arXiv subjects

Guo-Wei Wei

Publications and source records attributed to Guo-Wei Wei.

At least 73 records · Page 4Linked to original sources

arXiv2024

Multiscale Jones Polynomial and Persistent Jones Polynomial for Knot Data Analysis

Many structures in science, engineering, and art can be viewed as curves in 3-space. The entanglement of these curves plays a crucial role in determining the functionality and physical properties of materials. Many concepts in knot theory provide theoretical tools to explore the complexity and entanglement of curves in 3-space. However, classical knot theory primarily focuses on global topological properties and lacks the consideration of local structural information, which is critical in practical applications. In this work, two localized models based on the Jones polynomial, namely the multiscale Jones polynomial and the persistent Jones polynomial, are proposed. The stability of these models, especially the insensitivity of the multiscale and persistent Jones polynomial models to small perturbations in curve collections, is analyzed, thus ensuring their robustness for real-world applications.

math.GT↗

arXiv2024

Rapid response to fast viral evolution using AlphaFold 3-assisted topological deep learning

The fast evolution of SARS-CoV-2 and other infectious viruses poses a grand challenge to the rapid response in terms of viral tracking, diagnostics, and design and manufacture of monoclonal antibodies (mAbs) and vaccines, which are both time-consuming and costly. This underscores the need for efficient computational approaches. Recent advancements, like topological deep learning (TDL), have introduced powerful tools for forecasting emerging dominant variants, yet they require deep mutational scanning (DMS) of viral surface proteins and associated three-dimensional (3D) protein-protein interaction (PPI) complex structures. We propose an AlphaFold 3 (AF3)-assisted multi-task topological Laplacian (MT-TopLap) strategy to address this need. MT-TopLap combines deep learning with topological data analysis (TDA) models, such as persistent Laplacians (PL) to extract detailed topological and geometric characteristics of PPIs, thereby enhancing the prediction of DMS and binding free energy (BFE) changes upon virus mutations. Validation with four experimental DMS datasets of SARS-CoV-2 spike receptor-binding domain (RBD) and the human angiotensin-converting enzyme-2 (ACE2) complexes indicates that our AF3 assisted MT-TopLap strategy maintains robust performance, with only an average 1.1% decrease in Pearson correlation coefficients (PCC) and an average 9.3% increase in root mean square errors (RMSE), compared with the use of experimental structures. Additionally, AF3-assisted MT-TopLap achieved a PCC of 0.81 when tested with a SARS-CoV-2 HK.3 variant DMS dataset, confirming its capability to accurately predict BFE changes and adapt to new experimental data, thereby showcasing its potential for rapid and effective response to fast viral evolution.

q-bio.BM↗

arXiv2024

Persistent Directed Flag Laplacian (PDFL)-Based Machine Learning for Protein-Ligand Binding Affinity Prediction

Directionality in molecular and biomolecular networks plays a significant role in the accurate represention of the complex, dynamic, and asymmetrical nature of interactions present in protein-ligand binding, signal transduction, and biological pathways. Most traditional techniques of topological data analysis (TDA), such as persistent homology (PH) and persistent Laplacian (PL), overlook this aspect in their standard form. To address this, we present the persistent directed flag Laplacian (PDFL), which incorporates directed flag complexes to account for edges with directionality originated from polarization, gene regulation, heterogeneous interactions, etc. This study marks the first application of the PDFL, providing an in-depth analysis of spectral graph theory combined with machine learning. Besides its superior accuracy and reliability, the PDFL model offers simplicity by requiring only raw inputs without complex data processing. We validated our multi-kernel PDFL model for its scoring power against other state-of-art methods on three popular benchmarks, namely PDBbind v2007, v2013, and v2016. Computational results indicate that the proposed PDFL model outperforms competitors in protein-ligand binding affinity predictions, indicating that PDFL is a promising tool for protein engineering, drug discovery, and general applications in science and engineering.

q-bio.BM↗

arXiv2024

Persistent de Rham-Hodge Laplacians in Eulerian representation for manifold topological learning

Recently, topological data analysis has become a trending topic in data science and engineering. However, the key technique of topological data analysis, i.e., persistent homology, is defined on point cloud data, which does not work directly for data on manifolds. Although earlier evolutionary de Rham-Hodge theory deals with data on manifolds, it is inconvenient for machine learning applications because of the numerical inconsistency caused by remeshing the involving manifolds in the Lagrangian representation. In this work, we introduce persistent de Rham-Hodge Laplacian, or persistent Hodge Laplacian (PHL) as an abbreviation, for manifold topological learning. Our PHLs are constructed in the Eulerian representation via structure-persevering Cartesian grids, avoiding the numerical inconsistency over the multiscale manifolds. To facilitate the manifold topological learning, we propose a persistent Hodge Laplacian learning algorithm for data on manifolds or volumetric data. As a proof-of-principle application of the proposed manifold topological learning model, we consider the prediction of protein-ligand binding affinities with two benchmark datasets. Our numerical experiments highlight the power and promise of the proposed method.

math.DG↗

arXiv2024

Multiscale differential geometry learning for protein flexibility analysis

Protein flexibility is crucial for understanding protein structures, functions, and dynamics, and it can be measured through experimental methods such as X-ray crystallography. Theoretical approaches have also been developed to predict B-factor values, which reflect protein flexibility. Previous models have made significant strides in analyzing B-factors by fitting experimental data. In this study, we propose a novel approach for B-factor prediction using differential geometry theory, based on the assumption that the intrinsic properties of proteins reside on a family of low-dimensional manifolds embedded within the high-dimensional space of protein structures. By analyzing the mean and Gaussian curvatures of a set of kernel-function-defined low-dimensional manifolds, we develop effective and robust multiscale differential geometry (mDG) models. Our mDG model demonstrates a 27\% increase in accuracy compared to the classical Gaussian network model (GNM) in predicting B-factors for a dataset of 364 proteins. Additionally, by incorporating both global and local protein features, we construct a highly effective machine learning model for the blind prediction of B-factors. Extensive least-squares approximations and machine learning-based blind predictions validate the effectiveness of the mDG modeling approach for B-factor prediction.

q-bio.BM↗

arXiv2024

Graph-Based Bidirectional Transformer Decision Threshold Adjustment Algorithm for Class-Imbalanced Molecular Data

Data sets with imbalanced class sizes, where one class size is much smaller than that of others, occur exceedingly often in many applications, including those with biological foundations, such as disease diagnosis and drug discovery. Therefore, it is extremely important to be able to identify data elements of classes of various sizes, as a failure to do so can result in heavy costs. Nonetheless, many data classification procedures do not perform well on imbalanced data sets as they often fail to detect elements belonging to underrepresented classes. In this work, we propose the BTDT-MBO algorithm, incorporating Merriman-Bence-Osher (MBO) approaches and a bidirectional transformer, as well as distance correlation and decision threshold adjustments, for data classification tasks on highly imbalanced molecular data sets, where the sizes of the classes vary greatly. The proposed technique not only integrates adjustments in the classification threshold for the MBO algorithm in order to help deal with the class imbalance, but also uses a bidirectional transformer procedure based on an attention mechanism for self-supervised learning. In addition, the model implements distance correlation as a weight function for the similarity graph-based framework on which the adjusted MBO algorithm operates. The proposed method is validated using six molecular data sets and compared to other related techniques. The computational experiments show that the proposed technique is superior to competing approaches even in the case of a high class imbalance ratio.

cs.LG↗

arXiv2024

Topology-preserving Hodge Decomposition in the Eulerian Representation

The Hodge decomposition is a fundamental result in differential geometry and algebraic topology, particularly in the study of differential forms on a Riemannian manifold. Despite extensive research in the past few decades, topology-preserving Hodge decomposition of scalar and vector fields on manifolds with boundaries in the Eulerian representation remains a challenge due to the implicit incorporation of appropriate topology-preserving boundary conditions. In this work, we introduce a comprehensive 5-component topology-preserving Hodge decomposition that unifies normal and tangential components in the Cartesian representation. Implicit representations of planar and volumetric regions defined by level-set functions have been developed. Numerical experiments on various objects, including single-cell RNA velocity, validate the effectiveness of our approach, confirming the expected rigorous $L^2$-orthogonality and the accurate cohomology.

math.DG↗

arXiv2024

Mayer-homology learning prediction of protein-ligand binding affinities

Artificial intelligence-assisted drug design is revolutionizing the pharmaceutical industry. Effective molecular features are crucial for accurate machine learning predictions, and advanced mathematics plays a key role in designing these features. Persistent homology theory, which equips topological invariants with persistence, provides valuable insights into molecular structures. The calculation of Betti numbers is based on differential that typically satisfy $d^2 = 0$. Our recent work has extended this concept by employing Mayer homology with a generalized differential that satisfies $d^N = 0$ for $N \geq 2$, leading to the development of persistent Mayer homology (PMH) theory and richer topological information across various scales. In this study, we utilize PMH to create a novel multiscale topological vectorization for molecular representation, offering valuable tools for descriptive and predictive analysis in molecular data and machine learning prediction. Specifically, benchmark tests on established protein-ligand datasets, including PDBbind-2007, PDBbind-2013, and PDBbind-2016, demonstrate the superior performance of our Mayer homology models in predicting protein-ligand binding affinities.

q-bio.BM↗

arXiv2024

Position: Topological Deep Learning is the New Frontier for Relational Learning

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.

cs.LG↗

arXiv2024

Evolutionary Khovanov homology

Knot theory is a study of the embedding of closed circles into three-dimensional Euclidean space, motivated the ubiquity of knots in daily life and human civilization. However, the current knot theory focuses on the topology rather than metric. As such, the application of knot theory remains primitive and qualitative. Motivated by the need of quantitative knot data analysis (KDA), this work implements the metric into knot theory, the evolutionary Khovanov homology (EKH), to facilitate a multiscale KDA of real-world data. It is demonstrated that EKH exhibits non-trivial knot invariants at appropriate scales even if the global topological structure of a knot is simple. The proposed EKH has a great potential for KDA and knot learning.

math.GT↗

arXiv2024

Benchmarking AlphaFold3's protein-protein complex accuracy and machine learning prediction reliability for binding free energy changes upon mutation

AlphaFold 3 (AF3), the latest version of protein structure prediction software, goes beyond its predecessors by predicting protein-protein complexes. It could revolutionize drug discovery and protein engineering, marking a major step towards comprehensive, automated protein structure prediction. However, independent validation of AF3's predictions is necessary. Evaluated using the SKEMPI 2.0 database which involves 317 protein-protein complexes and 8338 mutations, AF3 complex structures give rise to a very good Pearson correlation coefficient of 0.86 for predicting protein-protein binding free energy changes upon mutation, slightly less than the 0.88 achieved earlier with the Protein Data Bank (PDB) structures. Nonetheless, AF3 complex structures led to a 8.6% increase in the prediction RMSE compared to original PDB complex structures. Additionally, some of AF3's complex structures have large errors, which were not captured in its ipTM performance metric. Finally, it is found that AF3's complex structures are not reliable for intrinsically flexible regions or domains.

q-bio.BM↗

arXiv2024

Persistent interaction topology in data analysis

Topological data analysis, as a tool for extracting topological features and characterizing geometric shapes, has experienced significant development across diverse fields. Its key mathematical techniques include persistent homology and the recently developed persistent Laplacians. However, classic mathematical models like simplicial complexes often struggle to provide a localized topological description for interactions or individual elements within a complex system involving a specific set of elements. In this work, we introduce persistent interaction homology and persistent interaction Laplacian that emphasize individual interacting elements in the system. We demonstrate the stability of persistent interaction homology as a persistent module. Furthermore, for a finite discrete set of points in the Euclidean space, we provide the construction of persistent interaction Vietoris-Rips complexes and compute their interaction homology and interaction Laplacians. The proposed methods hold significant promise for analyzing heterogeneously interactive data and emphasizing specific elements in data. Their utility for data science is demonstrated with applications to molecules.

math.AT↗

arXiv2023

Multiscale differential geometry learning of networks with applications to single-cell RNA sequencing data

Single-cell RNA sequencing (scRNA-seq) has emerged as a transformative technology, offering unparalleled insights into the intricate landscape of cellular diversity and gene expression dynamics. The analysis of scRNA-seq data poses challenges attributed to both sparsity and the extensive number of genes implicated. An increasing number of computational tools are devised for analyzing and interpreting scRNA-seq data. We present a multiscale differential geometry (MDG) strategy to exploit the geometric and biological properties inherent in scRNA-seq data. We assume that those intrinsic properties of cells lies on a family of low-dimensional manifolds embedded in the high-dimensional space of scRNA-seq data. Subsequently, we explore these properties via multiscale cell-cell interactive manifolds. Our multiscale curvature-based representation serves as a powerful approach to effectively encapsulate the complex relationships in the cell-cell network. We showcase the utility of our novel approach by demonstrating its effectiveness in classifying cell types. This innovative application of differential geometry in scRNA-seq analysis opens new avenues for understanding the intricacies of biological networks and holds great potential for network analysis in other fields.

q-bio.MN↗

arXiv2023

Persistent sheaf Laplacians

Recently various types of topological Laplacians have been studied from the perspective of data analysis. The spectral theory of these Laplacians has significantly extended the scope of algebraic topology and data analysis. Inspired by the theory of persistent Laplacians and cellular sheaves, this work develops the theory of persistent sheaf Laplacians for cellular sheaves, and describes how to construct sheaves for a point cloud where each point is associated with a quantity that can be devised to embed physical properties. As a result, the spectra of persistent sheaf Laplacians encode both geometrical and non-geometrical information of the given point cloud. The theory of persistent sheaf Laplacians is an elegant method for fusing different types of data and has huge potential for future development.

math.AT↗

arXiv2023

Persistent Dirac of Path and Hypergraph

This work introduces the development of path Dirac and hypergraph Dirac operators, along with an exploration of their persistence. These operators excel in distinguishing between harmonic and non-harmonic spectra, offering valuable insights into the subcomplexes within these structures. The paper showcases the functionality of these operators through a series of examples in various contexts. An important facet of this research involves examining the operators' sensitivity to filtration, emphasizing their capacity to adapt to topological changes. The paper also explores a significant application of persistent path Dirac and persistent hypergraph Dirac in the field of molecular science, specifically in the analysis of molecular structures. The study introduces strict preorders derived from molecular structures, which generate graphs and digraphs with intricate path structures. The depth of information within these path complexes reflects the complexity of different preorder classes influenced by molecular structures. This characteristic underscores the effectiveness of these tools in the realm of topological data analysis.

math.AT↗

arXiv2023

Persistent Mayer homology and persistent Mayer Laplacian

In algebraic topology, the differential (i.e., boundary operator) typically satisfies $d^{2}=0$. However, the generalized differential $d^{N}=0$ for an integer $N\geq 2$ has been studied in terms of Mayer homology on $N$-chain complexes for more than eighty years. We introduce Mayer Laplacians on $N$-chain complexes. We show that both Mayer homology and Mayer Laplacians offer considerable application potential, providing topological and geometric insights to spaces. We also introduce persistent Mayer homology and persistent Mayer Laplacians at various $N$. The Wasserstein distance and stability of persistence diagrams associated with Mayer homology are investigated. Our computational experiments indicate that the topological features offered by persistent Mayer homology and spectrum given by persistent Mayer Laplacians hold substantial promise for large, complex, and diverse data. We envision that the present work serves as an inaugural step towards integrating Mayer homology and Mayer Laplacians into the realm of topological data analysis.

math.AT↗

arXiv2023

Multiscale Topology in Interactomic Network: From Transcriptome to Antiaddiction Drug Repurposing

The escalating drug addiction crisis in the United States underscores the urgent need for innovative therapeutic strategies. This study embarked on an innovative and rigorous strategy to unearth potential drug repurposing candidates for opioid and cocaine addiction treatment, bridging the gap between transcriptomic data analysis and drug discovery. We initiated our approach by conducting differential gene expression analysis on addiction-related transcriptomic data to identify key genes. We propose a novel topological differentiation to identify key genes from a protein-protein interaction (PPI) network derived from DEGs. This method utilizes persistent Laplacians to accurately single out pivotal nodes within the network, conducting this analysis in a multiscale manner to ensure high reliability. Through rigorous literature validation, pathway analysis, and data-availability scrutiny, we identified three pivotal molecular targets, mTOR, mGluR5, and NMDAR, for drug repurposing from DrugBank. We crafted machine learning models employing two natural language processing (NLP)-based embeddings and a traditional 2D fingerprint, which demonstrated robust predictive ability in gauging binding affinities of DrugBank compounds to selected targets. Furthermore, we elucidated the interactions of promising drugs with the targets and evaluated their drug-likeness. This study delineates a multi-faceted and comprehensive analytical framework, amalgamating bioinformatics, topological data analysis and machine learning, for drug repurposing in addiction treatment, setting the stage for subsequent experimental validation. The versatility of the methods we developed allows for applications across a range of diseases and transcriptomic datasets.

q-bio.BM↗

arXiv2023

Poisson-Boltzmann based machine learning (PBML) model for electrostatic analysis

Electrostatics is of paramount importance to chemistry, physics, biology, and medicine. The Poisson-Boltzmann (PB) theory is a primary model for electrostatic analysis. However, it is highly challenging to compute accurate PB electrostatic solvation free energies for macromolecules due to the nonlinearity, dielectric jumps, charge singularity , and geometric complexity associated with the PB equation. The present work introduces a PB based machine learning (PBML) model for biomolecular electrostatic analysis. Trained with the second-order accurate MIBPB solver, the proposed PBML model is found to be more accurate and faster than several eminent PB solvers in electrostatic analysis. The proposed PBML model can provide highly accurate PB electrostatic solvation free energy of new biomolecules or new conformations generated by molecular dynamics with much reduced computational cost.

physics.chem-ph↗