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An iterative-based difference scheme for nonlinear fractional integro-differential equations of Volterra type

Partial Differential Equations in Applied Mathematics 2025年 13卷

作者： Saini, Gaurav Ghosh, Bappa Chand, Sunita Mohapatra, Jugal Center for Data Science Department of Computer Science and Engineering Siksha ‘O’ Anusandhan (Deemed to be University) India Center for Artificial Intelligence and Machine Learning Department of Computer Science and Engineering Siksha ‘O’ Anusandhan (Deemed to be University) India Department of Mathematics Siksha ‘O’ Anusandhan (Deemed to be University) India Department of Mathematics National Institute of Technology Rourkela India

This paper presents an iterative difference scheme for solving nonlinear fractional integro-differential equations of Volterra type, which are widely used in modeling memory-dependent phenomena in various scientific and engineering applications. The scheme employs Caputo's fractional derivative to handle the non-local nature of the fractional derivative and introduces an iterative approach to enhance accuracy and stability. By discretizing the domain of interest on a uniform mesh and the present non-local differential operator using a well-established L1 technique, we derive a nonlinear difference equation that captures the essential dynamics of the underlying continuous problem. The corresponding nonlinear equation is solved by employing the Daftardar-Gejji and Jafari (DGJ) method. The convergence and stability of the proposed scheme are rigorously analyzed under sufficiently smooth initial data, and the method produces reliable numerical solutions. Numerical experiments are conducted to validate the effectiveness of the scheme, demonstrating its efficiency. © 2025 The Authors

关键词： Composite trapezoidal formula Error estimation L1 technique Nonlinear integro-differential equations

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THIDS: Triplet High-Order Individual Differential Structural Brain Network

THIDS: Triplet High-Order Individual Differential Structural...

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IEEE International Symposium on Biomedical Imaging

作者： Dailin Wen Chunzhi Zhao Tulay Adali Daoqiang Zhang Vince D. Calhoun Shile Qi Department of Artificial Intelligence Nanjing University of Aeronautics and Astronautics Nanjing China Key Laboratory of Brain-Machine Intelligence Technology Ministry of Education Nanjing University of Aeronautics and Astronautics Nanjing China Department of CSEE University of Maryland Baltimore MD USA Tri-institutional Center for Translational Research in Neuroimaging and Data Science (TReNDS) Georgia State University Georgia Institute of Technology Emory University Atlanta GA USA

ISBN: (数字)9798331520526

ISBN: (纸本)9798331520533

The human brain is a highly integrated network, and the brain network models serve as a simplified representation of this complex system. However, traditional brain network approaches are limited to group-level mean comparisons and first-order interactions, failing to capture the individual differences with higher-order interactions among brain regions in both brain development and heterogeneous psychiatric disorders. Here, we propose a triplet high-order individual differential structural brain network (THIDS), which is a linear combination of the differential (reference-perturbed) and perturbed networks, while utilizing the interaction information among all triplets of brain regions to construct an individual difference structured brain network. Results show that THIDS consistently achieves the highest accuracy in schizophrenia diagnosis, gender classification and cognition prediction across two datasets, four classification models and seven cognitive domains, compared with four alternative brain network construction methods. These results demonstrate that the proposed THIDS approach reliably captures individual differential features in the brain, showing great potential to investigate especially heterogeneous brain disorders and individual brain development.

关键词： Biometrics Accuracy Perturbation methods Schizophrenia Predictive models Brain modeling Cognition Robustness Complex systems Biomedical imaging

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TVEG: Model Selection of the Time-Varying Exponential Family Distributions Graphical Models

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IEEE Transactions on Network science and Engineering 2025年

作者： Liu, Juan Mei, Guofeng Xia, Yuanqing Wu, Xiaoqun Lu, Jinhu Beijing Forestry University School of Technology Beijing100107 China Italy Zhongyuan University of Technology Henan 451191 China Wuhan University School of Mathematics and Statistics Wuhan430072 China Beihang University State Key Laboratory of Software Development Environment Beijing Advanced Innovation Center for Big Data and Brain Machine Intelligence School of Automation Science and Electrical Engineering Beijing100191 China

The undirected graphical model, a popular class of statistical model, offers a way to describe and explain the relationships among a set of variables. However, it remains a challenge to choose a certain graphical model to explain the relationships of variables adequately, especially when the relationships of variables are rewiring over time. This paper proposes the Time-Varying Exponential Family Distributions Graphical (TVEG) models, with time-varying structures and exponential family node-wise conditional distributions. TVEG models extend the scope of available graph models and can be applied to time-varying and exponential family distribution observation data in reality. We propose the Temporally Smoothed L1regularized exponential family graphical estimator (TSLEG), an estimator to infer the structure of TVEG from observations. We derive sufficient conditions for the TSLEG to recover the block partition and sparse pattern with high probability. We derive a message-passing optimization method to solve the TSLEG for time-varying Ising, Gaussian, exponential, and Poisson graphs based on the ADMM. The synthetic network simulations corroborate the theoretical analysis. Analysing of real data of stocks and the US Senate by the time-varying exponential model and Poisson model indicates the effectiveness and practicality of TVEG models. © 2025 IEEE. All rights reserved.

关键词： ADMM exponential family distributions Graphical model pseudo maximum likelihood estimation

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A THEORY OF INITIALISATION’S IMPACT ON SPECIALISATION

arXiv

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arXiv 2025年

作者： Jarvis, Devon Lee, Sebastian Dominé, Clémentine Carla Juliette Saxe, Andrew M. Mannelli, Stefano Sarao School of Computer Science and Applied Mathematics University of the Witwatersrand South Africa Center for Computational Neuroscience Flatiron Institute Simons Foundation Gatsby Computational Neuroscience Unit Sainsbury Wellcome Centre UCL United Kingdom Data Science and AI Computer Science and Engineering Chalmers University of Technology University of Gothenburg Sweden Machine Intelligence and Neural Discovery Institute University of the Witwatersrand South Africa CIFAR Azrieli Global Scholar CIFAR

Prior work has demonstrated a consistent tendency in neural networks engaged in continual learning tasks, wherein intermediate task similarity results in the highest levels of catastrophic interference. This phenomenon is attributed to the network’s tendency to reuse learned features across tasks. However, this explanation heavily relies on the premise that neuron specialisation occurs, i.e. the emergence of localised representations. Our investigation challenges the validity of this assumption. Using theoretical frameworks for the analysis of neural networks, we show a strong dependence of specialisation on the initial condition. More precisely, we show that weight imbalance and high weight entropy can favour specialised solutions. We then apply these insights in the context of continual learning, first showing the emergence of a monotonic relation between task-similarity and forgetting in non-specialised networks. Finally, we show that specialization by weight imbalance is beneficial on the commonly employed elastic weight consolidation regularisation technique. Copyright © 2025, The Authors. All rights reserved.

关键词： Neural networks

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Cross-Domain Animal Pose Estimation with Skeleton Anomaly-Aware Learning

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IEEE Transactions on Circuits and Systems for Video Technology 2025年

作者： Han, Le Chen, Kaixuan Zhao, Lei Jiang, Yangbo Wang, Pengfei Zheng, Nenggan Zhejiang Hangzhou310007 China Zhejiang University College of Computer Science and Technology Zhejiang Hangzhou310007 China Zhejiang University State Key Laboratory of Blockchain and Data Security Zhejiang Hangzhou310007 China Institute of Blockchain and Data Security. China Zhejiang University School of Software Technology Ningbo China Zhejiang University State Key Lab of Brain-Machine Intelligence Hangzhou310007 China Zhejiang Provincial Government ZJU Collaborative Innovation Center for Artificial Intelligence by MOE Hangzhou310007 China Bengbu University School of Computer and Information Engineering Bengbu233030 China

Animal pose estimation is often constrained by the scarcity of annotations and the diversity of scenarios and species. The pseudo-label generation based unsupervised domain adaptation paradigm, which discriminates the predicted keypoints of unlabeled data based on the skeleton position consistency, has demonstrated effectiveness for such problems. However, existing methods generate pseudo-labels with massive false positives, because they cannot effectively distinguish sample pairs with the same errors. In this study, we propose a cross-domain animal pose estimation model from a novel perspective of skeleton anomaly learning. We construct a graph contrastive learning mechanism to acquire the skeleton anomaly-aware knowledge, which enables the generation of accurate pseudo-labels for target domain and imposes graph constraint on unlabeled data. And a skeleton anomaly-feedback based domain adaptation framework is designed to facilitate implicit alignment of object-specific features and joint training of cross-domain. Besides, we propose a novel rat pose dataset named UDARP-9.4K to address the gap of small-sized animal pose datasets encompassing diverse experimental scenarios. The related datasets are reviewed and evaluated in detail. Extensive experiments are conducted on UDARP-9.4K and two public datasets to demonstrate the superiority of the proposed model in cross-scenarios and cross-species animal pose estimation tasks. Further analysis reveals the effectiveness of the proposed model for skeleton structure feature learning. The UDARP-9.4K dataset is available here. © 1991-2012 IEEE.

关键词： Invertebrates

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Homophily Induced Contrastive Attributed Graph Clustering

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IEEE Transactions on Circuits and Systems for Video Technology 2025年

作者： Chen, Man-Sheng Lai, Pei-Yuan Liao, De-Zhang Wang, Chang-Dong Lai, Jian-Huang Sun Yat-sen University School of Computer Science and Engineering Guangzhou China Guangxi Zhuang Autonomous Region Information Center Guangxi Key Laboratory of Digital Infrastructure Nanning China Guangdong Key Laboratory of Big Data Analysis and Processing Guangzhou China Key Laboratory of Machine Intelligence and Advanced Computing Ministry of Education China South China Technology Commercialization Center Guangzhou China Guangdong Key Laboratory of Information Security Technology Guangzhou China

Attributed graph clustering, aiming to discover the underlying graph structure and partition the graph nodes into several disjoint categories, is a basic task in graph data analysis. Although recent efforts over graph contrastive clustering have achieved decent performances, most of them get accustomed to construct the positive neighbor set by the generated pseudo clustering information, directly ignoring the ready-made neighbor nodes and the underlying semantics of edges in a graph. How to well deal with the graph neighbor-specific information to facilitate the performance of graph contrastive clustering is still a challenging problem. Therefore, in this work, we propose a novel Homophily Induced Contrastive Attributed Graph Clustering (HomoCAGC) method, where the power of homophily is exploited in facilitating the performance of contrastive attributed graph clustering, while the pseudo homophily in a graph is also explored and distinguished. Especially, the node feature as reliable information guidance is used to compute the underlying feature-oriented pair-wise node similarity, based on which the positive node pairs in contrastive regularizer are adjusted for better node representation characterization. According to the refined node representations, a triplet self-supervised clustering objective is well-designed to ensure the output embedding is cluster-oriented, and suitable for the downstream clustering task. Extensive experiments on seven benchmarks are conducted to demonstrate the effectiveness of HomoCAGC. © 1991-2012 IEEE.

关键词： Attributed graph clustering contrastive learning graph homophily self-supervised clustering

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WiViPose: A Video-aided Wi-Fi Framework for Environment-Independent 3D Human Pose Estimation

引用

IEEE Transactions on Multimedia 2025年

作者： Zhang, Lei Ning, Haoran Tang, Jiaxin Chen, Zhenxiang Zhong, Yaping Han, Yahong Tianjin University College of Intelligence and Computing the Tianjin Key Laboratory of Advanced Network Technology and Application Tianjin300050 China Key Laboratory of Computing Power Network and Information Security Ministry of Education China University of Jinan Shandong Provincial Key Laboratory of Ubiquitous Intelligent Computing the School of Information Science and Engineering Jinan250022 China Wuhan Sports University Sports Big-data Research Center Wuhan430079 China Tianjin University College of Intelligence and Computing the Tianjin Key Laboratory of Machine Learning Tianjin300350 China

The inherent complexity of Wi-Fi signals makes video-aided Wi-Fi 3D pose estimation difficult. The challenges include the limited generalizability of the task across diverse environments, its significant signal heterogeneity, and its inadequate ability to analyze local and geometric information. To overcome these challenges, we introduce WiViPose, a video-aided Wi-Fi framework for 3D pose estimation, which attains enhanced cross-environment generalization through cross-layer optimization. Bilinear temporal-spectral fusion (BTSF) is initially used to fuse the time-domain and frequency-domain features derived from Wi-Fi. Video features are derived from a multiresolution convolutional pose machine and enhanced by local self-attention. Cross-modality data fusion is facilitated through an attention-based transformer, with the process further refined under a supervisory mechanism. WiViPose demonstrates effectiveness by achieving an average percentage of correct keypoints (PCK)@50 of 91.01% across three typical indoor environments. © 2025 IEEE.

关键词： Frequency domain analysis

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Learning Counterfactual Outcomes Under Rank Preservation

arXiv

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arXiv 2025年

作者： Wu, Peng Li, Haoxuan Zheng, Chunyuan Zeng, Yan Chen, Jiawei Liu, Yang Guo, Ruocheng Zhang, Kun School of Mathematics and Statistics Beijing Technology and Business University China Center for Data Science Peking University China School of Mathematical Sciences Peking University China College of Computer Science and Technology Zhejiang University China Computer Science and Engineering University of California Santa Cruz Bolivia ByteDance Research China Department of Philosophy Carnegie Mellon University United States Machine Learning Department Mohamed bin Zayed University of Artificial Intelligence United Arab Emirates

Counterfactual inference aims to estimate the counterfactual outcome at the individual level given knowledge of an observed treatment and the factual outcome, with broad applications in fields such as epidemiology, econometrics, and management science. Previous methods rely on a known structural causal model (SCM) or assume the homogeneity of the exogenous variable and strict monotonicity between the outcome and exogenous variable. In this paper, we propose a principled approach for identifying and estimating the counterfactual outcome. We first introduce a simple and intuitive rank preservation assumption to identify the counterfactual outcome without relying on a known structural causal model. Building on this, we propose a novel ideal loss for theoretically unbiased learning of the counterfactual outcome and further develop a kernel-based estimator for its empirical estimation. Our theoretical analysis shows that the rank preservation assumption is not stronger than the homogeneity and strict monotonicity assumptions, and shows that the proposed ideal loss is convex, and the proposed estimator is unbiased. Extensive semi-synthetic and real-world experiments are conducted to demonstrate the effectiveness of the proposed method. Copyright © 2025, The Authors. All rights reserved.

关键词： Contrastive Learning

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DFingerNet: Noise-Adaptive Speech Enhancement for Hearing Aids

DFingerNet: Noise-Adaptive Speech Enhancement for Hearing Ai...

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International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Iosif Tsangko Andreas Triantafyllopoulos Michael Müller Hendrik Schröter Björn W. Schuller EIHW – Chair of Embedded Intelligence for Health Care and Wellbeing University of Augsburg Germany CHI – Chair of Health Informatics Technical University of Munich Germany MCML – Munich Center for Machine Learning Munich Germany WS Audiology Research and Development Erlangen Germany GLAM – Group on Language Audio & Music Imperial College London UK MDSI – Munich Data Science Institute Munich Germany

ISBN: (数字)9798350368741

ISBN: (纸本)9798350368758

The DeepFilterNet (DFN) architecture was recently proposed as a deep learning model suited for hearing aid devices. Despite its competitive performance on numerous benchmarks, it still follows a ‘one-size-fits-all’ approach, which aims to train a single, monolithic architecture that generalises across different noises and environments. However, its limited size and computation budget can hamper its generalisability. Recent work has shown that in-context adaptation can improve performance by conditioning the denoising process on additional information extracted from background recordings to mitigate this. These recordings can be offloaded outside the hearing aid, thus improving performance while adding minimal computational overhead. We introduce these principles to the DFN model, thus proposing the DFingerNet (DFiN) model, which shows superior performance on various benchmarks inspired by the DNS Challenge.

关键词： Performance evaluation Adaptation models Computational modeling Noise Noise reduction Computer architecture Speech enhancement Fingerprint recognition Hearing aids Recording

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DFingerNet: Noise-Adaptive Speech Enhancement for Hearing Aids

arXiv

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arXiv 2025年

作者： Tsangko, Iosif Triantafyllopoulos, Andreas Müller, Michael Schröter, Hendrik Schuller, Björn W. EIHW – Chair of Embedded Intelligence for Health Care and Wellbeing University of Augsburg Germany CHI – Chair of Health Informatics Technical University of Munich Germany MCML – Munich Center for Machine Learning Munich Germany WS Audiology Research and Development Erlangen Germany GLAM – Group on Language Audio & Music Imperial College London United Kingdom MDSI – Munich Data Science Institute Munich Germany

关键词： Budget control

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