arXiv subjects

Dandan Li

Publications and source records attributed to Dandan Li.

At least 19 recordsLinked to original sources

arXiv2026

Long-time asymptotics and invariant manifold for the fractional 2D Navier-Stokes equation

We consider the two-dimensional incompressible Navier-Stokes equations with supercritical fractional dissipation in the vorticity formulation. In self-similar variables, we analyze the linearized operator in weighted spaces, prove a spectral gap, and construct a finite-dimensional local slow invariant manifold for small solutions. As a consequence, solutions are attracted to this manifold and admit an explicit long-time asymptotic expansion determined by the leading eigenmodes; additional moment conditions yield faster decay. We also show Lipschitz dependence of the manifold on the dissipation exponent, and recover the classical Navier-Stokes dynamics in the limit as the exponent approaches one.

math.AP↗

arXiv2025

Towards Generalist Intelligence in Dentistry: Vision Foundation Models for Oral and Maxillofacial Radiology

Oral and maxillofacial radiology plays a vital role in dental healthcare, but radiographic image interpretation is limited by a shortage of trained professionals. While AI approaches have shown promise, existing dental AI systems are restricted by their single-modality focus, task-specific design, and reliance on costly labeled data, hindering their generalization across diverse clinical scenarios. To address these challenges, we introduce DentVFM, the first family of vision foundation models (VFMs) designed for dentistry. DentVFM generates task-agnostic visual representations for a wide range of dental applications and uses self-supervised learning on DentVista, a large curated dental imaging dataset with approximately 1.6 million multi-modal radiographic images from various medical centers. DentVFM includes 2D and 3D variants based on the Vision Transformer (ViT) architecture. To address gaps in dental intelligence assessment and benchmarks, we introduce DentBench, a comprehensive benchmark covering eight dental subspecialties, more diseases, imaging modalities, and a wide geographical distribution. DentVFM shows impressive generalist intelligence, demonstrating robust generalization to diverse dental tasks, such as disease diagnosis, treatment analysis, biomarker identification, and anatomical landmark detection and segmentation. Experimental results indicate DentVFM significantly outperforms supervised, self-supervised, and weakly supervised baselines, offering superior generalization, label efficiency, and scalability. Additionally, DentVFM enables cross-modality diagnostics, providing more reliable results than experienced dentists in situations where conventional imaging is unavailable. DentVFM sets a new paradigm for dental AI, offering a scalable, adaptable, and label-efficient model to improve intelligent dental healthcare and address critical gaps in global oral healthcare.

cs.CV↗

arXiv2025

Quasibound states of massless spin particles in Schwarzschild equivalent mediums

We show that, in Schwarzschild equivalent mediums, the massless spin particles obey the same dynamical equation, from which we obtain remarkably simple formulae for the frequencies of the quasibound states. We find that the quasibound frequencies of different bosons can be identical at the same quantum number $l$, and the same is true of different fermions, but a quasibound frequency for bosons can never equal a quasibound frequency for fermions. These results mean that, in Schwarzschild equivalent mediums with the quasibound-state boundary conditions, characteristics of electromagnetic waves are the same as those for all the massless bosonic waves, thereby allowing electromagnetic waves to simulate gravitational waves. Our predictions can be tested in future experiments, building upon the successful preparation of Schwarzschild equivalent mediums.

gr-qc↗

arXiv2025

STORM-BORN: A Challenging Mathematical Derivations Dataset Curated via a Human-in-the-Loop Multi-Agent Framework

High-quality math datasets are crucial for advancing the reasoning abilities of large language models (LLMs). However, existing datasets often suffer from three key issues: outdated and insufficient challenging content, neglecting human-like reasoning, and limited reliability due to single-LLM generation. To address these, we introduce STORM-BORN, an ultra-challenging dataset of mathematical derivations sourced from cutting-edge academic papers, which includes dense human-like approximations and heuristic cues. To ensure the reliability and quality, we propose a novel human-in-the-loop, multi-agent data generation framework, integrating reasoning-dense filters, multi-agent collaboration, and human mathematicians' evaluations. We curated a set of 2,000 synthetic samples and deliberately selected the 100 most difficult problems. Even most advanced models like GPT-o1 solved fewer than 5% of them. Fine-tuning on STORM-BORN boosts accuracy by 7.84% (LLaMA3-8B) and 9.12% (Qwen2.5-7B). As AI approaches mathematician-level reasoning, STORM-BORN provides both a high-difficulty benchmark and a human-like reasoning training resource. Our code and dataset are publicly available at https://github.com/lwhere/STORM-BORN.

cs.CL↗

arXiv2025

TANGO: A Robust Qubit Mapping Algorithm via Two-Stage Search and Bidirectional Look

Current quantum devices typically lack full qubit connectivity, making it difficult to directly execute logical circuits on quantum devices. This limitation necessitates quantum circuit mapping algorithms to insert SWAP gates, dynamically remapping logical qubits to physical qubits and transforming logical circuits into physical circuits that comply with device connectivity constraints. However, the insertion of SWAP gates increases both the gate count and circuit depth, ultimately reducing the fidelity of quantum algorithms. To achieve a balanced optimization of these two objectives, we propose the TANGO algorithm. By incorporating a layer-weight allocation strategy, the algorithm first formulates an evaluation function that balances the impact of qubit mapping on both mapped and unmapped nodes, thereby enhancing the quality of the initial mapping. Next, we design an innovative two-stage routing algorithm that prioritizes the number of executable gates as the primary evaluation metric while also considering quantum gate distance, circuit depth, and a novel bidirectional-look SWAP strategy, which optimizes SWAP gate selection in conjunction with preceding gates, improving the effectiveness of the mapping algorithm. Finally, by integrating advanced quantum gate optimization techniques, the algorithm's overall performance is further enhanced. Experimental results demonstrate that, compared to state-of-the-art methods, the proposed algorithm achieves multi-objective co-optimization of gate count and circuit depth across various benchmarks and quantum devices, exhibiting significant performance advantages.

quant-ph↗

arXiv2025

UnPuzzle: A Unified Framework for Pathology Image Analysis

Pathology image analysis plays a pivotal role in medical diagnosis, with deep learning techniques significantly advancing diagnostic accuracy and research. While numerous studies have been conducted to address specific pathological tasks, the lack of standardization in pre-processing methods and model/database architectures complicates fair comparisons across different approaches. This highlights the need for a unified pipeline and comprehensive benchmarks to enable consistent evaluation and accelerate research progress. In this paper, we present UnPuzzle, a novel and unified framework for pathological AI research that covers a broad range of pathology tasks with benchmark results. From high-level to low-level, upstream to downstream tasks, UnPuzzle offers a modular pipeline that encompasses data pre-processing, model composition,taskconfiguration,andexperimentconduction.Specifically, it facilitates efficient benchmarking for both Whole Slide Images (WSIs) and Region of Interest (ROI) tasks. Moreover, the framework supports variouslearningparadigms,includingself-supervisedlearning,multi-task learning,andmulti-modallearning,enablingcomprehensivedevelopment of pathology AI models. Through extensive benchmarking across multiple datasets, we demonstrate the effectiveness of UnPuzzle in streamlining pathology AI research and promoting reproducibility. We envision UnPuzzle as a cornerstone for future advancements in pathology AI, providing a more accessible, transparent, and standardized approach to model evaluation. The UnPuzzle repository is publicly available at https://github.com/Puzzle-AI/UnPuzzle.

eess.IV↗

arXiv2025

An Efficient Iterative Algorithm for Qubit Mapping via Layer-Weight Assignment and Search Space Reduction

Current quantum devices support interactions only between physically adjacent qubits, preventing quantum circuits from being directly executed on these devices. Therefore, SWAP gates are required to remap logical qubits to physical qubits, which in turn increases both quantum resource consumption and error rates. To minimize the insertion of additional SWAP gates, we propose HAIL, an efficient iterative qubit mapping algorithm. Leveraging the inherent parallelism in quantum circuits, a new layer-weight assignment method is integrated with subgraph isomorphism to derive an optimal initial qubit mapping. Moreover, we present a two-stage SWAP sequence search algorithm that effectively identifies the most efficient SWAP sequence by distilling feasible SWAP sequences at different stages. The whole qubit mapping algorithm is then refined through a few iterative bidirectional traversals, further reducing the number of SWAP gates required. Experimental results on the IBM Q20 architecture and various benchmarks show that HAIL-3 reduces the number of additional gates inserted in the $\mathcal{B}_{23}$ by 20.62\% compared to state-of-the-art algorithms. Moreover, we propose a partially extended SWAP sequence strategy combined with HAIL to reduce its time complexity, with experiments on the sparsely connected Google Sycamore architecture demonstrating reductions in both algorithm runtime and additional SWAP gates.

quant-ph↗

arXiv2024

Communication-Efficient Federated Learning with Adaptive Compression under Dynamic Bandwidth

Federated learning can train models without directly providing local data to the server. However, the frequent updating of the local model brings the problem of large communication overhead. Recently, scholars have achieved the communication efficiency of federated learning mainly by model compression. But they ignore two problems: 1) network state of each client changes dynamically; 2) network state among clients is not the same. The clients with poor bandwidth update local model slowly, which leads to low efficiency. To address this challenge, we propose a communication-efficient federated learning algorithm with adaptive compression under dynamic bandwidth (called AdapComFL). Concretely, each client performs bandwidth awareness and bandwidth prediction. Then, each client adaptively compresses its local model via the improved sketch mechanism based on his predicted bandwidth. Further, the server aggregates sketched models with different sizes received. To verify the effectiveness of the proposed method, the experiments are based on real bandwidth data which are collected from the network topology we build, and benchmark datasets which are obtained from open repositories. We show the performance of AdapComFL algorithm, and compare it with existing algorithms. The experimental results show that our AdapComFL achieves more efficient communication as well as competitive accuracy compared to existing algorithms.

cs.LG↗

arXiv2023

A Quantum Federated Learning Framework for Classical Clients

Quantum Federated Learning (QFL) enables collaborative training of a Quantum Machine Learning (QML) model among multiple clients possessing quantum computing capabilities, without the need to share their respective local data. However, the limited availability of quantum computing resources poses a challenge for each client to acquire quantum computing capabilities. This raises a natural question: Can quantum computing capabilities be deployed on the server instead? In this paper, we propose a QFL framework specifically designed for classical clients, referred to as CC-QFL, in response to this question. In each iteration, the collaborative training of the QML model is assisted by the shadow tomography technique, eliminating the need for quantum computing capabilities of clients. Specifically, the server constructs a classical representation of the QML model and transmits it to the clients. The clients encode their local data onto observables and use this classical representation to calculate local gradients. These local gradients are then utilized to update the parameters of the QML model. We evaluate the effectiveness of our framework through extensive numerical simulations using handwritten digit images from the MNIST dataset. Our framework provides valuable insights into QFL, particularly in scenarios where quantum computing resources are scarce.

quant-ph↗

arXiv2023

Physics-informed dynamic mode decomposition for short-term and long-term prediction of gas-solid flows

Integration of physics principles with data-driven methods has attracted great attention in recent few years. In this study, a physics-informed dynamic mode decomposition (piDMD) method, where the mass conservation law is integrated with a purely data-driven DMD method, is developed for fast prediction of the spatiotemporal dynamics of solid volume fraction distribution in bubbling fluidized beds. Assessment of the prediction ability using both piDMD and DMD is performed using the CFD-DEM results as the benchmark: Both DMD and piDMD can predict the short-term behaviour of solid volume fraction reasonably well, but piDMD outperforms the DMD in both qualitative and quantitative comparisons; With respect to their long-term ability, the piDMD-based prediction of the instantaneous solid volume fraction distributions is qualitatively correct although the accuracy needs to be improved, and the predicted time-averaged radial and axial profiles are satisfactory; Whereas the DMD-based prediction of instantaneous snapshots and time-averaged results is completely nonphysical. Present study provides a fast and relatively accurate method for predicting the hydrodynamics of gas-solid flows.

physics.flu-dyn↗

arXiv2022

FedGraph: an Aggregation Method from Graph Perspective

With the increasingly strengthened data privacy act and the difficult data centralization, Federated Learning (FL) has become an effective solution to collaboratively train the model while preserving each client's privacy. FedAvg is a standard aggregation algorithm that makes the proportion of dataset size of each client as aggregation weight. However, it can't deal with non-independent and identically distributed (non-i.i.d) data well because of its fixed aggregation weights and the neglect of data distribution. In this paper, we propose an aggregation strategy that can effectively deal with non-i.i.d dataset, namely FedGraph, which can adjust the aggregation weights adaptively according to the training condition of local models in whole training process. The FedGraph takes three factors into account from coarse to fine: the proportion of each local dataset size, the topology factor of model graphs, and the model weights. We calculate the gravitational force between local models by transforming the local models into topology graphs. The FedGraph can explore the internal correlation between local models better through the weighted combination of the proportion each local dataset, topology structure, and model weights. The proposed FedGraph has been applied to the MICCAI Federated Tumor Segmentation Challenge 2021 (FeTS) datasets, and the validation results show that our method surpasses the previous state-of-the-art by 2.76 mean Dice Similarity Score. The source code will be available at Github.

cs.CV↗

arXiv2021

MISSFormer: An Effective Medical Image Segmentation Transformer

The CNN-based methods have achieved impressive results in medical image segmentation, but they failed to capture the long-range dependencies due to the inherent locality of the convolution operation. Transformer-based methods are recently popular in vision tasks because of their capacity for long-range dependencies and promising performance. However, it lacks in modeling local context. In this paper, taking medical image segmentation as an example, we present MISSFormer, an effective and powerful Medical Image Segmentation tranSFormer. MISSFormer is a hierarchical encoder-decoder network with two appealing designs: 1) A feed-forward network is redesigned with the proposed Enhanced Transformer Block, which enhances the long-range dependencies and supplements the local context, making the feature more discriminative. 2) We proposed Enhanced Transformer Context Bridge, different from previous methods of modeling only global information, the proposed context bridge with the enhanced transformer block extracts the long-range dependencies and local context of multi-scale features generated by our hierarchical transformer encoder. Driven by these two designs, the MISSFormer shows a solid capacity to capture more discriminative dependencies and context in medical image segmentation. The experiments on multi-organ and cardiac segmentation tasks demonstrate the superiority, effectiveness and robustness of our MISSFormer, the experimental results of MISSFormer trained from scratch even outperform state-of-the-art methods pre-trained on ImageNet. The core designs can be generalized to other visual segmentation tasks. The code has been released on Github: https://github.com/ZhifangDeng/MISSFormer

cs.CV↗

arXiv2021

Federated Route Leak Detection in Inter-domain Routing with Privacy Guarantee

In the inter-domain network, a route leak occurs when a routing announcement is propagated outside of its intended scope, which is a violation of the agreed routing policy. The route leaks can disrupt the internet traffic and cause large outages. The accurately detection of route leaks requires the share of AS business relationship information of ASes. However, the business relationship information between ASes is confidential due to economic issues. Thus, ASes are usually unwilling to revealing this information to the other ASes, especially their competitors. Recent advancements in federated learning make it possible to share data while maintaining privacy. Motivated by this, in this paper we study the route leak problem by considering the privacy of business relationships between ASes, and propose a method for route leak detection with privacy guarantee by using blockchain-based federated learning framework, in which ASes can train a global detection model without revealing their business relationships directly. Moreover, the proposed method provides a self-validation scheme by labeling AS triples with local routing policies, which mitigates route leaks' lack of ground truth. We evaluate the proposed method under a variety of datasets including unbalanced and balanced datasets. The different deployment strategies of the proposed method under different topologies are also examined. The results show that the proposed method has a better performance in detecting route leaks than a single AS detection regardless of whether using balanced or unbalanced datasets. In the analysis of the deployment, the results show that ASes with more peers have more possible route leaks and can contribute more on the detection of route leaks with the proposed method.

cs.NI↗

arXiv2021

Bohmian Trajectories of the Time-oscillating Schr\"odinger Equations

Bohmian mechanics is a non-relativistic quantum theory based on a particle approach. In this paper we study the Schr\"odinger equation with rapidly oscillating potential and the associated Bohmian trajectory. We prove that the corresponding Bohmian trajectory converges locally in measure, and the limit coincides with the Bohmian trajectory for the effective Schr\"{o}dinger equation on a finite time interval. This is beneficial for the efficient simulation of the Bohmian trajectories in oscillating potential fields.

math-ph↗

arXiv2020

Soft-Root-Sign Activation Function

The choice of activation function in deep networks has a significant effect on the training dynamics and task performance. At present, the most effective and widely-used activation function is ReLU. However, because of the non-zero mean, negative missing and unbounded output, ReLU is at a potential disadvantage during optimization. To this end, we introduce a novel activation function to manage to overcome the above three challenges. The proposed nonlinearity, namely "Soft-Root-Sign" (SRS), is smooth, non-monotonic, and bounded. Notably, the bounded property of SRS distinguishes itself from most state-of-the-art activation functions. In contrast to ReLU, SRS can adaptively adjust the output by a pair of independent trainable parameters to capture negative information and provide zero-mean property, which leading not only to better generalization performance, but also to faster learning speed. It also avoids and rectifies the output distribution to be scattered in the non-negative real number space, making it more compatible with batch normalization (BN) and less sensitive to initialization. In experiments, we evaluated SRS on deep networks applied to a variety of tasks, including image classification, machine translation and generative modelling. Our SRS matches or exceeds models with ReLU and other state-of-the-art nonlinearities, showing that the proposed activation function is generalized and can achieve high performance across tasks. Ablation study further verified the compatibility with BN and self-adaptability for different initialization.

cs.CV↗

arXiv2019

Pullback Attractors for a Critical Degenerate Wave Equation with Time-dependent Damping

The aim of this paper is to analyze the long-time dynamical behavior of the solution for a degenerate wave equation with time-dependent damping term $\partial_{tt}u + β(t)\partial_tu = \mathcal{L}u(x,t) + f(u)$ on a bounded domain $Ω\subset\mathbb{R}^N$ with Dirichlet boundary conditions. Under some restrictions on $β(t)$ and critical growth restrictions on the nonlinear term $f$, we will prove the local and global well-posedness of the solution and derive the existence of a pullback attractor for the process associated with the degenerate damped hyperbolic problem.

math.DS↗

arXiv2019

Comb Convolution for Efficient Convolutional Architecture

Convolutional neural networks (CNNs) are inherently suffering from massively redundant computation (FLOPs) due to the dense connection pattern between feature maps and convolution kernels. Recent research has investigated the sparse relationship between channels, however, they ignored the spatial relationship within a channel. In this paper, we present a novel convolutional operator, namely comb convolution, to exploit the intra-channel sparse relationship among neurons. The proposed convolutional operator eliminates nearly 50% of connections by inserting uniform mappings into standard convolutions and removing about half of spatial connections in convolutional layer. Notably, our work is orthogonal and complementary to existing methods that reduce channel-wise redundancy. Thus, it has great potential to further increase efficiency through integrating the comb convolution to existing architectures. Experimental results demonstrate that by simply replacing standard convolutions with comb convolutions on state-of-the-art CNN architectures (e.g., VGGNets, Xception and SE-Net), we can achieve 50% FLOPs reduction while still maintaining the accuracy.

cs.CV↗

arXiv2019

Deterministic and random attractors for a wave equation with sign changing damping

The paper gives a detailed study of long-time dynamics generated by weakly damped wave equations in bounded 3D domains where the damping exponent depends explicitly on time and may change sign. It is shown that in the case when the non-linearity is superlinear, the considered equation remains dissipative if the weighted mean value of the dissipation rate remains positive and that the conditions of this type are not sufficient in the linear case. Two principally different cases are considered. In the case when this mean is uniform (which corresponds to deterministic dissipation rates), it is shown that the considered system possesses smooth uniform attractors as well as non-autonomous exponential attractors. In the case where the mean is not uniform (which corresponds to the random dissipation rate, for instance, when this dissipation rate is generated by the Bernoulli process), the tempered random attractor is constructed. In contrast to the usual situation, this random attractor is expected to have infinite Hausdorff and fractal dimension. The simplified model example which demonstrates infinite-dimensionality of the random attractor is also presented.

math.AP↗