Benjamin Jones,Guo-Wei Wei
Benjamin Jones
Topological data analysis (TDA) has had enormous success in science and engineering in the past decade. Persistent topological Laplacians (PTLs) overcome some limitations of persistent homology, a key technique in TDA, and provide substanti...
Li Shen,Jian Liu,Guo-Wei Wei
Li Shen
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 ≥ 2 has been studied in terms of Mayer homology on N -chain complexes f...
PERSISTENT SHEAF LAPLACIANS [0.03%]
持久层拉普拉斯算子
Xiaoqi Wei,Guo-Wei Wei
Xiaoqi Wei
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...
HETEROGENEOUS PERIDYNAMIC NEURAL OPERATORS: DISCOVER BIOTISSUE CONSTITUTIVE LAW AND MICROSTRUCTURE FROM DIGITAL IMAGE CORRELATION MEASUREMENTS [0.03%]
异构广义神经算子：从数字图像相关测量中发现生物组织本构定律和微观结构
Siavash Jafarzadeh,Stewart Silling,Lu Zhang et al.
Siavash Jafarzadeh et al.
Human tissues are highly organized structures with specific collagen fiber arrangements varying from point to point. The effects of such heterogeneity play an important role for tissue function, and hence it is of critical to discover and u...
Faisal Suwayyid,Guo-Wei Wei
Faisal Suwayyid
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...
Jian Liu,Li Shen,Guo-Wei Wei
Jian Liu
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 suscep...
Dong Chen,Jian Liu,Jie Wu et al.
Dong Chen et al.
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 topo...
GEOMETRIC STRUCTURE GUIDED MODEL AND ALGORITHMS FOR COMPLETE DECONVOLUTION OF GENE EXPRESSION DATA [0.03%]
用于基因表达数据完全去卷积的几何结构引导模型和算法
Duan Chen,Shaoyu Li,Xue Wang
Duan Chen
Complete deconvolution analysis for bulk RNA-seq data is important and helpful to distinguish whether the differences of disease-associated GEPs (gene expression profiles) in tissues of patients and normal controls are due to changes in cel...
PERSISTENT PATH LAPLACIAN [0.03%]
持久路径拉普拉斯算子
Rui Wang,Guo-Wei Wei
Rui Wang
Path homology proposed by S.-T.Yau and his co-workers provides a new mathematical model for directed graphs and networks. Persistent path homology (PPH) extends the path homology with filtration to deal with asymmetry structures. However, P...
Jelena Grbić,Jie Wu,Kelin Xia et al.
Jelena Grbić et al.
We establish a new theory which unifies various aspects of topological approaches for data science, by being applicable both to point cloud data and to graph data, including networks beyond pairwise interactions. We generalize simplicial co...