arXiv subjects

Guo-Wei Wei

Publications and source records attributed to Guo-Wei Wei.

At least 37 records · Page 2Linked to original sources

arXiv2026

VARIANT: Web Server for Decoding and Analyzing Viral Mutations at Genome and Protein Levels

A comprehensive analysis of viral mutations is essential for understanding viral evolution, disease epidemiology, diagnosis, drug resistance, etc. However, challenges remain in capturing complex mutation patterns and supporting diverse viral families with varying genome architectures. To address these needs, we present VARIANT, an web server for mutational analysis of RNA viral genomes and associated viral products across both single- and multi-segment virus genomes. The server takes as input a viral reference genome, a reference protein sequence, and/or multiple sequence alignment, and automatically provides full annotation of mutation types, including standard categories such as point mutations (missense, silent, and nonsense), insertions, deletions, or frameshift events in both coding and non-coding regions. In addition, VARIANT detects three biologically significant mutation patterns that are overlooked by conventional software/packages: ``row mutations'' (consecutive substitutions within a window of 3 nts), ``hot mutations'' (two non-consecutive substitutions within a window of 3 nts), and potential programmed ribosomal frameshifting (PRF) regions. The server currently contains automatic analysis of major viral pathogens, including SARS-CoV-2, HIV-1, Influenza H3N2, Ebola virus, and Chikungunya virus. It also allows users to analyze customized viruses. Users can track VARIANT analysis progress in real time, visualize mutation distributions, and download structured results in ZIP format. VARIANT also incorporates dual graph topology analysis to classify frameshifting element structures from dot-bracket notation input. This feature enables systematic comparison of RNA secondary structure motifs across viral families by mapping structures to a comprehensive library of dual graph topologies. The web server is freely available at https://variant.up.railway.app.

q-bio.QM↗

arXiv2026

Subspace Tensor Orthogonal Rotation Model (STORM) for Batch Alignment, Cell Type Deconvolution, and Gene Imputation in Spatial Transcriptomic Data

Spatial transcriptomics data analysis integrates cellular transcriptional activity with spatial coordinates to identify spatial domains, infer cell-type dynamics, and characterize gene expression patterns within tissues. Despite recent advances, significant challenges remain, including the treatment of batch effects, the handling of mixed cell-type signals, and the imputation of poorly measured or missing gene expression. This work addresses these challenges by introducing a novel Subspace Tensor Orthogonal Rotation Model (STORM) that aligns multiple slices which vary in their spatial dimensions and geometry by considering them at the level of physical patterns or microenvironments. To this end, STORM presents an irregular tensor factorization technique for decomposing a collection of gene expression matrices and integrating them into a shared latent space for downstream analysis. In contrast to black-box deep learning approaches, the proposed model is inherently interpretable. Numerical experiments demonstrate state-of-the-art performance in vertical and horizontal batch integration, cell-type deconvolution, and unmeasured gene imputation for spatial transcriptomics data.

q-bio.QM↗

arXiv2026

PETLS: PErsistent Topological Laplacian Software

Persistent topological Laplacians are operators that provide persistent Betti numbers and additional multiscale geometric information through the eigenvalues of the persistent topological Laplacian matrix. We introduce a framework and novel algorithm to aid in the computation of persistent topological Laplacians. We implement existing and new persistent Laplacian algorithms in an efficient and flexible C++ library with Python bindings, titled PETLS: PErsistent Topological Laplacian Software. As part of this library, we interface with several complexes commonly used in topological data analysis (TDA), such as simplicial, alpha, directed flag, Dowker, and cellular Sheaf. Because increased efficiency broadens the set of computationally feasible applications, we provide recommendations on how to use algorithms and complexes for data analysis in machine learning.

math.AT↗

arXiv2026

Multi-dimensional Persistent Sheaf Laplacians for Image Analysis

We propose a multi-dimensional persistent sheaf Laplacian (MPSL) framework on simplicial complexes for image analysis. The proposed method is motivated by the strong sensitivity of commonly used dimensionality reduction techniques, such as principal component analysis (PCA), to the choice of reduced dimension. Rather than selecting a single reduced dimension or averaging results across dimensions, we exploit complementary advantages of multiple reduced dimensions. At a given dimension, image samples are regarded as simplicial complexes, and persistent sheaf Laplacians are utilized to extract a multiscale localized topological spectral representation for individual image samples. Statistical summaries of the resulting spectra are then aggregated across scales and dimensions to form multiscale multi-dimensional image representations. We evaluate the proposed framework on the COIL20 and ETH80 image datasets using standard classification protocols. Experimental results show that the proposed method provides more stable performance across a wide range of reduced dimensions and achieves consistent improvements to PCA-based baselines in moderate dimensional regimes.

cs.CV↗

arXiv2026

Persistent Sheaf Laplacian Analysis of Protein Stability and Solubility Changes upon Mutation

Genetic mutations frequently disrupt protein structure, stability, and solubility, acting as primary drivers for a wide spectrum of diseases. Despite the critical importance of these molecular alterations, existing computational models often lack interpretability, and fail to integrate essential physicochemical interaction. To overcome these limitations, we propose SheafLapNet, a unified predictive framework grounded in the mathematical theory of Topological Deep Learning (TDL) and Persistent Sheaf Laplacian (PSL). Unlike standard Topological Data Analysis (TDA) tools such as persistent homology, which are often insensitive to heterogeneous information, PSL explicitly encodes specific physical and chemical information such as partial charges directly into the topological analysis. SheafLapNet synergizes these sheaf-theoretic invariants with advanced protein transformer features and auxiliary physical descriptors to capture intrinsic molecular interactions in a multiscale and mechanistic manner. To validate our framework, we employ rigorous benchmarks for both regression and classification tasks. For stability prediction, we utilize the comprehensive S2648 and S350 datasets. For solubility prediction, we employ the PON-Sol2 dataset, which provides annotations for increased, decreased, or neutral solubility changes. By integrating these multi-perspective features, SheafLapNet achieves state-of-the-art performance across these diverse benchmarks, demonstrating that sheaf-theoretic modeling significantly enhances both interpretability and generalizability in predicting mutation-induced structural and functional changes.

math.SP↗

arXiv2025

Persistent commutative algebra on graphs and hypergraphs

We introduce a persistent commutative algebra for studying the algebraic and combinatorial evolution of edge ideals of graphs and hypergraphs under filtration. Building on the Persistent Stanley--Reisner Theory (PSRT), we develop the notion of persistent edge ideals and analyze their graded Betti numbers across the filtration of graphs or hypergraphs. To enable this analysis, we establish a persistent extension of Hochster's formula, providing a functorial correspondence between algebraic and topological persistence. We further examine the behavior of Betti splittings in the persistent setting, proving a general inequality that extends the classical splitting result to the filtration of monomial ideals. Motivated by graph-theoretic interpretations, we introduce persistent minimal vertex covers, which encode the temporal structure of combinatorial dependencies within evolving graphs or hypergraphs. Applications to alignment-free genomic classification and molecular isomer discrimination demonstrate the interpretability and representatbility of persistent edge ideals as algebraic invariants, bridging combinatorial commutative algebra and data science.

math.AC↗

arXiv2025

Multiscale Grassmann Manifolds for Single-Cell Data Analysis

Single-cell data analysis seeks to characterize cellular heterogeneity based on high-dimensional gene expression profiles. Conventional approaches represent each cell as a vector in Euclidean space, which limits their ability to capture intrinsic correlations and multiscale geometric structures. We propose a multiscale framework based on Grassmann manifolds that integrates machine learning with subspace geometry for single-cell data analysis. By generating embeddings under multiple representation scales, the framework combines their features from different geometric views into a unified Grassmann manifold. A power-based scale sampling function is introduced to control the selection of scales and balance in- formation across resolutions. Experiments on nine benchmark single-cell RNA-seq datasets demonstrate that the proposed approach effectively preserves meaningful structures and provides stable clustering performance, particularly for small to medium-sized datasets. These results suggest that Grassmann manifolds offer a coherent and informative foundation for analyzing single cell data.

cs.LG↗

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

GBNL: Graded Betti Number Learning of Complex Biological Data

While persistent homology is widely used for data shape analysis, persistent commutative algebra (PCA) has seen limited adoption in machine learning and data science. Unlike persistent homology, which delivers topological invariants in the form of Betti numbers, PCA provides both algebraic invariants and graded Betti numbers. However, graded Betti numbers have seldom been applied to real-world data. In this work, we introduce the first-of-its-kind application of commutative algebra graded Betti numbers in machine learning and data science. Specifically, we present Graded Betti Number Learning (GBNL) for protein-nucleic acid binding prediction. Protein-DNA/RNA interactions are fundamental to cellular processes such as replication, transcription, translation, and gene regulation, and their understanding and prediction remain challenging. GBNL represents each nucleic acid sequence as a family of $k$-mer-specific sets and derives persistent graded Betti invariants from PCA, generating multiscale topological representations of local nucleotide organization. To incorporate cross-molecule context, these graded Betti representations are paired with transformer-based protein embeddings, linking nucleotide-level signals with global protein patterns. The proposed graded Betti representations effectively detect single-site mutations and distinguish complete mutation patterns. Operating on primary sequences with minimal preprocessing, GBNL bridges commutative algebra, reduced algebraic topology, combinatorics, and machine learning, establishing a new paradigm for comparative sequence analysis. Numerical studies using three datasets highlight the success of GBNL in protein-nucleic acid binding prediction.

math.AC↗

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

Predicting Protein-Nucleic Acid Flexibility Using Persistent Sheaf Laplacians

Understanding the flexibility of protein-nucleic acid complexes, often characterized by atomic B-factors, is essential for elucidating their structure, dynamics, and functions, such as reactivity and allosteric pathways. Traditional models such as Gaussian Network Models (GNM) and Elastic Network Models (ENM) often fall short in capturing multiscale interactions, especially in large or complex biomolecular systems. In this work, we apply the Persistent Sheaf Laplacian (PSL) framework for the B-factor prediction of protein-nucleic acid complexes. The PSL model integrates multiscale analysis, algebraic topology, combinatoric Laplacians, and sheaf theory for data representation. It reveals topological invariants in its harmonic spectra and captures the homotopic shape evolution of data with its non-harmonic spectra. Its localization enables accurate B-factor predictions. We benchmark our method on three diverse datasets, including protein-RNA and nucleic-acid-only structures, and demonstrate that PSL consistently outperforms existing models such as GNM and multiscale FRI (mFRI), achieving up to a 21% improvement in Pearson correlation coefficient for B-factor prediction. These results highlight the robustness and adaptability of PSL in modeling complex biomolecular interactions and suggest its potential utility in broader applications such as mutation impact analysis and drug design.

q-bio.BM↗

arXiv2025

Topological Sequence Analysis of Genomes: Category theory Approaches

Sequence data, such as DNA, RNA, and protein sequences, exhibit intricate, multi-scale structures that pose significant challenges for conventional analysis methods, particularly those relying on alignment or purely statistical representations. In this work, we introduce category-based topological sequence analysis (CTSA ) of genomes. CTSA models a sequence as a resolution category, capturing its hierarchical structure through a categorical construction. Substructure complexes are then derived from this categorical representation, and their persistent homology is computed to extract multi-scale topological features. Our models depart from traditional alignment-free approaches by incorporating structured mathematical formalisms rooted in sequence topology. The resulting topological signatures provide informative representations across a variety of tasks, including the phylogenetic analysis of SARS-CoV-2 variants and the prediction of protein-nucleic acid binding affinities. Comparative studies were carried out against six state-of-the-art methods. Experimental results demonstrate that CTSA achieves excellent and consistent performance in these tasks, suggesting its general applicability and robustness. Beyond sequence analysis, the proposed framework opens new directions for the integration of categorical and homological theories for biological sequence analysis.

q-bio.GN↗

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

Computational Drug Repurposing for Alzheimer's Disease via Sheaf Theoretic Population-Scale Analysis of snRNA-seq Data

Single-cell and single-nucleus RNA sequencing (scRNA-seq /snRNA-seq) are widely used to reveal heterogeneity in cells, showing a growing potential for precision and personalized medicine. Nonetheless, sustainable drug discovery must be based on a population-level understanding of molecular mechanisms, which calls for the population-scale analysis of scRNA-seq/snRNA-seq data. This work introduces a sequential target-drug selection model for drug repurposing against Alzheimer's Disease (AD) targets inferred from population-level snRNA-seq studies of AD progression in microglia cells as well as different cell types taken from an AD affected brain vascular tissue atlas, involving hundreds of thousands of nuclei from multi-patient and multi-regional studies. We utilize Persistent Sheaf Laplacians (PSL) to facilitate a Protein-Protein Interaction (PPI) analysis of AD targets inferred from differential gene expression (DEG), and then use machine learning models to predict repurpose-able DrugBank compounds for molecular targeting. We screen the efficacy of different DrugBank small compounds and further examine their central nervous system (CNS)-relevant ADMET (Absorption, Distribution, Metabolism, Excretion, and Toxicity), resulting in a list of lead candidates for AD treatment. The list of significant genes establishes a target domain for effective machine learning based AD drug repurposing analysis of DrugBank small compounds to treat AD related molecular targets.

q-bio.MN↗

arXiv2025

Interaction Topological Transformer for Multiscale Learning in Porous Materials

Porous materials exhibit vast structural diversity and support critical applications in gas storage, separations, and catalysis. However, predictive modeling remains challenging due to the multiscale nature of structure-property relationships, where performance is governed by both local chemical environments and global pore-network topology. These complexities, combined with sparse and unevenly distributed labeled data, hinder generalization across material families. We propose the Interaction Topological Transformer (ITT), a unified data-efficient framework that leverages novel interaction topology to capture materials information across multiple scales and multiple levels, including structural, elemental, atomic, and pairwise-elemental organization. ITT extracts scale-aware features that reflect both compositional and relational structure within complex porous frameworks, and integrates them through a built-in Transformer architecture that supports joint reasoning across scales. Trained using a two-stage strategy, i.e., self-supervised pretraining on 0.6 million unlabeled structures followed by supervised fine-tuning, ITT achieves state-of-the-art, accurate, and transferable predictions for adsorption, transport, and stability properties. This framework provides a principled and scalable path for learning-guided discovery in structurally and chemically diverse porous materials.

cs.LG↗

arXiv2025

Persistent Khovanov homology of tangles

Knot data analysis (KDA), which studies data with curve-type structures such as knots, links, and tangles, has emerging as a promising geometric topology approach in data science. While evolutionary Khovanov homology has been developed to analyze the global persistent topological features of links, it has limitations in capturing the local topological characteristics of knots and links. To address this challenge, we introduce the persistent Khovanov homology of tangles, providing a new mathematical framework for characterizing local features in curve-type data. While tangle homology is inherently abstract, we provide a concrete functor which maps the category of tangles to the category of modules, enabling the computation of tangle homology. Additionally, we employ planar algebra to construct a category of tangles without invoking fixed boundaries, thereby giving rise to a persistent Khovanov homology functor that enables practical applications. This framework provides a theoretical foundation and practical strategies for the topological analysis of curve-type data.

math.GT↗

arXiv2025

Computing Khovanov homology of tangles

The computation of Khovanov homology for tangles has significant potential applications, yet explicit computational studies remain limited. In this work, we present a method for computing the Khovanov homology of tangles via an arc reduction approach, and we derive the Poincaré polynomial for simple tangles. Furthermore, we compute the Poincaré polynomials of tangles with at most three crossings.

math.GT↗

arXiv2025

Khovanov homology of tangles: algorithm and computation

Knot, link, and tangle theory is crucial in both mathematical theory and practical application, including quantum physics, molecular biology, and structural chemistry. Unlike knots and links, tangles impose more relaxed constraints, allowing the presence of arcs, which makes them particularly valuable for broader applications. Although Khovanov homology for knots and links has been extensively studied, its computation for tangles remains largely unexplored. In our recent work, we provide a topological quantum field theory (TQFT) construction for the Khovanov homology of tangles, offering a more concrete method for its computation. The primary contribution of this work is a comprehensive approach to the computation of the Khovanov homology of tangles, offering both a detailed computation procedure and a practical guide for implementing algorithms through codes to facilitate the calculation. This contribution paves the way for further studies and applications of Khovanov homology in the context of tangles.

math.GT↗