arXiv subjects

Guo-Wei Wei

Publications and source records attributed to Guo-Wei Wei.

At least 91 records · Page 5Linked to original sources

arXiv2023

Interaction homotopy and interaction homology

Interactions in complex systems are widely observed across various fields, drawing increased attention from researchers. In mathematics, efforts are made to develop various theories and methods for studying the interactions between spaces. In this work, we present an algebraic topology framework to explore interactions between spaces. We introduce the concept of interaction spaces and investigate their homotopy, singular homology, and simplicial homology. Furthermore, we demonstrate that interaction singular homology serves as an invariant under interaction homotopy. We believe that the proposed framework holds potential for practical applications.

math.AT↗

arXiv2023

ChatGPT for Computational Topology

ChatGPT represents a significant milestone in the field of artificial intelligence (AI), finding widespread applications across diverse domains. However, its effectiveness in mathematical contexts has been somewhat constrained by its susceptibility to conceptual errors. Concurrently, topological data analysis (TDA), a relatively new discipline, has garnered substantial interest in recent years. Nonetheless, the advancement of TDA is impeded by the limited understanding of computational algorithms and coding proficiency among theoreticians. This work endeavors to bridge the gap between theoretical topological concepts and their practical implementation in computational topology through the utilization of ChatGPT. We showcase how a pure theoretician, devoid of computational experience and coding skills, can effectively transform mathematical formulations and concepts into functional code for computational topology with the assistance of ChatGPT. Our strategy outlines a productive process wherein a mathematician trains ChatGPT on pure mathematical concepts, steers ChatGPT towards generating computational topology code, and subsequently validates the generated code using established examples. Our specific case studies encompass the computation of Betti numbers, Laplacian matrices, and Dirac matrices for simplicial complexes, as well as the persistence of various homologies and Laplacians. Furthermore, we explore the application of ChatGPT in computing recently developed topological theories for hypergraphs and digraphs. This work serves as an initial step towards effectively transforming pure mathematical theories into practical computational tools, with the ultimate goal of enabling real applications across diverse fields.

math.AT↗

arXiv2023

Integration of persistent Laplacian and pre-trained transformer for protein solubility changes upon mutation

Protein mutations can significantly influence protein solubility, which results in altered protein functions and leads to various diseases. Despite of tremendous effort, machine learning prediction of protein solubility changes upon mutation remains a challenging task as indicated by the poor scores of normalized Correct Prediction Ratio (CPR). Part of the challenge stems from the fact that there is no three-dimensional (3D) structures for the wild-type and mutant proteins. This work integrates persistent Laplacians and pre-trained Transformer for the task. The Transformer, pretrained with hunderds of millions of protein sequences, embeds wild-type and mutant sequences, while persistent Laplacians track the topological invariant change and homotopic shape evolution induced by mutations in 3D protein structures, which are rendered from AlphaFold2. The resulting machine learning model was trained on an extensive data set labeled with three solubility types. Our model outperforms all existing predictive methods and improves the state-of-the-art up to 15%.

q-bio.BM↗

arXiv2023

Combinatorial and Hodge Laplacians: Similarity and Difference

As key subjects in spectral geometry and combinatorial graph theory respectively, the (continuous) Hodge Laplacian and the combinatorial Laplacian share similarities in revealing the topological dimension and geometric shape of data and in their realization of diffusion and minimization of harmonic measures. It is believed that they also both associate with vector calculus, through the gradient, curl, and divergence, as argued in the popular usage of "Hodge Laplacians on graphs" in the literature. Nevertheless, these Laplacians are intrinsically different in their domains of definitions and applicability to specific data formats, hindering any in-depth comparison of the two approaches. To facilitate the comparison and bridge the gap between the combinatorial Laplacian and Hodge Laplacian for the discretization of continuous manifolds with boundary, we further introduce Boundary-Induced Graph (BIG) Laplacians using tools from Discrete Exterior Calculus (DEC). BIG Laplacians are defined on discrete domains with appropriate boundary conditions to characterize the topology and shape of data. The similarities and differences of the combinatorial Laplacian, BIG Laplacian, and Hodge Laplacian are then examined. Through an Eulerian representation of 3D domains as level-set functions on regular grids, we show experimentally the conditions for the convergence of BIG Laplacian eigenvalues to those of the Hodge Laplacian for elementary shapes.

math.DG↗

arXiv2023

Analyzing Single Cell RNA Sequencing with Topological Nonnegative Matrix Factorization

Single-cell RNA sequencing (scRNA-seq) is a relatively new technology that has stimulated enormous interest in statistics, data science, and computational biology due to the high dimensionality, complexity, and large scale associated with scRNA-seq data. Nonnegative matrix factorization (NMF) offers a unique approach due to its meta-gene interpretation of resulting low-dimensional components. However, NMF approaches suffer from the lack of multiscale analysis. This work introduces two persistent Laplacian regularized NMF methods, namely, topological NMF (TNMF) and robust topological NMF (rTNMF). By employing a total of 12 datasets, we demonstrate that the proposed TNMF and rTNMF significantly outperform all other NMF-based methods. We have also utilized TNMF and rTNMF for the visualization of popular Uniform Manifold Approximation and Projection (UMAP) and t-distributed stochastic neighbor embedding (t-SNE).

stat.ML↗

arXiv2023

K-Nearest-Neighbors Induced Topological PCA for scRNA Sequence Data Analysis

Single-cell RNA sequencing (scRNA-seq) is widely used to reveal heterogeneity in cells, which has given us insights into cell-cell communication, cell differentiation, and differential gene expression. However, analyzing scRNA-seq data is a challenge due to sparsity and the large number of genes involved. Therefore, dimensionality reduction and feature selection are important for removing spurious signals and enhancing downstream analysis. Traditional PCA, a main workhorse in dimensionality reduction, lacks the ability to capture geometrical structure information embedded in the data, and previous graph Laplacian regularizations are limited by the analysis of only a single scale. We propose a topological Principal Components Analysis (tPCA) method by the combination of persistent Laplacian (PL) technique and L$_{2,1}$ norm regularization to address multiscale and multiclass heterogeneity issues in data. We further introduce a k-Nearest-Neighbor (kNN) persistent Laplacian technique to improve the robustness of our persistent Laplacian method. The proposed kNN-PL is a new algebraic topology technique which addresses the many limitations of the traditional persistent homology. Rather than inducing filtration via the varying of a distance threshold, we introduced kNN-tPCA, where filtrations are achieved by varying the number of neighbors in a kNN network at each step, and find that this framework has significant implications for hyper-parameter tuning. We validate the efficacy of our proposed tPCA and kNN-tPCA methods on 11 diverse benchmark scRNA-seq datasets, and showcase that our methods outperform other unsupervised PCA enhancements from the literature, as well as popular Uniform Manifold Approximation (UMAP), t-Distributed Stochastic Neighbor Embedding (tSNE), and Projection Non-Negative Matrix Factorization (NMF) by significant margins.

q-bio.QM↗

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

Artificial intelligence-aided protein engineering: from topological data analysis to deep protein language models

Protein engineering is an emerging field in biotechnology that has the potential to revolutionize various areas, such as antibody design, drug discovery, food security, ecology, and more. However, the mutational space involved is too vast to be handled through experimental means alone. Leveraging accumulative protein databases, machine learning (ML) models, particularly those based on natural language processing (NLP), have considerably expedited protein engineering. Moreover, advances in topological data analysis (TDA) and artificial intelligence-based protein structure prediction, such as AlphaFold2, have made more powerful structure-based ML-assisted protein engineering strategies possible. This review aims to offer a comprehensive, systematic, and indispensable set of methodological components, including TDA and NLP, for protein engineering and to facilitate their future development.

q-bio.BM↗

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↗

arXiv2023

Mathematics-assisted directed evolution and protein engineering

Directed evolution is a molecular biology technique that is transforming protein engineering by creating proteins with desirable properties and functions. However, it is experimentally impossible to perform the deep mutational scanning of the entire protein library due to the enormous mutational space, which scales as $20^N$ , where N is the number of amino acids. This has led to the rapid growth of AI-assisted directed evolution (AIDE) or AI-assisted protein engineering (AIPE) as an emerging research field. Aided with advanced natural language processing (NLP) techniques, including long short-term memory, autoencoder, and transformer, sequence-based embeddings have been dominant approaches in AIDE and AIPE. Persistent Laplacians, an emerging technique in topological data analysis (TDA), have made structure-based embeddings a superb option in AIDE and AIPE. We argue that a class of persistent topological Laplacians (PTLs), including persistent Laplacians, persistent path Laplacians, persistent sheaf Laplacians, persistent hypergraph Laplacians, persistent hyperdigraph Laplacians, and evolutionary de Rham-Hodge theory, can effectively overcome the limitations of the current TDA and offer a new generation of more powerful TDA approaches. In the general framework of topological deep learning, mathematics-assisted directed evolution (MADE) has a great potential for future protein engineering.

q-bio.BM↗

arXiv2023

Persistent Laplacian-enhanced Algorithm for Scarcely Labeled Data Classification

The success of many machine learning (ML) methods depends crucially on having large amounts of labeled data. However, obtaining enough labeled data can be expensive, time-consuming, and subject to ethical constraints for many applications. One approach that has shown tremendous value in addressing this challenge is semi-supervised learning (SSL); this technique utilizes both labeled and unlabeled data during training, often with much less labeled data than unlabeled data, which is often relatively easy and inexpensive to obtain. In fact, SSL methods are particularly useful in applications where the cost of labeling data is especially expensive, such as medical analysis, natural language processing (NLP), or speech recognition. A subset of SSL methods that have achieved great success in various domains involves algorithms that integrate graph-based techniques. These procedures are popular due to the vast amount of information provided by the graphical framework and the versatility of their applications. In this work, we propose an algebraic topology-based semi-supervised method called persistent Laplacian-enhanced graph MBO (PL-MBO) by integrating persistent spectral graph theory with the classical Merriman-Bence- Osher (MBO) scheme. Specifically, we use a filtration procedure to generate a sequence of chain complexes and associated families of simplicial complexes, from which we construct a family of persistent Laplacians. Overall, it is a very efficient procedure that requires much less labeled data to perform well compared to many ML techniques, and it can be adapted for both small and large datasets. We evaluate the performance of the proposed method on data classification, and the results indicate that the proposed technique outperforms other existing semi-supervised algorithms.

cs.LG↗

arXiv2023

Persistent topological Laplacian analysis of SARS-CoV-2 variants

Topological data analysis (TDA) is an emerging field in mathematics and data science. Its central technique, persistent homology, has had tremendous success in many science and engineering disciplines. However, persistent homology has limitations, including its incapability of describing the homotopic shape evolution of data during filtration. Persistent topological Laplacians (PTLs), such as persistent Laplacian and persistent sheaf Laplacian, were proposed to overcome the drawback of persistent homology. In this work, we examine the modeling and analysis power of PTLs in the study of the protein structures of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) spike receptor binding domain (RBD) and its variants, i.e., Alpha, Beta, Gamma, BA.1, and BA.2. First, we employ PTLs to study how the RBD mutation-induced structural changes of RBD-angiotensin-converting enzyme 2 (ACE2) binding complexes are captured in the changes of spectra of the PTLs among SARS-CoV-2 variants. Additionally, we use PTLs to analyze the binding of RBD and ACE2-induced structural changes of various SARS-CoV-2 variants. Finally, we explore the impacts of computationally generated RBD structures on PTL-based machine learning, including deep learning, and predictions of deep mutational scanning datasets for the SARS-CoV-2 Omicron BA.2 variant. Our results indicate that PTLs have advantages over persistent homology in analyzing protein structural changes and provide a powerful new TDA tool for data science.

q-bio.QM↗

arXiv2023

Persistent hyperdigraph homology and persistent hyperdigraph Laplacians

Hypergraphs are useful mathematical models for describing complex relationships among members of a structured graph, while hyperdigraphs serve as a generalization that can encode asymmetric relationships in the data. However, obtaining topological information directly from hyperdigraphs remains a challenge. To address this issue, we introduce hyperdigraph homology in this work. We also propose topological hyperdigraph Laplacians, which can extract both harmonic spectra and non-harmonic spectra from directed and internally organized data. Moreover, we introduce persistent hyperdigraph homology and persistent hyperdigraph Laplacians through filtration, enabling the capture of topological persistence and homotopic shape evolution of directed and structured data across multiple scales. The proposed methods offer new multiscale algebraic topology tools for topological data analysis.

math.AT↗

arXiv2023

Machine-learning Repurposing of DrugBank Compounds for Opioid Use Disorder

Opioid use disorder (OUD) is a chronic and relapsing condition that involves the continued and compulsive use of opioids despite harmful consequences. The development of medications with improved efficacy and safety profiles for OUD treatment is urgently needed. Drug repurposing is a promising option for drug discovery due to its reduced cost and expedited approval procedures. Computational approaches based on machine learning enable the rapid screening of DrugBank compounds, identifying those with the potential to be repurposed for OUD treatment. We collected inhibitor data for four major opioid receptors and used advanced machine learning predictors of binding affinity that fuse the gradient boosting decision tree algorithm with two natural language processing (NLP)-based molecular fingerprints and one traditional 2D fingerprint. Using these predictors, we systematically analyzed the binding affinities of DrugBank compounds on four opioid receptors. Based on our machine learning predictions, we were able to discriminate DrugBank compounds with various binding affinity thresholds and selectivities for different receptors. The prediction results were further analyzed for ADMET (absorption, distribution, metabolism, excretion, and toxicity), which provided guidance on repurposing DrugBank compounds for the inhibition of selected opioid receptors. The pharmacological effects of these compounds for OUD treatment need to be tested in further experimental studies and clinical trials. Our machine learning studies provide a valuable platform for drug discovery in the context of OUD treatment.

q-bio.BM↗

arXiv2023

Machine-learning Analysis of Opioid Use Disorder Informed by MOR, DOR, KOR, NOR and ZOR-Based Interactome Networks

Opioid use disorder (OUD) continuously poses major public health challenges and social implications worldwide with dramatic rise of opioid dependence leading to potential abuse. Despite that a few pharmacological agents have been approved for OUD treatment, the efficacy of said agents for OUD requires further improvement in order to provide safer and more effective pharmacological and psychosocial treatments. Preferable therapeutic treatments of OUD rely on the advances in understanding the neurobiological mechanism of opioid dependence. Proteins including mu, delta, kappa, nociceptin, and zeta opioid receptors are the direct targets of opioids. Each receptor has a large protein-protein interaction (PPI) network, that behaves differently when subjected to various treatments, thus increasing the complexity in the drug development process for an effective opioid addiction treatment. The report below analyzes the work by presenting a PPI-network informed machine-learning study of OUD. We have examined more than 500 proteins in the five opioid receptor networks and subsequently collected 74 inhibitor datasets. Machine learning models were constructed by pairing gradient boosting decision tree (GBDT) algorithm with two advanced natural language processing (NLP)-based molecular fingerprints. With these models, we systematically carried out evaluations of screening and repurposing potential of drug candidates for four opioid receptors. In addition, absorption, distribution, metabolism, excretion, and toxicity (ADMET) properties were also considered in the screening of potential drug candidates. Our study can be a valuable and promising tool of pharmacological development for OUD treatments.

q-bio.BM↗

arXiv2023

Topological data analysis hearing the shapes of drums and bells

Mark Kac asked a famous question in 1966 entitled Can one hear the shape of a drum?, a spectral geometry problem that has intrigued mathematicians for the last six decades and is important to many other fields, such as architectural acoustics, audio forensics, pattern recognition, radiology, and imaging science. A related question is how to hear the shape of a drum. We show that the answer was given in the set of 65 Zenghouyi chime bells dated back to 475-433 B.C. in China. The set of chime bells gradually varies their sizes and weights to enable melodies, intervals, and temperaments. The same design principle was used in many other musical instruments, such as xylophones, pan flutes, pianos, etc. We reveal that there is a fascinating connection between the progression pattern of many musical instruments and filtration (or spectral sequence) in topological data analysis (TDA). We argue that filtration-induced evolutionary de Rham-Hodge theory provides a new mathematical foundation for musical instruments. Its discrete counterpart, persistent Laplacians and many other persistent topological Laplacians, including persistent sheaf Laplacians and persistent path Laplacians are briefly discussed.

math.HO↗