nldr.bib

@article{Kutz2016,
author = {Kutz, J. Nathan and Brunton, Steven L.},
doi = {10.1137/15M1023543},
editor = {Kutz, J. Nathan (University of Washington) and Brunton, Steven (University of Washington) and Brunton, Bingi (University of Washington) and Proctor, Joshua L. (Institute for Disease Modeling)},
file = {:home/ba13026/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Kutz, Brunton - 2016 - Dynamic mode decomposition.pdf:pdf},
issn = {15360040},
journal = {SIAM Journal on Applied Dynamical Systems},
keywords = {Dynamic mode decomposition,Dynamical systems,Koopman operator,Multiresolution analysis},
number = {2},
pages = {713--735},
title = {{Dynamic mode decomposition}},
url = {file:///Users/bas/Downloads/DYNAMIC MODE DECOMPOSITION DATA.pdf},
volume = {15},
year = {2016}
}
@misc{SCHMID2019,
author = {SCHMID, PETER J.},
file = {:home/ba13026/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/SCHMID - 2019 - KOOPMAN ANALYSIS AND THE SPARSITY-PROMOTING.pdf:pdf},
number = {October},
title = {{KOOPMAN ANALYSIS AND THE SPARSITY-PROMOTING}},
year = {2019}
}
@article{Schmid2010,
abstract = {The description of coherent features of fluid flow is essential to our understanding of fluid-dynamical and transport processes. A method is introduced that is able to extract dynamic information from flow fields that are either generated by a (direct) numerical simulation or visualized/measured in a physical experiment. The extracted dynamic modes, which can be interpreted as a generalization of global stability modes, can be used to describe the underlying physical mechanisms captured in the data sequence or to project large-scale problems onto a dynamical system of significantly fewer degrees of freedom. The concentration on subdomains of the flow field where relevant dynamics is expected allows the dissection of a complex flow into regions of localized instability phenomena and further illustrates the flexibility of the method, as does the description of the dynamics within a spatial framework. Demonstrations of the method are presented consisting of a plane channel flow, flow over a two-dimensional cavity, wake flow behind a flexible membrane and a jet passing between two cylinders. {\textcopyright} 2010 Cambridge University Press.},
author = {Schmid, Peter J.},
doi = {10.1017/S0022112010001217},
file = {:home/ba13026/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/SCHMID - 2010 - Dynamic mode decomposition of numerical and experimental data.pdf:pdf},
issn = {14697645},
journal = {Journal of Fluid Mechanics},
keywords = {dmd},
mendeley-tags = {dmd},
month = {aug},
pages = {5--28},
publisher = {Cambridge University Press},
title = {{Dynamic mode decomposition of numerical and experimental data}},
url = {https://www.cambridge.org/core/product/identifier/S0022112010001217/type/journal{\_}article},
volume = {656},
year = {2010}
}
@article{Klus2019,
abstract = {We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition). This approach is applicable to deterministic and stochastic dynamical systems. It can be used for computing eigenvalues, eigenfunctions, and modes of the generator and for system identification. In addition to learning the governing equations of deterministic systems, which then reduces to SINDy (sparse identification of nonlinear dynamics), it is possible to identify the drift and diffusion terms of stochastic differential equations from data. Moreover, we apply gEDMD to derive coarse-grained models of high-dimensional systems, and also to determine efficient model predictive control strategies. We highlight relationships with other methods and demonstrate the efficacy of the proposed methods using several guiding examples and prototypical molecular dynamics problems.},
archivePrefix = {arXiv},
arxivId = {1909.10638},
author = {Klus, Stefan and N{\"{u}}ske, Feliks and Peitz, Sebastian and Niemann, Jan-Hendrik and Clementi, Cecilia and Sch{\"{u}}tte, Christof},
eprint = {1909.10638},
file = {:home/ba13026/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Klus et al. - 2019 - Data-driven approximation of the Koopman generator Model reduction, system identification, and control.pdf:pdf},
month = {sep},
title = {{Data-driven approximation of the Koopman generator: Model reduction, system identification, and control}},
url = {http://arxiv.org/abs/1909.10638},
year = {2019}
}
@article{ROWLEY2009,
abstract = {{\textless}p{\textgreater} We present a technique for describing the global behaviour of complex nonlinear flows by decomposing the flow into modes determined from spectral analysis of the Koopman operator, an infinite-dimensional linear operator associated with the full nonlinear system. These modes, referred to as Koopman modes, are associated with a particular observable, and may be determined directly from data (either numerical or experimental) using a variant of a standard Arnoldi method. They have an associated temporal frequency and growth rate and may be viewed as a nonlinear generalization of global eigenmodes of a linearized system. They provide an alternative to proper orthogonal decomposition, and in the case of periodic data the Koopman modes reduce to a discrete temporal Fourier transform. The Arnoldi method used for computations is identical to the dynamic mode decomposition recently proposed by Schmid {\&} Sesterhenn ( {\textless}italic{\textgreater}Sixty-First Annual Meeting of the APS Division of Fluid Dynamics{\textless}/italic{\textgreater} , 2008), so dynamic mode decomposition can be thought of as an algorithm for finding Koopman modes. We illustrate the method on an example of a jet in crossflow, and show that the method captures the dominant frequencies and elucidates the associated spatial structures. {\textless}/p{\textgreater}},
author = {ROWLEY, CLARENCE W. and MEZI{\'{C}}, IGOR and BAGHERI, SHERVIN and SCHLATTER, PHILIPP and HENNINGSON, DAN S.},
doi = {10.1017/S0022112009992059},
file = {:home/ba13026/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/ROWLEY et al. - 2009 - Spectral analysis of nonlinear flows.pdf:pdf},
issn = {0022-1120},
journal = {Journal of Fluid Mechanics},
month = {dec},
pages = {115--127},
publisher = {Cambridge University Press},
title = {{Spectral analysis of nonlinear flows}},
url = {https://www.cambridge.org/core/product/identifier/S0022112009992059/type/journal{\_}article},
volume = {641},
year = {2009}
}
@article{Garcia-Garrido2018,
abstract = {The goal of this paper is to apply Lagrangian Descriptors (LDs), a technique based on Dynamical Systems Theory (DST) to reveal the phase space structures present in the well-known Arnold's cat map. This discrete dynamical system, which represents a classical example of an Anosov diffeomorphism that is strongly mixing, will provide us with a benchmark model to test the performance of LDs and their capability to detect fixed points, periodic orbits and their stable and unstable manifolds present in chaotic maps. In this work we show, both from a theoretical and a numerical perspective, how LDs reveal the invariant manifolds of the periodic orbits of the cat map. The application of this methodology in this setting clearly illustrates the chaotic behavior of the cat map and highlights some technical numerical difficulties that arise in the identification of its phase space structures.},
author = {Garc{\'{i}}a-Garrido, V{\'{i}}ctor J. and Balibrea-Iniesta, Francisco and Wiggins, Stephen and Mancho, Ana M. and Lopesino, Carlos},
doi = {10.1134/S1560354718060096},
file = {:home/ba13026/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Garc{\'{i}}a-Garrido et al. - 2018 - Detection of Phase Space Structures of the Cat Map with Lagrangian Descriptors.pdf:pdf},
issn = {14684845},
journal = {Regular and Chaotic Dynamics},
keywords = {37D10,37Mxx,37N10,37XX,70K43,Lagrangian descriptors,chaotic sets,dynamical systems,maps,mixing,stable and unstable manifolds},
number = {6},
pages = {751--766},
title = {{Detection of Phase Space Structures of the Cat Map with Lagrangian Descriptors}},
volume = {23},
year = {2018}
}
@article{Williams2014,
abstract = {The Koopman operator is a linear but infinite dimensional operator that governs the evolution of scalar observables defined on the state space of an autonomous dynamical system, and is a powerful tool for the analysis and decomposition of nonlinear dynamical systems. In this manuscript, we present a data driven method for approximating the leading eigenvalues, eigenfunctions, and modes of the Koopman operator. The method requires a data set of snapshot pairs and a dictionary of scalar observables, but does not require explicit governing equations or interaction with a "black box" integrator. We will show that this approach is, in effect, an extension of Dynamic Mode Decomposition (DMD), which has been used to approximate the Koopman eigenvalues and modes. Furthermore, if the data provided to the method are generated by a Markov process instead of a deterministic dynamical system, the algorithm approximates the eigenfunctions of the Kolmogorov backward equation, which could be considered as the "stochastic Koopman operator" [1]. Finally, four illustrative examples are presented: two that highlight the quantitative performance of the method when presented with either deterministic or stochastic data, and two that show potential applications of the Koopman eigenfunctions.},
archivePrefix = {arXiv},
arxivId = {1408.4408},
author = {Williams, Matthew O. and Kevrekidis, Ioannis G. and Rowley, Clarence W.},
doi = {10.1007/s00332-015-9258-5},
eprint = {1408.4408},
file = {:home/ba13026/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Williams, Kevrekidis, Rowley - 2014 - A Data-Driven Approximation of the Koopman Operator Extending Dynamic Mode Decomposition.pdf:pdf},
month = {aug},
title = {{A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition}},
url = {http://arxiv.org/abs/1408.4408 http://dx.doi.org/10.1007/s00332-015-9258-5},
year = {2014}
}
@article{Champion2019,
abstract = {Governing equations are essential to the study of physical systems, providing models that can generalize to predict previously unseen behaviors. There are many systems of interest across disciplines where large quantities of data have been collected, but the underlying governing equations remain unknown. This work introduces an approach to discover governing models from data. The proposed method addresses a key limitation of prior approaches by simultaneously discovering coordinates that admit a parsimonious dynamical model. Developing parsimonious and interpretable governing models has the potential to transform our understanding of complex systems, including in neuroscience, biology, and climate science.

The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable identification of both the structure and parameters of a nonlinear dynamical system from data. The resulting models have the fewest terms necessary to describe the dynamics, balancing model complexity with descriptive ability, and thus promoting interpretability and generalizability. This provides an algorithmic approach to Occam's razor for model discovery. However, this approach fundamentally relies on an effective coordinate system in which the dynamics have a simple representation. In this work, we design a custom deep autoencoder network to discover a coordinate transformation into a reduced space where the dynamics may be sparsely represented. Thus, we simultaneously learn the governing equations and the associated coordinate system. We demonstrate this approach on several example high-dimensional systems with low-dimensional behavior. The resulting modeling framework combines the strengths of deep neural networks for flexible representation and sparse identification of nonlinear dynamics (SINDy) for parsimonious models. This method places the discovery of coordinates and models on an equal footing.},
author = {Champion, Kathleen and Lusch, Bethany and Kutz, J. Nathan and Brunton, Steven L.},
doi = {10.1073/PNAS.1906995116},
file = {:home/ba13026/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Champion et al. - 2019 - Data-driven discovery of coordinates and governing equations.pdf:pdf},
issn = {0027-8424},
journal = {Proceedings of the National Academy of Sciences},
month = {oct},
pages = {201906995},
pmid = {31636218},
publisher = {National Academy of Sciences},
title = {{Data-driven discovery of coordinates and governing equations}},
url = {https://www.pnas.org/content/early/2019/10/18/1906995116.short?rss=1},
year = {2019}
}
@article{Munoz-Gil2019,
abstract = {In order to study transport in complex environments, it is extremely important to determine the physical mechanism underlying diffusion, and precisely characterize its nature and parameters. Often, this task is strongly impacted by data consisting of trajectories with short length and limited localization precision. In this paper, we propose a machine learning method based on a random forest architecture, which is able to associate even very short trajectories to the underlying diffusion mechanism with a high accuracy. In addition, the method is able to classify the motion according to normal or anomalous diffusion, and determine its anomalous exponent with a small error. The method provides highly accurate outputs even when working with very short trajectories and in the presence of experimental noise. We further demonstrate the application of transfer learning to experimental and simulated data not included in the training/testing dataset. This allows for a full, high-accuracy characterization of experimental trajectories without the need of any prior information.},
archivePrefix = {arXiv},
arxivId = {1903.02850},
author = {Mu{\~{n}}oz-Gil, Gorka and Garcia-March, Miguel Angel and Manzo, Carlo and Mart{\'{i}}n-Guerrero, Jos{\'{e}} D. and Lewenstein, Maciej},
eprint = {1903.02850},
file = {:home/ba13026/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Mu{\~{n}}oz-Gil et al. - 2019 - Machine learning method for single trajectory characterization.pdf:pdf},
pages = {1--9},
title = {{Machine learning method for single trajectory characterization}},
url = {http://arxiv.org/abs/1903.02850},
volume = {1},
year = {2019}
}
@article{Mahendran2017,
abstract = {The fabrication of monodisperse transmembrane barrels formed from short synthetic peptides has not been demonstrated previously. This is in part because of the complexity of the interactions between peptides and lipids within the hydrophobic environment of a membrane. Here we report the formation of a transmembrane pore through the self-assembly of 35 amino acid $\alpha$-helical peptides. The design of the peptides is based on the C-terminal D4 domain of the Escherichia coli polysaccharide transporter Wza. By using single-channel current recording, we define discrete assembly intermediates and show that the pore is most probably a helix barrel that contains eight D4 peptides arranged in parallel. We also show that the peptide pore is functional and capable of conducting ions and binding blockers. Such $\alpha$-helix barrels engineered from peptides could find applications in nanopore technologies such as single-molecule sensing and nucleic-acid sequencing.},
author = {Mahendran, Kozhinjampara R. and Niitsu, Ai and Kong, Lingbing and Thomson, Andrew R. and Sessions, Richard B. and Woolfson, Derek N. and Bayley, Hagan},
doi = {10.1038/nchem.2647},
file = {:home/ba13026/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Mahendran et al. - 2017 - A monodisperse transmembrane $\alpha$-helical peptide barrel (Supplement).pdf:pdf},
issn = {17554349},
journal = {Nature Chemistry},
keywords = {wza},
mendeley-tags = {wza},
number = {5},
pages = {411--419},
title = {{A monodisperse transmembrane $\alpha$-helical peptide barrel (Supplement)}},
volume = {9},
year = {2017}
}
@article{Mahendran2016,
abstract = {The assembly of transmembrane barrels formed from short synthetic peptides has not been previously demonstrated. Now, a transmembrane pore has been fabricated via the self-assembly of peptides. The 35-amino-acid $\alpha$-helical peptides are based on the C-terminal D4 domain of the Escherichia coli polysaccharide transporter Wza.},
author = {Mahendran, Kozhinjampara R. and Niitsu, Ai and Kong, Lingbing and Thomson, Andrew R. and Sessions, Richard B. and Woolfson, Derek N. and Bayley, Hagan},
doi = {10.1038/nchem.2647},
file = {:home/ba13026/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Mahendran et al. - 2016 - A monodisperse transmembrane $\alpha$-helical peptide barrel.pdf:pdf},
issn = {1755-4330},
journal = {Nature Chemistry},
keywords = {Biosensors,Membranes},
month = {nov},
number = {5},
pages = {411--419},
publisher = {Nature Publishing Group},
title = {{A monodisperse transmembrane $\alpha$-helical peptide barrel}},
url = {http://www.nature.com/doifinder/10.1038/nchem.2647},
volume = {9},
year = {2016}
}
@article{Niitsu2017,
abstract = {The rational (de novo) design of membrane-spanning proteins lags behind that for water-soluble globular proteins. This is due to gaps in our knowledge of membrane-protein structure, and experimental difficulties in studying such proteins compared to water-soluble counterparts. One limiting factor is the small number of experimentally determined three-dimensional structures for transmembrane proteins. By contrast, many tens of thousands of globular protein structures provide a rich source of 'scaffolds' for protein design, and the means to garner sequence-to-structure relationships to guide the design process. The $\alpha$-helical coiled coil is a protein-structure element found in both globular and membrane proteins, where it cements a variety of helix-helix interactions and helical bundles. Our deep understanding of coiled coils has enabled a large number of successfulde novodesigns. For one class, the $\alpha$-helical barrels-that is, symmetric bundles of five or more helices with central accessible channels-there are both water-soluble and membrane-spanning examples. Recent computational designs of water-soluble $\alpha$-helical barrels with five to seven helices have advanced the design field considerably. Here we identify and classify analogous and more complicated membrane-spanning $\alpha$-helical barrels from the Protein Data Bank. These provide tantalizing but tractable targets for protein engineering andde novoprotein design.This article is part of the themed issue 'Membrane pores: from structure and assembly, to medicine and technology'.},
author = {Niitsu, Ai and Heal, Jack W and Fauland, Kerstin and Thomson, Andrew R and Woolfson, Derek N},
doi = {10.1098/rstb.2016.0213},
file = {:home/ba13026/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Niitsu et al. - 2017 - Membrane-spanning $\alpha$-helical barrels as tractable protein-design targets.pdf:pdf},
issn = {1471-2970},
journal = {Philosophical transactions of the Royal Society of London. Series B, Biological sciences},
keywords = {coiled coil,de novo protein design,transmembrane proteins,$\alpha$-helical barrel},
month = {aug},
number = {1726},
pages = {20160213},
pmid = {28630153},
publisher = {The Royal Society},
title = {{Membrane-spanning $\alpha$-helical barrels as tractable protein-design targets.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/28630153 http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=PMC5483516},
volume = {372},
year = {2017}
}
@incollection{M.S.Shell2019,
author = {{M.S. Shell}},
file = {:home/ba13026/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/M.S. Shell - 2019 - Exploring the energy landscape.pdf:pdf},
title = {{Exploring the energy landscape}},
url = {https://sites.engineering.ucsb.edu/{~}shell/che210d/Exploring{\_}the{\_}energy{\_}landscape.pdf},
year = {2019}
}
@article{Planitz1979,
author = {Planitz, M.},
doi = {10.2307/3617890},
file = {:home/ba13026/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Planitz - 1979 - Inconsistent Systems of Linear Equations.pdf:pdf},
journal = {The Mathematical Gazette},
month = {oct},
number = {425},
pages = {181},
title = {{Inconsistent Systems of Linear Equations}},
url = {https://www.jstor.org/stable/3617890?origin=crossref},
volume = {63},
year = {1979}
}
@article{Ernst2017,
abstract = {While adequately chosen reaction coordinates are expected to reveal the mechanism of a dynamical process, it proves to be notoriously difficult to model the complex structural rearrangements of a macromolecule by a low-dimensional collective coordinate. Adopting the hinge-bending motion of T4 lysozyme (T4L) as a prominent example and performing a 50 $\mu$s long unbiased molecular dynamics (MD) simulation of T4L, a general strategy to identify reaction coordinates of protein functional dynamics is developed. As a systematic method to reduce the dimensionality of the dynamics, first various types of principal component analyses are employed, and it is shown that the applicability and outcome of the approach crucially depends on the type of input coordinates used. In a second step, prospective candidates for a reaction coordinate are tested by studying the molecule's response to external pulling along the coordinate, using targeted MD simulations. While trying to directly enforce the open-closed transition does ...},
author = {Ernst, Matthias and Wolf, Steffen and Stock, Gerhard},
doi = {10.1021/acs.jctc.7b00571},
file = {:home/ba13026/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Ernst, Wolf, Stock - 2017 - Identification and Validation of Reaction Coordinates Describing Protein Functional Motion Hierarchical Dyna.pdf:pdf},
issn = {1549-9618},
journal = {Journal of Chemical Theory and Computation},
month = {oct},
number = {10},
pages = {5076--5088},
publisher = {American Chemical Society},
title = {{Identification and Validation of Reaction Coordinates Describing Protein Functional Motion: Hierarchical Dynamics of T4 Lysozyme}},
url = {https://pubs.acs.org/doi/10.1021/acs.jctc.7b00571},
volume = {13},
year = {2017}
}
@article{James1978,
abstract = {If we have a system of m linear equations to solve, it is a great simplification to write them in matrix form},
author = {James, M.},
doi = {10.1017/S0025557200086460},
file = {:home/ba13026/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/James - 1978 - The generalised inverse.pdf:pdf},
issn = {0025-5572},
journal = {The Mathematical Gazette},
month = {jun},
number = {420},
pages = {109--114},
publisher = {Cambridge University Press},
title = {{The generalised inverse}},
url = {https://www.cambridge.org/core/product/identifier/S0025557200086460/type/journal{\_}article},
volume = {62},
year = {1978}
}
@article{Kutz2014,
abstract = {Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems. However, existing DMD theory deals primarily with sequential time series for which the measurement dimension is much larger than the number of measurements taken. We present a theoretical framework in which we define DMD as the eigendecomposition of an approximating linear operator. This generalizes DMD to a larger class of datasets, including nonsequential time series. We demonstrate the utility of this approach by presenting novel sampling strategies that increase computational efficiency and mitigate the effects of noise, respectively. We also introduce the concept of linear consistency, which helps explain the potential pitfalls of applying DMD to rank-deficient datasets, illustrating with examples. Such computations are not considered in the existing literature but can be understood using our more general framework. In addition, we show that our theory strengthens the connections between DMD and Koopman operator theory. It also establishes connections between DMD and other techniques, including the eigensystem realization algorithm (ERA), a system identification method, and linear inverse modeling (LIM), a method from climate science. We show that under certain conditions, DMD is equivalent to LIM.},
author = {Kutz, J. Nathan and Brunton, Steven L. and Luchtenburg, Dirk M. and Rowley, Clarence W. and Tu, Jonathan H.},
doi = {10.3934/jcd.2014.1.391},
file = {:home/ba13026/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Kutz et al. - 2014 - On dynamic mode decomposition Theory and applications.pdf:pdf},
issn = {2158-2491},
journal = {Journal of Computational Dynamics},
keywords = {Dynamic mode decomposition,Koopman operator,order models.,reduced,spectral analysis,time series analysis},
month = {dec},
number = {2},
pages = {391--421},
publisher = {Journal of Computational Dynamics},
title = {{On dynamic mode decomposition: Theory and applications}},
url = {http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=10631},
volume = {1},
year = {2014}
}
@book{Strang2006,
author = {Strang, Gilbert},
file = {:home/ba13026/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Strang - 2006 - Linear Algebra and its applications.pdf:pdf},
title = {{Linear Algebra and its applications}},
url = {http://www.math.hcmus.edu.vn/{~}bxthang/Linear algebra and its applications.pdf},
year = {2006}
}
@incollection{Henkelman2002,
address = {Dordrecht},
author = {Henkelman, Graeme and J{\'{o}}hannesson, G{\'{i}}sli and J{\'{o}}nsson, Hannes},
booktitle = {Theoretical Methods in Condensed Phase Chemistry},
doi = {10.1007/0-306-46949-9_10},
file = {:home/ba13026/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Henkelman, J{\'{o}}hannesson, J{\'{o}}nsson - 2002 - Methods for Finding Saddle Points and Minimum Energy Paths.pdf:pdf},
pages = {269--302},
publisher = {Kluwer Academic Publishers},
title = {{Methods for Finding Saddle Points and Minimum Energy Paths}},
url = {http://link.springer.com/10.1007/0-306-46949-9{\_}10},
year = {2002}
}
@article{Ross2009,
abstract = {Linear dimensionality reduction techniques, notably principal component analysis, are widely used in climate data analysis as a means to aid in the interpretation of datasets of high dimensionality. These linear methods may not be appropriate for the analysis of data arising from nonlinear processes occurring in the climate system. Numerous techniques for nonlinear dimensionality reduction have been developed recently that may provide a potentially useful tool for the identification of low-dimensional manifolds in climate data sets arising from nonlinear dynamics. In this thesis I apply three such techniques to the study of El Nino/Southern Oscillation variability in tropical Pacific sea surface temperatures and thermocline depth, comparing observational data with simulations from coupled atmosphere-ocean general circulation models from the CMIP3 multi-model ensemble. The three methods used here are a nonlinear principal component analysis (NLPCA) approach based on neural networks, the Isomap isometric mapping algorithm, and Hessian locally linear embedding. I use these three methods to examine El Nino variability in the different data sets and assess the suitability of these nonlinear dimensionality reduction approaches for climate data analysis. I conclude that although, for the application presented here, analysis using NLPCA, Isomap and Hessian locally linear embedding does not provide additional information beyond that already provided by principal component analysis, these methods are effective tools for exploratory data analysis.},
archivePrefix = {arXiv},
arxivId = {0901.0537},
author = {Ross, Ian},
eprint = {0901.0537},
file = {:home/ba13026/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Ross - 2009 - Nonlinear Dimensionality Reduction Methods in Climate Data Analysis.pdf:pdf},
month = {jan},
title = {{Nonlinear Dimensionality Reduction Methods in Climate Data Analysis}},
url = {http://arxiv.org/abs/0901.0537},
year = {2009}
}