arXiv subjects

Hongsong Feng

Publications and source records attributed to Hongsong Feng.

At least 19 recordsLinked to original sources

arXiv2026

Persistent magnitude homology on finite metric space

Magnitude homology is an emerging approach that captures the intrinsic topological and geometric features of metric spaces. It offers a distinct theoretical lens for interpreting structural information within topological and geometric data analysis. This work introduces persistent magnitude homology, an extension of magnitude homology that captures multi-scale geometric and topological features of metric spaces. We construct the category of finite metric spaces with isometric embeddings and show that magnitude homology defines a functor to the category of abelian groups, naturally leading to the definition of persistent magnitude homology. We also introduce weighted persistent modules and weighted barcodes to offer both an algebraic and visual description of persistent magnitude homology. Additionally, we present an isometry theorem that relates interleaving distances and bottleneck distances, and establish stability results for persistent magnitude homology and magnitude profile. These results establish the stability of magnitude-based descriptors, bridging the gap between theory and practical application.

math.AT↗

arXiv2026

CAKR: Commutative algebra k-mer representations for genomics

Despite the availability of various sequence analysis models, comparative genomic analysis remains a challenge in genomics, genetics, and phylogenetics. Commutative algebra, a fundamental tool in algebraic geometry and number theory, has rarely been used in data and biological sciences. In this study, we introduce commutative algebra $k$-mer representations as a nonlinear algebraic framework for analyzing genomic sequences. This representation bridges commutative algebra, algebraic topology, combinatorics, and machine learning to establish a mathematical framework for comparative genomic analysis. We evaluate its effectiveness on three tasks including genetic variant classification, phylogenetic tree reconstruction, and viral classification, typically requiring alignment-based, alignment-free, and machine-learning approaches, respectively. In this work, we show that commutative algebra k-mer representations outperform five state-of-the-art sequence analysis methods across twelve primary datasets, with two additional supplementary fragment-placement benchmarks, especially in viral classification, and maintain relatively stable predictive accuracy as dataset size increases, underscoring scalability and robustness.

q-bio.QM↗

arXiv2026

Commutative Algebra Learning for Protein Flexibility Analysis

Protein flexibility, commonly quantified by B-factors, is closely related to protein structure and function. However, accurate B-factor prediction remains challenging due to the multiscale nature of protein structures and the complexity of atomic interactions. In this work, we propose a commutative algebra-based learning framework, termed CAL, for protein B-factor prediction. Unlike many biomolecular prediction tasks that rely primarily on global structural representations, B-factor prediction requires an accurate characterization of the local geometric environments surrounding individual atoms. To address this challenge, CAL employs commutative algebra theory to construct localized algebraic descriptors at multiple spatial scales. On a benchmark dataset of 364 proteins, CAL improves prediction accuracy by 34.5\% over the classical Gaussian network model (GNM). Extensive experiments demonstrate that CAL achieves robust and consistent performance across diverse datasets and is competitive with existing state-of-the-art methods. Furthermore, by integrating CAL with machine learning, we develop a blind prediction model capable of cross-protein B-factor prediction. Overall, CAL provides an effective, efficient, and mathematically principled framework for protein flexibility prediction and offers a powerful approach for analyzing and predicting localized structural properties in complex biomolecular systems.

q-bio.BM↗

arXiv2026

Persistent local Laplacian prediction of protein-ligand binding affinities

Accurate prediction of protein-ligand binding affinity remains a central challenge in structure-based drug discovery. The effectiveness of machine learning models critically depends on the quality of molecular descriptors, for which advanced mathematical frameworks provide powerful tools. In this work, we employ a novel mathematical theory, termed the persistent local Laplacian (PLL), to construct molecular descriptors that capture localized geometric and topological features of biomolecular structures. The PLL framework addresses key limitations of traditional topological data analysis methods, such as persistent homology and the persistent Laplacian, which are often insensitive to local structural variations, while maintaining high computational efficiency. The resulting molecular descriptors are integrated with advanced machine learning algorithms to develop accurate predictive models for protein-ligand binding affinity. The proposed models are systematically evaluated on three well-established benchmark datasets, demonstrating consistently strong and competitive predictive performance. Computational results show that the PLL-based models outperform existing approaches, highlighting their potential as a powerful tool for drug discovery, protein engineering, and broader applications in science and engineering.

q-bio.BM↗

arXiv2026

Local Laplacian: theory and models for data analysis

While topological data analysis has emerged as a powerful paradigm for structural inference, its foundational tools, notably persistent homology and the persistent Laplacian, are frequently insensitive to localized structural fluctuations and suffer from prohibitive computational costs on large-scale datasets. To bridge this gap, we introduce the persistent local Laplacian formalism, which is designed to extract fine-grained local topological and geometric signatures while enabling a highly efficient, parallelizable computational workflow. On the theoretical front, we prove a generalized persistent Hodge isomorphism, establishing that the harmonic space of the persistent local Laplacian is isomorphic to the persistent local homology. Furthermore, we derive a unitary equivalence between the persistent local Laplacian and the persistent Laplacian of its corresponding link complex at a shifted dimension. This spectral conjugacy establishes the mathematical foundation for developing efficient computational schemes to resolve persistent local spectral invariants. We further extend this construction to point clouds and graph-structured data, characterizing their persistent local spectral properties through combinatorial filtrations. The resulting architecture is inherently decoupled, facilitating massive parallelization and rendering it uniquely scalable for large-scale network analysis and distributed computational environments.

math.AT↗

arXiv2025

Commutative Algebra Modeling in Materials Science -- A Case Study on Metal-Organic Frameworks (MOFs)

Metal-organic frameworks (MOFs) are a class of important crystalline and highly porous materials whose hierarchical geometry and chemistry hinder interpretable predictions in materials properties. Commutative algebra is a branch of abstract algebra that has been rarely applied in data and material sciences. We introduce the first ever commutative algebra modeling and prediction in materials science. Specifically, category-specific commutative algebra (CSCA) is proposed as a new framework for MOF representation and learning. It integrates element-based categorization with multiscale algebraic invariants to encode both local coordination motifs and global network organization of MOFs. These algebraically consistent, chemically aware representations enable compact, interpretable, and data efficient modeling of MOF properties such as Henry's constants and uptake capacities for common gases. Compared to traditional geometric and graph-based approaches, CSCA achieves comparable or superior predictive accuracy while substantially improving interpretability and stability across data sets. By aligning commutative algebra with the chemical hierarchy, the CSCA establishes a rigorous and generalizable paradigm for understanding structure and property relationships in porous materials and provides a nonlinear algebra-based framework for data-driven material discovery.

cond-mat.mtrl-sci↗

arXiv2025

CAP: Commutative Algebra Prediction of Protein-Nucleic Acid Binding Affinities

An accurate prediction of protein-nucleic acid binding affinity is vital for deciphering genomic processes, yet existing approaches often struggle in reconciling high accuracy with interpretability and computational efficiency. In this study, we introduce commutative algebra prediction (CAP), which couples persistent Stanley-Reisner theory with advanced sequence embedding for predicting protein-nucleic acid binding affinities. CAP encodes proteins through transformer-learned embeddings that retain long-range evolutionary context and represents DNA and RNA with $\textit{k}$-mer algebra embeddings derived from persistent facet ideals, which capture fine-scale nucleotide geometry. We demonstrate that CAP surpasses the SVSBI protein-nucleic acid benchmark and, in a further test, maintains reasonable performance on newly curated protein-RNA and protein-nucleic acid datasets. Leveraging only primary sequences, CAP generalizes to any protein-nucleic acid pair with minimal preprocessing, enabling genome-scale analyses without 3D structural data and promising faster virtual screening for drug discovery and protein engineering.

q-bio.QM↗

arXiv2025

Commutative algebra neural network reveals genetic origins of diseases

Genetic mutations can disrupt protein structure, stability, and solubility, contributing to a wide range of diseases. Existing predictive models often lack interpretability and fail to integrate physical and chemical interactions critical to molecular mechanisms. Moreover, current approaches treat disease association, stability changes, and solubility alterations as separate tasks, limiting model generalizability. In this study, we introduce a unified framework based on multiscale commutative algebra to capture intrinsic physical and chemical interactions for the first time. Leveraging Persistent Stanley-Reisner Theory, we extract multiscale algebraic invariants to build a Commutative Algebra neural Network (CANet). Integrated with transformer features and auxiliary physical features, we apply CANet to tackle three key domains for the first time: disease-associated mutations, mutation-induced protein stability changes, and solubility changes upon mutations. Across six benchmark tasks, CANet and its gradient boosting tree counterpart, CATree, consistently attain state-of-the-art performance, achieving up to 7.5% improvement in predictive accuracy. Our approach offers multiscale, mechanistic, interpretable,and generalizable models for predicting disease-mutation associations.

q-bio.QM↗

arXiv2025

CAML: Commutative algebra machine learning -- a case study on protein-ligand binding affinity prediction

Recently, Suwayyid and Wei have introduced commutative algebra as an emerging paradigm for machine learning and data science. In this work, we integrate commutative algebra machine learning (CAML) for the prediction of protein-ligand binding affinities. Specifically, we apply persistent Stanley-Reisner theory, a key concept in combinatorial commutative algebra, to the affinity predictions of protein-ligand binding and metalloprotein-ligand binding. We introduce three new algorithms, i.e., element-specific commutative algebra, category-specific commutative algebra, and commutative algebra on bipartite complexes, to address the complexity of data involved in (metallo) protein-ligand complexes. We show that the proposed CAML outperforms other state-of-the-art methods in (metallo) protein-ligand binding affinity predictions.

q-bio.BM↗

arXiv2025

Persistent Sheaf Laplacian Analysis of Protein Flexibility

Protein flexibility, measured by the B-factor or Debye-Waller factor, is essential for protein functions such as structural support, enzyme activity, cellular communication, and molecular transport. Theoretical analysis and prediction of protein flexibility are crucial for protein design, engineering, and drug discovery. In this work, we introduce the persistent sheaf Laplacian (PSL), an effective tool in topological data analysis, to model and analyze protein flexibility. By representing the local topology and geometry of protein atoms through the multiscale harmonic and non-harmonic spectra of PSLs, the proposed model effectively captures protein flexibility and provides accurate, robust predictions of protein B-factors. Our PSL model demonstrates an increase in accuracy of 32% compared to the classical Gaussian network model (GNM) in predicting B-factors for a dataset of 364 proteins. Additionally, we construct a blind machine learning prediction method utilizing global and local protein features. Extensive computations and comparisons validate the effectiveness of the proposed PSL model for B-factor predictions.

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

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

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↗

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

ChatGPT in Drug Discovery: A Case Study on Anti-Cocaine Addiction Drug Development with Chatbots

The birth of ChatGPT, a cutting-edge language model-based chatbot developed by OpenAI, ushered in a new era in AI. However, due to potential pitfalls, its role in rigorous scientific research is not clear yet. This paper vividly showcases its innovative application within the field of drug discovery. Focused specifically on developing anti-cocaine addiction drugs, the study employs GPT-4 as a virtual guide, offering strategic and methodological insights to researchers working on generative models for drug candidates. The primary objective is to generate optimal drug-like molecules with desired properties. By leveraging the capabilities of ChatGPT, the study introduces a novel approach to the drug discovery process. This symbiotic partnership between AI and researchers transforms how drug development is approached. Chatbots become facilitators, steering researchers towards innovative methodologies and productive paths for creating effective drug candidates. This research sheds light on the collaborative synergy between human expertise and AI assistance, wherein ChatGPT's cognitive abilities enhance the design and development of potential pharmaceutical solutions. This paper not only explores the integration of advanced AI in drug discovery but also reimagines the landscape by advocating for AI-powered chatbots as trailblazers in revolutionizing therapeutic innovation.

cs.AI↗

arXiv2023

Knot data analysis using multiscale Gauss link integral

In the past decade, topological data analysis (TDA) has emerged as a powerful approach in data science. The main technique in TDA is persistent homology, which tracks topological invariants over the filtration of point cloud data using algebraic topology. Although knot theory and related subjects are a focus of study in mathematics, their success in practical applications is quite limited due to the lack of localization and quantization. We address these challenges by introducing knot data analysis (KDA), a new paradigm that incorporating curve segmentation and multiscale analysis into the Gauss link integral. The resulting multiscale Gauss link integral (mGLI) recovers the global topological properties of knots and links at an appropriate scale but offers multiscale feature vectors to capture the local structures and connectivities of each curve segment at various scales. The proposed mGLI significantly outperforms other state-of-the-art methods in benchmark protein flexibility analysis, including earlier persistent homology-based methods. Our approach enables the integration of artificial intelligence (AI) and KDA for general curve-like objects and data.

math.GT↗

arXiv2023

Machine Learning Study of the Extended Drug-target Interaction Network informed by Pain Related Voltage-Gated Sodium Channels

Pain is a significant global health issue, and the current treatment options for pain management have limitations in terms of effectiveness, side effects, and potential for addiction. There is a pressing need for improved pain treatments and the development of new drugs. Voltage-gated sodium channels, particularly Nav1.3, Nav1.7, Nav1.8, and Nav1.9, play a crucial role in neuronal excitability and are predominantly expressed in the peripheral nervous system. Targeting these channels may provide a means to treat pain while minimizing central and cardiac adverse effects. In this study, we construct protein-protein interaction (PPI) networks based on pain-related sodium channels and develop a corresponding drug-target interaction (DTI) network to identify potential lead compounds for pain management. To ensure reliable machine learning predictions, we carefully select 111 inhibitor datasets from a pool of over 1,000 targets in the PPI network. We employ three distinct machine learning algorithms combined with advanced natural language processing (NLP)-based embeddings, specifically pre-trained transformer and autoencoder representations. Through a systematic screening process, we evaluate the side effects and repurposing potential of over 150,000 drug candidates targeting Nav1.7 and Nav1.8 sodium channels. Additionally, we assess the ADMET (absorption, distribution, metabolism, excretion, and toxicity) properties of these candidates to identify leads with near-optimal characteristics. Our strategy provides an innovative platform for the pharmacological development of pain treatments, offering the potential for improved efficacy and reduced side effects.

q-bio.BM↗

arXiv2023

Multi-objective Molecular Optimization for Opioid Use Disorder Treatment Using Generative Network Complex

Opioid Use Disorder (OUD) has emerged as a significant global public health issue, with complex multifaceted conditions. Due to the lack of effective treatment options for various conditions, there is a pressing need for the discovery of new medications. In this study, we propose a deep generative model that combines a stochastic differential equation (SDE)-based diffusion modeling with the latent space of a pretrained autoencoder model. The molecular generator enables efficient generation of molecules that are effective on multiple targets, specifically the mu, kappa, and delta opioid receptors. Furthermore, we assess the ADMET (absorption, distribution, metabolism, excretion, and toxicity) properties of the generated molecules to identify drug-like compounds. To enhance the pharmacokinetic properties of some lead compounds, we employ a molecular optimization approach. We obtain a diverse set of drug-like molecules. We construct binding affinity predictors by integrating molecular fingerprints derived from autoencoder embeddings, transformer embeddings, and topological Laplacians with advanced machine learning algorithms. Further experimental studies are needed to evaluate the pharmacological effects of these drug-like compounds for OUD treatment. Our machine learning platform serves as a valuable tool in designing and optimizing effective molecules for addressing OUD.

cs.LG↗