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UMAP-assisted K-means clustering of large-scale SARS-CoV-2 mutation datasets

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arXiv 2020年

作者： Hozumi, Yuta Wang, Rui Yin, Changchuan Wei, Guo-Wei Department of Mathematics Michigan State University MI48824 United States Department of Mathematics Statistics and Computer Science University of Illinois at Chicago ChicagoIL60607 United States Department of Electrical and Computer Engineering Michigan State University MI48824 United States Department of Biochemistry and Molecular Biology Michigan State University MI48824 United States

Coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has a worldwide devastating effect. The understanding of evolution and transmission of SARS-CoV-2 is of paramount importance for the COVID-19 control, combating, and prevention. Due to the rapid growth of both the number of SARS-CoV-2 genome sequences and the number of unique mutations, the phylogenetic analysis of SARS-CoV-2 genome isolates faces an emergent large-data challenge. We introduce a dimension-reduced k-means clustering strategy to tackle this challenge. We examine the performance and effectiveness of three dimension-reduction algorithms: principal component analysis (PCA), t-distributed stochastic neighbor embedding (t-SNE), and uniform manifold approximation and projection (UMAP). By using four benchmark datasets, we found that UMAP is the best-suited technique due to its stable, reliable, and efficient performance, its ability to improve clustering accuracy, especially for large Jaccard distanced-based datasets, and its superior clustering visualization. The UMAP-assisted k-means clustering enables us to shed light on increasingly large datasets from SARS-CoV-2 genome isolates. Copyright © 2020, The Authors. All rights reserved.

关键词： Coronavirus

Mutations on COVID-19 diagnostic targets

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arXiv 2020年

作者： Wang, Rui Hozumi, Yuta Yin, Changchuan Wei, Guo-Wei Department of Mathematics Michigan State University MI48824 United States Department of Mathematics Statistics and Computer Science University of Illinois at Chicago ChicagoIL60607 United States Department of Biochemistry and Molecular Biology Michigan State University MI48824 United States Department of Electrical and Computer Engineering Michigan State University MI48824 United States

Effective, sensitive, and reliable diagnostic reagents are of paramount importance for combating the ongoing coronavirus disease 2019 (COVID-19) pandemic at the time there is no preventive vaccine nor specific drug available for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). It would be an absolute tragedy if currently used diagnostic reagents are undermined in any manner. Based on the genotyping of 7818 SARS-CoV-2 genome samples collected up to May 1, 2020, we reveal that essentially all of the current COVID-19 diagnostic targets have had mutations. We further show that SARS-CoV-2 has the most devastating mutations on the targets of various nucleocapsid (N) gene primers and probes, which have been unfortunately used by countries around the world to diagnose COVID-19. Our findings explain what has seriously gone wrong with a specific diagnostic reagent made in China. To understand whether SARS-CoV-2 genes have mutated unevenly, we have computed the mutation ratio and mutation h-index of all SARS-CoV genes, indicating that the N gene is the most non-conservative gene in the SARS-CoV-2 genome. Our findings enable researchers to target the most conservative SARS-CoV-2 genes and proteins for the design and development of COVID-19 diagnostic reagents, preventive vaccines, and therapeutic medicines. Copyright © 2020, The Authors. All rights reserved.

关键词： Coronavirus

Decoding SARS-CoV-2 transmission, evolution and ramification on COVID-19 diagnosis, vaccine, and medicine

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arXiv 2020年

Tremendous effort has been given to the development of diagnostic tests, preventive vaccines, and therapeutic medicines for coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syn-drome coronavirus 2 (SARS-CoV-2). Much of this development has been based on the reference genome collected on January 5, 2020. Based on the genotyping of 6156 genome samples collected up to April 24, 2020, we report that SARS-CoV-2 has had 4459 alarmingly mutations which can be clustered into five sub-types. We introduce mutation ratio and mutation h-index to characterize the protein conservativeness and unveil that SARS-CoV-2 envelope protein, main protease, and endoribonuclease protein are relatively con-servative, while SARS-CoV-2 nucleocapsid protein, spike protein, and papain-like protease are relatively non-conservative. In particular, the nucleocapsid protein has more than half its genes changed in the past few months, signaling devastating impacts on the ongoing development of COVID-19 diagnosis, vaccines, and drugs. Copyright © 2020, The Authors. All rights reserved.

关键词： Coronavirus

L-Fuzzy Concept Analysis as a Decision-Making Tool in the Development of Bio-Based Materials

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Research Square

Research Square 2020年

作者： Leceta, Itsaso Alcalde, Cristina Urdanpilleta, Marta Guerrero, Pedro de la Caba, Koro Burusco, Ana Department of Applied Mathematics University of the Basque Country UPV/EHU San Sebastian Spain Department of Applied Physics I University of the Basque Country UPV/EHU San Sebastian Spain Department of Chemical and Environmental Engineering University of the Basque Country UPV/EHU San Sebastian Spain Department of Statistics Computer Science and Mathematics Public University of Navarra Pamplona Spain

The use of L-fuzzy concept analysis for the determination of the formulations of gelatin-based films that fulfill specific functional properties is reported. The requirements of water contact angle (CA), water vapour transmission rate (WVTR), L* and b* colour values, tensile strength (TS), elongation at break (EB) and gloss values were specified for both fatty food packaging and wound healing applications. Once the required formulations were estimated by L-fuzzy concepts, the experimental results showed a high accordance with the predicted values of the final properties, as well as with the requirements. The errors were lower than 20% in all cases, except in colour (for food packaging) and gloss and elongation at break (for wound healing), in which the final properties were even better that the estimations. This analysis allowed finding the required formulations in a highly cost-effective way. © 2020, CC BY.

关键词： Contact angle

Tractably modelling dependence in networks beyond exchangeability

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arXiv 2020年

作者： Wu, Weichi Olhede, Sofia Wolfe, Patrick Center for Statistical Sciences Department of Industrial Engineering Tsinghua University China Institute of Mathematics Chair of Statistical Data Science EPFL Swaziland Departments of Statistics and Computer Science Purdue University United States

We propose a general framework for modelling network data that is designed to describe aspects of non-exchangeable networks. Conditional on latent (unobserved) variables, the edges of the network are generated by their finite growth history (with latent orders) while the marginal probabilities of the adjacency matrix are modeled by a generalization of a graph limit function (or a graphon). In particular, we study the estimation, clustering and degree behavior of the network in our setting. We determine (i) the minimax estimator of a composite graphon with respect to squared error loss;(ii) that spectral clustering is able to consistently detect the latent membership when the block-wise constant composite graphon is considered under additional conditions;and (iii) we are able to construct models with heavy-tailed empirical degrees under specific scenarios and parameter choices. This explores why and under which general conditions non-exchangeable network data can be described by a stochastic block model. The new modelling framework is able to capture empirically important characteristics of network data such as sparsity combined with heavy tailed degree distribution, and add understanding as to what generative mechanisms will make them *** Codes 62G05, 62R07, 62E20, 62G20, secondary 53C20 Copyright © 2020, The Authors. All rights reserved.

关键词： Clustering algorithms

Characterizing SARS-CoV-2 mutations in the united states

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arXiv 2020年

作者： Wang, Rui Chen, Jiahui Gao, Kaifu Hozumi, Yuta Yin, Changchuan Wei, Guo-Wei Department of Mathematics Michigan State University MI48824 United States Department of Mathematics Statistics and Computer Science University of Illinois at Chicago ChicagoIL60607 United States Department of Electrical and Computer Engineering Michigan State University MI48824 United States Department of Biochemistry and Molecular Biology Michigan State University MI48824 United States

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been mutating since it was first sequenced in early January 2020. The genetic variants have developed into a few distinct clusters with different properties. Since the United States (US) has the highest number of viral infected patients globally, it is essential to understand the US SARS-CoV-2. Using genotyping, sequence-alignment, time-evolution, k-means clustering, protein-folding stability, algebraic topology, and network theory, we reveal that the US SARS-CoV-2 has four substrains and five top US SARS-CoV-2 mutations were first detected in China (2 cases), Singapore (2 cases), and the United Kingdom (1 case). The next three top US SARS-CoV-2 mutations were first detected in the US. These eight top mutations belong to two disconnected groups. The first group consisting of 5 concurrent mutations is prevailing, while the other group with three concurrent mutations gradually fades out. Our analysis suggests that female immune systems are more active than those of males in responding to SARS-CoV-2 infections. We identify that one of the top mutations, 27964C>T-(S24L) on ORF8, has an unusually strong gender dependence. Based on the analysis of all mutations on the spike protein, we further uncover that three of four US SASR-CoV-2 substrains become more infectious. Our study calls for effective viral control and containing strategies in the US. Copyright © 2020, The Authors. All rights reserved.

关键词： Machine learning

Author Correction: H∞ observer-based control for fuzzy Hadamard fractional-order systems

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Computational and Applied mathematics 2025年第5期44卷 1-1页

作者： Rhaima, Mohamed Gassara, Hamdi Mchiri, Lassaad Hajjaji, Ahmed El Makhlouf, Abdellatif Ben Department of Statistics and Operations Research College of Science King Saud University Riyadh Saudi Arabia Laboratory of Sciences Techniques of Automatic Control and Computer Engineering National School of Engineering of Sfax University of Sfax Sfax Tunisia Panthéon-Assas University Paris II Paris France Modeling Information and Systems Laboratory University of Picardie Jules Verne UFR of Sciences Amiens France Department of Mathematics Faculty of Sciences Sfax University Sfax Tunisia

An optimal algorithm for strict circular seriation

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arXiv 2021年

作者： Armstrong, Santiago Guzmán, Cristóbal Long, Carlos A. Sing Institute for Mathematical and Computational Engineering Pontificia Universidad Católica de Chile Santiago Chile Anid - Millennium Science Initiative Program Millennium Nucleus Center for the Discovery of Structures in Complex Data Santiago Chile Department of Applied Mathematics University of Twente Netherlands Institute for Biological and Medical Engineering Pontificia Universidad Católica de Chile Santiago Chile

We study the problem of circular seriation, where we are given a matrix of pairwise dissimilarities between n objects, and the goal is to find a circular order of the objects in a manner that is consistent with their dissimilarity. This problem is a generalization of the classical linear seriation problem where the goal is to find a linear order, and for which optimal O(n2) algorithms are known. Our contributions can be summarized as follows. First, we introduce circular Robinson matrices as the natural class of dissimilarity matrices for the circular seriation problem. Second, for the case of strict circular Robinson dissimilarity matrices we provide an optimal O(n2) algorithm for the circular seriation problem. Finally, we propose a statistical model to analyze the well-posedness of the circular seriation problem for large n. In particular, we establish O(log(n)/n) rates on the distance between any circular ordering found by solving the circular seriation problem to the underlying order of the model, in the Kendall-tau *** Codes 68R01, 05C85, 05C50, 05C25, 65C20 Copyright © 2021, The Authors. All rights reserved.

关键词： Trees (mathematics)

Third generation of vortex identification methods:Omega and Liutex/Rortex based systems

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Journal of Hydrodynamics 2019年第2期31卷 205-223页

作者： Chaoqun Liu Yi-sheng Gao Xiang-rui Dong Yi-qian Wang Jian-ming Liu Yu-ning Zhang Xiao-shu Cai Nan Gui Department of Mathematics University of Texas at ArlingtonArlington 76019TexasUSA College of Energy and Power Engineering University of Shanghai for Science and TechnologyShanghai 200093China School of Aerospace Engineering Tsinghua UniversityBeijing 100084China School of Mathematics and Statistics Jiangsu Normal UniversityXuzhou 221116China Key Laboratory of Condition Monitoring and Control for Power Plant Equipment(Ministry of Education) School of EnergyPower and Mechanical EngineeringNorth China Electric Power UniversityBeijing 102206China Institute of Nuclear and New Energy Technology Collaborative Innovation Center of Advanced Nuclear Energy TechnologyKey Laboratory of Advanced Reactor Engineering and Safety of Ministry of EducationTsinghua UniversityBeijing 100084China

A vortex is intuitively recognized as the rotational/swirling motion of fluids,but a rigorous and universally-accepted definition is still not *** tube/filament has been regarded equivalent to a vortex since Helmholtz proposed the concepts of vorticity tube/filament in 1858 and the vorticity-based methods can be categorized as the first generation of vortex identification *** the last three decades,a lot of vortex identification methods,including 0,A,and Aci criteria,have been proposed to overcome the problems associated with the vorticity-based *** of these criteria are based on the Cauchy-Stokes decomposition and/or eigenvalues of the velocity gradient tensor and can be considered as the second generation of vortex identification *** from 2014,the Vortex and Turbulence Research Team at the University of Texas at Arlington(the UTA team)focus on the development of a new generation of vortex identification *** first fruit of this effort,a new Omega(/2)vortex identification method,which defined a vortex as a connected region where the vorticity overtakes the deformation,was published in *** 2017 and 2018,a Liutex(previously called Rortex)vector was proposed to provide a mathematical definition of the local rigid rotation part of the fluid motion,including both the local rotational axis and the rotational ***/Rortex is a new physical quantity with scalar,vector and tensor forms exactly representing the local rigid rotation of ***,a decomposition of the vorticity to a rotational part namely Liutex/Rortex and an anti-symmetric shear part(RS decomposition)was introduced in 2018,and a universal decomposition of the velocity gradient tensor to a rotation part(7?)and a non-rotation part(NR、was also given in 2018 as a counterpart of the traditional Cauchy-Stokes *** in early 2019,a Liutex/Rortex based Omega method called Omega-Liutex,which combines the respective advantages o

关键词： Vortex definition vortex identification Omega Liutex/Rortex direct numerical simulation turbulence