solution to such problem, whose principal part admits a critical decay $O(|x|^{-1})$. The result is related to an open problem raised by V. I. Yudovich in [{\it Eleven great problems of mathematical hydrodynamics}, Mosc. Math. J. 3 (2003), no. 2, 711--737], where Problem 2b states that: {\em Prove or disprove the global existence of stationary and periodic flows of a viscous incompressible fluid in the presence of interior sources and sinks.} Our result partially gives a positive answer to this open in the exterior disk for the case when the interior source or sink is a perturbation of the constant state.

math.AP

Acoustic Characterization of the Resonator in the Chinese Transverse Flute (dizi)

The dizi is a traditional Chinese transverse flute and is most distinguished from the western flute by the presence of a hole covered by a wrinkled membrane. In this study, we analyze the linear acoustical behavior of the dizi resonator through a detailed acoustical model that incorporates drilled toneholes, back end-holes, membrane hole, and upstream embouchure hole. The input admittance of the dizi is measured and modeled using the Transfer Matrix Method (TMM) and Transfer Matrix Method with external Interactions (TMMI). In comparison to measurements, the TMMI is shown to more accurately model the dizi than the TMM when compared to measurements. Our analysis reveals that attaching the membrane shifts admittance peaks to lower frequencies, reduces their magnitude, and influences tuning and harmonicity for different peaks and fingerings. The study further shows that the upstream branch, which includes the embouchure hole, complicates the evaluation of the tonehole lattice cutoff frequency, suggesting that it may not need to be considered for flute instruments. Cutoff frequencies exhibit distinct groupings across fingerings, influenced by the different tonehole lattices in the dizi: finger-hole lattice and end-hole lattice.

physics.app-ph

A refined uniqueness result of Leray's problem in an infinite-long pipe with the Navier-slip boundary

We consider the generalized Leray's problem with the Navier-slip boundary condition in an infinite pipe $\mathcal{D}=Σ\times\mathbb{R}$. We show that if the flux $Φ$ of the solution is no larger than a critical value that is \emph{independent with the friction ratio} of the Navier-slip boundary condition, the solution to the problem must be the parallel Poiseuille flow with the given flux. Compared with known related 3D results, this seems to be the first conclusion with the size of critical flux being uniform with the friction ratio $α\in]0,\infty]$, and it is surprising since the prescribed uniqueness breaks down immediately when $α=0$, even if $Φ=0$. Our proof relies primarily on a refined gradient estimate of the Poiseuille flow with the Navier-slip boundary condition. Additionally, we prove the critical flux $Φ_0\geq\fracπ{16}$ provided that $Σ$ is a unit disk.

math.AP

Reducing Barriers to the Use of Marginalised Music Genres in AI

AI systems for high quality music generation typically rely on extremely large musical datasets to train the AI models. This creates barriers to generating music beyond the genres represented in dominant datasets such as Western Classical music or pop music. We undertook a 4 month international research project summarised in this paper to explore the eXplainable AI (XAI) challenges and opportunities associated with reducing barriers to using marginalised genres of music with AI models. XAI opportunities identified included topics of improving transparency and control of AI models, explaining the ethics and bias of AI models, fine tuning large models with small datasets to reduce bias, and explaining style-transfer opportunities with AI models. Participants in the research emphasised that whilst it is hard to work with small datasets such as marginalised music and AI, such approaches strengthen cultural representation of underrepresented cultures and contribute to addressing issues of bias of deep learning models. We are now building on this project to bring together a global International Responsible AI Music community and invite people to join our network.

cs.SD

On local well-posedness of 3D ideal Hall-MHD system with an azimuthal magnetic field

In this paper, we study the local well-posedness of classical solutions to the ideal Hall-MHD equations whose magnetic field is supposed to be azimuthal in the $L^2$-based Sobolev spaces. By introducing a good unknown coupling with the original unknowns, we overcome difficulties arising from the lack of magnetic resistance, and establish a self-closed $H^m$ with $(3\leq m\in\mathbb{N})$ local energy estimate of the system. Here, a key cancellation related to $\theta$ derivatives is discovered. In order to apply this cancellation, part of the high-order energy estimates is performed in the cylindrical coordinate system, even though our solution is not assumed to be axially symmetric. During the proof, high-order derivative tensors of unknowns in the cylindrical coordinates system are carefully calculated, which would be useful in further researches on related topics.

math.AP

A Holistic Evaluation of Piano Sound Quality

This paper aims to develop a holistic evaluation method for piano sound quality to assist in purchasing decisions. Unlike previous studies that focused on the effect of piano performance techniques on sound quality, this study evaluates the inherent sound quality of different pianos. To derive quality evaluation systems, the study uses subjective questionnaires based on a piano sound quality dataset. The method selects the optimal piano classification models by comparing the fine-tuning results of different pre-training models of Convolutional Neural Networks (CNN). To improve the interpretability of the models, the study applies Equivalent Rectangular Bandwidth (ERB) analysis. The results reveal that musically trained individuals are better able to distinguish between the sound quality differences of different pianos. The best fine-tuned CNN pre-trained backbone achieves a high accuracy of 98.3% as the piano classifier. However, the dataset is limited, and the audio is sliced to increase its quantity, resulting in a lack of diversity and balance, so we use focal loss to reduce the impact of data imbalance. To optimize the method, the dataset will be expanded, or few-shot learning techniques will be employed in future research.

cs.SD

A refined long time asymptotic bound for 3D axially symmetric Boussinesq system with zero thermal diffusivity

In this paper, we obtain a refined temporal asymptotic upper bound of the global axially symmetric solution to the Boussinesq system with no thermal diffusivity. We show the spacial $W^{1,p}$-Sobolev ($2\leq p<\infty$) norm of the velocity can only grow at most algebraically as $t\to+\infty$. Under a signed potential condition imposed on the initial data, we further derive that the aforementioned norm is uniformly bounded at all times. Higher order estimates are also given: We find the $H^1$ norm of the temperature fluctuation grows sub-exponentially as $t\to+\infty$. Meanwhile, for any $m\geq 1$, we deduce that the $H^m$-temporal growth of the solution is slower than a double exponential function. As a result, these improve the results in \cite{HR:2010AIHP} where the authors only provided rough temporal asymptotic upper bounds while proving the global well-posedness.

math.AP