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Ahmed F, Bhuiyan MAN, Coskunuzer B. Topo-CNN: Retinal Image Analysis with Topological Deep Learning. JOURNAL OF IMAGING INFORMATICS IN MEDICINE 2025:10.1007/s10278-025-01575-7. [PMID: 40563040 DOI: 10.1007/s10278-025-01575-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2025] [Revised: 05/27/2025] [Accepted: 05/29/2025] [Indexed: 06/28/2025]
Abstract
The analysis of fundus images is vital for early detection of retinal diseases such as diabetic retinopathy (DR), glaucoma, and age-related macular degeneration (AMD), but traditional methods are resource-intensive. We propose an automated and interpretable diagnostic framework that leverages novel feature representations to improve performance. Our main contribution is a topological feature extraction technique based on Topological Data Analysis (TDA), which captures geometric and structural patterns in fundus images. These features are computationally efficient and interpretable. We integrate them with pretrained CNN features (e.g., ResNet-50) into a hybrid deep model, Topo-CNN, combining global image context with topological structure. We evaluate Topo-CNN on three benchmarks: APTOS (binary and five-class DR), ORIGA (Glaucoma), and IChallenge-AMD. Our model achieves 98.7% accuracy/98.9 AUC on binary DR, 95.5 AUC on five-class DR, 93.8% accuracy/93.6 AUC on AMD, and 82.3% accuracy/95.8 specificity on glaucoma. Ablation studies confirm the added value of topological features, and our Topo-CNN consistently outperforms existing methods across tasks.
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Affiliation(s)
- Faisal Ahmed
- Department of Data Science and Mathematics, Embry-Riddle Aeronautical University, 3700 Willow Creek Rd, 86301, Prescott, AZ, USA
| | - Mohammad Alfrad Nobel Bhuiyan
- Department of Medicine, Louisiana State University Health Sciences Center at Shreveport, 1501 Kings Highway, 71103, Shreveport, LA, USA.
| | - Baris Coskunuzer
- Department of Mathematical Sciences, The University of Texas at Dallas, 800 W Campbell Rd, 75080, Richardson, TX, USA.
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Wang R, Tian Y, Liò P, Bianconi G. Dirac-equation signal processing: Physics boosts topological machine learning. PNAS NEXUS 2025; 4:pgaf139. [PMID: 40371396 PMCID: PMC12076202 DOI: 10.1093/pnasnexus/pgaf139] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/09/2024] [Accepted: 04/18/2025] [Indexed: 05/16/2025]
Abstract
Topological signals are variables or features associated with both nodes and edges of a network. Recently, in the context of topological machine learning, great attention has been devoted to signal processing of such topological signals. Most of the previous topological signal processing algorithms treat node and edge signals separately and work under the hypothesis that the true signal is smooth and/or well approximated by a harmonic eigenvector of the higher-order Laplacian, which may be violated in practice. Here, we propose Dirac-equation signal processing, a framework for efficiently reconstructing true signals on nodes and edges, also if they are not smooth or harmonic, by processing them jointly. The proposed physics-inspired algorithm is based on the spectral properties of the topological Dirac operator. It leverages the mathematical structure of the topological Dirac equation to boost the performance of the signal processing algorithm. We discuss how the relativistic dispersion relation obeyed by the topological Dirac equation can be used to assess the quality of the signal reconstruction. Finally, we demonstrate the improved performance of the algorithm with respect to previous algorithms. Specifically, we show that Dirac-equation signal processing can also be used efficiently if the true signal is a nontrivial linear combination of more than one eigenstate of the Dirac equation, as it generally occurs for real signals.
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Affiliation(s)
- Runyue Wang
- Centre for Complex Systems, School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
| | - Yu Tian
- Nordita, KTH Royal Institute of Technology and Stockholm University, Stockholm SE-106 91, Sweden
- Center for Systems Biology Dresden, 108 Pfotenhauerstraße, Dresden 01307, Germany
| | - Pietro Liò
- Department of Computer Science and Technology, University of Cambridge, Cambridge CB3 0FA, United Kingdom
| | - Ginestra Bianconi
- Centre for Complex Systems, School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
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3
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Xu S, Jiang L, Zhang Z, Luo X, Wu H, Tan Z. Network Toxicology and Molecular Docking Strategy for Analyzing the Toxicity and Mechanisms of Bisphenol A in Alzheimer's Disease. J Biochem Mol Toxicol 2025; 39:e70247. [PMID: 40192506 DOI: 10.1002/jbt.70247] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2025] [Accepted: 03/27/2025] [Indexed: 05/17/2025]
Abstract
Alzheimer's disease (AD) is a chronic and progressive neurodegenerative disorder marked by memory deterioration and cognitive impairment. Bisphenol A (BPA), a common environmental pollutant, has been linked to neurotoxicity and may contribute to AD development. This study aims to uncover potential toxicological targets and molecular mechanisms of BPA-induced AD. BPA's potential neurotoxic effects were predicted using ProTox and ADMETlab. Target prediction for BPA was conducted through the STITCH and Swiss Target Prediction platforms, while AD-related targets were compiled from GeneCards, OMIM, and the Therapeutic Target Database (TTD). Protein-protein interaction (PPI) networks were constructed using STRING and visualized in Cytoscape, and gene ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway analyses were performed. Molecular docking was employed to evaluate the binding interactions between BPA and the identified core targets. Through systematic bioinformatics analyses, 137 candidate targets for BPA-elicited AD were identified. Screening via PPI network analysis highlighted five key targets: STAT3, AKT1, INS, EGFR, and PTEN. GO and KEGG pathway enrichment revealed significant involvement in oxidative stress, neuronal apoptosis, neurodegenerative processes, and pathways such as PI3K/AKT, MAPK, lipid and atherosclerosis, and AD signaling. Molecular docking simulations confirmed strong binding affinities between BPA and these core targets. This study sheds light on the molecular mechanisms underlying BPA's neurotoxic effects in the context of AD and provides a foundation for further research into preventive and therapeutic strategies. The integration of network toxicology and molecular docking offers a robust framework for unraveling toxic pathways of uncharacterized environmental and chemical agents.
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Affiliation(s)
- Sumei Xu
- Phase I Clinical Trial Center, Xiangya Hospital, Central South University, Changsha, Hunan, China
- National Clinical Research Center for Geriatric Disorders, Xiangya Hospital, Central South University, Changsha, Hunan, China
- Department of Biomedical Informatics, University at Buffalo, Buffalo, New York, USA
| | - Liping Jiang
- Department of Clinical Pharmacology, Xiangya Hospital, Central South University, Changsha, Hunan, China
- Hunan Key Laboratory of Pharmacogenetics, Institute of Clinical Pharmacology, Central South University, Changsha, Hunan, China
- Engineering Research Center of Applied Technology of Pharmacogenomics, Ministry of Education, Changsha, Hunan, China
| | - Zhuo Zhang
- Department of Clinical Pharmacology, Xiangya Hospital, Central South University, Changsha, Hunan, China
- Hunan Key Laboratory of Pharmacogenetics, Institute of Clinical Pharmacology, Central South University, Changsha, Hunan, China
- Engineering Research Center of Applied Technology of Pharmacogenomics, Ministry of Education, Changsha, Hunan, China
| | - Xin Luo
- Department of Clinical Pharmacology, Xiangya Hospital, Central South University, Changsha, Hunan, China
- Hunan Key Laboratory of Pharmacogenetics, Institute of Clinical Pharmacology, Central South University, Changsha, Hunan, China
- Engineering Research Center of Applied Technology of Pharmacogenomics, Ministry of Education, Changsha, Hunan, China
| | - Huilan Wu
- Department of Clinical Pharmacology, Xiangya Hospital, Central South University, Changsha, Hunan, China
- Hunan Key Laboratory of Pharmacogenetics, Institute of Clinical Pharmacology, Central South University, Changsha, Hunan, China
- Engineering Research Center of Applied Technology of Pharmacogenomics, Ministry of Education, Changsha, Hunan, China
| | - Zhirong Tan
- Department of Clinical Pharmacology, Xiangya Hospital, Central South University, Changsha, Hunan, China
- Hunan Key Laboratory of Pharmacogenetics, Institute of Clinical Pharmacology, Central South University, Changsha, Hunan, China
- Engineering Research Center of Applied Technology of Pharmacogenomics, Ministry of Education, Changsha, Hunan, China
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Qin Y, Fasy BT, Wenk C, Summa B. Rapid and Precise Topological Comparison with Merge Tree Neural Networks. IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2025; 31:1322-1332. [PMID: 39298308 DOI: 10.1109/tvcg.2024.3456395] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/21/2024]
Abstract
Merge trees are a valuable tool in the scientific visualization of scalar fields; however, current methods for merge tree comparisons are computationally expensive, primarily due to the exhaustive matching between tree nodes. To address this challenge, we introduce the Merge Tree Neural Network (MTNN), a learned neural network model designed for merge tree comparison. The MTNN enables rapid and high-quality similarity computation. We first demonstrate how to train graph neural networks, which emerged as effective encoders for graphs, in order to produce embeddings of merge trees in vector spaces for efficient similarity comparison. Next, we formulate the novel MTNN model that further improves the similarity comparisons by integrating the tree and node embeddings with a new topological attention mechanism. We demonstrate the effectiveness of our model on real-world data in different domains and examine our model's generalizability across various datasets. Our experimental analysis demonstrates our approach's superiority in accuracy and efficiency. In particular, we speed up the prior state-of-the-art by more than 100× on the benchmark datasets while maintaining an error rate below 0.1%.
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Matuk J, Kurtek S, Bharath K. Topo-Geometric Analysis of Variability in Point Clouds Using Persistence Landscapes. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2024; 46:11035-11046. [PMID: 39196754 PMCID: PMC11636526 DOI: 10.1109/tpami.2024.3451328] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/30/2024]
Abstract
Topological data analysis provides a set of tools to uncover low-dimensional structure in noisy point clouds. Prominent amongst the tools is persistence homology, which summarizes birth-death times of homological features using data objects known as persistence diagrams. To better aid statistical analysis, a functional representation of the diagrams, known as persistence landscapes, enable use of functional data analysis and machine learning tools. Topological and geometric variabilities inherent in point clouds are confounded in both persistence diagrams and landscapes, and it is important to distinguish topological signal from noise to draw reliable conclusions on the structure of the point clouds when using persistence homology. We develop a framework for decomposing variability in persistence diagrams into topological signal and topological noise through alignment of persistence landscapes using an elastic Riemannian metric. Aligned landscapes (amplitude) isolate the topological signal. Reparameterizations used for landscape alignment (phase) are linked to a resolution parameter used to generate persistence diagrams, and capture topological noise in the form of geometric, global scaling and sampling variabilities. We illustrate the importance of decoupling topological signal and topological noise in persistence diagrams (landscapes) using several simulated examples. We also demonstrate that our approach provides novel insights in two real data studies.
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Hong Y, Wang D, Lin Y, Yang Q, Wang Y, Xie Y, Shu W, Gao S, Hua C. Environmental triggers and future risk of developing autoimmune diseases: Molecular mechanism and network toxicology analysis of bisphenol A. ECOTOXICOLOGY AND ENVIRONMENTAL SAFETY 2024; 288:117352. [PMID: 39550874 DOI: 10.1016/j.ecoenv.2024.117352] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2024] [Revised: 11/02/2024] [Accepted: 11/13/2024] [Indexed: 11/19/2024]
Abstract
Bisphenol A (BPA), a chemical compound in plastics and resins, widely exist in people's production and life which have great potential to damage human and animal health. It has been proved that BPA could affect human immune function and promote the occurrence and development of autoimmune diseases (ADs). However, the mechanism and pathophysiology remain unknown. Therefore, this study aims to advance network toxicology strategies to efficiently investigate the putative toxicity and underlying molecular mechanisms of environmental pollutants, focusing on ADs induced by BPA exposure. Leveraging databases including ChEMBL, STITCH, SwissTargetPrediction, GeneCards, and OMIM, we identified potential targets associated with BPA exposure and ADs, including rheumatoid arthritis (RA), systemic lupus erythematosus (SLE), multiple sclerosis (MS), Hashimoto's thyroiditis (HT), inflammatory bowel disease (IBD), and type 1 diabetes (T1D). Subsequent refinement using STRING and Cytoscape software highlighted core targets respectively, and Metascape was utilized for enrichment analysis. Gene expression data from the GEO database revealed the upregulation or downregulation of these targets across these ADs. Molecular docking performed with Autodock confirmed robust binding between BPA and core targets, notably PPARG, CTNNB1, ESR1, EGFR, SRC, and CCND1. These findings suggest that BPA exposure may serve as an environmental trigger in the development of autoimmunity, underscoring potential environmental risk factors for the onset of autoimmune conditions.
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Affiliation(s)
- Yanggang Hong
- The Second School of Medicine, Wenzhou Medical University, Zhejiang Province 325035, China
| | - Deqi Wang
- The First School of Medicine, Wenzhou Medical University, Zhejiang Province 325035, China
| | - Yinfang Lin
- The First School of Medicine, Wenzhou Medical University, Zhejiang Province 325035, China
| | - Qianru Yang
- The First School of Medicine, Wenzhou Medical University, Zhejiang Province 325035, China
| | - Yi Wang
- The First School of Medicine, Wenzhou Medical University, Zhejiang Province 325035, China
| | - Yuanyuan Xie
- School of Basic Medical Sciences, Wenzhou Medical University, Wenzhou, Zhejiang Province 325035, China
| | - Wanyi Shu
- School of Ophthalmology & Optometry, School of Biomedical Engineering, Wenzhou Medical University, Wenzhou, Zhejiang Province 325035, China
| | - Sheng Gao
- Laboratory Animal Center, Wenzhou Medical University, Wenzhou, Zhejiang Province 325035, China.
| | - Chunyan Hua
- School of Basic Medical Sciences, Wenzhou Medical University, Wenzhou, Zhejiang Province 325035, China.
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Manrique-Castano D, Bhaskar D, ElAli A. Dissecting glial scar formation by spatial point pattern and topological data analysis. Sci Rep 2024; 14:19035. [PMID: 39152163 PMCID: PMC11329771 DOI: 10.1038/s41598-024-69426-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2023] [Accepted: 08/05/2024] [Indexed: 08/19/2024] Open
Abstract
Glial scar formation represents a fundamental response to central nervous system (CNS) injuries. It is mainly characterized by a well-defined spatial rearrangement of reactive astrocytes and microglia. The mechanisms underlying glial scar formation have been extensively studied, yet quantitative descriptors of the spatial arrangement of reactive glial cells remain limited. Here, we present a novel approach using point pattern analysis (PPA) and topological data analysis (TDA) to quantify spatial patterns of reactive glial cells after experimental ischemic stroke in mice. We provide open and reproducible tools using R and Julia to quantify spatial intensity, cell covariance and conditional distribution, cell-to-cell interactions, and short/long-scale arrangement, which collectively disentangle the arrangement patterns of the glial scar. This approach unravels a substantial divergence in the distribution of GFAP+ and IBA1+ cells after injury that conventional analysis methods cannot fully characterize. PPA and TDA are valuable tools for studying the complex spatial arrangement of reactive glia and other nervous cells following CNS injuries and have potential applications for evaluating glial-targeted restorative therapies.
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Affiliation(s)
- Daniel Manrique-Castano
- Neuroscience Axis, Research Center of CHU de Québec-Université Laval, Quebec City, QC, Canada.
- Department of Psychiatry and Neuroscience, Faculty of Medicine, Université Laval, Quebec City, QC, Canada.
| | | | - Ayman ElAli
- Neuroscience Axis, Research Center of CHU de Québec-Université Laval, Quebec City, QC, Canada.
- Department of Psychiatry and Neuroscience, Faculty of Medicine, Université Laval, Quebec City, QC, Canada.
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8
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Hong Y, Yuan Q, Wang L, Yang Z, Xu P, Guan X, Chen C. Integrative bioinformatics analysis to identify ferroptosis-related genes in non-obstructive azoospermia. J Assist Reprod Genet 2024; 41:2145-2161. [PMID: 38902567 PMCID: PMC11339017 DOI: 10.1007/s10815-024-03155-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2024] [Accepted: 05/23/2024] [Indexed: 06/22/2024] Open
Abstract
PURPOSE The objective of this study was to discern ferroptosis-related genes (FRGs) linked to non-obstructive azoospermia and investigate the associated molecular mechanisms. METHOD A dataset related to azoospermia was retrieved from the Gene Expression Omnibus database, and FRGs were sourced from GeneCards. Ferroptosis-related differentially expressed genes (FRDEGs) were discerned. Subsequently, these genes underwent analyses encompassing Gene Ontology and Kyoto Encyclopedia of Genes and Genomes, as well as protein-protein interaction (PPI) networks and assessments of functional similarity. Following the identification of hub genes, an exploration of immune infiltration, single-cell expression, diagnostic utility, and interactions involving hub genes, RNA-binding proteins (RBPs), transcription factors (TFs), microRNAs (miRNAs), and drugs was conducted. RESULTS A total of 35 differentially expressed FRGs were discerned. These genes demonstrated enrichment in functions and pathways associated with ferroptosis. From the PPI network, eight hub genes were selected. Functional similarity analysis highlighted the potential pivotal roles of HMOX1 and GPX4 in azoospermia. Analysis of immune cell infiltration indicated a significant decrease in activated dendritic cells in the azoospermia group, with notable correlations between hub genes, particularly SAT1 and HMGCR, and immune cell infiltration. Unique expression patterns of hub genes across various cell types in the human testis were observed, with GPX4 prominently enriched in spermatid/sperm. Eight hub genes exhibited robust diagnostic value (AUC > 0.75). Lastly, a comprehensive hub gene-miRNA-TF-RBP-drug network was constructed. CONCLUSION In summary, our investigation unveiled eight FRDEGs associated with azoospermia, which hold potential as biomarkers for the diagnosis and treatment of azoospermia.
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Affiliation(s)
- Yanggang Hong
- The Second School of Medicine, Wenzhou Medical University, Wenzhou, 325000, Zhejiang, China
- Key Laboratory of Children Genitourinary Diseases of Wenzhou, Wenzhou, 325000, Zhejiang, China
| | - Qichao Yuan
- Department of Pediatric Urology, the Second Affiliated Hospital and Yuying Children's Hospital of Wenzhou Medical University, Wenzhou, 325000, Zhejiang, China
- Key Laboratory of Children Genitourinary Diseases of Wenzhou, Wenzhou, 325000, Zhejiang, China
| | - Lingfei Wang
- Department of Pediatric Urology, the Second Affiliated Hospital and Yuying Children's Hospital of Wenzhou Medical University, Wenzhou, 325000, Zhejiang, China
- Key Laboratory of Children Genitourinary Diseases of Wenzhou, Wenzhou, 325000, Zhejiang, China
| | - Zihan Yang
- Department of Pediatric Urology, the Second Affiliated Hospital and Yuying Children's Hospital of Wenzhou Medical University, Wenzhou, 325000, Zhejiang, China
- Key Laboratory of Children Genitourinary Diseases of Wenzhou, Wenzhou, 325000, Zhejiang, China
| | - Peiyu Xu
- The Second School of Medicine, Wenzhou Medical University, Wenzhou, 325000, Zhejiang, China
- Key Laboratory of Children Genitourinary Diseases of Wenzhou, Wenzhou, 325000, Zhejiang, China
| | - Xiaoju Guan
- Department of Pediatric Urology, the Second Affiliated Hospital and Yuying Children's Hospital of Wenzhou Medical University, Wenzhou, 325000, Zhejiang, China.
- Key Laboratory of Children Genitourinary Diseases of Wenzhou, Wenzhou, 325000, Zhejiang, China.
| | - Congde Chen
- Department of Pediatric Urology, the Second Affiliated Hospital and Yuying Children's Hospital of Wenzhou Medical University, Wenzhou, 325000, Zhejiang, China.
- Key Laboratory of Children Genitourinary Diseases of Wenzhou, Wenzhou, 325000, Zhejiang, China.
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Papamarkou T, Birdal T, Bronstein M, Carlsson G, Curry J, Gao Y, Hajij M, Kwitt R, Liò P, Di Lorenzo P, Maroulas V, Miolane N, Nasrin F, Ramamurthy KN, Rieck B, Scardapane S, Schaub MT, Veličković P, Wang B, Wang Y, Wei GW, Zamzmi G. Position: Topological Deep Learning is the New Frontier for Relational Learning. PROCEEDINGS OF MACHINE LEARNING RESEARCH 2024; 235:39529-39555. [PMID: 40196046 PMCID: PMC11973457] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Subscribe] [Scholar Register] [Indexed: 04/09/2025]
Abstract
Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models. This paper posits that TDL is the new frontier for relational learning. TDL may complement graph representation learning and geometric deep learning by incorporating topological concepts, and can thus provide a natural choice for various machine learning settings. To this end, this paper discusses open problems in TDL, ranging from practical benefits to theoretical foundations. For each problem, it outlines potential solutions and future research opportunities. At the same time, this paper serves as an invitation to the scientific community to actively participate in TDL research to unlock the potential of this emerging field.
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Affiliation(s)
| | - Tolga Birdal
- Department of Computing, Imperial College London, London, UK
| | | | - Gunnar Carlsson
- Department of Mathematics, Stanford University, Stanford, USA
- BlueLightAI Inc, USA
| | | | - Yue Gao
- School of Software, Tsinghua University, Beijing, China
| | | | - Roland Kwitt
- Department of Artificial Intelligence and Human Interfaces, University of Salzburg, Austria
| | - Pietro Liò
- Department of Computer Science and Technology, University of Cambridge, Cambridge, UK
| | - Paolo Di Lorenzo
- Department of Information Engineering, Electronics and Telecommunications, Sapienza University of Rome, Rome, Italy
| | | | - Nina Miolane
- Department of Electrical and Computer Engineering, UC Santa Barbara, Santa Barbara, USA
| | - Farzana Nasrin
- Department of Mathematics, University of Hawai’i at Mānoa, Hawai’i, USA
| | | | - Bastian Rieck
- Helmholtz Munich, Munich Germany
- Technical University of Munich, Munich Germany
| | - Simone Scardapane
- Department of Information Engineering, Electronics and Telecommunications, Sapienza University of Rome, Rome, Italy
| | | | - Petar Veličković
- Department of Computer Science and Technology, University of Cambridge, Cambridge, UK
- Google Deep-Mind
| | - Bei Wang
- School of Computing, University of Utah, Utah, USA
| | - Yusu Wang
- Computer Science and Engineering Department, University of California San Diego, San Diego, USA
| | - Guo-Wei Wei
- Department of Mathematics, Michigan State University, East Lansing, Michigan, USA
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Levenson RM, Singh Y, Rieck B, Hathaway QA, Farrelly C, Rozenblit J, Prasanna P, Erickson B, Choudhary A, Carlsson G, Sarkar D. Advancing Precision Medicine: Algebraic Topology and Differential Geometry in Radiology and Computational Pathology. J Transl Med 2024; 104:102060. [PMID: 38626875 PMCID: PMC12054847 DOI: 10.1016/j.labinv.2024.102060] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2023] [Revised: 04/08/2024] [Accepted: 04/10/2024] [Indexed: 05/19/2024] Open
Abstract
Precision medicine aims to provide personalized care based on individual patient characteristics, rather than guideline-directed therapies for groups of diseases or patient demographics. Images-both radiology- and pathology-derived-are a major source of information on presence, type, and status of disease. Exploring the mathematical relationship of pixels in medical imaging ("radiomics") and cellular-scale structures in digital pathology slides ("pathomics") offers powerful tools for extracting both qualitative and, increasingly, quantitative data. These analytical approaches, however, may be significantly enhanced by applying additional methods arising from fields of mathematics such as differential geometry and algebraic topology that remain underexplored in this context. Geometry's strength lies in its ability to provide precise local measurements, such as curvature, that can be crucial for identifying abnormalities at multiple spatial levels. These measurements can augment the quantitative features extracted in conventional radiomics, leading to more nuanced diagnostics. By contrast, topology serves as a robust shape descriptor, capturing essential features such as connected components and holes. The field of topological data analysis was initially founded to explore the shape of data, with functional network connectivity in the brain being a prominent example. Increasingly, its tools are now being used to explore organizational patterns of physical structures in medical images and digitized pathology slides. By leveraging tools from both differential geometry and algebraic topology, researchers and clinicians may be able to obtain a more comprehensive, multi-layered understanding of medical images and contribute to precision medicine's armamentarium.
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Affiliation(s)
- Richard M Levenson
- Department of Pathology and Laboratory Medicine, University of California Davis, Davis, California.
| | - Yashbir Singh
- Department of Radiology, Mayo Clinic, Rochester, Minnesota.
| | - Bastian Rieck
- Helmholtz Munich and Technical University of Munich, Munich, Germany
| | - Quincy A Hathaway
- Department of Medical Education, West Virginia University, Morgantown, West Virginia
| | | | | | - Prateek Prasanna
- Department of Biomedical Informatics, Stony Brook University, Stony Brook, New York
| | | | | | - Gunnar Carlsson
- Department of Mathematics, Stanford University, Stanford, California
| | - Deepa Sarkar
- Institute of Genomic Health, Ichan school of Medicine, Mount Sinai, New York
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11
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Siva NK, Singh Y, Hathaway QA, Sengupta PP, Yanamala N. A novel multi-task machine learning classifier for rare disease patterning using cardiac strain imaging data. Sci Rep 2024; 14:10672. [PMID: 38724564 PMCID: PMC11082231 DOI: 10.1038/s41598-024-61201-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2023] [Accepted: 05/02/2024] [Indexed: 05/12/2024] Open
Abstract
To provide accurate predictions, current machine learning-based solutions require large, manually labeled training datasets. We implement persistent homology (PH), a topological tool for studying the pattern of data, to analyze echocardiography-based strain data and differentiate between rare diseases like constrictive pericarditis (CP) and restrictive cardiomyopathy (RCM). Patient population (retrospectively registered) included those presenting with heart failure due to CP (n = 51), RCM (n = 47), and patients without heart failure symptoms (n = 53). Longitudinal, radial, and circumferential strains/strain rates for left ventricular segments were processed into topological feature vectors using Machine learning PH workflow. In differentiating CP and RCM, the PH workflow model had a ROC AUC of 0.94 (Sensitivity = 92%, Specificity = 81%), compared with the GLS model AUC of 0.69 (Sensitivity = 65%, Specificity = 66%). In differentiating between all three conditions, the PH workflow model had an AUC of 0.83 (Sensitivity = 68%, Specificity = 84%), compared with the GLS model AUC of 0.68 (Sensitivity = 52% and Specificity = 76%). By employing persistent homology to differentiate the "pattern" of cardiac deformations, our machine-learning approach provides reasonable accuracy when evaluating small datasets and aids in understanding and visualizing patterns of cardiac imaging data in clinically challenging disease states.
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Affiliation(s)
- Nanda K Siva
- School of Medicine, West Virginia University, Morgantown, WV, USA
- Division of Cardiology, Heart and Vascular Institute, West Virginia University, Morgantown, WV, USA
| | - Yashbir Singh
- Division of Cardiology, Heart and Vascular Institute, West Virginia University, Morgantown, WV, USA
- Department of Radiology, Mayo Clinic, Rochester, MN, USA
| | - Quincy A Hathaway
- School of Medicine, West Virginia University, Morgantown, WV, USA
- Division of Cardiology, Heart and Vascular Institute, West Virginia University, Morgantown, WV, USA
| | - Partho P Sengupta
- Division of Cardiovascular Disease and Hypertension, Rutgers Robert Wood Johnson Medical School, 125 Patterson St, New Brunswick, NJ, 08901, USA.
| | - Naveena Yanamala
- Division of Cardiovascular Disease and Hypertension, Rutgers Robert Wood Johnson Medical School, 125 Patterson St, New Brunswick, NJ, 08901, USA.
- Institute for Software Research, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, USA.
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12
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Bou Dagher L, Madern D, Malbos P, Brochier-Armanet C. Persistent homology reveals strong phylogenetic signal in 3D protein structures. PNAS NEXUS 2024; 3:pgae158. [PMID: 38689707 PMCID: PMC11058471 DOI: 10.1093/pnasnexus/pgae158] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/02/2023] [Accepted: 04/01/2024] [Indexed: 05/02/2024]
Abstract
Changes that occur in proteins over time provide a phylogenetic signal that can be used to decipher their evolutionary history and the relationships between organisms. Sequence comparison is the most common way to access this phylogenetic signal, while those based on 3D structure comparisons are still in their infancy. In this study, we propose an effective approach based on Persistent Homology Theory (PH) to extract the phylogenetic information contained in protein structures. PH provides efficient and robust algorithms for extracting and comparing geometric features from noisy datasets at different spatial resolutions. PH has a growing number of applications in the life sciences, including the study of proteins (e.g. classification, folding). However, it has never been used to study the phylogenetic signal they may contain. Here, using 518 protein families, representing 22,940 protein sequences and structures, from 10 major taxonomic groups, we show that distances calculated with PH from protein structures correlate strongly with phylogenetic distances calculated from protein sequences, at both small and large evolutionary scales. We test several methods for calculating PH distances and propose some refinements to improve their relevance for addressing evolutionary questions. This work opens up new perspectives in evolutionary biology by proposing an efficient way to access the phylogenetic signal contained in protein structures, as well as future developments of topological analysis in the life sciences.
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Affiliation(s)
- Léa Bou Dagher
- Université Claude Bernard Lyon 1, CNRS, VetAgro Sup, Laboratoire de Biométrie et BiologieÉvolutive, UMR5558, F-69622 Villeurbanne, France
- Université Claude Bernard Lyon 1, CNRS, Institut Camille Jordan, UMR5208, F-69622 Villeurbanne, France
- Université Libanaise, Laboratoire de Mathématiques, École Doctorale en Science et Technologie, PO BOX 5 Hadath, Liban
| | - Dominique Madern
- University Grenoble Alpes, CEA, CNRS, IBS, 38000 Grenoble, France
| | - Philippe Malbos
- Université Claude Bernard Lyon 1, CNRS, Institut Camille Jordan, UMR5208, F-69622 Villeurbanne, France
| | - Céline Brochier-Armanet
- Université Claude Bernard Lyon 1, CNRS, VetAgro Sup, Laboratoire de Biométrie et BiologieÉvolutive, UMR5558, F-69622 Villeurbanne, France
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Parastar H, Christmann J, Weller P. Automated 2D peak detection in gas chromatography-ion mobility spectrometry through persistent homology. Anal Chim Acta 2024; 1289:342204. [PMID: 38245205 DOI: 10.1016/j.aca.2024.342204] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2023] [Revised: 12/11/2023] [Accepted: 01/02/2024] [Indexed: 01/22/2024]
Abstract
BACKGROUND Gas chromatography-ion mobility spectrometry (GC-IMS) is a powerful analytical technique which has gained widespread use in a variety of fields. Detecting peaks in GC-IMS data is essential for chemical identification. Topological data analysis (TDA) has the ability to record alterations in topology throughout the entire spectrum of GC-IMS data and retain this data in diagrams known as persistence diagrams. To put it differently, TDA naturally identifies characteristics such as mountains, volcanoes, and their higher-dimensional equivalents within the original data and measures their significance. RESULTS In the present contribution, a novel approach based on persistent homology (a flagship technique of TDA) is suggested for automatic 2D peak detection in GC-IMS. For this purpose, two different GC-IMS data examples (urine and olive oil) are used to show the performance of the proposed method. The outputs of the algorithm are GC-IMS chromatogram with detected peaks, persistence plot showing the importance (intensity) of the detected peaks and a table with retention times (RT), drift times (DT), and persistence scores of detected peaks. The RT and DT can be used for identification of the peaks and persistence scores for quantitation. Additionally, watershed segmentation is applied to the GC-IMS images to index individual peaks and segment overlapping compounds allowing for a more accurate identification and quantification of individual peaks. SIGNIFICANCE Inspection of the results for GC-IMS datasets showed the accurate and reliable performance of the proposed strategy based on persistent homology for automatic 2D GC-IMS peak detection for qualitative and quantitative analysis. In addition, this approach can be easily extended to other types of hyphenated chromatographic and/or spectroscopic data.
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Affiliation(s)
- Hadi Parastar
- Department of Chemistry, Sharif University of Technology, P.O. Box 11155-9516, Tehran, Iran; Institute for Instrumental Analytics and Bioanalytics, Mannheim University of Applied Sciences, 68163, Mannheim, Germany.
| | - Joscha Christmann
- Institute for Instrumental Analytics and Bioanalytics, Mannheim University of Applied Sciences, 68163, Mannheim, Germany
| | - Philipp Weller
- Institute for Instrumental Analytics and Bioanalytics, Mannheim University of Applied Sciences, 68163, Mannheim, Germany.
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14
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Catanzaro MJ, Rizzo S, Kopchick J, Chowdury A, Rosenberg DR, Bubenik P, Diwadkar VA. Topological Data Analysis Captures Task-Driven fMRI Profiles in Individual Participants: A Classification Pipeline Based on Persistence. Neuroinformatics 2024; 22:45-62. [PMID: 37924429 PMCID: PMC11268454 DOI: 10.1007/s12021-023-09645-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 10/11/2023] [Indexed: 11/06/2023]
Abstract
BOLD-based fMRI is the most widely used method for studying brain function. The BOLD signal while valuable, is beset with unique vulnerabilities. The most notable of these is the modest signal to noise ratio, and the relatively low temporal and spatial resolution. However, the high dimensional complexity of the BOLD signal also presents unique opportunities for functional discovery. Topological Data Analyses (TDA), a branch of mathematics optimized to search for specific classes of structure within high dimensional data may provide particularly valuable applications. In this investigation, we acquired fMRI data in the anterior cingulate cortex (ACC) using a basic motor control paradigm. Then, for each participant and each of three task conditions, fMRI signals in the ACC were summarized using two methods: a) TDA based methods of persistent homology and persistence landscapes and b) non-TDA based methods using a standard vectorization scheme. Finally, using machine learning (with support vector classifiers), classification accuracy of TDA and non-TDA vectorized data was tested across participants. In each participant, TDA-based classification out-performed the non-TDA based counterpart, suggesting that our TDA analytic pipeline better characterized task- and condition-induced structure in fMRI data in the ACC. Our results emphasize the value of TDA in characterizing task- and condition-induced structure in regional fMRI signals. In addition to providing our analytical tools for other users to emulate, we also discuss the unique role that TDA-based methods can play in the study of individual differences in the structure of functional brain signals in the healthy and the clinical brain.
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Affiliation(s)
- Michael J Catanzaro
- Iowa State University, Ames, IA, USA.
- Geometric Data Analytics, 343 West Main Street, Durham, NC, 27701, USA.
| | - Sam Rizzo
- Vanderbilt University, Nashville, TN, USA
| | - John Kopchick
- Wayne State University School of Medicine, Detroit, MI, USA
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15
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Madeleine T, Podoliak N, Buchnev O, Membrillo Solis I, Orlova T, van Rossem M, Kaczmarek M, D’Alessandro G, Brodzki J. Topological Learning for the Classification of Disorder: An Application to the Design of Metasurfaces. ACS NANO 2023; 18. [PMID: 38108267 PMCID: PMC10796169 DOI: 10.1021/acsnano.3c08776] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2023] [Revised: 12/01/2023] [Accepted: 12/06/2023] [Indexed: 12/19/2023]
Abstract
Structural disorder can improve the optical properties of metasurfaces, whether it is emerging from some large-scale fabrication methods or explicitly designed and built lithographically. For example, correlated disorder, induced by a minimum inter-nanostructure distance or by hyperuniformity properties, is particularly beneficial for light extraction. Inspired by topology, we introduce numerical descriptors to provide quantitative measures of disorder with universal properties, suitable to treat both uncorrelated and correlated disorder at all length scales. The accuracy of these topological descriptors is illustrated both theoretically and experimentally by using them to design plasmonic metasurfaces with controlled disorder that we then correlate to the strength of their surface lattice resonances. These descriptors are an example of topological tools that can be used for the fast and accurate design of disordered structures or as aid in improving their fabrication methods.
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Affiliation(s)
- Tristan Madeleine
- Mathematical
Sciences, University of Southampton, Southampton SO17 1BJ, United Kingdom
| | - Nina Podoliak
- Physics
and Astronomy, University of Southampton, Southampton SO17 1BJ, United Kingdom
| | - Oleksandr Buchnev
- Optoelectronics
Research Centre and Centre for Photonic Metamaterials, University of Southampton, Southampton SO17 1BJ, United Kingdom
| | | | - Tetiana Orlova
- Physics
and Astronomy, University of Southampton, Southampton SO17 1BJ, United Kingdom
- Infochemistry
Scientific Center, ITMO University, 9 Lomonosova Street, Saint-Petersburg, 191002, Russia
| | - Maria van Rossem
- Physics
and Astronomy, University of Southampton, Southampton SO17 1BJ, United Kingdom
| | - Malgosia Kaczmarek
- Physics
and Astronomy, University of Southampton, Southampton SO17 1BJ, United Kingdom
| | | | - Jacek Brodzki
- Mathematical
Sciences, University of Southampton, Southampton SO17 1BJ, United Kingdom
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16
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Ohki T, Kunii N, Chao ZC. Efficient, continual, and generalized learning in the brain - neural mechanism of Mental Schema 2.0. Rev Neurosci 2023; 34:839-868. [PMID: 36960579 DOI: 10.1515/revneuro-2022-0137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2022] [Accepted: 02/26/2023] [Indexed: 03/25/2023]
Abstract
There has been tremendous progress in artificial neural networks (ANNs) over the past decade; however, the gap between ANNs and the biological brain as a learning device remains large. With the goal of closing this gap, this paper reviews learning mechanisms in the brain by focusing on three important issues in ANN research: efficiency, continuity, and generalization. We first discuss the method by which the brain utilizes a variety of self-organizing mechanisms to maximize learning efficiency, with a focus on the role of spontaneous activity of the brain in shaping synaptic connections to facilitate spatiotemporal learning and numerical processing. Then, we examined the neuronal mechanisms that enable lifelong continual learning, with a focus on memory replay during sleep and its implementation in brain-inspired ANNs. Finally, we explored the method by which the brain generalizes learned knowledge in new situations, particularly from the mathematical generalization perspective of topology. Besides a systematic comparison in learning mechanisms between the brain and ANNs, we propose "Mental Schema 2.0," a new computational property underlying the brain's unique learning ability that can be implemented in ANNs.
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Affiliation(s)
- Takefumi Ohki
- International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo Institutes for Advanced Study, The University of Tokyo, Tokyo 113-0033, Japan
| | - Naoto Kunii
- Department of Neurosurgery, The University of Tokyo, Tokyo 113-0033, Japan
| | - Zenas C Chao
- International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo Institutes for Advanced Study, The University of Tokyo, Tokyo 113-0033, Japan
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17
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Jeon ES, Choi H, Shukla A, Wang Y, Buman MP, Turaga P. Constrained Adaptive Distillation Based on Topological Persistence for Wearable Sensor Data. IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2023; 72:2532014. [PMID: 38818128 PMCID: PMC11137740 DOI: 10.1109/tim.2023.3329818] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2024]
Abstract
Wearable sensor data analysis with persistence features generated by topological data analysis (TDA) has achieved great successes in various applications, however, it suffers from large computational and time resources for extracting topological features. In this paper, our approach utilizes knowledge distillation (KD) that involves the use of multiple teacher networks trained with the raw time-series and persistence images generated by TDA, respectively. However, direct transfer of knowledge from the teacher models utilizing different characteristics as inputs to the student model results in a knowledge gap and limited performance. To address this problem, we introduce a robust framework that integrates multimodal features from two different teachers and enables a student to learn desirable knowledge effectively. To account for statistical differences in multimodalities, entropy based constrained adaptive weighting mechanism is leveraged to automatically balance the effects of teachers and encourage the student model to adequately adopt the knowledge from two teachers. To assimilate dissimilar structural information generated by different style models for distillation, batch and channel similarities within a mini-batch are used. We demonstrate the effectiveness of the proposed method on wearable sensor data.
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Affiliation(s)
- Eun Som Jeon
- Geometric Media Lab, School of Arts, Media and Engineering and School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85281 USA
| | - Hongjun Choi
- Lawrence Livermore National Laboratory, Livermore, CA, USA
| | - Ankita Shukla
- Geometric Media Lab, School of Arts, Media and Engineering and School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85281 USA
| | - Yuan Wang
- Department of Epidemiology and Biostatistics, University of South Carolina, Columbia, SC 29208 USA
| | - Matthew P Buman
- College of Health Solutions, Arizona State University, Phoenix, AZ 85004 USA
| | - Pavan Turaga
- Geometric Media Lab, School of Arts, Media and Engineering and School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85281 USA
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18
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Zhong Y, Zhao J, Deng H, Wu Y, Zhu L, Yang M, Liu Q, Luo G, Ma W, Li H. Integrative bioinformatics analysis to identify novel biomarkers associated with non-obstructive azoospermia. Front Immunol 2023; 14:1088261. [PMID: 36969237 PMCID: PMC10031032 DOI: 10.3389/fimmu.2023.1088261] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2022] [Accepted: 02/22/2023] [Indexed: 03/11/2023] Open
Abstract
AimThis study aimed to identify autophagy-related genes (ARGs) associated with non-obstructive azoospermia and explore the underlying molecular mechanisms.MethodsTwo datasets associated with azoospermia were downloaded from the Gene Expression Omnibus database, and ARGs were obtained from the Human Autophagy-dedicated Database. Autophagy-related differentially expressed genes were identified in the azoospermia and control groups. These genes were subjected to Gene Ontology and Kyoto Encyclopedia of Genes and Genomes, protein–protein interaction (PPI) network, and functional similarity analyses. After identifying the hub genes, immune infiltration and hub gene–RNA-binding protein (RBP)–transcription factor (TF)–miRNA–drug interactions were analyzed.ResultsA total 46 differentially expressed ARGs were identified between the azoospermia and control groups. These genes were enriched in autophagy-associated functions and pathways. Eight hub genes were selected from the PPI network. Functional similarity analysis revealed that HSPA5 may play a key role in azoospermia. Immune cell infiltration analysis revealed that activated dendritic cells were significantly decreased in the azoospermia group compared to those in the control groups. Hub genes, especially ATG3, KIAA0652, MAPK1, and EGFR were strongly correlated with immune cell infiltration. Finally, a hub gene–miRNA–TF–RBP–drug network was constructed.ConclusionThe eight hub genes, including EGFR, HSPA5, ATG3, KIAA0652, and MAPK1, may serve as biomarkers for the diagnosis and treatment of azoospermia. The study findings suggest potential targets and mechanisms for the occurrence and development of this disease.
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Affiliation(s)
- Yucheng Zhong
- Assisted Reproductive Technology Center, Southern Medical University Affiliated Maternal and Child Health Hospital of Foshan, Foshan, Guangdong, China
| | - Jun Zhao
- Assisted Reproductive Technology Center, Southern Medical University Affiliated Maternal and Child Health Hospital of Foshan, Foshan, Guangdong, China
| | - Hao Deng
- Assisted Reproductive Technology Center, Southern Medical University Affiliated Maternal and Child Health Hospital of Foshan, Foshan, Guangdong, China
| | - Yaqin Wu
- Assisted Reproductive Technology Center, Southern Medical University Affiliated Maternal and Child Health Hospital of Foshan, Foshan, Guangdong, China
| | - Li Zhu
- Assisted Reproductive Technology Center, Southern Medical University Affiliated Maternal and Child Health Hospital of Foshan, Foshan, Guangdong, China
| | - Meiqiong Yang
- Assisted Reproductive Technology Center, Southern Medical University Affiliated Maternal and Child Health Hospital of Foshan, Foshan, Guangdong, China
| | - Qianru Liu
- Assisted Reproductive Technology Center, Southern Medical University Affiliated Maternal and Child Health Hospital of Foshan, Foshan, Guangdong, China
| | - Guoqun Luo
- Assisted Reproductive Technology Center, Southern Medical University Affiliated Maternal and Child Health Hospital of Foshan, Foshan, Guangdong, China
| | - Wenmin Ma
- Assisted Reproductive Technology Center, Southern Medical University Affiliated Maternal and Child Health Hospital of Foshan, Foshan, Guangdong, China
- Assist Reproductive Medical Center, Zhaoqing West River Hospital, Zhaoqing, Guangdong, China
- *Correspondence: Wenmin Ma, ; Huan Li,
| | - Huan Li
- Assisted Reproductive Technology Center, Southern Medical University Affiliated Maternal and Child Health Hospital of Foshan, Foshan, Guangdong, China
- *Correspondence: Wenmin Ma, ; Huan Li,
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19
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Ye X, Sun F, Xiang S. TREPH: A Plug-In Topological Layer for Graph Neural Networks. ENTROPY (BASEL, SWITZERLAND) 2023; 25:331. [PMID: 36832697 PMCID: PMC9954936 DOI: 10.3390/e25020331] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/11/2023] [Revised: 02/04/2023] [Accepted: 02/08/2023] [Indexed: 06/18/2023]
Abstract
Topological Data Analysis (TDA) is an approach to analyzing the shape of data using techniques from algebraic topology. The staple of TDA is Persistent Homology (PH). Recent years have seen a trend of combining PH and Graph Neural Networks (GNNs) in an end-to-end manner to capture topological features from graph data. Though effective, these methods are limited by the shortcomings of PH: incomplete topological information and irregular output format. Extended Persistent Homology (EPH), as a variant of PH, addresses these problems elegantly. In this paper, we propose a plug-in topological layer for GNNs, termed Topological Representation with Extended Persistent Homology (TREPH). Taking advantage of the uniformity of EPH, a novel aggregation mechanism is designed to collate topological features of different dimensions to the local positions determining their living processes. The proposed layer is provably differentiable and more expressive than PH-based representations, which in turn is strictly stronger than message-passing GNNs in expressive power. Experiments on real-world graph classification tasks demonstrate the competitiveness of TREPH compared with the state-of-the-art approaches.
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Affiliation(s)
- Xue Ye
- National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China
- School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 101408, China
| | - Fang Sun
- School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
| | - Shiming Xiang
- National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China
- School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 101408, China
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20
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Rammal A, Assaf R, Goupil A, Kacim M, Vrabie V. Machine learning techniques on homological persistence features for prostate cancer diagnosis. BMC Bioinformatics 2022; 23:476. [DOI: 10.1186/s12859-022-04992-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2022] [Accepted: 10/18/2022] [Indexed: 11/14/2022] Open
Abstract
AbstractThe rapid evolution of image processing equipment and techniques ensures the development of novel picture analysis methodologies. One of the most powerful yet computationally possible algebraic techniques for measuring the topological characteristics of functions is persistent homology. It's an algebraic invariant that can capture topological details at different spatial resolutions. Persistent homology investigates the topological features of a space using a set of sampled points, such as pixels. It can track the appearance and disappearance of topological features caused by changes in the nested space created by an operation known as filtration, in which a parameter scale, in our case the intensity of pixels, is increased to detect changes in the studied space over a range of varying scales. In addition, at the level of machine learning there were many studies and articles witnessing recently the combination between homological persistence and machine learning algorithms. On another level, prostate cancer is diagnosed referring to a scoring criterion describing the severity of the cancer called Gleason score. The classical Gleason system defines five histological growth patterns (grades). In our study we propose to study the Gleason score on some glands issued from a new optical microscopy technique called SLIM. This new optical microscopy technique that combines two classic ideas in light imaging: Zernike’s phase contrast microscopy and Gabor’s holography. Persistent homology features are computed on these images. We suggested machine learning methods to classify these images into the corresponding Gleason score. Machine learning techniques applied on homological persistence features was very effective in the detection of the right Gleason score of the prostate cancer in these kinds of images and showed an accuracy of above 95%.
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21
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Pinto L, Gopalan S, Balasubramaniam P. Quantification on the Generalization Performance of Deep Neural Network with Tychonoff Separation Axioms. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2022.06.065] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
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22
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Leykam D, Rondón I, Angelakis DG. Dark soliton detection using persistent homology. CHAOS (WOODBURY, N.Y.) 2022; 32:073133. [PMID: 35907713 DOI: 10.1063/5.0097053] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2022] [Accepted: 07/01/2022] [Indexed: 06/15/2023]
Abstract
Classifying images often requires manual identification of qualitative features. Machine learning approaches including convolutional neural networks can achieve accuracy comparable to human classifiers but require extensive data and computational resources to train. We show how a topological data analysis technique, persistent homology, can be used to rapidly and reliably identify qualitative features in experimental image data. The identified features can be used as inputs to simple supervised machine learning models, such as logistic regression models, which are easier to train. As an example, we consider the identification of dark solitons using a dataset of 6257 labeled atomic Bose-Einstein condensate density images.
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Affiliation(s)
- Daniel Leykam
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543
| | - Irving Rondón
- School of Computational Sciences, Korea Institute for Advanced Study, 85 Hoegi-ro, Seoul 02455, Republic of Korea
| | - Dimitris G Angelakis
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543
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23
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Le MQ, Taylor D. Persistent homology of convection cycles in network flows. Phys Rev E 2022; 105:044311. [PMID: 35590622 DOI: 10.1103/physreve.105.044311] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2021] [Accepted: 03/29/2022] [Indexed: 06/15/2023]
Abstract
Convection is a well-studied topic in fluid dynamics, yet it is less understood in the context of network flows. Here, we incorporate techniques from topological data analysis (namely, persistent homology) to automate the detection and characterization of convective flows (also called cyclic or chiral flows) over networks, particularly those that arise for irreversible Markov chains. As two applications, we study convection cycles arising under the PageRank algorithm and we investigate chiral edge flows for a stochastic model of a bimonomer's configuration dynamics. Our experiments highlight how system parameters-e.g., the teleportation rate for PageRank and the transition rates of external and internal state changes for a monomer-can act as homology regularizers of convection, which we summarize with persistence barcodes and homological bifurcation diagrams. Our approach establishes a connection between the study of convection cycles and homology, the branch of mathematics that formally studies cycles, which has diverse potential applications throughout the sciences and engineering.
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Affiliation(s)
- Minh Quang Le
- Department of Mathematics, University at Buffalo, State University of New York, Buffalo, New York 14260, USA
| | - Dane Taylor
- Department of Mathematics, University at Buffalo, State University of New York, Buffalo, New York 14260, USA
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Extending conventional surface roughness ISO parameters using topological data analysis for shot peened surfaces. Sci Rep 2022; 12:5538. [PMID: 35365741 PMCID: PMC8976008 DOI: 10.1038/s41598-022-09551-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2021] [Accepted: 03/21/2022] [Indexed: 11/30/2022] Open
Abstract
The roughness of material surfaces is of greatest relevance for applications. These include wear, friction, fatigue, cytocompatibility, or corrosion resistance. Today’s descriptors of the International Organization for Standardization show varying performance in discriminating surface roughness patterns. We introduce here a set of surface parameters which are extracted from the appropriate persistence diagram with enhanced discrimination power. Using the finite element method implemented in Abaqus Explicit 2019, we modelled American Rolling Mill Company pure iron specimens (volume 1.5 × 1.5 × 1.0 mm3) exposed to a shot peening procedure. Surface roughness evaluation after each shot impact and single indents were controlled numerically. Conventional and persistence-based evaluation is implemented in Python code and available as open access supplement. Topological techniques prove helpful in the comparison of different shot peened surface samples. Conventional surface area roughness parameters might struggle in distinguishing different shot peening surface topographies, in particular for coverage values > 69%. Above that range, the calculation of conventional parameters leads to overlapping descriptor values. In contrast, lifetime entropy of persistence diagrams and Betti curves provide novel, discriminative one-dimensional descriptors at all coverage ranges. We compare how conventional parameters and persistence parameters describe surface roughness. Conventional parameters are outperformed. These results highlight how topological techniques might be a promising extension of surface roughness methods.
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25
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Morilla I. Repairing the human with artificial intelligence in oncology. Artif Intell Cancer 2021; 2:60-68. [DOI: 10.35713/aic.v2.i5.60] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 10/15/2021] [Revised: 10/26/2021] [Accepted: 10/27/2021] [Indexed: 02/06/2023] Open
Affiliation(s)
- Ian Morilla
- Laboratoire Analyse, Géométrie et Applications - Institut Galilée, Sorbonne Paris Nord University, Paris 75006, France
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26
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Chazal F, Michel B. An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists. Front Artif Intell 2021; 4:667963. [PMID: 34661095 PMCID: PMC8511823 DOI: 10.3389/frai.2021.667963] [Citation(s) in RCA: 77] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2021] [Accepted: 07/16/2021] [Indexed: 11/30/2022] Open
Abstract
With the recent explosion in the amount, the variety, and the dimensionality of available data, identifying, extracting, and exploiting their underlying structure has become a problem of fundamental importance for data analysis and statistical learning. Topological data analysis (tda) is a recent and fast-growing field providing a set of new topological and geometric tools to infer relevant features for possibly complex data. It proposes new well-founded mathematical theories and computational tools that can be used independently or in combination with other data analysis and statistical learning techniques. This article is a brief introduction, through a few selected topics, to basic fundamental and practical aspects of tda for nonexperts.
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Affiliation(s)
- Frédéric Chazal
- Inria Saclay - Île-de-France Research Centre, Palaiseau, France
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Lymberopoulos E, Gentili GI, Alomari M, Sharma N. Topological Data Analysis Highlights Novel Geographical Signatures of the Human Gut Microbiome. Front Artif Intell 2021; 4:680564. [PMID: 34490420 PMCID: PMC8417942 DOI: 10.3389/frai.2021.680564] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2021] [Accepted: 07/28/2021] [Indexed: 01/22/2023] Open
Abstract
Background: There is growing interest in the connection between the gut microbiome and human health and disease. Conventional approaches to analyse microbiome data typically entail dimensionality reduction and assume linearity of the observed relationships, however, the microbiome is a highly complex ecosystem marked by non-linear relationships. In this study, we use topological data analysis (TDA) to explore differences and similarities between the gut microbiome across several countries. Methods: We used curated adult microbiome data at the genus level from the GMrepo database. The dataset contains OTU and demographical data of over 4,400 samples from 19 studies, spanning 12 countries. We analysed the data with tmap, an integrative framework for TDA specifically designed for stratification and enrichment analysis of population-based gut microbiome datasets. Results: We find associations between specific microbial genera and groups of countries. Specifically, both the USA and UK were significantly co-enriched with the proinflammatory genera Lachnoclostridium and Ruminiclostridium, while France and New Zealand were co-enriched with other, butyrate-producing, taxa of the order Clostridiales. Conclusion: The TDA approach demonstrates the overlap and distinctions of microbiome composition between and within countries. This yields unique insights into complex associations in the dataset, a finding not possible with conventional approaches. It highlights the potential utility of TDA as a complementary tool in microbiome research, particularly for large population-scale datasets, and suggests further analysis on the effects of diet and other regionally varying factors.
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Affiliation(s)
- Eva Lymberopoulos
- Department of Clinical and Movement Neurosciences, Institute of Neurology, University College London, London, United Kingdom.,CDT AI-Enabled Healthcare Systems, Institute of Health Informatics, University College London, London, United Kingdom
| | - Giorgia Isabella Gentili
- Department of Clinical and Movement Neurosciences, Institute of Neurology, University College London, London, United Kingdom
| | - Muhannad Alomari
- Department of Clinical and Movement Neurosciences, Institute of Neurology, University College London, London, United Kingdom.,R Data Labs, Rolls-Royce Ltd, Derby, United Kingdom
| | - Nikhil Sharma
- Department of Clinical and Movement Neurosciences, Institute of Neurology, University College London, London, United Kingdom.,National Hospital for Neurology and Neurosurgery, University College London Hospitals NHS Foundation Trust, London, United Kingdom
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