BIMSA > Shing Toung Yau
Professor Shing Toung Yau

Group: Statistics, Probability and Data Science

Office: A3-2-206

Email: stephenyau@bimsa.cn

Research Field: Complex Geometry, Control Theory, Computer Science, Financial Mathematics, Bioinformation

CV

Biography

Stephen Yau received his PhD degree from the State University of New York at Stony Brook in 1976. He has served as a member of the Institute for Advanced Study at Princeton, an assistant professor at Harvard University under Benjamin Pierce, and later joined the University of Illinois at Chicago, where he taught for over 30 years in the departments of mathematics, statistics, and computer science.
Stephen Yau has made significant original contributions in international cutting-edge research fields, including mathematics, applied mathematics and control theory, computer science, financial mathematics, and bio informatics. He solved some famous conjectures in complex geometry and singularity theory, and was the first to successfully use Lie algebras to study hypersurface singularities in algebraic geometry, a algebra that is now known as Yau algebra among his peers. He solved the Mitter conjecture, completely solving the theoretical problem of nonlinear filters, which will have far-reaching implications for modern industries, including national defense. In the field of bio informatics, his work on the 2D representation of DNA and protein was published in the world's top journal, "Nucleic Acids Research". Recently, he pioneered the natural vector method for representing genomes and proteins. He has published over 200 academic papers, including top international mathematics journals such as PNAS, Annals of Mathematics, and Inventiones Mathematicae.

Education Experience

  • 1974 - 1976      Stony Brook University      Doctor
  • 1973 - 1974      Stony Brook University      Master
  • 1970 - 1973      CUHK

Publication

  • [1] Jiayi Kang, Xiaopei Jiao, and Stephen S.-T. Yau, Estimation of the Linear System via Optimal Transportation and Its Application for Missing Data Observations, IEEE Transactions on Automatic Control (2025)
  • [2] Shi, J.*, Jiao, X.*, & Yau, S. S.-T., A Novel Logarithmic Transformed Deep Galerkin Approach to Optimal Filtering Problem, accepted by Proceeding of 2024 IEEE 63rd Conference on Decision and Control (CDC) (2024)
  • [3] Y Tao, J Kang, SST Yau, The Stochastic Stability Analysis for Outlier Robustness of Kalman-type Filtering Framework Based on Correntropy-Induced Cost, IEEE Transactions on Automatic Control (2024)
  • [4] Jiayi Kang, Andrew Salmon and Stephen S.-T. Yau, Nonexistence of finite-dimensional estimation algebras on closed smooth manifolds, arXiv preprint arXiv:2410.08689 (2024)
  • [5] Xiuqiong Chen, Jiayi Kang and Stephen S.-T. Yau, Time-varying feedback particle filter, Automatica, 167, 111740 (2024)
  • [6] Xiuqiong Chen*, Zeju Sun*, Yangtianze Tao, and Stephen Shing-Toung Yau, A Uniform Framework of Yau-Yau Algorithm Based on Deep Learning with the Capability of Overcoming the Curse of Dimensionality, accepted by IEEE Transactions on Automatic Control(2024)
  • [7] Mengcen Guan*, Nan Sun*, and Stephen S-T. Yau#, Geometric analysis of SARS-CoV-2 variants, Gene, 909, 148291 (2024)
  • [8] Hongyu Yu, and Stephen Shing-Toung Yau, The optimal metric for viral genome space, Computational and Structural Biotechnology Journal, 23(2024), 2083-2096
  • [9] Stephen S.-T. Yau, Xin Zhao, Kun Tian, Hongyu Yu, Mathematical Principles in Bioinformatics, Springer(2024)
  • [10] Ruohan Ren, Hongyu Yu, Jiahao Teng, Sihui Mao, Zixuan Bian, Yangtianze Tao, and Stephen Shing-Toung Yau, CAPE: a deep learning framework with Chaos-Attention net for Promoter Evolution, Briefings in Bioinformatics(2024), 1-10
  • [11] Stephen S-T. Yau, Xiaopei Jiao, Finite dimensional estimation algebra on arbitrary state dimension with nonmaximal rank: linear structure of Wong matrix, accepted by International Journal of Control(2023)
  • [12] Stephen S-T. Yau, Hongyu Yu and Xiaopei Jiao, Complete classification of finite dimensional estimation algebras with state dimension n, linear rank n-1 and constant Wong matrix, accepted by IEEE Transactions on Automatic Control(2023)
  • [13] Stephen S-T. Yau, Yangtianze Tao, and Jiayi Kang, Maximum Correntropy Ensemble Kalman Filter, accepted by proceedings of the 2023 62nd IEEE Conference on Decision and Control(2023)
  • [14] Stephen S-T. Yau, Guorui Ma, Yang Wang, and Huaiqing Zuo, Hodge moduli algebras and complete invariants of singularities, accepted by Asian Journal of Mathematics(2023)
  • [15] Harris Song*, Nan Sun*, Wenping Yu and Stephen S-T. Yau#, , A Novel Natural Graph for Efficient Clustering of Virus Genome Sequences, Current Bioinformatics, 687-703 (2023)
  • [16] Jiayi Kang, Xiaopei Jiao and Stephen S-T. Yau, Finite Dimensional Estimation Algebra For Time-varying Filtering System and Optimal Transport Particle Filter: A Tangent Flow Point of View, IEEE Transactions on Aerospace and Electronic Systems(2023)
  • [17] Nan Sun, Hongyu Yu, Ruohan Ren, Tao Zhou, Mengcen Guan, Leqi Zhao, Stephen S.-T. Yau#, Grand Biological Universe: Genome space geometry unravels looking for a single metric is likely to be futile in evolution, bioRxiv (2023)
  • [18] Stephen S-T. Yau, Guorui Ma and Huaiqing Zuo, k-th singular locus moduli algebras of singularities and their derivation Lie algebras, Journal of Mathematical Physics, 64:031701(2023), 1-13
  • [19] Yangtianze Tao , Jiayi Kang , and Stephen Shing-Toung Yau, Neural Projection Filter: Learning Unknown Dynamics Driven by Noisy Observations, IEEE Transactions on Neural Networks and Learning Systems, 35(2023), 7, 9508-9522
  • [20] Y Tao, J Kang, SST Yau, Neural projection filter: Learning unknown dynamics driven by noisy observations, IEEE Transactions on Neural Networks and Learning Systems (2023)
  • [21] Stephen S-T. Yau, Chun-Ting Hu, Shao-Jun Pei, Jing-Long Wang, Li-Dong Zu, Wei-Wei Shen, Lin Yuan, Feng Gao, Li-Ren Jiang and Guo-Hui Fu, Quantitative proteomics profiling reveals the inhibition of trastuzumab antitumor effcacy by phosphorylated RPS6 in gastric carcinoma, Cancer Chemotherapy and Pharmacology, 92(2023), 341-355
  • [22] Stephen S-T. Yau, Qiwei Zhu and Huaiqing Zuo, Classification of weighted dual graphs consisting of -2 curves and exactly one -3-Curve, Izvestiya: Mathematics, 87(2023), 5, 1078-1116
  • [23] Stephen S-T. Yau, Naveed Hussain and Huaiqing Zuo, On derivation Lie algebras of isolated complete intersection singularities, Letters in Mathematical Physics, 113:99(2023), 1-34
  • [24] Stephen S-T. Yau, Zeju Sun, Solving Nonlinear Filtering Problems with Correlated Noise Based on Hermite-Galerkin Spectral Method, Automatica, 156(2023), 111176, 1-14
  • [25] Stephen S-T. Yau, Yangtianze Tao, Outlier-Robust Iterative Extended Kalman Filtering, IEEE Signal Processing Letters, 30(2023), 743-747
  • [26] Stephen S-T. Yau, Jiayi Kang and Andrew Salmon, Log-concave posterior densities arising in continuous filtering and a maximum a posteriori algorithm, SIAM Journal on Control and Optimization, 64(2023), 4, 2407-2424
  • [27] Stephen S-T. Yau, Haoyu Zhou and Ruohan Ren, Utilizing the codon adaptation index (CAI) to evaluate the susceptibility to HIV-1 and SARSCoV- 2 related coronaviruses in possible target cells in humans, Frontiers in Cellular and Infection Microbiology, section Virus and Host, 12:1085397(2023), 1-19
  • [28] Stephen S-T. Yau, Sijing Li, Zhongjian Wang and Zhiwen Zhang, Solving nonlinear filtering problems using a tensor train decomposition method, IEEE Transactions on Automatic Control, 68(2023), 7, 4405-4412
  • [29] Stephen S-T. Yau, Xiuqiong Chen, On the stability of linear feedback particle filter, Asian Journal of Mathematics, 27(2023), 1, 95-120
  • [30] Stephen S-T. Yau, Guorui Ma and Huaiqing Zuo, Nonexistence of negative weight derivations of the local k-th Hessian algebras associated to isolated singularities, Pacific Journal of Mathematics, 323(2023), 1, 129-172
  • [31] B.H. Lian, Naveed Hussain and Huaiqing Zuo, Derivations of local k-th Hessain algebras of singularities, Rocky Mountain Journal of Mathematics, 53(2023), 1, 65-87
  • [32] Stephen S-T. Yau, Naveed Hussain*, Zhiwen Liu* and Huaiqing Zuo, -th Milnor numbers and-th Tjurina numbers of weighted homogeneous singularities, Geometriae Dedicata, 217(34), 1-35 (2023)
  • [33] Stephen S-T. Yau, Naveed Hussain, Guorui Ma and Huaiqing Zuo, Higher Nash blow-up local algebras of singularities and its derivation Lie algebras, Journal of Algebra, 618(2023), 165-194
  • [34] Stephen S-T. Yau, Xiaopei Jiao, Structure of finite dimensional exact estimation algebra on state dimension 3 and linear rank 2, International Journal of Control, 96(2023), 2, 362-373
  • [35] Meng Fang*, Jiawei Xu*, Nan Sun and Stephen S.-T. Yau#, Generating Minimal Models of H1N1 NS1 Gene Sequences Using Alignment-based and Alignment-free Algorithms, Genes, 14:186(2023), 1-11
  • [36] Xiuqiong Chen, Yangtianze Tao, Wenjie Xu, and Stephen Shing-Toung Yau, Recurrent Neural Networks are Universal Approximators with Stochastic Inputs, IEEE Transactions on Neural Networks and Learning Systems, 34(2023), 10, 7992-8006
  • [37] Nan Sun, Xin Zhao and Stephen S.-T. Yau#, An efficient numerical representation of genome sequence: Natural vector with covariance component, PeerJ, 10, e13544 (2022)
  • [38] Kang, Jiayi, Xiuqiong Chen, Yangtianze Tao, and Stephen Shing-Toung Yau, Optimal transportation particle filter for linear filtering systems with correlated noises, IEEE Transactions on Aerospace and Electronic Systems, 58(6), 5190-5203 (2022)
  • [39] Nan Sun, Jie Yang and Stephen S.-T. Yau#, Identification of HIV rapid mutations using differences in nucleotide distribution over time, Genes, 13(2), 170 (2022)
  • [40] Xiankui Meng, Stephen S.-T. Yau, Kohn-Rossi Cohomology and Complex Plateau Problem, Pure and Applied Mathematics Quarterly, 2022, vol 18, 2, 683-718
  • [41] Chen, Xiuqiong, Yangtianze Tao, Wenjie Xu, and Stephen Shing-Toung Yau, accepted by IEEE Trans. Neural Netw. Learn. Syst., (), -, (2022)
  • [42] Shuanghe Fan, Stephen S.-T. Yau, Huaiqing Zuo, Non-existence of negative weight derivations of the local 1-st Hessian algebra of singularities, Asian Journal of Mathematics, 2022, , 1-81, to appear
  • [43] Jian Liu, Ke-Lin Xia, Jie Wu, Stephen Shing-Toung Yau, and Guo-Wei Wei, Biomolecular topology: modelling and analysis, Acta Mathematica Sinica, 38(2022), 10, 1901-1938
  • [44] Stephen S-T. Yau, Chuangqiang Hu and Huaiqing Zuo, Complex structures of a twenty dimensional family of Calabi-Yau 3-folds, Communications in Analysis and Geometry, 30(2022), 8, 1825-1831
  • [45] Stephen S-T. Yau, Mengcen Guan and Leqi Zhao, Classification of Protein Sequences by a Novel Alignment-Free Method on Bacterial and Virus Families, Genes, 13:1744(2022), 1-12
  • [46] Stephen S-T. Yau, Shuanghe Fan and Huaiqing Zuo, Non-existence of negative weight derivations of the local 1-st Hessian algebra of singularities, Asian Journal of Mathematics, 26(2022), 3, 289-372
  • [47] Stephen S-T. Yau, Xiuqiong Chen, Xue Luo and Ji Shi, General convergence result for continuousdiscrete feedback particle filter, International Journal of Control, 95(2022), 11, 2972-2986
  • [48] Stephen S-T. Yau, Xiaona Bao, Lily He and Jingan Cui, Nucleotide Amino Acid K-mer Vector: An alignment-free method for comparing genomic sequences, Communications in Information and Systems, 22(2022), 3, 317-337
  • [49] Stephen S-T. Yau, Naveed Hussain and Huaiqing Zuo, New k-th Yau algebras of isolated hypersurface singularities and weak Torelli-type theorem, Mathematical Research Letters, 29(2022), 2, 455-486
  • [50] Stephen S-T. Yau, Naveed Hussain and Huaiqing Zuo, Classification of the nilradical of k-th Yau algebras arising from singularities, Pure and Applied Mathematics Quarterly, 18(2022), 3, 835-862
  • [51] Stephen S-T. Yau, Ruzhang Zhao and Shaojun Pei, New Genome Sequence Detection via Natural Vector Convex Hull Method, IEEE/ACM Transactions on Computational Biology and Bioinformatics, 19(2022), 3, 1782-1793
  • [52] Stephen S-T. Yau, Xiankui Meng, Kohn-Rossi Cohomology and Complex Plateau Problem, Pure and Applied Mathematics Quarterly, 18(2022), 2, 683-718
  • [53] Nan Sun and Stephen S.-T. Yau#, In-depth Investigation of the Point Mutation Pattern of HIV-1, Frontiers in Cellular and Infection Microbiology, 12:1033481(2022), 1-11
  • [54] Ruohan Ren, Changchuan Yin, and Stephen Shing-Toung Yau, kmer2vec: a novel method for comparing DNA sequences by word2vec embedding, Journal of Computational Biology, 29(2022), 9, 1001-1021
  • [55] Nan Sun, Jie Yang, Stephen S.-T. Yau, Identification of HIV rapid mutations using differences in nucleotide distribution over time, genes, Genes, (), -, (2022)
  • [56] Hussain, Naveed, Stephen S-T. Yau, and Huaiqing Zuo, Classification of the nilradical of $ k $-th Yau algebras arising from singularities., Pure Appl. Math. Q., (), -, (2022)
  • [57] Hussain, Naveed, Stephen S-T. Yau, and Huaiqing Zuo, Generalized Cartan Matrices Associated to k-th Yau Algebras of Singularities and Characterization Theorem., Algebr. Represent. Theory, (), -, (2022)
  • [58] Hussain, Naveed, Stephen S-T. Yau, and Huaiqing Zuo, An inequality conjecture and a weak Torelli-type theorem for isolated complete intersection singularities., J. Geom. Phys., (), -, (2022)
  • [59] Rui Dong, Shaojun Pei, Mengcen Guan, Shek-Chung Yau, Changchuan Yin, Rong L. He, Stephen S.-T. Yau, Full chromosomal relationships between populations and the origin of humans, Front. Genet., (), -, (2022)
  • [60] Xiuqiong Chen*, Jiayi Kang*, Mina Teicher, and Stephen S.-T. Yau, A New Linear Regression Kalman Filter with Symmetric Samples, Symmetry, 13(11), 2139 (2021)
  • [61] Xiaopei Jiao*, Shaojun Pei*, Zeju Sun, Jiayi Kang and Stephen S.-T. Yau, Determination of the nucleotide or amino acid composition of genome or protein sequences by using natural vector method and convex hull principle, Fundamental Research, 1(5), 559-564 (2021)
  • [62] Nan Sun*, Shaojun Pei*, Lily He, Changchuan Yin, Rong Lucy He, Stephen S.-T. Yau, Geometric construction of viral genome space and its applications, Computational and Structural Biotechnology Journal 2021, 19, 4226-4234.
  • [63] Bingyi Chen,Stephen S.-T. Yau, Shing-Tung Yau, Huaiqing Zuo, 4d N=2 SCFT and singularity theory Part IV: Isolated rational Gorenstein non-complete intersection singularities with at least one-dimensional deformation and nontrivial T-2, Adv. Math., (), -, (2021)
  • [64] Shaojun Pei, Stephen S.-T. Yau, Analysis of the Genomic Distance Between Bat Coronavirus RaTG13 and SARS-CoV-2 Reveals Multiple Origins of COVID-19, Acta Math. Sci., (), -, (2021)
  • [65] Naveed Hussain, Stephen S.-T. Yau；Huaiqing Zuo, Derivation Lie Algebras of New k-TH Local Algebras of Isolated Hypersurface Singularities, Pac. J. Math., (), -, (2021)
  • [66] Ji Shi, Xiuqiong Chen, Stephen S.-T. Yau, A Novel Real-Time Filtering Method to General Nonlinear Filtering Problem Without Memory, IEEE Access, (), -, (2021)
  • [67] Naveed Hussain, Stephen S.-T. Yau, Huaiqing Zuo, ON THE DIMENSION OF A NEW CLASS OF DERIVATION LIE ALGEBRAS ASSOCIATED TO SINGULARITIES, Mathematics, (), -, (2021)
  • [68] Xiuqiong Chen*, Jiayi Kang*, Mina Teicher, Stephen S.-T. Yau, Symmetry-Basel, (), -, (2021)
  • [69] Jiao, Xiaopei, and Stephen S-T. Yau, Structure of finite dimensional exact estimation algebra on state dimension 3 and linear rank 2., INTERNATIONAL JOURNAL OF CONTROL (2021)
  • [70] Chen, Xiuqiong, Xue Luo, Ji Shi, and Stephen S-T. Yau, General convergence result for continuous-discrete feedback particle filter., Int. J. Control, (), -, (2021)
  • [71] Nan Sun*, Shaojun Pei*, Lily He, Changchuan Yin, Rong Lucy He and Stephen S.-T. Yau#, Geometric construction of viral genome space and its applications, Computational and Structural Biotechnology Journal, 19, 4226-4234 (2021)
  • [72] Kun Tian* , Xin Zhao*, Stephen S.‑T. Yau, Amino acid torsion angles enable prediction of protein fold classification, Scientific Reports (2020)
  • [73] Nan Sun*, Rui Dong*, Shaojun Pei, Changchuan Yin and Stephen S.-T. Yau#, A new method based on coding sequence density to cluster bacteria, Journal of Computational Biology, 27(12), 1688-1698 (2020)
  • [74] Shaojun Pei, Rui Dong, Yiming Bao, Rong He, and Stephen Shing-Toung Yau, Classification of genomic components and prediction of genes of Begomovirus based on subsequence natural vector and support vector machine, PeerJ, 8(2020), 1-15
  • [75] Tung Hoang, Changchuan Yin, and Stephen Shing-Toung Yau, Splice sites detection using chaos game representation and neural network, Genomics, 112(2020), 1847-1852
  • [76] Kun Tian*, Xin Zhao*, Stephen S.-T. Yau, Convex hull analysis of evolutionary and phylogenetic relationships between biological groups, Journal of Theoretical Biology (2018)
  • [77] Xin Zhao, Kun Tian, Stephen S.-T. Yau, A new efficient method for analyzing fungi species using correlations between nucleotides, BMC Evolutionary Biology (2018)
  • [78] S. S.-T. Yau, B. Yuan and H. Zuo , On the polynomial sharp upper estimate conjecture in 7-dimensional simplex, Journal of number theory, 160, 254-286 (2016)
  • [79] Chenglong Yu, Mo Deng, Lu Zheng, Rong Lucy He, Jie Yang, and Stephen Shing-Toung Yau, DFA7, A New Method to Distinguish between Intron-containing and Intronless Genes, PLoS ONE, 9(2014), 1-10
  • [80] GUO-QING HU; STEPHEN S. T. YAU; WEN-LIN CHIOU, FINITE-DIMENSIONAL FILTERS WITH NONLINEAR DRIFT XIII: CLASSIFICATION OF FINITE-DIMENSIONAL ESTIMATION ALGEBRAS OF MAXIMAL RANK WITH STATE SPACE DIMENSION FIVE, Asian Journal of Math, 04(2000), 04, 905-932
  • [81] N Hussain, SST Yau, H Zuo, Three types of derivation lie algebras of isolated hypersurface singularities, Rendiconti del Circolo Matematico di Palermo Series 2, 74(1), 1-20 (2025)
  • [82] X Li, T Zhou, X Feng, ST Yau, SST Yau, Exploring geometry of genome space via Grassmann manifolds, The Innovation, 5(5) (2024)
  • [83] W Cao, S Liu, C Liu, Z He, SST Yau, SE Li, Convolutional bayesian filtering, arXiv (2024)
  • [84] X Jiao, SST Yau, Finite-dimensional estimation algebra on arbitrary state dimension with nonmaximal rank: linear structure of Wong matrix, International Journal of Control, 97(11), 2669-2676 (2024)
  • [85] W Cao, T Zhang, Z Sun, C Liu, SST Yau, SE Li, Nonlinear Bayesian Filtering with Natural Gradient Gaussian Approximation, arXiv (2024)
  • [86] C Hu, SST Yau, H Zuo, On the$k$-th Tjurina number of weighted homogeneous singularities, arXiv (2024)
  • [87] H Yu, SST Yau, Automated recognition of chromosome fusion using an alignment-free natural vector method, Frontiers in Genetics, 15, 1364951 (2024)
  • [88] Q Shi, SST Yau, H Zuo, On$T$-maps and ideals of antiderivatives of hypersurface singularities, Известия Российской академии наук. Серия математическая, 88(6), 190-226 (2024)
  • [89] X Jiao, SST Yau, Weak form Mitter conjecture on nonmaximal rank estimation algebra: state dimension 4 and rank 3, 系统科学与复杂性 (2024)
  • [90] J Shi, X Jiao, SST Yau, DGLG: A Novel Deep Generalized Legendre-Galerkin Approach To Optimal Filtering Problem, IEEE Transactions on Automatic Control (2024)
  • [91] SST Yau, X Zhao, K Tian, H Yu, Sequence alignment, Mathematical Principles in Bioinformatics, 27-42 (2023)
  • [92] H Zhou, R Ren, SST Yau, Utilizing the codon adaptation index to evaluate the susceptibility to HIV-1 and SARS-CoV-2 related coronaviruses in possible target cells in humans, Frontiers in cellular and infection microbiology, 12, 1085397 (2023)
  • [93] SST Yau, Q Zhu, H Zuo, Classification of weighted dual graphs consisting of$-2$-curves and exactly one$-3$-curve, Известия Российской академии наук. Серия математическая, 87(5), 232-270 (2023)
  • [94] CT Hu, SJ Pei, JL Wang, LD Zu, WW Shen, L Yuan, F Gao, LR Jiang, ..., Quantitative proteomics profiling reveals the inhibition of trastuzumab antitumor efficacy by phosphorylated RPS6 in gastric carcinoma, Cancer chemotherapy and pharmacology, 92(5), 341-355 (2023)
  • [95] Z Sun, SST Yau, Solving nonlinear filtering problems with correlated noise based on Hermite–Galerkin spectral method, Automatica, 156, 111176 (2023)
  • [96] N Hussain, SST Yau, H Zuo, DERIVATIONS OF LOCAL$k$-TH HESSIAN ALGEBRAS OF SINGULARITIES, Rocky Mountain Journal of Mathematics, 53(1), 65-87 (2023)
  • [97] H Yu, X Jiao, SST Yau, Complete Classification of Finite Dimensional Estimation Algebras With State Dimension n, Linear Rank n-1, and Constant Wong Matrix, IEEE Transactions on Automatic Control, 69(1), 295-302 (2023)
  • [98] X Chen, X Luo, J Shi, SST Yau, General convergence result for continuous-discrete feedback particle filter, International Journal of Control, 95(11), 2972-2986 (2022)
  • [99] N Hussain, SST Yau, H Zuo, An inequality conjecture and a weak Torelli-type theorem for isolated complete intersection singularities, Journal of Geometry and Physics, 178, 104542 (2022)
  • [100] N Hussain, SST Yau, H Zuo, Generalized Cartan Matrices Associated to-th Yau Algebras of Singularities and Characterization Theorem, Algebras and Representation Theory, 25(6), 1461-1492 (2022)
  • [101] B Chen, SST Yau, ST Yau, H Zuo, $4d$$N=2$SCFT and singularity theory Part IV: Isolated rational Gorenstein non-complete intersection singularities with at least one-dimensional deformation and …, Mathematical Research Letters, 28(1), 1-23 (2022)
  • [102] Z Xiao, SST Yau, Q Zhu, H Zuo, On the Nakai Conjecture for some singularities, ANNALI SCUOLA NORMALE SUPERIORE-CLASSE DI SCIENZE, 18(18) (2022)
  • [103] N Hussain, SST Yau, H Zuo, Inequality conjectures on derivations of local-th Hessain algebras associated to isolated hypersurface singularities, Mathematische Zeitschrift, 298, 1813-1829 (2021)
  • [104] N Hussain, SST YAU, H Zuo, TH YAU NUMBER OF ISOLATED HYPERSURFACE SINGULARITIES AND AN INEQUALITY CONJECTURE, Journal of the Australian Mathematical Society, 110(1), 94-118 (2021)
  • [105] N Hussain, SST Yau, H Zuo, On two inequality conjectures for the-th Yau numbers of isolated hypersurface singularities, Geometriae Dedicata, 212, 57-71 (2021)
  • [106] N Hussain, SST Yau, H Zuo, On the Generalized Cartan Matrices Arising from-th Yau Algebras of Isolated Hypersurface Singularities, Algebras and Representation Theory, 24, 1101-1124 (2021)
  • [107] W Dong, X Chen, SST Yau, The novel classes of finite dimensional filters with non-maximal rank estimation algebra on state dimension four and rank of one, International Journal of Control, 94(5), 1156-1165 (2021)
  • [108] C Yin, SST Yau, Inverted repeats in coronavirus SARS-CoV-2 genome manifest the evolution events, Journal of Theoretical Biology, 530, 110885 (2021)
  • [109] B Chen, N Hussain, SST Yau, H Zuo, Variation of complex structures and variation of Lie algebras II: new Lie algebras arising from singularities, Journal of Differential Geometry, 115(3), 437-473 (2020)
  • [110] B Chen, H Chen, SST Yau, H Zuo, The nonexistence of negative weight derivations on positive dimensional isolated singularities: generalized Wahl conjecture, Journal of Differential Geometry, 115(2), 195-224 (2020)
  • [111] N Hussain, SST Yau, H Zuo, On the new-th Yau algebras of isolated hypersurface singularities, Mathematische Zeitschrift, 294(1), 331-358 (2020)
  • [112] R Dong, S Pei, C Yin, RL He, SST Yau, Analysis of the hosts and transmission paths of SARS-CoV-2 in the COVID-19 outbreak, Genes, 11(6), 637 (2020)
  • [113] Z Sun, S Pei, RL He, SST Yau, A novel numerical representation for proteins: three-dimensional chaos game representation and its extended natural vector, Computational and Structural Biotechnology Journal, 18, 1904-1913 (2020)
  • [114] N Hussain, SST Yau, H Zuo, Generalized Cartan matrices arising from new derivation Lie algebras of isolated hypersurface singularities, Pacific Journal of Mathematics, 305(1), 189-217 (2020)
  • [115] G Ma, SST Yau, H Zuo, On the non-existence of negative weight derivations of the new moduli algebras of singularities, Journal of Algebra, 564, 199-246 (2020)
  • [116] L He, R Dong, RL He, SST Yau, A novel alignment-free method for HIV-1 subtype classification, Infection, Genetics and Evolution, 77, 104080 (2020)
  • [117] W Dong, X Luo, SST Yau, Solving nonlinear filtering problems in real time by Legendre Galerkin spectral method, IEEE Transactions on Automatic Control, 66(4), 1559-1572 (2020)
  • [118] C Hu, S Yang, SST Yau, Weight enumerators for nonbinary asymmetric quantum codes and their applications, Advances in Applied Mathematics, 121, 102085 (2020)
  • [119] J Shi, SST Yau, Finite dimensional estimation algebras with state dimension 3 and rank 2, Mitter conjecture, International Journal of Control, 93(9), 2177-2186 (2020)
  • [120] L He, R Dong, RL He, SST Yau, Positional correlation natural vector: a novel method for genome comparison, International Journal of Molecular Sciences, 21(11), 3859 (2020)
  • [121] X Jiao, SST Yau, New Classes of Finite Dimensional Filters with Nonmaximal Rank Estimation Algebra on State Dimension$n$and Linear Rank$n-2$, SIAM Journal on Control and Optimization, 58(6), 3413-3427 (2020)
  • [122] N Hussain, X Luo, SST Yau, M Zhang, H Zuo, On classification of toric surface codes of dimension seven, Communications in Analysis and Geometry, 28(2), 263-319 (2020)
  • [123] C Yin, SST Yau, Inverted repeats in coronavirus SARS-CoV-2 genome and implications in evolution, arXiv (2020)
  • [124] W Dong, X Chen, SST Yau, Novel Classification of Finite Dimensional Filters with Non-maximal Rank Estimation Algebra, 2020 American Control Conference (ACC), 3349-3354 (2020)
  • [125] W Dong, SST Yau, A Novel Image Description With the Stretched Natural Vector Method: Application to Face Recognition, IEEE Access, 8, 100084-100094 (2020)
  • [126] YY Zhang, J Wen, SST Yau, Phylogenetic analysis of protein sequences based on a novel k-mer natural vector method, Genomics, 111(6), 1298-1305 (2019)
  • [127] H Chen, S Yau, H Zuo, Non-existence of negative weight derivations on positively graded Artinian algebras, Transactions of the American Mathematical Society, 372(4), 2493-2535 (2019)
  • [128] R Dong, L He, RL He, SST Yau, A novel approach to clustering genome sequences using inter-nucleotide covariance, Frontiers in Genetics, 10 (2019)
  • [129] X Zhao, K Tian, RL He, SST Yau, Convex hull principle for classification and phylogeny of eukaryotic proteins, Genomics, 111(6), 1777-1784 (2019)
  • [130] Z Wang, X Luo, SST Yau, Z Zhang, Proper orthogonal decomposition method to nonlinear filtering problems in medium-high dimension, IEEE Transactions on Automatic Control, 65(4), 1613-1624 (2019)
  • [131] S Pei, W Dong, X Chen, RL He, SST Yau, Fast and accurate genome comparison using genome images: The Extended Natural Vector Method, Molecular phylogenetics and evolution, 141, 106633 (2019)
  • [132] S Pei, R Dong, RL He, SST Yau, Large-scale genome comparison based on cumulative Fourier power and phase spectra: central moment and covariance vector, Computational and structural biotechnology journal, 17, 982-994 (2019)
  • [133] K Tian, X Zhao, Y Zhang, S Yau, Comparing protein structures and inferring functions with a novel three-dimensional Yau–Hausdorff method, Journal of Biomolecular Structure and Dynamics (2019)
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  • [301] WS Wong, X Wu, SST Yau, Hessian matrix non-decomposition theorem, Mathematical Research Letters, 6(6), 663-673 (1999)
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  • [303] T Jiang, SST Yau, Intersection lattices and topological structures of complements of arrangements in$\mathbb {CP}^2$, Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, 26(2), 357-381 (1998)
  • [304] ST Yau, SST Yau, Finite Dimensional Filters with Nonlinear Drift, XI: Explicit Solution of the Generalized Kolmogorov Equation in Brockett–Mitter Program, Advances in Mathematics, 140(2), 156-189 (1998)
  • [305] HS Luk, SST Yau, Counterexample to boundary regularity of a strongly pseudoconvex CR submanifold: An addendum to the paper of Harvey-Lawson, arXiv (1998)
  • [306] ST Yau, SST Yau, Existence and decay estimates for time dependent parabolic equation with application to Duncan–Mortensen–Zakai equation, Asian Journal of Mathematics, 2(4), 1079-1150 (1998)
  • [307] HS Luk, SST Yau, Explicit construction of graph invariant for strongly pseudoconvex compact 3-dimensional rational CR manifolds, Compositio Mathematica, 114(1), 77-111 (1998)
  • [308] H Chen, HS Luk, S Yau, Explicit computation of generalized Hamming weights for some algebraic geometric codes, Advances in Applied Mathematics, 21(1), 124-145 (1998)
  • [309] J Chen, SST Yau, CW Leung, Finite-dimensional filters with nonlinear drift VIII: Classification of finite-dimensional estimation algebras of maximal rank with state-space dimension 4, SIAM journal on control and optimization, 35(4), 1132-1141 (1997)
  • [310] J Chen, SST Yau, Finite-Dimensional Filters with Nonlinear Drift VII: Mitter Conjecture and Structure of$\eta$, SIAM journal on control and optimization, 35(4), 1116-1131 (1997)
  • [311] A Rasoulian, SST Yau, Finite dimensional filters with non-linear drift IX Construction of finite dimensional estimation algebras of non-maximal rank, Systems & control letters, 30(2-3), 109-118 (1997)
  • [312] QL Zhang, SK Chang, SST Yau, An Experimental Result in Image Indexing Using GEP-2D Strings, Image Databases And Multi-Media Search, 127-146 (1997)
  • [313] T Jiang, SST Yau, Complement of arrangement of hyperplanes, Singularities and complex geometry (Beijing, 1994), 5, 93-104 (1997)
  • [314] HS Luk, SST Yau, Complete algebraic CR invariants of real codimension 3 strongly pseudoconvex CR manifold, Studies in Advanced Mathematics, 5, 175-182 (1997)
  • [315] J Chen, SST Yau, CW Leung, Finite-dimensional filters with nonlinear drift IV: Classification of finite-dimensional estimation algebras of maximal rank with state–space dimension 3, SIAM journal on control and optimization, 34(1), 179-198 (1996)
  • [316] J Chen, SST Yau, Finite-dimensional filters with nonlinear drift, VI: Linear structure of Ω, Mathematics of Control, Signals and Systems, 9(4), 370-385 (1996)
  • [317] YJ Xu, SST Yau, Micro-local characterization of quasi-homogeneous singularities, American Journal of Mathematics, 118(2), 389-399 (1996)
  • [318] YJ Xu, SST Yau, A sharp estimate of the number of integral points in a 4-dimensional tetrahedra., Journal für die reine und angewandte Mathematik (Crelles Journal), 1996, 473 … (1996)
  • [319] QL Zhang, SK Chang, SST Yau, A unified approach to iconic indexing, retrieval, and maintenance of spatial relationships in image databases, Journal of Visual Communication and Image Representation, 7(4), 307-324 (1996)
  • [320] SST Yau, A Rasoulian, The structure of/spl Omega/-matrix in nonlinear filters, Proceedings of 35th IEEE Conference on Decision and Control, 1, 1083-1087 (1996)
  • [321] HS Luk, SST Yau, Invariant Kohn-Rossi cohomology and obstruction to embedding of compact real (2n-1)-dimensional CR manifolds in CN, Journal of the Mathematical Society of Japan, 48(1), 61-68 (1996)
  • [322] QL Zhang, SK Chang, SST Yau, Iconic indexing and maintenance of spatial relationships in image databases, Multimedia Storage and Archiving Systems, 2916, 385-396 (1996)
  • [323] SST Yau, GQ Hu, Direct Method without the Riccati equation for a Linear Filtering System with Arbitrary Initial Conditions, IFAC Proceedings Volumes, 29(1), 3858-3863 (1996)
  • [324] H Chen, YJ Xu, SST Yau, Nonexistence of negative weight derivation of moduli algebras of weighted homogeneous singularities, Journal of Algebra, 172(2), 243-254 (1995)
  • [325] HS Luk, SST Yau, Invariants of strongly pseudoconvex CR manifolds, World Sci Publ (1995)
  • [326] SST Yau, Finite-dimensional filters with nonlinear drift. I: A class of filters including both Kalman-Bucy and Benes filters, J. Math. Systems, Estimation, and Control, 4, 181-203 (1994)
  • [327] WL Chiou, SST Yau, Finite-dimensional filters with nonlinear drift. II: Brockett’s problem on classification of finite-dimensional estimation algebras, SIAM journal on control and optimization, 32(1), 297-310 (1994)
  • [328] T Jiang, SST Yau, Diffeomorphic types of the complements of arrangements of hyperplanes, Compositio mathematica, 92(2), 133-155 (1994)
  • [329] HS Luk, SST Yau, Y Yu, Algebraic Classification and Obstructions to Embedding of Strongly Pseudoconvex Compact 3‐dimensional CR Manifolds in C, Mathematische Nachrichten, 170(1), 183-200 (1994)
  • [330] T Bielecki, J Chen, SST Yau, Random wavelet transformation and its properties, Wavelet Applications in Signal and Image Processing II, 2303, 345-353 (1994)
  • [331] SST Yau, Y Yu, Gorenstein quotient singularities in dimension three, 1993, Memoirs of the American Mathematical Society, 110(530), 505-505 (1994)
  • [332] SST Yau, Y Yu, Gorenstein quotient singularities in dimension three, American Mathematical Soc. (1993)
  • [333] YJ Xu, SST Yau, Durfee conjecture and coordinate free characterization of homogeneous singularities, Journal of Differential Geometry, 37(2), 375-396 (1993)
  • [334] T Jiang, SST Yau, Topological invariance of intersection lattices of arrangements in 𝐂𝐏², Bulletin of the American Mathematical Society, 29(1), 88-93 (1993)
  • [335] SST Yau, Y Yu, GORENSTEIN QUOTIENT SINGULARITIES IN DIMENSION-3, Memoirs of the American Mathematical Society, 105(505), 1-88 (1993)
  • [336] T Bielecki, J Chen, S Yau, EB Lin, Wavelet and wavelet Stieltjes transforms, Proceedings of 32nd IEEE Conference on Decision and Control, 3062-3063 (1993)
  • [337] HS Luk, SST Yau, COHOMOLOGY AND SPLITTING CRITERION FOR HOLOMORPHIC VECTOR-BUNDLES ON CPN, MATHEMATISCHE NACHRICHTEN, 161, 233-238 (1993)
  • [338] J Chen, CW Leung, S Yau, The classification of low dimensional estimation algebras, Proceedings of 32nd IEEE Conference on Decision and Control, 732-734 (1993)
  • [339] YJ Xu, SST Yau, A sharp estimate of the number of integral points in a tetrahedron., Journal für die reine und angewandte Mathematik (Crelles Journal), 1992, 423 … (1992)
  • [340] J Sampson, SST Yau, Y Yu, Classification of gradient space as sℓ (2, C) module I, American Journal of Mathematics, 1147-1161 (1992)
  • [341] Y Xu, SST Yau, Topological types of seven classes of isolated singularities with C*-action, The Rocky Mountain Journal of Mathematics, 22(3), 1147-1215 (1992)
  • [342] A Libgober, S Yau, An obstruction to smoothing of Gorenstein surface singularities, Commentarii Mathematici Helvetici, 67, 670-670 (1992)
  • [343] RT Dong, LF Tam, WS Wong, SST Yau, Structure and classification theorems of finite-dimensional exact estimation algebras, SIAM journal on control and optimization, 29(4), 866-877 (1991)
  • [344] SST Yau, Solvability of Lie algebras arising from isolated singularities and nonisolatedness of singularities defined by sℓ (2, C) invariant polynomials, American Journal of Mathematics, 773-778 (1991)
  • [345] SST Yau, A remark on moduli of complex hypersurfaces, American Journal of Mathematics, 287-292 (1991)
  • [346] S Bloch, IV Dolgachev, W Fulton, C Seeley, SST Yau, Algebraic methods in the study of simple-elliptic singularities, Algebraic Geometry (1991)
  • [347] SST Yau, Regularity for the Harvey-Lawson solutions to the complex Plateau problem, Journal of Differential Geometry, 34(2), 425-429 (1991)
  • [348] LF Tam, WS Wong, SST Yau, On a necessary and sufficient condition for finite dimensionality of estimation algebras, SIAM journal on control and optimization, 28(1), 173-185 (1990)
  • [349] C Seeley, SST Yau, Variation of complex structures and variation of Lie algebras, Inventiones mathematicae, 99, 545-565 (1990)
  • [350] M Benson, SST Yau, Equivalences between isolated hypersurface singularities, Mathematische Annalen, 287(1), 107-134 (1990)
  • [351] A Libgober, SST Yau, An obstruction for smoothing of Gorenstein surface singularities, Commentarii Mathematici Helvetici, 65, 413-433 (1990)
  • [352] Rome Air Development Center, SST Yau, Knowledge Based Quality Assurance Tools, Air Force Systems Command (1990)
  • [353] Y Xu, SST Yau, Classification of topological types of isolated quasi-homogeneous two dimensional hypersurface singularities, manuscripta mathematica, 64(4), 445-469 (1989)
  • [354] SST Yau, The multiplicity of isolated two-dimensional hypersurface singularities: Zariski problem, American Journal of Mathematics, 753-767 (1989)
  • [355] YJ Xu, SST Yau, THE INEQUALITY μ> 12p− 4 FOR HYPERSURFACE g WEAKLY ELLIPTIC SINGULARITIES, Singularities: Proceedings of the IMA Participating Institutions Conference (1989)
  • [356] SST Yau, Topological types and multiplicities of isolated quasi-homogeneous surface singularities (1988)
  • [357] SST Yau, Classification of Jacobian Ideals Invariant by$sl(2, \ \mathbf {C})$Actions, American Mathematical Soc. (1988)
  • [358] SST Yau, Classification of Jacobian ideals invariant by sl (2, C) actions, (No Title) (1988)
  • [359] HB Lawson, SST Yau, Holomorphic symmetries, Annales scientifiques de l'École Normale Supérieure, 20(4), 557-577 (1987)
  • [360] SST Yau, Solvable Lie algebras and generalized Cartan matrices arising from isolated singularities, Mathematische Zeitschrift, 191(4), 489-506 (1986)
  • [361] M Benson, SST Yau, Lie algebra and their representations arising from isolated singularities: Computer method in calculating the Lie algebras and their cohomology, Advance studies in Pure Mathematics, 8, 3-58 (1986)
  • [362] SST Yau, Singularities Defined by sℓ (2, C) Invariant Polynomials and Solvability of Lie Algebras Arising From Isolated Singularities, American Journal of Mathematics, 1215-1239 (1986)
  • [363] IM Singer, B Wong, ST Yau, SST Yau, An estimate of the gap of the first two eigenvalues in the Schrödinger operator, Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, 12(2), 319-333 (1985)
  • [364] SST Yau, Criteria for right-left equivalence and right equivalence of holomorphic functions with isolated critical points, Proceedings of Symposia in Pure Mathematics, 41, 291-297 (1984)
  • [365] SST Yau, Continuous family of finite-dimensional representations of a solvable Lie algebra arising from singularities, Proceedings of the National Academy of Sciences, 80(24), 7694-7696 (1983)
  • [366] SST Yau, Milnor algebras and equivalence relations among holomorphic functions (1983)
  • [367] SST Yau, On irregularity and geometric genus of isolated singularities, Proe. Symp. Pure Math, 40(Part 2) (1983)
  • [368] JN Mather, SST Yau, Classification of isolated hypersurface singularities by their moduli algebras, Inventiones mathematicae, 69(2), 243-251 (1982)
  • [369] SST Yau, Various numerical invariants for isolated singularities, American Journal of Mathematics, 1063-1100 (1982)
  • [370] SST Yau, sInvariant for Isolated n-Dimensional Singularities and Its Application to Moduli Problem, American Journal of Mathematics, 829-841 (1982)
  • [371] SST Yau, Kohn-Rossi cohomology and its application to the complex Plateau problem, I, Annals of Mathematics, 67-110 (1981)
  • [372] JN Mather, SST Yau, Criterion for biholomorphic equivalence of isolated hypersurface singularities, Proceedings of the National Academy of Sciences, 78(10), 5946-5947 (1981)
  • [373] SST Yau, Sheaf cohomology on 1-convex manifolds, Ann. of Math. Stud, 100 (1981)
  • [374] SST Yau, Existence of$L2$-integrable holomorphic forms and lower estimates of$TV1$ (1981)
  • [375] SST Yau, Deformations and equitopological deformations of strongly pseudoconvex manifolds, Nagoya Mathematical Journal, 82, 113-129 (1981)
  • [376] SST Yau, On maximally elliptic singularities, Transactions of the American Mathematical Society, 257(2), 269-329 (1980)
  • [377] SST Yau, Index theory for the boundaries of complex analytic varieties, Proceedings of the National Academy of Sciences, 77(3), 1248-1249 (1980)
  • [378] SST Yau, On strongly elliptic singularities, American Journal of Mathematics, 101(4), 855-884 (1979)
  • [379] SST Yau, Hypersurface weighted dual graphs of normal singularities of surfaces, American Journal of Mathematics, 101(4), 761-812 (1979)
  • [380] SST Yau, Normal two-dimensional elliptic singularities, Transactions of the American Mathematical Society, 254, 117-134 (1979)
  • [381] SST Yau, Gorenstein singularities with geometric genus equal to two, American Journal of Mathematics, 101(4), 813-854 (1979)
  • [382] SST Yau, The signature of Milnor fibres and duality theorem for strongly pseudoconvex manifolds, Inventiones mathematicae, 46(1), 81-97 (1978)
  • [383] SST Yau, Normal singularities of surfaces, Proc. Sympos. Pure Math, 32, 195-198 (1978)
  • [384] SST Yau, Two theorems on higher dimensional singularities, Mathematische Annalen, 231(1), 55-59 (1977)
  • [385] SST Yau, On almost minimally elliptic singularities (1977)
  • [386] JM Garnett III, A Ben-Israel, SS Yau, A hyperpower iterative method for computing matrix products involving the generalized inverse, SIAM Journal on Numerical Analysis, 8(1), 104-109 (1971)
  • [387] SL Hakimi, SS Yau, Distance matrix of a graph and its realizability, Quarterly of applied mathematics, 22(4), 305-317 (1965)
  • [388] Stephen S-T. Yau, Naveed Hussain and Huaiqing Zuo, Geometric nilpotent Lie algebras and zerodimensional simple complete intersection singularities, Forum Mathematicum, 34, 2, 323-345
  • [389] S Yau, H Zuo, Recent results on rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds, ALM, 36, 173-197
  • [390] X Luo, SST Yau, Hermite spectral method to 1D forward Kolmogorov equation and its application to nonlinear filtering problems, unpublished, available online
  • [391] STY Stephen, X Chen, X Jiao, J Kang, Z Sun, Y Tao, Principles of Nonlinear Filtering Theory,

 

Update Time: 2025-07-24 13:00:07