Pub Date : 2007-06-15DOI: 10.1142/9789812793492_0010
O. Flomenbom, R. Silbey
Single molecule data made of on and off events are ubiquitous. Famous examples include enzyme turnover, probed via fluorescence, and opening and closing of ion-channel, probed via the flux of ions. The data reflects the dynamics in the underlying multi-substate on-off kinetic scheme (KS) of the process, but the determination of the underlying KS is difficult, and sometimes even impossible, due to the loss of information in the mapping of the mutli-dimensional KS onto two dimensions. A way to deal with this problem considers canonical (unique) forms. (Unique canonical form is constructed from an infinitely long trajectory, but many KSs.) Here we introduce canonical forms of reduced dimensions that can handle any KS (i.e. also KSs with symmetry and irreversible transitions). We give the mapping of KSs into reduced dimensions forms, which is based on topology of KSs, and the tools for extracting the reduced dimensions form from finite data. The canonical forms of reduced dimensions constitute a powerful tool in discriminating between KSs.
{"title":"Unique Mechanisms From Finite Two-State Trajectories","authors":"O. Flomenbom, R. Silbey","doi":"10.1142/9789812793492_0010","DOIUrl":"https://doi.org/10.1142/9789812793492_0010","url":null,"abstract":"Single molecule data made of on and off events are ubiquitous. Famous examples include enzyme turnover, probed via fluorescence, and opening and closing of ion-channel, probed via the flux of ions. The data reflects the dynamics in the underlying multi-substate on-off kinetic scheme (KS) of the process, but the determination of the underlying KS is difficult, and sometimes even impossible, due to the loss of information in the mapping of the mutli-dimensional KS onto two dimensions. A way to deal with this problem considers canonical (unique) forms. (Unique canonical form is constructed from an infinitely long trajectory, but many KSs.) Here we introduce canonical forms of reduced dimensions that can handle any KS (i.e. also KSs with symmetry and irreversible transitions). We give the mapping of KSs into reduced dimensions forms, which is based on topology of KSs, and the tools for extracting the reduced dimensions form from finite data. The canonical forms of reduced dimensions constitute a powerful tool in discriminating between KSs.","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126721834","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}
Pub Date : 2006-08-23DOI: 10.1002/9783527609970.CH17
M. Ding, Yonghong Chen, S. Bressler
Multi-electrode neurophysiological recordings produce massive quantities of data. Multivariate time series analysis provides the basic framework for analyzing the patterns of neural interactions in these data. It has long been recognized that neural interactions are directional. Being able to assess the directionality of neuronal interactions is thus a highly desired capability for understanding the cooperative nature of neural computation. Research over the last few years has shown that Granger causality is a key technique to furnish this capability. The main goal of this article is to provide an expository introduction to the concept of Granger causality. Mathematical frameworks for both bivariate Granger causality and conditional Granger causality are developed in detail with particular emphasis on their spectral representations. The technique is demonstrated in numerical examples where the exact answers of causal influences are known. It is then applied to analyze multichannel local field potentials recorded from monkeys performing a visuomotor task. Our results are shown to be physiologically interpretable and yield new insights into the dynamical organization of large-scale oscillatory cortical networks.
{"title":"Granger Causality: Basic Theory and Application to Neuroscience","authors":"M. Ding, Yonghong Chen, S. Bressler","doi":"10.1002/9783527609970.CH17","DOIUrl":"https://doi.org/10.1002/9783527609970.CH17","url":null,"abstract":"Multi-electrode neurophysiological recordings produce massive quantities of data. Multivariate time series analysis provides the basic framework for analyzing the patterns of neural interactions in these data. It has long been recognized that neural interactions are directional. Being able to assess the directionality of neuronal interactions is thus a highly desired capability for understanding the cooperative nature of neural computation. Research over the last few years has shown that Granger causality is a key technique to furnish this capability. The main goal of this article is to provide an expository introduction to the concept of Granger causality. Mathematical frameworks for both bivariate Granger causality and conditional Granger causality are developed in detail with particular emphasis on their spectral representations. The technique is demonstrated in numerical examples where the exact answers of causal influences are known. It is then applied to analyze multichannel local field potentials recorded from monkeys performing a visuomotor task. Our results are shown to be physiologically interpretable and yield new insights into the dynamical organization of large-scale oscillatory cortical networks.","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123138573","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}
Pub Date : 2005-10-17DOI: 10.4018/978-1-59904-042-4.CH002
Jean-Philippe Vert
Support vector machines and kernel methods are increasingly popular in genomics and computational biology, due to their good performance in real-world applications and strong modularity that makes them suitable to a wide range of problems, from the classification of tumors to the automatic annotation of proteins. Their ability to work in high dimension, to process non-vectorial data, and the natural framework they provide to integrate heterogeneous data are particularly relevant to various problems arising in computational biology. In this chapter we survey some of the most prominent applications published so far, highlighting the particular developments in kernel methods triggered by problems in biology, and mention a few promising research directions likely to expand in the future.
{"title":"Kernel Methods in Genomics and Computational Biology","authors":"Jean-Philippe Vert","doi":"10.4018/978-1-59904-042-4.CH002","DOIUrl":"https://doi.org/10.4018/978-1-59904-042-4.CH002","url":null,"abstract":"Support vector machines and kernel methods are increasingly popular in genomics and computational biology, due to their good performance in real-world applications and strong modularity that makes them suitable to a wide range of problems, from the classification of tumors to the automatic annotation of proteins. Their ability to work in high dimension, to process non-vectorial data, and the natural framework they provide to integrate heterogeneous data are particularly relevant to various problems arising in computational biology. In this chapter we survey some of the most prominent applications published so far, highlighting the particular developments in kernel methods triggered by problems in biology, and mention a few promising research directions likely to expand in the future.","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"257 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133473500","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}
Pub Date : 2005-04-08DOI: 10.1007/978-3-540-73750-6_14
Alexander N Gorban, A. Zinovyev
{"title":"PCA and K-Means Decipher Genome","authors":"Alexander N Gorban, A. Zinovyev","doi":"10.1007/978-3-540-73750-6_14","DOIUrl":"https://doi.org/10.1007/978-3-540-73750-6_14","url":null,"abstract":"","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129653525","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}
Pub Date : 2004-06-06DOI: 10.1007/978-3-642-55606-7_3
P. Theodosopoulos, T. Theodosopoulos
{"title":"Evolution at the Edge of Chaos: A Paradigm for the Maturation of the Humoral Immune Response","authors":"P. Theodosopoulos, T. Theodosopoulos","doi":"10.1007/978-3-642-55606-7_3","DOIUrl":"https://doi.org/10.1007/978-3-642-55606-7_3","url":null,"abstract":"","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130237801","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}
K. Garikipati, H. Narayanan, E. Arruda, K. Grosh, S. Calve
{"title":"Material Forces in the Context of Biotissue Remodelling","authors":"K. Garikipati, H. Narayanan, E. Arruda, K. Grosh, S. Calve","doi":"10.1007/0-387-26261-X_8","DOIUrl":"https://doi.org/10.1007/0-387-26261-X_8","url":null,"abstract":"","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129303023","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}
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