论文检索

Tianwen Zhu, Guangyu Wu, Zhiwei Cao, Ruihang Wang, Jimin Jia, Yong Luo, Yonggang Wen

Existing battery State of Health (SOH) prediction approaches often struggle to provide both accurate predictions and reliable uncertainty estimates. This paper presents a novel Multi-Task Learning (MTL) framework that jointly tackles SOH prediction and provides a proxy metric for uncertainty through a unified architecture. The framework combines a Physics-Informed Neural Network (PINN) for SOH prediction with a deep autoencoding Gaussian mixture model for uncertainty modeling. Particularly, the energy score from the Gaussian mixture model serves as a proxy metric for uncertainty, where a higher score indicates potential prediction unreliability. Moreover, to enhance task-specific learning, we employ a multi-head attention mechanism that adaptively captures distinct feature relationships. Our experiments show improvements in prediction performance compared to the state-of-the-art baseline. A comprehensive evaluation on six XJTU battery benchmark datasets demonstrates that our framework achieves a prediction accuracy of 99.50% (MAPE: 0.0050) while providing reliable uncertainty quantification through the proxy metric.

Mingming Zhu, Jiahua Rao, Xiaoyu Chen, Qianmu Yuan, Yuedong Yang

Protein design is revolutionizing biotechnology, yet existing approaches struggle to balance structural foldability with functional performance. Structure-based models excel at generating stable protein backbones but often overlook critical functional properties, while protein language models capture evolutionary and functional signals but frequently predict sequences lacking structural stability. Integrating these complementary approaches remains challenging due to their inherently conflicting objectives. We present MAProt, a multi-agent framework that synergistically combines structure-based and protein language model-based methods for protein design. Each agent specializes in a distinct aspect of the design objective: the structure-based agent (e.g., ProteinMPNN) ensures compatibility with the target backbone, while protein language model-based agents (e.g., ESM, SaProt) capture evolutionary plausibility and functional potential. To reconcile conflicts and achieve optimal trade-offs, we introduce a Pareto-based negotiation module that enables effective multi-objective coordination and consensus among agents. Extensive experiments on benchmark datasets demonstrate that MAProt achieves a remarkable improvement over state-of-the-art baselines, and generalizes robustly across a range of tasks, including thermodynamic folding stability design, functional protein design, and high-affinity antibody design. These results highlight the power of collaborative optimization for advancing rational protein engineering.

Jiang Zhu, Yulin Jin, Qingqing Ye, Zhibiao Guo, Kun Fang, Ruochen Du, Yingnan Zhao, Haibo Hu

Contrastive learning (CL) is a popular learning paradigm that excels in extracting meaningful representations from unlabeled data. Recent studies have shown that CL is highly vulnerable to backdoor attacks. Current defenses against backdoor attacks in CL are primarily reactive and post-training. That is, the detection and elimination of backdoors are executed in the deployment phase of a given well-trained model. However, these post-training defenses are usually prone to degrading model utility and resource-intensive, causing that the backdoor detection and elimination from a fully-trained model is quite challenging. To address this issue, we argue for a fundamental perspective, i.e., integrating the defense into the model's training phase, and propose a novel framework to mitigate the backdoor in CL, namely Density-Based Identification and Fine-Tuning (DIFT). Specifically, DIFT identifies potential poisoned samples during the early training phase via detecting embeddings with abnormal poisoning characteristic in the feature space. Then, to remove backdoors and preserve model utility, the detected poisoned samples are leveraged to fine-tune the model, and the remaining clean samples are further involved into training the model after the fine-tuning. DIFT, as a proactive training-time defense, avoids the problematic backdoor removal and the high computational cost associated with those reactive post-training methods. We empirically evaluate DIFT on various CL algorithms against backdoor attack. Experimental results demonstrate that our method exhibits promising defense effectiveness while maintaining model's clean data accuracy.

Jiajie Zhu, Xia Du, Xiaoyuan Liu, Ji-Zhe Zhou, Qizhen Xu, Zheng Lin, Chi-Man Pun

The rapid advancements in artificial intelligence have significantly accelerated the adoption of speech recognition technology, leading to its widespread integration across various applications. However, this surge in usage also highlights a critical issue: audio data is highly vulnerable to unauthorized exposure and analysis, posing significant privacy risks for businesses and individuals. This paper introduces an Information-Obfuscation Reversible Adversarial Example (IO-RAE) framework, the pioneering method designed to safeguard audio privacy using reversible adversarial examples. IO-RAE leverages large language models to generate misleading yet contextually coherent content, effectively preventing unauthorized eavesdropping by humans and Automatic Speech Recognition (ASR) systems. Additionally, we propose the Cumulative Signal Attack technique, which mitigates high-frequency noise and enhances attack efficacy by targeting low-frequency signals. Our approach ensures the protection of audio data without degrading its quality or usability. Experimental evaluations demonstrate the superiority of our method, achieving a targeted misguidance rate of 96.5% and a remarkable 100% untargeted misguidance rate in obfuscating target keywords across multiple ASR models, including a commercial black-box system from Google. Furthermore, the quality of the recovered audio, measured by the Perceptual Evaluation of Speech Quality score, reached 4.45, comparable to high-quality original recordings. Notably, the recovered audio processed by ASR systems exhibited an error rate of 0%, indicating nearly lossless recovery. These results highlight the practical applicability and effectiveness of our IO-RAE framework in protecting sensitive audio privacy.

Qingsong Zhong, Haomin Yu, Yan Lin, Wangmeng Shen, Long Zeng, Jilin Hu

Structure-Based Drug Design (SBDD) has emerged as a popular approach in drug discovery, leveraging three-dimensional protein structures to generate drug ligands. However, existing generative models encounter several key challenges: (1) Incorporating boundary condition constraints, (2) Integrating hierarchical structural conditions and (3) Ensuring spatial modeling fidelity. To overcome these limitations, we propose SculptDrug, a spatial condition-aware generative model based on Bayesian Flow Networks (BFNs). First, SculptDrug follows a BFNs-based framework and employs a progressive denoising strategy to ensure spatial modeling fidelity, iteratively refining atom positions while enhancing local interactions for precise spatial alignment. Second, we introduce the Boundary Awareness Block, which incorporates protein surface constraints into the generative process to ensure that the generated ligands are geometrically compatible with the target protein. Finally, we design a Hierarchical Encoder that captures global structural context while preserving fine-grained molecular interactions, ensuring overall consistency and accurate ligand-protein conformations. We evaluate SculptDrug on the CrossDocked dataset, and experimental results demonstrate that SculptDrug outperforms state-of-the-art baselines, proving the efficacy of spatial condition-aware modeling.

Xinzhe Zheng, Shiyu Jiang, Gustavo Seabra, Chenglong Li, Yanjun Li

Deep generative models are rapidly advancing structure-based drug design, offering substantial promise for generating small molecule ligands that bind to specific protein targets. However, most current approaches assume a rigid protein binding pocket, neglecting the intrinsic flexibility of proteins and the conformational rearrangements induced by ligand binding, limiting their applicability in practical drug discovery. Here, we propose Apo2Mol, a diffusion-based generative framework for 3D molecule design that explicitly accounts for conformational flexibility in protein binding pockets. To support this, we curate a dataset of over 24,000 experimentally resolved apo-holo structure pairs from the Protein Data Bank, enabling the characterization of protein structure changes associated with ligand binding. Apo2Mol employs a full-atom hierarchical graph-based diffusion model that simultaneously generates 3D ligand molecules and their corresponding holo pocket conformations from input apo states. Empirical studies demonstrate that Apo2Mol can achieve state-of-the-art performance in generating high-affinity ligands and accurately capture realistic protein pocket conformational changes.

Shiyan Zheng, Herun Wan, Minnan Luo, Junhang Huang

While existing social bot detectors perform well on benchmarks, their robustness across diverse real-world scenarios remains limited due to unclear ground truth and varied misleading cues. In particular, the impact of shortcut learning, where models rely on spurious correlations instead of capturing causal task-relevant features, has received limited attention. To address this gap, we conduct an in-depth study to assess how detectors are influenced by potential shortcuts based on textual features, which are most susceptible to manipulation by social bots. We design a series of shortcut scenarios by constructing spurious associations between user labels and superficial textual cues to evaluate model robustness. Results show that shifts in irrelevant feature distributions significantly degrade social bot detector performance, with an average relative accuracy drop of 32 % in the baseline models. To tackle this challenge, we propose mitigation strategies based on large language models, leveraging counterfactual data augmentation. These methods mitigate the problem from data and model perspectives across three levels, including data distribution at both the individual user text and overall dataset levels, as well as model’s ability to extract causal information. Our strategies achieve an average relative performance improvement of 56 % under shortcut scenarios.

Xuanle Zhao, Shuxin Zeng, Xinyuan Cai, Xiang Cheng, Duzhen Zhang, Xiuyi Chen, Bo Xu

While Vision Language Models (VLMs) have demonstrated remarkable capabilities in general visual understanding, their application in the chemical domain has been limited, with previous works predominantly focusing on text and thus overlooking critical visual information, such as molecular structures. Current approaches that directly adopt standard VLMs for chemical tasks suffer from two primary issues: (i) computational inefficiency of processing entire chemical images with non-informative backgrounds. (ii) a narrow scope on molecular-level tasks that restricts progress in chemical reasoning. In this work, we propose TinyChemVL, an efficient and powerful chemical VLM that leverages visual token reduction and reaction-level tasks to improve model efficiency and reasoning capacity. Also, we propose ChemRxn-V, a reaction-level benchmark for assessing vision-based reaction recognition and prediction tasks. Directly predicting reaction products from molecular images poses a non-trivial challenge, as it requires models to integrate both recognition and reasoning capacities. Our results demonstrate that, with only 4B parameters, TinyChemVL achieves superior performance on both molecular and reaction tasks, while also demonstrating faster inference and training speeds compared to existing models. Notably, TinyChemVL outperforms ChemVLM while utilizing only 1/16th of the visual tokens. This work builds efficient yet powerful VLMs for chemical domains by co-designing model architecture and task complexity.

Ziwei Zhang, Zhao Li, Zhuojun Jiang, Jiangyi Yin, Xuebin Wang, Jiangchao Chen, Qingyun Liu

Stringent regulations like General Data Protection Regulation (GDPR) mandate that an application's code-level data handling must align with its natural-language privacy policy, creating a critical auditing challenge. However, existing methods, predominantly reliant on static analysis, suffer from a critical limitation: in their pursuit of soundness via over-approximation, they exhibit "semantic blindness"—detecting what data flows exist but not why. This leads to an overwhelming volume of false positives, rendering automated auditing impractical. To bridge this gap, we introduce PriAgent, a novel framework that approaches compliance auditing as a multi-stage, AI-driven reasoning task. Instead of a monolithic model, PriAgent deploys a team of specialized agents that execute a divide-and-conquer strategy. They systematically prune the analysis space by abstracting data flows, pinpoint semantic loci critical for inspection, and perform on-demand summarization of large code blocks to ensure scalability. PriAgent leverages Retrieval-Augmented Generation (RAG) with a curated knowledge base of Android APIs, equipping agents to discern potentially non-compliant behavior from benign functionality. By correlating code-level evidence with the app's stated privacy policy, PriAgent delivers a holistic and explainable verdict for each potential violation. Our evaluations demonstrate that PriAgent significantly reduces false positives, enabling a more scalable and precise compliance audit.

Zhishuai Zhang, Xintian Li, Shilong Liu, Aodong Zhang, Lu Jie, Nan Sun

In this paper, we propose AMS-IO-Agent, a domain-specialized LLM-based agent for structure-aware input/output (I/O) subsystem generation in analog and mixed-signal (AMS) integrated circuits (ICs). The central contribution of this work is a framework that connects natural language design intent with industrial-level AMS IC design deliverables. AMS-IO-Agent integrates two key capabilities: (1) a structured domain knowledge base that captures reusable constraints and design conventions; (2) design intent structuring, which converts ambiguous user intent into verifiable logic steps using JSON and Python as intermediate formats. We further introduce AMS-IO-Bench, a benchmark for wirebond-packaged AMS I/O ring automation. On this benchmark, AMS-IO-Agent achieves over 70% DRC+LVS pass rate and reduces design turnaround time from hours to minutes, outperforming the baseline LLM. Furthermore, an agent-generated I/O ring was fabricated and validated in a 28 nm CMOS tape-out, demonstrating the practical effectiveness of the approach in real AMS IC design flows. To our knowledge, this is the first reported human-agent collaborative AMS IC design in which an LLM-based agent completes a nontrivial subtask with outputs directly used in silicon.

Yunzhong Zhang, You Zhou, Changqing Su, Zhen Cheng, Zhaofei Yu, Bo Xiong, Tiejun Huang, Xun Cao

Particle Image Velocimetry (PIV) is a widely adopted non-invasive imaging technique that tracks the motion of tracer particles across image sequences to capture the velocity distribution of fluid flows. It is commonly employed to analyze complex flow structures and validate numerical simulations. This study explores the untapped potential of spike cameras—ultra-high-speed, high-dynamic-range vision sensors—in high-speed fluid velocimetry. We propose a deep learning framework, Spike Imaging Velocimetry (SIV), tailored for high-resolution fluid motion estimation. To enhance the network’s performance, we design three novel modules specifically adapted to the characteristics of fluid dynamics and spike streams: the Detail-Preserving Hierarchical Transform (DPHT), the Graph Encoder (GE), and the Multi-scale Velocity Refinement (MSVR). Furthermore, we introduce a spike-based PIV dataset, Particle Scenes with Spike and Displacement (PSSD), which contains labeled samples from three representative fluid-dynamics scenarios: steady turbulence, high-speed flow, and high-dynamic-range conditions. Our proposed method outperforms existing baselines across all these scenarios, demonstrating its effectiveness.

Yiwen Zhang, Keyan Ding, Yihang Wu, Xiang Zhuang, Yi Yang, Qiang Zhang, Huajun Chen

Retrieving molecular structures from tandem mass spectra is a crucial step in rapid compound identification. Existing retrieval methods, such as traditional mass spectral library matching, suffer from limited spectral library coverage, while recent cross-modal representation learning frameworks often encounter modality misalignment, resulting in suboptimal retrieval accuracy and generalization. To address these limitations, we propose GLMR, a Generative Language Model-based Retrieval framework that mitigates the cross-modal misalignment through a two-stage process. In the pre-retrieval stage, a contrastive learning-based model identifies top candidate molecules as contextual priors for the input mass spectrum. In the generative retrieval stage, these candidate molecules are integrated with the input mass spectrum to guide a generative model in producing refined molecular structures, which are then used to re-rank the candidates based on molecular similarity. Experiments on both MassSpecGym and the proposed MassRET-20k dataset demonstrate that GLMR significantly outperforms existing methods, achieving over 40% improvement in top-1 accuracy and exhibiting strong generalizability.

Ruobei Zhang, Shengeng Tang, Huan Yan, Xiang Zhang, Jiabao Guo

The challenge in WiFi-based cross-domain Behavior Recognition lies in the significant interference of domain-specific signals on gesture variation. However, previous methods alleviate this interference by mapping the phase from multiple domains into a common feature space. If the Doppler Frequency Shift (DFS) signal is used to dynamically supplement the phase features to achieve better generalization, it enables the model to not only explore a wider feature space but also to avoid potential degradation of gesture semantic information. Specifically, we propose a novel Salient-aware Adaptive WiFi Sensing for Cross-domain Behavior Recognition (Wi-CBR), which constructs a dual-branch self-attention module that captures temporal features from phase information reflecting dynamic path length variations while extracting kinematic features from DFS correlated with motion velocity. Moreover, we design a Saliency Guidance Module that employs group attention mechanisms to mine critical activity features and utilizes gating mechanisms to optimize information entropy, facilitating feature fusion and enabling effective interaction between salient and non-salient behavioral characteristics. Extensive experiments on two large-scale public datasets (Widar3.0 and XRF55) demonstrate the superior performance of our method in both in-domain and cross-domain scenarios.

Qinyi Zhang, Duanyu Feng, Ronghui Han, Yangshuai Wang, Hao Wang

Simulating microstructure evolution (MicroEvo) is vital for materials design but demands high numerical accuracy, efficiency, and physical fidelity. Although recent studies on deep learning (DL) offers a promising alternative to traditional solvers, the field lacks standardized benchmarks. Existing studies are flawed due to a lack of comparing specialized MicroEvo DL models with state-of-the-art spatio-temporal architectures, an overemphasis on numerical accuracy over physical fidelity, and a failure to analyze error propagation over time. To address these gaps, we introduce MicroEvoEval, the first comprehensive benchmark for image-based microstructure evolution prediction. We evaluate 14 models, encompassing both domain-specific and general-purpose architectures, across four representative MicroEvo tasks with datasets specifically structured for both short- and long-term assessment. Our multi-faceted evaluation framework goes beyond numerical accuracy and computational cost, incorporating a curated set of structure-preserving metrics to assess physical fidelity. Our extensive evaluations yield several key insights. Notably, we find that modern architectures (e.g., VMamba), not only achieve superior long-term stability and physical fidelity but also operate with an order-of-magnitude greater computational efficiency. The results highlight the necessity of holistic evaluation and identify these modern architectures as a highly promising direction for developing efficient and reliable surrogate models in data-driven materials science.

Qin-Yi Zhang, Hong Wang, Siyao Liu, Haichuan Lin, Linying Cao, Xiao-Hu Zhou, Chen Chen, Shuang-Yi Wang, Zeng-Guang Hou

Fluid–structure interaction (FSI) systems involve distinct physical domains, fluid and solid, governed by different partial differential equations and coupled at a dynamic interface. While learning-based solvers offer a promising alternative to costly numerical simulations, existing methods struggle to capture the heterogeneous dynamics of FSI within a unified framework. This challenge is further exacerbated by inconsistencies in response across domains due to interface coupling and by disparities in learning difficulty across fluid and solid regions, leading to instability during prediction. To address these challenges, we propose the Heterogeneous Graph Attention Solver (HGATSolver). HGATSolver encodes the system as a heterogeneous graph, embedding physical structure directly into the model via distinct node and edge types for fluid, solid, and interface regions. This enables specialized message-passing mechanisms tailored to each physical domain. To stabilize explicit time stepping, we introduce a novel physics-conditioned gating mechanism that serves as a learnable, adaptive relaxation factor. Furthermore, an Inter-domain Gradient-Balancing Loss dynamically balances the optimization objectives across domains based on predictive uncertainty. Extensive experiments on two constructed FSI benchmarks and a public dataset demonstrate that HGATSolver achieves state-of-the-art performance, establishing an effective framework for surrogate modeling of coupled multi-physics systems.

Qiang Zhang, Feng Yang, Weihong Huang, Jing Feng, Juan Liu

Protein subcellular localization prediction is essential for understanding protein function and cellular organization. However, existing methods exhibit two major limitations: (1) they overlook the critical role of evolutionarily conserved protein domains, which are fundamental functional and structural units that significantly influence functions and subcellular localization, and (2) they rarely learn residue order and backbone coordinates simultaneously, neglecting the complementary information inherent in multi-modal representations. In this paper, we propose a novel Domain-Aware Multi-View Contrastive Representation Learning for Protein Subcellular Localization prediction, named DMVCL. Firstly, it devises domain-sequence/structure attention modules, which identify functionally significant regions in protein structures/sequences that critically determine subcellular localization. Secondly, it introduces a multi-view contrastive learning framework that unites inter-view and intra-view objectives. Inter-view contrastive learning aligns protein sequences with their corresponding structures by maximizing mutual information, thereby capturing the consistency of protein residue order and backbone coordinates. Intra-view contrastive learning enhances the representation discriminability of each modality by explicitly separating proteins with no common location and attracting those with any shared localization. Extensive experiments demonstrate that DMVCL significantly outperforms existing baselines. Ablation studies and visualizations further highlight the contributions of domain-sequence/structure attention and multi-view contrastive learning in achieving superior predictive performance.

Longlong Zhang, Xi Wang, Haotong Du, Yangyi Xu, Zhuo Liu, Yang Liu

Social bot detection is pivotal for safeguarding the integrity of online information ecosystems. Although recent graph neural network (GNN) solutions achieve strong results, they remain hindered by two practical challenges: (i) severe class imbalance arising from the high cost of generating bots, and (ii) topological noise introduced by bots that skillfully mimic human behavior and forge deceptive links. We propose the Reinforcement-guided graph Augmentation social Bot detector (RABot), a multi-granularity graph-augmentation framework that addresses both issues in a unified manner. RABot employs a neighborhood-aware oversampling strategy that linearly interpolates minority-class embeddings within local subgraphs, thereby stabilizing the decision boundary under low-resource regimes. Concurrently, a reinforcement-learning-driven edge-filtering module combines similarity-based edge features with adaptive threshold optimization to excise spurious interactions during message passing, yielding a cleaner topology. Extensive experiments on three real-world benchmarks and four GNN backbones demonstrate that RABot consistently surpasses state-of-the-art baselines. In addition, since its augmentation and filtering modules are orthogonal to the underlying architecture, RABot can be seamlessly integrated into existing GNN pipelines to boost performance with minimal overhead.

Jirong Zha, Yuxuan Fan, Tianyu Zhang, Geng Chen, Yingfeng Chen, Chen Gao, Xinlei Chen

Multimodal Large Language Models (MLLMs) have shown promise in single-agent vision tasks, yet benchmarks for evaluating multi-agent collaborative perception remain scarce. This gap is critical, as multi-drone systems provide enhanced coverage, robustness, and collaboration compared to single-sensor setups. Existing multi-image benchmarks mainly target basic perception tasks using high-quality single-agent images, thus failing to evaluate MLLMs in more complex, egocentric collaborative scenarios, especially under real-world degraded perception conditions. To address these challenges, we introduce AirCopBench, the first comprehensive benchmark designed to evaluate MLLMs in embodied aerial collaborative perception under challenging perceptual conditions. AirCopBench includes 14.6k+ questions derived from both simulator and real-world data, spanning four key task dimensions: Scene Understanding, Object Understanding, Perception Assessment, and Collaborative Decision, across 14 task types. We construct the benchmark using data from challenging degraded-perception scenarios with annotated collaborative events, generating large-scale questions through model-, rule-, and human-based methods under rigorous quality control. Evaluations on 40 MLLMs show significant performance gaps in collaborative perception tasks, with the best model trailing humans by 24.38% on average and exhibiting inconsistent results across tasks. Fine-tuning experiments further confirm the feasibility of sim-to-real transfer in aerial collaborative perception.

Chengsheng Yuan, Zhaonan Ji, Qi Cui, Zhili Zhou, Xinting Li, Zhihua Xia

Generative image steganography has attracted significant attention for its exceptional resistance to steganalysis. However, current generative steganography methods still face limitations in terms of the lack of provable security guarantees under statistical analysis and vulnerability to real-world, unforeseen channel attacks. To address these issues, this paper proposes a novel generative image steganography framework that leverages the Latent Diffusion Model (LDM). Notably, we have uncover a consistent trend: regardless of whether an image has undergone attacks such as compression or noise addition, the sign pattern of values in its latent vector encoded by the LDM remains largely invariant. Capitalizing on this trend, we have devised an adaptive distribution-preserving mapping (ADPM) mechanism, capable of converting a secret message into a latent vector that follows standard normal distribution in an adjustable way. Since both the secret latent vector and the latent vector randomly generated during regular image generation follow the same distribution, satisfying the optimal input conditions for the diffusion model, the proposed method can achieve provable security. Experimental results demonstrate the outstanding performance of our approach in terms of robustness, security, and extraction accuracy.

Shuai Yu, Xiaoliang He, Kangjie Dong, Yi Yu

Semi-supervised singing melody extraction (SSME) is one of the key tasks in the field of music information retrieval (MIR). Recently, several SSME methods have been proposed and achieved remarkable successes. However, existing methods are still facing two critical issues: firstly, there is a lack of an effective data augmentation method for SSME, which results in insufficient utilization of unlabeled data. Secondly, existing SSME methods discards too much unlabeled data in the stage of consistency regularization, which hinders the further improvements of SSME task. In this paper, we present \emph{ELH-SME}, a novel framework that better utilizes the unlabeled musical data for SSME task. Specifically, our proposed ELH-SME framework consists of three modules: (1) we first propose a diffusion-based multi-bands augmentation (DMA) method to increase the amounts of training data. The proposed DMA methods employs a diffusion model to generate perturbation at the specific frequency bands in an end-to-end manner, thereby avoiding sharply perturbations to the spectrogram. (2) To improve the utilization rate of unlabeled data, we suggest a global-class confidence (GCC) module. During the phase of consistency regularization, we consider both the global-wise and class-wise confidence values, improving the utilization rate of unlabeled data. (3) To further improve the utilization of unlabeled data, we also propose to enhance the representation capability of unlabeled data by extracting channel-level features from labeled data via channel cross attention (CCA). We evaluate our proposed framework on several well-known public available datasets, and the conducted experiments demonstrate the effectiveness of our method.