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Diagnostic of the Lévy area for geophysical flow models in view of defining high order stochastic discrete-time schemes 基于高阶随机离散时间格式的地球物理流动模型lsamvy区域诊断
Foundations of data science (Springfield, Mo.) Pub Date : 2023-01-01 DOI: 10.3934/fods.2023011
Pierre-Marie Boulvard, Etienne Mémin
{"title":"Diagnostic of the Lévy area for geophysical flow models in view of defining high order stochastic discrete-time schemes","authors":"Pierre-Marie Boulvard, Etienne Mémin","doi":"10.3934/fods.2023011","DOIUrl":"https://doi.org/10.3934/fods.2023011","url":null,"abstract":"In this paper we characterize numerically through two criteria the Lévy area related to unresolved fluctuation velocities associated to a stochastic coarse-scale representation of geophysical fluid flow dynamics. We study in particular whether or not the process associated to the random unresolved velocity components exhibits a Lévy area corresponding to a Wiener process, and if the law of this process can reasonably be approached by a centered Dirac measure. This exploration enables us to answer positively to a conjecture made for the constitution of high-order discrete time evolution schemes for stochastic representation defined from stochastic transport.","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136306282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Hierarchical regularization networks for sparsification based learning on noisy datasets 基于噪声数据集学习的分层正则化网络
Foundations of data science (Springfield, Mo.) Pub Date : 2023-01-01 DOI: 10.3934/fods.2023009
P. Shekhar, M. Babu, Abani Patra
{"title":"Hierarchical regularization networks for sparsification based learning on noisy datasets","authors":"P. Shekhar, M. Babu, Abani Patra","doi":"10.3934/fods.2023009","DOIUrl":"https://doi.org/10.3934/fods.2023009","url":null,"abstract":"","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70248298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Persistent hyperdigraph homology and persistent hyperdigraph Laplacians 持久超向位同调和持久超向位拉普拉斯算子
Foundations of data science (Springfield, Mo.) Pub Date : 2023-01-01 DOI: 10.3934/fods.2023010
Dong Chen, Jian Liu, Jie Wu, Guo-Wei Wei
{"title":"Persistent hyperdigraph homology and persistent hyperdigraph Laplacians","authors":"Dong Chen, Jian Liu, Jie Wu, Guo-Wei Wei","doi":"10.3934/fods.2023010","DOIUrl":"https://doi.org/10.3934/fods.2023010","url":null,"abstract":"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.","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136053367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Unsupervised learning of observation functions in state space models by nonparametric moment methods 非参数矩法在状态空间模型中观测函数的无监督学习
Foundations of data science (Springfield, Mo.) Pub Date : 2023-01-01 DOI: 10.3934/fods.2023002
Qingci An, Yannis Kevrekidis, Fei Lu, Mauro Maggioni
{"title":"Unsupervised learning of observation functions in state space models by nonparametric moment methods","authors":"Qingci An, Yannis Kevrekidis, Fei Lu, Mauro Maggioni","doi":"10.3934/fods.2023002","DOIUrl":"https://doi.org/10.3934/fods.2023002","url":null,"abstract":"We investigate the unsupervised learning of non-invertible observation functions in nonlinear state space models. Assuming abundant data of the observation process along with the distribution of the state process, we introduce a nonparametric generalized moment method to estimate the observation function via constrained regression. The major challenge comes from the non-invertibility of the observation function and the lack of data pairs between the state and observation. We address the fundamental issue of identifiability from quadratic loss functionals and show that the function space of identifiability is the closure of a RKHS that is intrinsic to the state process. Numerical results show that the first two moments and temporal correlations, along with upper and lower bounds, can identify functions ranging from piecewise polynomials to smooth functions, leading to convergent estimators. The limitations of this method, such as non-identifiability due to symmetry and stationarity, are also discussed.","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135534595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Noise calibration for SPDEs: A case study for the rotating shallow water model spde的噪声校正:以旋转浅水模型为例
Foundations of data science (Springfield, Mo.) Pub Date : 2023-01-01 DOI: 10.3934/fods.2023012
Dan Crisan, Oana Lang, Alexander Lobbe, Peter-Jan van Leeuwen, Roland Potthast
{"title":"Noise calibration for SPDEs: A case study for the rotating shallow water model","authors":"Dan Crisan, Oana Lang, Alexander Lobbe, Peter-Jan van Leeuwen, Roland Potthast","doi":"10.3934/fods.2023012","DOIUrl":"https://doi.org/10.3934/fods.2023012","url":null,"abstract":"","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":"161 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134980769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Weight set decomposition for weighted rank and rating aggregation: An interpretable and visual decision support tool 加权排名和评级聚合的权重集分解:一个可解释和可视化的决策支持工具
Foundations of data science (Springfield, Mo.) Pub Date : 2023-01-01 DOI: 10.3934/fods.2023001
Tyler A. Perini, A. Langville, Glenn Kramer, Jeff Shrager, Mark Shapiro
{"title":"Weight set decomposition for weighted rank and rating aggregation: An interpretable and visual decision support tool","authors":"Tyler A. Perini, A. Langville, Glenn Kramer, Jeff Shrager, Mark Shapiro","doi":"10.3934/fods.2023001","DOIUrl":"https://doi.org/10.3934/fods.2023001","url":null,"abstract":"","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70248223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
GEOMETRIC STRUCTURE GUIDED MODEL AND ALGORITHMS FOR COMPLETE DECONVOLUTION OF GENE EXPRESSION DATA. 基因表达数据完全反褶积的几何结构导向模型和算法
Foundations of data science (Springfield, Mo.) Pub Date : 2022-09-01 DOI: 10.3934/fods.2022013
Duan Chen, Shaoyu Li, Xue Wang
{"title":"GEOMETRIC STRUCTURE GUIDED MODEL AND ALGORITHMS FOR COMPLETE DECONVOLUTION OF GENE EXPRESSION DATA.","authors":"Duan Chen, Shaoyu Li, Xue Wang","doi":"10.3934/fods.2022013","DOIUrl":"10.3934/fods.2022013","url":null,"abstract":"<p><p>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 cellular composition of tissue samples, or due to GEPs changes in specific cells. One of the major techniques to perform complete deconvolution is nonnegative matrix factorization (NMF), which also has a wide-range of applications in the machine learning community. However, the NMF is a well-known strongly ill-posed problem, so a direct application of NMF to RNA-seq data will suffer severe difficulties in the interpretability of solutions. In this paper, we develop an NMF-based mathematical model and corresponding computational algorithms to improve the solution identifiability of deconvoluting bulk RNA-seq data. In our approach, we combine the biological concept of marker genes with the solvability conditions of the NMF theories, and develop a geometric structures guided optimization model. In this strategy, the geometric structure of bulk tissue data is first explored by the spectral clustering technique. Then, the identified information of marker genes is integrated as solvability constraints, while the overall correlation graph is used as manifold regularization. Both synthetic and biological data are used to validate the proposed model and algorithms, from which solution interpretability and accuracy are significantly improved.</p>","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":"1 1","pages":"441-466"},"PeriodicalIF":0.0,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10798655/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42614124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
ASPECTS OF TOPOLOGICAL APPROACHES FOR DATA SCIENCE. 数据科学拓扑方法的各个方面。
Foundations of data science (Springfield, Mo.) Pub Date : 2022-06-01 DOI: 10.3934/fods.2022002
Jelena Grbić, Jie Wu, Kelin Xia, Guo-Wei Wei
{"title":"ASPECTS OF TOPOLOGICAL APPROACHES FOR DATA SCIENCE.","authors":"Jelena Grbić, Jie Wu, Kelin Xia, Guo-Wei Wei","doi":"10.3934/fods.2022002","DOIUrl":"10.3934/fods.2022002","url":null,"abstract":"<p><p>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 complexes and hypergraphs to super-hypergraphs and establish super-hypergraph homology as an extension of simplicial homology. Driven by applications, we also introduce super-persistent homology.</p>","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":"4 2","pages":"165-216"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9881677/pdf/nihms-1825620.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10592051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A log-Gaussian Cox process with sequential Monte Carlo for line narrowing in spectroscopy 谱线窄化的对数高斯-考克斯过程
Foundations of data science (Springfield, Mo.) Pub Date : 2022-02-26 DOI: 10.3934/fods.2023008
T. Harkonen, Emma Hannula, M. Moores, E. Vartiainen, L. Roininen
{"title":"A log-Gaussian Cox process with sequential Monte Carlo for line narrowing in spectroscopy","authors":"T. Harkonen, Emma Hannula, M. Moores, E. Vartiainen, L. Roininen","doi":"10.3934/fods.2023008","DOIUrl":"https://doi.org/10.3934/fods.2023008","url":null,"abstract":"We propose a statistical model for narrowing line shapes in spectroscopy that are well approximated as linear combinations of Lorentzian or Voigt functions. We introduce a log-Gaussian Cox process to represent the peak locations thereby providing uncertainty quantification for the line narrowing. Bayesian formulation of the method allows for robust and explicit inclusion of prior information as probability distributions for parameters of the model. Estimation of the signal and its parameters is performed using a sequential Monte Carlo algorithm followed by an optimization step to determine the peak locations. Our method is validated using a simulation study and applied to a mineralogical Raman spectrum.","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45413111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Data based quantification of synchronization 基于数据的同步量化
Foundations of data science (Springfield, Mo.) Pub Date : 2022-01-01 DOI: 10.3934/fods.2022020
{"title":"Data based quantification of synchronization","authors":"","doi":"10.3934/fods.2022020","DOIUrl":"https://doi.org/10.3934/fods.2022020","url":null,"abstract":"","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70248163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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