9129767 UWS2UD76 items 1 0 date desc year Abarbanel https://habarbanel.scrippsprofiles.ucsd.edu/wp-content/plugins/zotpress/
%7B%22status%22%3A%22success%22%2C%22instance%22%3A%22zotpress-dc99f2c4b60c2dfd74874400d74b0057%22%2C%22meta%22%3A%7B%22request_last%22%3A200%2C%22request_next%22%3A50%2C%22used_cache%22%3Atrue%7D%2C%22data%22%3A%5B%7B%22key%22%3A%22GDHM8LWB%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Clark%20et%20al.%22%2C%22parsedDate%22%3A%222022-06-16%22%2C%22numChildren%22%3A1%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EClark%2C%20R.%2C%20Fuller%2C%20L.%2C%20Platt%2C%20J.%20A.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282022%29.%20Reduced-Dimension%2C%20Biophysical%20Neuron%20Models%20Constructed%20From%20Observed%20Data.%20%3Ci%3ENeural%20Computation%3C%5C%2Fi%3E%2C%20%3Ci%3E34%3C%5C%2Fi%3E%287%29%2C%201545%26%23x2013%3B1587.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1162%5C%2Fneco_a_01515%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1162%5C%2Fneco_a_01515%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Reduced-Dimension%2C%20Biophysical%20Neuron%20Models%20Constructed%20From%20Observed%20Data%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22Randall%22%2C%22lastName%22%3A%22Clark%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22Lawson%22%2C%22lastName%22%3A%22Fuller%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22Jason%20A.%22%2C%22lastName%22%3A%22Platt%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22Henry%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22Abstract%5Cn%20%20%20%20%20%20%20%20%20%20%20%20Using%20methods%20from%20nonlinear%20dynamics%20and%20interpolation%20techniques%20from%20applied%20mathematics%2C%20we%20show%20how%20to%20use%20data%20alone%20to%20construct%20discrete%20time%20dynamical%20rules%20that%20forecast%20observed%20neuron%20properties.%20These%20data%20may%20come%20from%20simulations%20of%20a%20Hodgkin-Huxley%20%28HH%29%20neuron%20model%20or%20from%20laboratory%20current%20clamp%20experiments.%20In%20each%20case%2C%20the%20reduced-dimension%2C%20data-driven%20forecasting%20%28DDF%29%20models%20are%20shown%20to%20predict%20accurately%20for%20times%20after%20the%20training%20period.%5Cn%20%20%20%20%20%20%20%20%20%20%20%20When%20the%20available%20observations%20for%20neuron%20preparations%20are%2C%20for%20example%2C%20membrane%20voltage%20V%28t%29%20only%2C%20we%20use%20the%20technique%20of%20time%20delay%20embedding%20from%20nonlinear%20dynamics%20to%20generate%20an%20appropriate%20space%20in%20which%20the%20full%20dynamics%20can%20be%20realized.%5Cn%20%20%20%20%20%20%20%20%20%20%20%20The%20DDF%20constructions%20are%20reduced-dimension%20models%20relative%20to%20HH%20models%20as%20they%20are%20built%20on%20and%20forecast%20only%20observables%20such%20as%20V%28t%29.%20They%20do%20not%20require%20detailed%20specification%20of%20ion%20channels%2C%20their%20gating%20variables%2C%20and%20the%20many%20parameters%20that%20accompany%20an%20HH%20model%20for%20laboratory%20measurements%2C%20yet%20all%20of%20this%20important%20information%20is%20encoded%20in%20the%20DDF%20model.%20As%20the%20DDF%20models%20use%20and%20forecast%20only%20voltage%20data%2C%20they%20can%20be%20used%20in%20building%20networks%20with%20biophysical%20connections.%20Both%20gap%20junction%20connections%20and%20ligand%20gated%20synaptic%20connections%20among%20neurons%20involve%20presynaptic%20voltages%20and%20induce%20postsynaptic%20voltage%20response.%20Biophysically%20based%20DDF%20neuron%20models%20can%20replace%20other%20reduced-dimension%20neuron%20models%2C%20say%2C%20of%20the%20integrate-and-fire%20type%2C%20in%20developing%20and%20analyzing%20large%20networks%20of%20neurons.%5Cn%20%20%20%20%20%20%20%20%20%20%20%20When%20one%20does%20have%20detailed%20HH%20model%20neurons%20for%20network%20components%2C%20a%20reduced-dimension%20DDF%20realization%20of%20the%20HH%20voltage%20dynamics%20may%20be%20used%20in%20network%20computations%20to%20achieve%20computational%20efficiency%20and%20the%20exploration%20of%20larger%20biological%20networks.%22%2C%22date%22%3A%222022-06-16%22%2C%22language%22%3A%22en%22%2C%22DOI%22%3A%2210.1162%5C%2Fneco_a_01515%22%2C%22ISSN%22%3A%220899-7667%2C%201530-888X%22%2C%22url%22%3A%22https%3A%5C%2F%5C%2Fdirect.mit.edu%5C%2Fneco%5C%2Farticle%5C%2F34%5C%2F7%5C%2F1545%5C%2F111332%5C%2FReduced-Dimension-Biophysical-Neuron-Models%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-07-13T19%3A20%3A24Z%22%7D%7D%2C%7B%22key%22%3A%22PYZJXMJH%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Penny%20et%20al.%22%2C%22parsedDate%22%3A%222022-03%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EPenny%2C%20S.%20G.%2C%20Smith%2C%20T.%20A.%2C%20Chen%2C%20T.%20C.%2C%20Platt%2C%20J.%20A.%2C%20Lin%2C%20H.%20Y.%2C%20Goodliff%2C%20M.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282022%29.%20Integrating%20recurrent%20neural%20networks%20with%20data%20assimilation%20for%20scalable%20data-driven%20state%20estimation.%20%3Ci%3EJournal%20of%20Advances%20in%20Modeling%20Earth%20Systems%3C%5C%2Fi%3E%2C%20%3Ci%3E14%3C%5C%2Fi%3E%283%29%2C%2025.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1029%5C%2F2021ms002843%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1029%5C%2F2021ms002843%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Integrating%20recurrent%20neural%20networks%20with%20data%20assimilation%20for%20scalable%20data-driven%20state%20estimation%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22S.%20G.%22%2C%22lastName%22%3A%22Penny%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22T.%20A.%22%2C%22lastName%22%3A%22Smith%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22T.%20C.%22%2C%22lastName%22%3A%22Chen%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%20A.%22%2C%22lastName%22%3A%22Platt%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20Y.%22%2C%22lastName%22%3A%22Lin%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22M.%22%2C%22lastName%22%3A%22Goodliff%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22Data%20assimilation%20%28DA%29%20is%20integrated%20with%20machine%20learning%20in%20order%20to%20perform%20entirely%20data-driven%20online%20state%20estimation.%20To%20achieve%20this%2C%20recurrent%20neural%20networks%20%28RNNs%29%20are%20implemented%20as%20pretrained%20surrogate%20models%20to%20replace%20key%20components%20of%20the%20DA%20cycle%20in%20numerical%20weather%20prediction%20%28NWP%29%2C%20including%20the%20conventional%20numerical%20forecast%20model%2C%20the%20forecast%20error%20covariance%20matrix%2C%20and%20the%20tangent%20linear%20and%20adjoint%20models.%20It%20is%20shown%20how%20these%20RNNs%20can%20be%20initialized%20using%20DA%20methods%20to%20directly%20update%20the%20hidden%5C%2Freservoir%20state%20with%20observations%20of%20the%20target%20system.%20The%20results%20indicate%20that%20these%20techniques%20can%20be%20applied%20to%20estimate%20the%20state%20of%20a%20system%20for%20the%20repeated%20initialization%20of%20short-term%20forecasts%2C%20even%20in%20the%20absence%20of%20a%20traditional%20numerical%20forecast%20model.%20Further%2C%20it%20is%20demonstrated%20how%20these%20integrated%20RNN-DA%20methods%20can%20scale%20to%20higher%20dimensions%20by%20applying%20domain%20localization%20and%20parallelization%2C%20providing%20a%20path%20for%20practical%20applications%20in%20NWP.%22%2C%22date%22%3A%222022%5C%2F03%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1029%5C%2F2021ms002843%22%2C%22ISSN%22%3A%22%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A04Z%22%7D%7D%2C%7B%22key%22%3A%22XBC4GWRK%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Platt%20et%20al.%22%2C%22parsedDate%22%3A%222022%22%2C%22numChildren%22%3A1%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EPlatt%2C%20J.%20A.%2C%20Penny%2C%20S.%20G.%2C%20Smith%2C%20T.%20A.%2C%20Chen%2C%20T.-C.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282022%29.%20A%20systematic%20exploration%20of%20reservoir%20computing%20for%20forecasting%20complex%20spatiotemporal%20dynamics.%20%3Ci%3ENeural%20Networks%3C%5C%2Fi%3E%2C%20%3Ci%3E153%3C%5C%2Fi%3E%2C%20530%26%23x2013%3B552.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1016%5C%2Fj.neunet.2022.06.025%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1016%5C%2Fj.neunet.2022.06.025%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22A%20systematic%20exploration%20of%20reservoir%20computing%20for%20forecasting%20complex%20spatiotemporal%20dynamics%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22Jason%20A.%22%2C%22lastName%22%3A%22Platt%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22Stephen%20G.%22%2C%22lastName%22%3A%22Penny%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22Timothy%20A.%22%2C%22lastName%22%3A%22Smith%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22Tse-Chun%22%2C%22lastName%22%3A%22Chen%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22Henry%20D.I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22%22%2C%22date%22%3A%2209%5C%2F2022%22%2C%22language%22%3A%22en%22%2C%22DOI%22%3A%2210.1016%5C%2Fj.neunet.2022.06.025%22%2C%22ISSN%22%3A%2208936080%22%2C%22url%22%3A%22https%3A%5C%2F%5C%2Flinkinghub.elsevier.com%5C%2Fretrieve%5C%2Fpii%5C%2FS0893608022002404%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-08-31T22%3A51%3A17Z%22%7D%7D%2C%7B%22key%22%3A%22INRTL2HN%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Platt%20et%20al.%22%2C%22parsedDate%22%3A%222021-12%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EPlatt%2C%20J.%20A.%2C%20Wong%2C%20A.%20D.%2C%20Clark%2C%20R.%2C%20Penny%2C%20S.%20G.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282021%29.%20Robust%20forecasting%20using%20predictive%20generalized%20synchronization%20in%20reservoir%20computing.%20%3Ci%3EChaos%3C%5C%2Fi%3E%2C%20%3Ci%3E31%3C%5C%2Fi%3E%2812%29%2C%2016.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1063%5C%2F5.0066013%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1063%5C%2F5.0066013%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Robust%20forecasting%20using%20predictive%20generalized%20synchronization%20in%20reservoir%20computing%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%20A.%22%2C%22lastName%22%3A%22Platt%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22A.%20D.%22%2C%22lastName%22%3A%22Wong%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22R.%22%2C%22lastName%22%3A%22Clark%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22S.%20G.%22%2C%22lastName%22%3A%22Penny%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22Reservoir%20computers%20%28RCs%29%20are%20a%20class%20of%20recurrent%20neural%20networks%20%28RNNs%29%20that%20can%20be%20used%20for%20forecasting%20the%20future%20of%20observed%20time%20series%20data.%20As%20with%20all%20RNNs%2C%20selecting%20the%20hyperparameters%20in%20the%20network%20to%20yield%20excellent%20forecasting%20presents%20a%20challenge%20when%20training%20on%20new%20inputs.%20We%20analyze%20a%20method%20based%20on%20predictive%20generalized%20synchronization%20%28PGS%29%20that%20gives%20direction%20in%20designing%20and%20evaluating%20the%20architecture%20and%20hyperparameters%20of%20an%20RC.%20To%20determine%20the%20occurrences%20of%20PGS%2C%20we%20rely%20on%20the%20auxiliary%20method%20to%20provide%20a%20computationally%20efficient%20pre-training%20test%20that%20guides%20hyperparameter%20selection.%20We%20provide%20a%20metric%20for%20evaluating%20the%20RC%20using%20the%20reproduction%20of%20the%20input%20system%27s%20Lyapunov%20exponents%20that%20demonstrates%20robustness%20in%20prediction.%22%2C%22date%22%3A%222021%5C%2F12%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1063%5C%2F5.0066013%22%2C%22ISSN%22%3A%221054-1500%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A08Z%22%7D%7D%2C%7B%22key%22%3A%22EICWFKND%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Abarbanel%22%2C%22parsedDate%22%3A%222021-05%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3E%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282021%29.%20A%20personal%20retrospective%20on%20the%2060th%20anniversary%20of%20the%20journal%20Biological%20Cybernetics.%20%3Ci%3EBiological%20Cybernetics%3C%5C%2Fi%3E%2C%202.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1007%5C%2Fs00422-021-00878-6%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1007%5C%2Fs00422-021-00878-6%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22A%20personal%20retrospective%20on%20the%2060th%20anniversary%20of%20the%20journal%20Biological%20Cybernetics%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22%22%2C%22date%22%3A%222021%5C%2F05%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1007%5C%2Fs00422-021-00878-6%22%2C%22ISSN%22%3A%220340-1200%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A07Z%22%7D%7D%2C%7B%22key%22%3A%227HQ7AGBG%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Ty%20et%20al.%22%2C%22parsedDate%22%3A%222019-10%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3ETy%2C%20A.%20J.%20A.%2C%20Fang%2C%20Z.%2C%20Gonzalez%2C%20R.%20A.%2C%20Rozdeba%2C%20P.%20J.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282019%29.%20Machine%20learning%20of%20time%20series%20using%20time-delay%20embedding%20and%20precision%20annealing.%20%3Ci%3ENeural%20Computation%3C%5C%2Fi%3E%2C%20%3Ci%3E31%3C%5C%2Fi%3E%2810%29%2C%202004%26%23x2013%3B2024.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1162%5C%2Fneco_a_01224%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1162%5C%2Fneco_a_01224%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Machine%20learning%20of%20time%20series%20using%20time-delay%20embedding%20and%20precision%20annealing%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22A.%20J.%20A.%22%2C%22lastName%22%3A%22Ty%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22Z.%22%2C%22lastName%22%3A%22Fang%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22R.%20A.%22%2C%22lastName%22%3A%22Gonzalez%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22P.%20J.%22%2C%22lastName%22%3A%22Rozdeba%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22Tasking%20machine%20learning%20to%20predict%20segments%20of%20a%20time%20series%20requires%20estimating%20the%20parameters%20of%20a%20ML%20model%20with%20input%5C%2Foutput%20pairs%20from%20the%20time%20series.%20We%20borrow%20two%20techniques%20used%20in%20statistical%20data%20assimilation%20in%20order%20to%20accomplish%20this%20task%3A%20time-delay%20embedding%20to%20prepare%20our%20input%20data%20and%20precision%20annealing%20as%20a%20training%20method.%20The%20precision%20annealing%20approach%20identifies%20the%20global%20minimum%20of%20the%20action%20%28-log%5BP%5D%29.%20In%20this%20way%2C%20we%20are%20able%20to%20identify%20the%20number%20of%20training%20pairs%20required%20to%20produce%20good%20generalizations%20%28predictions%29%20for%20the%20time%20series.%20We%20proceed%20from%20a%20scalar%20time%20series%20s%28tn%29%3Btn%3Dt0%2Bn%20Delta%20t%20and%2C%20using%20methods%20of%20nonlinear%20time%20series%20analysis%2C%20show%20how%20to%20produce%20a%20DE%3E1-dimensional%20time-delay%20embedding%20space%20in%20which%20the%20time%20series%20has%20no%20false%20neighbors%20as%20does%20the%20observed%20s%28tn%29%20time%20series.%20In%20that%20DE-dimensional%20space%2C%20we%20explore%20the%20use%20of%20feedforward%20multilayer%20perceptrons%20as%20network%20models%20operating%20on%20DE-dimensional%20input%20and%20producing%20DE-dimensional%20outputs.%22%2C%22date%22%3A%222019%5C%2F10%22%2C%22language%22%3A%22%22%2C%22DOI%22%3A%2210.1162%5C%2Fneco_a_01224%22%2C%22ISSN%22%3A%220899-7667%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A05Z%22%7D%7D%2C%7B%22key%22%3A%226TYYSTKI%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Abarbanel%20et%20al.%22%2C%22parsedDate%22%3A%222018-08%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3E%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%2C%20Rozdeba%2C%20P.%20J.%2C%20%26amp%3B%20Shirman%2C%20S.%20%282018%29.%20Machine%20learning%3A%20Deepest%20learning%20as%20statistical%20data%20assimilation%20problems.%20%3Ci%3ENeural%20Computation%3C%5C%2Fi%3E%2C%20%3Ci%3E30%3C%5C%2Fi%3E%288%29%2C%202025%26%23x2013%3B2055.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1162%5C%2Fneco_a_01094%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1162%5C%2Fneco_a_01094%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Machine%20learning%3A%20Deepest%20learning%20as%20statistical%20data%20assimilation%20problems%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22P.%20J.%22%2C%22lastName%22%3A%22Rozdeba%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22S.%22%2C%22lastName%22%3A%22Shirman%22%7D%5D%2C%22abstractNote%22%3A%22We%20formulate%20an%20equivalence%20between%20machine%20learning%20and%20the%20formulation%20of%20statistical%20data%20assimilation%20as%20used%20widely%20in%20physical%20and%20biological%20sciences.%20The%20correspondence%20is%20that%20layer%20number%20in%20a%20feedforward%20artificial%20network%20setting%20is%20the%20analog%20of%20time%20in%20the%20data%20assimilation%20setting.%20This%20connection%20has%20been%20noted%20in%20the%20machine%20learning%20literature.%20We%20add%20a%20perspective%20that%20expands%20on%20how%20methods%20from%20statistical%20physics%20and%20aspects%20of%20Lagrangian%20and%20Hamiltonian%20dynamics%20play%20a%20role%20in%20how%20networks%20can%20be%20trained%20and%20designed.%20Within%20the%20discussion%20of%20this%20equivalence%2C%20we%20show%20that%20adding%20more%20layers%20%28making%20the%20network%20deeper%29%20is%20analogous%20to%20adding%20temporal%20resolution%20in%20a%20data%20assimilation%20framework.%20Extending%20this%20equivalence%20to%20recurrent%20networks%20is%20also%20discussed.%20We%20explore%20how%20one%20can%20find%20a%20candidate%20for%20the%20global%20minimum%20of%20the%20cost%20functions%20in%20the%20machine%20learning%20context%20using%20a%20method%20from%20data%20assimilation.%20Calculations%20on%20simple%20models%20from%20both%20sides%20of%20the%20equivalence%20are%20reported.%20Also%20discussed%20is%20a%20framework%20in%20which%20the%20time%20or%20layer%20label%20is%20taken%20to%20be%20continuous%2C%20providing%20a%20differential%20equation%2C%20the%20Euler-Lagrange%20equation%20and%20its%20boundary%20conditions%2C%20as%20a%20necessary%20condition%20for%20a%20minimum%20of%20the%20cost%20function.%20This%20shows%20that%20the%20problem%20being%20solved%20is%20a%20two-point%20boundary%20value%20problem%20familiar%20in%20the%20discussion%20of%20variational%20methods.%20The%20use%20of%20continuous%20layers%20is%20denoted%20%5C%22deepest%20learning.%5C%22%20These%20problems%20respect%20a%20symplectic%20symmetry%20in%20continuous%20layer%20phase%20space.%20Both%20Lagrangian%20versions%20and%20Hamiltonian%20versions%20of%20these%20problems%20are%20presented.%20Their%20well-studied%20implementation%20in%20a%20discrete%20time%5C%2Flayer%2C%20while%20respecting%20the%20symplectic%20structure%2C%20is%20addressed.%20The%20Hamiltonian%20version%20provides%20a%20direct%20rationale%20for%20backpropagation%20as%20a%20solution%20method%20for%20a%20certain%20two-point%20boundary%20value%20problem.%22%2C%22date%22%3A%222018%5C%2F08%22%2C%22language%22%3A%22%22%2C%22DOI%22%3A%2210.1162%5C%2Fneco_a_01094%22%2C%22ISSN%22%3A%220899-7667%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A05Z%22%7D%7D%2C%7B%22key%22%3A%22YULFGFSX%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Abarbanel%20et%20al.%22%2C%22parsedDate%22%3A%222017-12%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3E%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%2C%20Shirman%2C%20S.%2C%20Breen%2C%20D.%2C%20Kadakia%2C%20N.%2C%20Rey%2C%20D.%2C%20Armstrong%2C%20E.%2C%20%26amp%3B%20Margoliash%2C%20D.%20%282017%29.%20A%20unifying%20view%20of%20synchronization%20for%20data%20assimilation%20in%20complex%20nonlinear%20networks.%20%3Ci%3EChaos%3C%5C%2Fi%3E%2C%20%3Ci%3E27%3C%5C%2Fi%3E%2812%29.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1063%5C%2F1.5001816%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1063%5C%2F1.5001816%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22A%20unifying%20view%20of%20synchronization%20for%20data%20assimilation%20in%20complex%20nonlinear%20networks%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22S.%22%2C%22lastName%22%3A%22Shirman%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22D.%22%2C%22lastName%22%3A%22Breen%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22N.%22%2C%22lastName%22%3A%22Kadakia%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22D.%22%2C%22lastName%22%3A%22Rey%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22E.%22%2C%22lastName%22%3A%22Armstrong%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22D.%22%2C%22lastName%22%3A%22Margoliash%22%7D%5D%2C%22abstractNote%22%3A%22Networks%20of%20nonlinear%20systems%20contain%20unknown%20parameters%20and%20dynamical%20degrees%20of%20freedom%20that%20may%20not%20be%20observable%20with%20existing%20instruments.%20From%20observable%20state%20variables%2C%20we%20want%20to%20estimate%20the%20connectivity%20of%20a%20model%20of%20such%20a%20network%20and%20determine%20the%20full%20state%20of%20the%20model%20at%20the%20termination%20of%20a%20temporal%20observation%20window%20during%20which%20measurements%20transfer%20information%20to%20a%20model%20of%20the%20network.%20The%20model%20state%20at%20the%20termination%20of%20a%20measurement%20window%20acts%20as%20an%20initial%20condition%20for%20predicting%20the%20future%20behavior%20of%20the%20network.%20This%20allows%20the%20validation%20%28or%20invalidation%29%20of%20the%20model%20as%20a%20representation%20of%20the%20dynamical%20processes%20producing%20the%20observations.%20Once%20the%20model%20has%20been%20tested%20against%20new%20data%2C%20it%20may%20be%20utilized%20as%20a%20predictor%20of%20responses%20to%20innovative%20stimuli%20or%20forcing.%20We%20describe%20a%20general%20framework%20for%20the%20tasks%20involved%20in%20the%20%5C%22inverse%5C%22%20problem%20of%20determining%20properties%20of%20a%20model%20built%20to%20represent%20measured%20output%20from%20physical%2C%20biological%2C%20or%20other%20processes%20when%20the%20measurements%20are%20noisy%2C%20the%20model%20has%20errors%2C%20and%20the%20state%20of%20the%20model%20is%20unknown%20when%20measurements%20begin.%20This%20framework%20is%20called%20statistical%20data%20assimilation%20and%20is%20the%20best%20one%20can%20do%20in%20estimating%20model%20properties%20through%20the%20use%20of%20the%20conditional%20probability%20distributions%20of%20the%20model%20state%20variables%2C%20conditioned%20on%20observations.%20There%20is%20a%20very%20broad%20arena%20of%20applications%20of%20the%20methods%20described.%20These%20include%20numerical%20weather%20prediction%2C%20properties%20of%20nonlinear%20electrical%20circuitry%2C%20and%20determining%20the%20biophysical%20properties%20of%20functional%20networks%20of%20neurons.%20Illustrative%20examples%20will%20be%20given%20of%20%281%29%20estimating%20the%20connectivity%20among%20neurons%20with%20known%20dynamics%20in%20a%20network%20of%20unknown%20connectivity%2C%20and%20%282%29%20estimating%20the%20biophysical%20properties%20of%20individual%20neurons%20in%20vitro%20taken%20from%20a%20functional%20network%20underlying%20vocalization%20in%20songbirds.%20Published%20by%20AIP%20Publishing.%22%2C%22date%22%3A%222017%5C%2F12%22%2C%22language%22%3A%22%22%2C%22DOI%22%3A%2210.1063%5C%2F1.5001816%22%2C%22ISSN%22%3A%221054-1500%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A10Z%22%7D%7D%2C%7B%22key%22%3A%22Z5FSSWG7%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Armstrong%20et%20al.%22%2C%22parsedDate%22%3A%222017-10%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EArmstrong%2C%20E.%2C%20Patwardhan%2C%20A.%20V.%2C%20Johns%2C%20L.%2C%20Kishimoto%2C%20C.%20T.%2C%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%2C%20%26amp%3B%20Fuller%2C%20G.%20M.%20%282017%29.%20An%20optimization-based%20approach%20to%20calculating%20neutrino%20flavor%20evolution.%20%3Ci%3EPhysical%20Review%20D%3C%5C%2Fi%3E%2C%20%3Ci%3E96%3C%5C%2Fi%3E%288%29.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1103%5C%2FPhysRevD.96.083008%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1103%5C%2FPhysRevD.96.083008%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22An%20optimization-based%20approach%20to%20calculating%20neutrino%20flavor%20evolution%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22E.%22%2C%22lastName%22%3A%22Armstrong%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22A.%20V.%22%2C%22lastName%22%3A%22Patwardhan%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22L.%22%2C%22lastName%22%3A%22Johns%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22C.%20T.%22%2C%22lastName%22%3A%22Kishimoto%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22G.%20M.%22%2C%22lastName%22%3A%22Fuller%22%7D%5D%2C%22abstractNote%22%3A%22We%20assess%20the%20utility%20of%20an%20optimization-based%20data%20assimilation%20%28D.A.%29%20technique%20for%20treating%20the%20problem%20of%20nonlinear%20neutrino%20flavor%20transformation%20in%20core-collapse%20supernovae.%20D.A.%20uses%20measurements%20obtained%20from%20a%20physical%20system%20to%20estimate%20the%20state%20variable%20evolution%20and%20parameter%20values%20of%20the%20associated%20model.%20Formulated%20as%20an%20optimization%20procedure%2C%20D.A.%20can%20offer%20an%20integration-blind%20approach%20to%20predicting%20model%20evolution%2C%20which%20offers%20an%20advantage%20for%20models%20that%20thwart%20solution%20via%20traditional%20numerical%20integration%20techniques.%20Further%2C%20D.A.%20performs%20most%20optimally%20for%20models%20whose%20equations%20of%20motion%20are%20nonlinearly%20coupled.%20In%20this%20exploratory%20work%2C%20we%20consider%20a%20simple%20steady-state%20model%20with%20two%20monoenergetic%20neutrino%20beams%20coherently%20interacting%20with%20each%20other%20and%20a%20background%20medium.%20As%20this%20model%20can%20be%20solved%20via%20numerical%20integration%2C%20we%20have%20an%20independent%20consistency%20check%20for%20D.A.%20solutions.%20We%20find%20that%20the%20procedure%20can%20capture%20key%20features%20of%20flavor%20evolution%20over%20the%20entire%20trajectory%2C%20even%20given%20measurements%20of%20neutrino%20flavor%20only%20at%20the%20endpoint%2C%20and%20with%20an%20assumed%20known%20initial%20flavor%20distribution.%20Further%2C%20the%20procedure%20permits%20an%20examination%20of%20the%20sensitivity%20of%20flavor%20evolution%20to%20estimates%20of%20unknown%20model%20parameters%2C%20locates%20degeneracies%20in%20parameter%20space%2C%20and%20can%20identify%20the%20specific%20measurements%20required%20to%20break%20those%20degeneracies.%22%2C%22date%22%3A%222017%5C%2F10%22%2C%22language%22%3A%22%22%2C%22DOI%22%3A%2210.1103%5C%2FPhysRevD.96.083008%22%2C%22ISSN%22%3A%222470-0010%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A07Z%22%7D%7D%2C%7B%22key%22%3A%22NRB42Y7N%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Kadakia%20et%20al.%22%2C%22parsedDate%22%3A%222017-01%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EKadakia%2C%20N.%2C%20Rey%2C%20D.%2C%20Ye%2C%20J.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282017%29.%20Symplectic%20Structure%20Of%20Statistical%20Variational%20Data%20Assimilation.%20%3Ci%3EQuarterly%20Journal%20of%20the%20Royal%20Meteorological%20Society%3C%5C%2Fi%3E%2C%20%3Ci%3E143%3C%5C%2Fi%3E%28703%29%2C%20756%26%23x2013%3B771.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1002%5C%2Fqj.2962%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1002%5C%2Fqj.2962%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Symplectic%20Structure%20Of%20Statistical%20Variational%20Data%20Assimilation%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22N.%22%2C%22lastName%22%3A%22Kadakia%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22D.%22%2C%22lastName%22%3A%22Rey%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%22%2C%22lastName%22%3A%22Ye%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22Data%20assimilation%20variational%20principles%20%284D-Var%29%20exhibit%20a%20natural%20symplectic%20structure%20among%20the%20state%20variables%20x%28t%29%20and.%20x%28t%29.%20We%20explore%20the%20implications%20of%20this%20structure%20in%20both%20Lagrangian%20coordinates%20%7Bx%28t%29%2C%20x%28t%29%7D%20andHamiltonian%20canonical%20coordinates%20%7Bx%28t%29%2C%20p%28t%29%7D%20through%20a%20numerical%20examination%20of%20the%20chaotic%20Lorenz%201996%20model%20in%20ten%20dimensions.%20We%20find%20that%20there%20are%20a%20number%20of%20subtleties%20associated%20with%20discretization%2C%20boundary%20conditions%2C%20and%20symplecticity%2C%20suggesting%20differing%20approaches%20when%20working%20in%20the%20the%20Lagrangian%20versus%20the%20Hamiltonian%20description.%20We%20investigate%20these%20differences%20in%20detail%2C%20and%20accordingly%20develop%20a%20protocol%20for%20searching%20for%20optimal%20trajectories%20in%20a%20Hamiltonian%20space.%20We%20find%20that%20casting%20the%20problem%20into%20canonical%20coordinates%20can%2C%20in%20some%20situations%2C%20considerably%20improve%20the%20quality%20of%20predictions.%22%2C%22date%22%3A%222017%5C%2F01%22%2C%22language%22%3A%22%22%2C%22DOI%22%3A%2210.1002%5C%2Fqj.2962%22%2C%22ISSN%22%3A%220035-9009%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A09Z%22%7D%7D%2C%7B%22key%22%3A%226GPFGBYA%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22An%20et%20al.%22%2C%22parsedDate%22%3A%222017-01%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EAn%2C%20Z.%2C%20Rey%2C%20D.%2C%20Ye%2C%20J.%20X.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282017%29.%20Estimating%20the%20state%20of%20a%20geophysical%20system%20with%20sparse%20observations%3A%20time%20delay%20methods%20to%20achieve%20accurate%20initial%20states%20for%20prediction.%20%3Ci%3ENonlinear%20Processes%20in%20Geophysics%3C%5C%2Fi%3E%2C%20%3Ci%3E24%3C%5C%2Fi%3E%281%29%2C%209%26%23x2013%3B22.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.5194%5C%2Fnpg-24-9-2017%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.5194%5C%2Fnpg-24-9-2017%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Estimating%20the%20state%20of%20a%20geophysical%20system%20with%20sparse%20observations%3A%20time%20delay%20methods%20to%20achieve%20accurate%20initial%20states%20for%20prediction%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22Z.%22%2C%22lastName%22%3A%22An%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22D.%22%2C%22lastName%22%3A%22Rey%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%20X.%22%2C%22lastName%22%3A%22Ye%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22The%20problem%20of%20forecasting%20the%20behavior%20of%20a%20complex%20dynamical%20system%20through%20analysis%20of%20observational%20time-series%20data%20becomes%20difficult%20when%20the%20system%20expresses%20chaotic%20behavior%20and%20the%20measurements%20are%20sparse%2C%20in%20both%20space%20and%5C%2For%20time.%20Despite%20the%20fact%20that%20this%20situation%20is%20quite%20typical%20across%20many%20fields%2C%20including%20numerical%20weather%20prediction%2C%20the%20issue%20of%20whether%20the%20available%20observations%20are%20%5C%22sufficient%5C%22%20for%20generating%20successful%20forecasts%20is%20still%20not%20well%20understood.%20An%20analysis%20by%20Whartenby%20et%20al.%20%282013%29%20found%20that%20in%20the%20context%20of%20the%20nonlinear%20shallow%20water%20equations%20on%20a%20beta%20plane%2C%20standard%20nudging%20techniques%20require%20observing%20approximately%2070%25%20of%20the%20full%20set%20of%20state%20variables.%20Here%20we%20examine%20the%20same%20system%20using%20a%20method%20introduced%20by%20Rey%20et%20al.%20%282014a%29%2C%20which%20generalizes%20standard%20nudging%20methods%20to%20utilize%20time%20delayed%20measurements.%20We%20show%20that%20in%20certain%20circumstances%2C%20it%20provides%20a%20sizable%20reduction%20in%20the%20number%20of%20observations%20required%20to%20construct%20accurate%20estimates%20and%20high-quality%20predictions.%20In%20particular%2C%20we%20find%20that%20this%20estimate%20of%2070%25%20can%20be%20reduced%20to%20about%2033%25%20using%20time%20delays%2C%20and%20even%20further%20if%20Lagrangian%20drifter%20locations%20are%20also%20used%20as%20measurements.%22%2C%22date%22%3A%222017%5C%2F01%22%2C%22language%22%3A%22%22%2C%22DOI%22%3A%2210.5194%5C%2Fnpg-24-9-2017%22%2C%22ISSN%22%3A%221023-5809%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A03Z%22%7D%7D%2C%7B%22key%22%3A%22RI99ACGT%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Kadakia%20et%20al.%22%2C%22parsedDate%22%3A%222016-12%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EKadakia%2C%20N.%2C%20Armstrong%2C%20E.%2C%20Breen%2C%20D.%2C%20Morone%2C%20U.%2C%20Daou%2C%20A.%2C%20Margoliash%2C%20D.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282016%29.%20Nonlinear%20statistical%20data%20assimilation%20for%20HVCRA%20neurons%20in%20the%20avian%20song%20system.%20%3Ci%3EBiological%20Cybernetics%3C%5C%2Fi%3E%2C%20%3Ci%3E110%3C%5C%2Fi%3E%286%29%2C%20417%26%23x2013%3B434.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1007%5C%2Fs00422-016-0697-3%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1007%5C%2Fs00422-016-0697-3%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Nonlinear%20statistical%20data%20assimilation%20for%20HVCRA%20neurons%20in%20the%20avian%20song%20system%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22N.%22%2C%22lastName%22%3A%22Kadakia%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22E.%22%2C%22lastName%22%3A%22Armstrong%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22D.%22%2C%22lastName%22%3A%22Breen%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22U.%22%2C%22lastName%22%3A%22Morone%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22A.%22%2C%22lastName%22%3A%22Daou%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22D.%22%2C%22lastName%22%3A%22Margoliash%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22With%20the%20goal%20of%20building%20a%20model%20of%20the%20HVC%20nucleus%20in%20the%20avian%20song%20system%2C%20we%20discuss%20in%20detail%20a%20model%20of%20HVCRA%20projection%20neurons%20comprised%20of%20a%20somatic%20compartment%20with%20fast%20Na%2B%20and%20K%2B%20currents%20and%20a%20dendritic%20compartment%20with%20slower%20Ca2%2B%20dynamics.%20We%20show%20this%20model%20qualitatively%20exhibits%20many%20observed%20electrophysiological%20behaviors.%20We%20then%20show%20in%20numerical%20procedures%20how%20one%20can%20design%20and%20analyze%20feasible%20laboratory%20experiments%20that%20allow%20the%20estimation%20of%20all%20of%20the%20many%20parameters%20and%20unmeasured%20dynamical%20variables%2C%20given%20observations%20of%20the%20somatic%20voltage%20V-s%28t%29%20alone.%20A%20key%20to%20this%20procedure%20is%20to%20initially%20estimate%20the%20slow%20dynamics%20associated%20with%20Ca%2C%20blocking%20the%20fast%20Na%20and%20K%20variations%2C%20and%20then%20with%20the%20Ca%20parameters%20fixed%20estimate%20the%20fast%20Na%20and%20K%20dynamics.%20This%20separation%20of%20time%20scales%20provides%20a%20numerically%20robust%20method%20for%20completing%20the%20full%20neuron%20model%2C%20and%20the%20efficacy%20of%20the%20method%20is%20tested%20by%20prediction%20when%20observations%20are%20complete.%20The%20simulation%20provides%20a%20framework%20for%20the%20slice%20preparation%20experiments%20and%20illustrates%20the%20use%20of%20data%20assimilation%20methods%20for%20the%20design%20of%20those%20experiments.%22%2C%22date%22%3A%222016%5C%2F12%22%2C%22language%22%3A%22%22%2C%22DOI%22%3A%2210.1007%5C%2Fs00422-016-0697-3%22%2C%22ISSN%22%3A%220340-1200%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A06Z%22%7D%7D%2C%7B%22key%22%3A%22SWVWYXSJ%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Armstrong%20and%20Abarbanel%22%2C%22parsedDate%22%3A%222016-11%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EArmstrong%2C%20E.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282016%29.%20Model%20of%20the%20songbird%20nucleus%20HVC%20as%20a%20network%20of%20central%20pattern%20generators.%20%3Ci%3EJournal%20of%20Neurophysiology%3C%5C%2Fi%3E%2C%20%3Ci%3E116%3C%5C%2Fi%3E%285%29%2C%202405%26%23x2013%3B2419.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1152%5C%2Fjn.00438.2016%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1152%5C%2Fjn.00438.2016%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Model%20of%20the%20songbird%20nucleus%20HVC%20as%20a%20network%20of%20central%20pattern%20generators%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22E.%22%2C%22lastName%22%3A%22Armstrong%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22We%20propose%20a%20functional%20architecture%20of%20the%20adult%20songbird%20nucleus%20HVC%20in%20which%20the%20core%20element%20is%20a%20%5C%22functional%20syllable%20unit%5C%22%20%28FSU%29.%20In%20this%20model%2C%20HVC%20is%20organized%20into%20FSUs%2C%20each%20of%20which%20provides%20the%20basis%20for%20the%20production%20of%20one%20syllable%20in%20vocalization.%20Within%20each%20FSU%2C%20the%20inhibitory%20neuron%20population%20takes%20one%20of%20two%20operational%20states%3A%201%29%20simultaneous%20firing%20wherein%20all%20inhibitory%20neurons%20fire%20simultaneously%2C%20and%202%29%20competitive%20firing%20of%20the%20inhibitory%20neurons.%20Switching%20between%20these%20basic%20modes%20of%20activity%20is%20accomplished%20via%20changes%20in%20the%20synaptic%20strengths%20among%20the%20inhibitory%20neurons.%20The%20inhibitory%20neurons%20connect%20to%20excitatory%20projection%20neurons%20such%20that%20during%20state%201%20the%20activity%20of%20projection%20neurons%20is%20suppressed%2C%20while%20during%20state%202%20patterns%20of%20sequential%20firing%20of%20projection%20neurons%20can%20occur.%20The%20latter%20state%20is%20stabilized%20by%20feedback%20from%20the%20projection%20to%20the%20inhibitory%20neurons.%20Song%20composition%20for%20specific%20species%20is%20distinguished%20by%20the%20manner%20in%20which%20different%20FSUs%20are%20functionally%20connected%20to%20each%20other.%20Ours%20is%20a%20computational%20model%20built%20with%20biophysically%20based%20neurons.%20We%20illustrate%20that%20many%20observations%20of%20HVC%20activity%20are%20explained%20by%20the%20dynamics%20of%20the%20proposed%20population%20of%20FSUs%2C%20and%20we%20identify%20aspects%20of%20the%20model%20that%20are%20currently%20testable%20experimentally.%20In%20addition%2C%20and%20standing%20apart%20from%20the%20core%20features%20of%20an%20FSU%2C%20we%20propose%20that%20the%20transition%20between%20modes%20may%20be%20governed%20by%20the%20biophysical%20mechanism%20of%20neuromodulation.%22%2C%22date%22%3A%222016%5C%2F11%22%2C%22language%22%3A%22%22%2C%22DOI%22%3A%2210.1152%5C%2Fjn.00438.2016%22%2C%22ISSN%22%3A%220022-3077%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A05Z%22%7D%7D%2C%7B%22key%22%3A%22BDSI45NW%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Nogaret%20et%20al.%22%2C%22parsedDate%22%3A%222016-09%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3ENogaret%2C%20A.%2C%20Meliza%2C%20C.%20D.%2C%20Margoliash%2C%20D.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282016%29.%20Automatic%20construction%20of%20predictive%20neuron%20models%20through%20large%20scale%20assimilation%20of%20electrophysiological%20data.%20%3Ci%3EScientific%20Reports%3C%5C%2Fi%3E%2C%20%3Ci%3E6%3C%5C%2Fi%3E.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1038%5C%2Fsrep32749%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1038%5C%2Fsrep32749%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Automatic%20construction%20of%20predictive%20neuron%20models%20through%20large%20scale%20assimilation%20of%20electrophysiological%20data%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22A.%22%2C%22lastName%22%3A%22Nogaret%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22C.%20D.%22%2C%22lastName%22%3A%22Meliza%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22D.%22%2C%22lastName%22%3A%22Margoliash%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22We%20report%20on%20the%20construction%20of%20neuron%20models%20by%20assimilating%20electrophysiological%20data%20with%20large-scale%20constrained%20nonlinear%20optimization.%20The%20method%20implements%20interior%20point%20line%20parameter%20search%20to%20determine%20parameters%20from%20the%20responses%20to%20intracellular%20current%20injections%20of%20zebra%20finch%20HVC%20neurons.%20We%20incorporated%20these%20parameters%20into%20a%20nine%20ionic%20channel%20conductance%20model%20to%20obtain%20completed%20models%20which%20we%20then%20use%20to%20predict%20the%20state%20of%20the%20neuron%20under%20arbitrary%20current%20stimulation.%20Each%20model%20was%20validated%20by%20successfully%20predicting%20the%20dynamics%20of%20the%20membrane%20potential%20induced%20by%2020-50%20different%20current%20protocols.%20The%20dispersion%20of%20parameters%20extracted%20from%20different%20assimilation%20windows%20was%20studied.%20Differences%20in%20constraints%20from%20current%20protocols%2C%20stochastic%20variability%20in%20neuron%20output%2C%20and%20noise%20behave%20as%20a%20residual%20temperature%20which%20broadens%20the%20global%20minimum%20of%20the%20objective%20function%20to%20an%20ellipsoid%20domain%20whose%20principal%20axes%20follow%20an%20exponentially%20decaying%20distribution.%20The%20maximum%20likelihood%20expectation%20of%20extracted%20parameters%20was%20found%20to%20provide%20an%20excellent%20approximation%20of%20the%20global%20minimum%20and%20yields%20highly%20consistent%20kinetics%20for%20both%20neurons%20studied.%20Large%20scale%20assimilation%20absorbs%20the%20intrinsic%20variability%20of%20electrophysiological%20data%20over%20wide%20assimilation%20windows.%20It%20builds%20models%20in%20an%20automatic%20manner%20treating%20all%20data%20as%20equal%20quantities%20and%20requiring%20minimal%20additional%20insight.%22%2C%22date%22%3A%222016%5C%2F09%22%2C%22language%22%3A%22%22%2C%22DOI%22%3A%2210.1038%5C%2Fsrep32749%22%2C%22ISSN%22%3A%222045-2322%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A00Z%22%7D%7D%2C%7B%22key%22%3A%22EXLJ7E5C%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Ye%20et%20al.%22%2C%22parsedDate%22%3A%222015-11%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EYe%2C%20J.%20X.%2C%20Rey%2C%20D.%2C%20Kadakia%2C%20N.%2C%20Eldridge%2C%20M.%2C%20Morone%2C%20U.%20I.%2C%20Rozdeba%2C%20P.%2C%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%2C%20%26amp%3B%20Quinn%2C%20J.%20C.%20%282015%29.%20Systematic%20variational%20method%20for%20statistical%20nonlinear%20state%20and%20parameter%20estimation.%20%3Ci%3EPhysical%20Review%20E%3C%5C%2Fi%3E%2C%20%3Ci%3E92%3C%5C%2Fi%3E%285%29.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1103%5C%2FPhysRevE.92.052901%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1103%5C%2FPhysRevE.92.052901%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Systematic%20variational%20method%20for%20statistical%20nonlinear%20state%20and%20parameter%20estimation%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%20X.%22%2C%22lastName%22%3A%22Ye%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22D.%22%2C%22lastName%22%3A%22Rey%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22N.%22%2C%22lastName%22%3A%22Kadakia%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22M.%22%2C%22lastName%22%3A%22Eldridge%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22U.%20I.%22%2C%22lastName%22%3A%22Morone%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22P.%22%2C%22lastName%22%3A%22Rozdeba%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%20C.%22%2C%22lastName%22%3A%22Quinn%22%7D%5D%2C%22abstractNote%22%3A%22In%20statistical%20data%20assimilation%20one%20evaluates%20the%20conditional%20expected%20values%2C%20conditioned%20on%20measurements%2C%20of%20interesting%20quantities%20on%20the%20path%20of%20a%20model%20through%20observation%20and%20prediction%20windows.%20This%20often%20requires%20working%20with%20very%20high%20dimensional%20integrals%20in%20the%20discrete%20time%20descriptions%20of%20the%20observations%20and%20model%20dynamics%2C%20which%20become%20functional%20integrals%20in%20the%20continuous-time%20limit.%20Two%20familiar%20methods%20for%20performing%20these%20integrals%20include%20%281%29%20Monte%20Carlo%20calculations%20and%20%282%29%20variational%20approximations%20using%20the%20method%20of%20Laplace%20plus%20perturbative%20corrections%20to%20the%20dominant%20contributions.%20We%20attend%20here%20to%20aspects%20of%20the%20Laplace%20approximation%20and%20develop%20an%20annealing%20method%20for%20locating%20the%20variational%20path%20satisfying%20the%20Euler-Lagrange%20equations%20that%20comprises%20the%20major%20contribution%20to%20the%20integrals.%20This%20begins%20with%20the%20identification%20of%20the%20minimum%20action%20path%20starting%20with%20a%20situation%20where%20the%20model%20dynamics%20is%20totally%20unresolved%20in%20state%20space%2C%20and%20the%20consistent%20minimum%20of%20the%20variational%20problem%20is%20known.%20We%20then%20proceed%20to%20slowly%20increase%20the%20model%20resolution%2C%20seeking%20to%20remain%20in%20the%20basin%20of%20the%20minimum%20action%20path%2C%20until%20a%20path%20that%20gives%20the%20dominant%20contribution%20to%20the%20integral%20is%20identified.%20After%20a%20discussion%20of%20some%20general%20issues%2C%20we%20give%20examples%20of%20the%20assimilation%20process%20for%20some%20simple%2C%20instructive%20models%20from%20the%20geophysical%20literature.%20Then%20we%20explore%20a%20slightly%20richer%20model%20of%20the%20same%20type%20with%20two%20distinct%20time%20scales.%20This%20is%20followed%20by%20a%20model%20characterizing%20the%20biophysics%20of%20individual%20neurons.%22%2C%22date%22%3A%222015%5C%2F11%22%2C%22language%22%3A%22%22%2C%22DOI%22%3A%2210.1103%5C%2FPhysRevE.92.052901%22%2C%22ISSN%22%3A%221539-3755%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A10Z%22%7D%7D%2C%7B%22key%22%3A%22IN9JX6ZA%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Schumann-Bischoff%20et%20al.%22%2C%22parsedDate%22%3A%222015-05%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3ESchumann-Bischoff%2C%20J.%2C%20Parlitz%2C%20U.%2C%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%2C%20Kostuk%2C%20M.%2C%20Rey%2C%20D.%2C%20Eldridge%2C%20M.%2C%20%26amp%3B%20Luther%2C%20S.%20%282015%29.%20Basin%20structure%20of%20optimization%20based%20state%20and%20parameter%20estimation.%20%3Ci%3EChaos%3C%5C%2Fi%3E%2C%20%3Ci%3E25%3C%5C%2Fi%3E%285%29.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1063%5C%2F1.4920942%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1063%5C%2F1.4920942%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Basin%20structure%20of%20optimization%20based%20state%20and%20parameter%20estimation%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%22%2C%22lastName%22%3A%22Schumann-Bischoff%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22U.%22%2C%22lastName%22%3A%22Parlitz%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22M.%22%2C%22lastName%22%3A%22Kostuk%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22D.%22%2C%22lastName%22%3A%22Rey%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22M.%22%2C%22lastName%22%3A%22Eldridge%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22S.%22%2C%22lastName%22%3A%22Luther%22%7D%5D%2C%22abstractNote%22%3A%22Most%20data%20based%20state%20and%20parameter%20estimation%20methods%20require%20suitable%20initial%20values%20or%20guesses%20to%20achieve%20convergence%20to%20the%20desired%20solution%2C%20which%20typically%20is%20a%20global%20minimum%20of%20some%20cost%20function.%20Unfortunately%2C%20however%2C%20other%20stable%20solutions%20%28e.g.%2C%20local%20minima%29%20may%20exist%20and%20provide%20suboptimal%20or%20even%20wrong%20estimates.%20Here%2C%20we%20demonstrate%20for%20a%209-dimensional%20Lorenz-96%20model%20how%20to%20characterize%20the%20basin%20size%20of%20the%20global%20minimum%20when%20applying%20some%20particular%20optimization%20based%20estimation%20algorithm.%20We%20compare%20three%20different%20strategies%20for%20generating%20suitable%20initial%20guesses%2C%20and%20we%20investigate%20the%20dependence%20of%20the%20solution%20on%20the%20given%20trajectory%20segment%20%28underlying%20the%20measured%20time%20series%29.%20To%20address%20the%20question%20of%20how%20many%20state%20variables%20have%20to%20be%20measured%20for%20optimal%20performance%2C%20different%20types%20of%20multivariate%20time%20series%20are%20considered%20consisting%20of%201%2C%202%2C%20or%203%20variables.%20Based%20on%20these%20time%20series%2C%20the%20local%20observability%20of%20state%20variables%20and%20parameters%20of%20the%20Lorenz-96%20model%20is%20investigated%20and%20confirmed%20using%20delay%20coordinates.%20This%20result%20is%20in%20good%20agreement%20with%20the%20observation%20that%20correct%20state%20and%20parameter%20estimation%20results%20are%20obtained%20if%20the%20optimization%20algorithm%20is%20initialized%20with%20initial%20guesses%20close%20to%20the%20true%20solution.%20In%20contrast%2C%20initialization%20with%20other%20exact%20solutions%20of%20the%20model%20equations%20%28different%20from%20the%20true%20solution%20used%20to%20generate%20the%20time%20series%29%20typically%20fails%2C%20i.e.%2C%20the%20optimization%20procedure%20ends%20up%20in%20local%20minima%20different%20from%20the%20true%20solution.%20Initialization%20using%20random%20values%20in%20a%20box%20around%20the%20attractor%20exhibits%20success%20rates%20depending%20on%20the%20number%20of%20observables%20and%20the%20available%20time%20series%20%28trajectory%20segment%29.%20%28C%29%202015%20AIP%20Publishing%20LLC.%22%2C%22date%22%3A%222015%5C%2F05%22%2C%22language%22%3A%22%22%2C%22DOI%22%3A%2210.1063%5C%2F1.4920942%22%2C%22ISSN%22%3A%221054-1500%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A00Z%22%7D%7D%2C%7B%22key%22%3A%22V9FLWP2V%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Nogaret%20et%20al.%22%2C%22parsedDate%22%3A%222015-02%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3ENogaret%2C%20A.%2C%20O%26%23x2019%3BCallaghan%2C%20E.%20L.%2C%20Lataro%2C%20R.%20M.%2C%20Salgado%2C%20H.%20C.%2C%20Meliza%2C%20C.%20D.%2C%20Duncan%2C%20E.%2C%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%2C%20%26amp%3B%20Paton%2C%20J.%20F.%20R.%20%282015%29.%20Silicon%20central%20pattern%20generators%20for%20cardiac%20diseases.%20%3Ci%3EJournal%20of%20Physiology-London%3C%5C%2Fi%3E%2C%20%3Ci%3E593%3C%5C%2Fi%3E%284%29%2C%20763%26%23x2013%3B774.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1113%5C%2Fjphysiol.2014.282723%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1113%5C%2Fjphysiol.2014.282723%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Silicon%20central%20pattern%20generators%20for%20cardiac%20diseases%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22A.%22%2C%22lastName%22%3A%22Nogaret%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22E.%20L.%22%2C%22lastName%22%3A%22O%27Callaghan%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22R.%20M.%22%2C%22lastName%22%3A%22Lataro%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20C.%22%2C%22lastName%22%3A%22Salgado%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22C.%20D.%22%2C%22lastName%22%3A%22Meliza%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22E.%22%2C%22lastName%22%3A%22Duncan%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%20F.%20R.%22%2C%22lastName%22%3A%22Paton%22%7D%5D%2C%22abstractNote%22%3A%22Cardiac%20rhythm%20management%20devices%20provide%20therapies%20for%20both%20arrhythmias%20and%20resynchronisation%20but%20not%20heart%20failure%2C%20which%20affects%20millions%20of%20patients%20worldwide.%20This%20paper%20reviews%20recent%20advances%20in%20biophysics%20and%20mathematical%20engineering%20that%20provide%20a%20novel%20technological%20platform%20for%20addressing%20heart%20disease%20and%20enabling%20beat-to-beat%20adaptation%20of%20cardiac%20pacing%20in%20response%20to%20physiological%20feedback.%20The%20technology%20consists%20of%20silicon%20hardware%20central%20pattern%20generators%20%28hCPGs%29%20that%20may%20be%20trained%20to%20emulate%20accurately%20the%20dynamical%20response%20of%20biological%20central%20pattern%20generators%20%28bCPGs%29.%20We%20discuss%20the%20limitations%20of%20present%20CPGs%20and%20appraise%20the%20advantages%20of%20analog%20over%20digital%20circuits%20for%20application%20in%20bioelectronic%20medicine.%20To%20test%20the%20system%2C%20we%20have%20focused%20on%20the%20cardio-respiratory%20oscillators%20in%20the%20medulla%20oblongata%20that%20modulate%20heart%20rate%20in%20phase%20with%20respiration%20to%20induce%20respiratory%20sinus%20arrhythmia%20%28RSA%29.%20We%20describe%20here%20a%20novel%2C%20scalable%20hCPG%20comprising%20physiologically%20realistic%20%28Hodgkin-Huxley%20type%29%20neurones%20and%20synapses.%20Our%20hCPG%20comprises%20two%20neurones%20that%20antagonise%20each%20other%20to%20provide%20rhythmic%20motor%20drive%20to%20the%20vagus%20nerve%20to%20slow%20the%20heart.%20We%20show%20how%20recent%20advances%20in%20modelling%20allow%20the%20motor%20output%20to%20adapt%20to%20physiological%20feedback%20such%20as%20respiration.%20In%20rats%2C%20we%20report%20on%20the%20restoration%20of%20RSA%20using%20an%20hCPG%20that%20receives%20diaphragmatic%20electromyography%20input%20and%20use%20it%20to%20stimulate%20the%20vagus%20nerve%20at%20specific%20time%20points%20of%20the%20respiratory%20cycle%20to%20slow%20the%20heart%20rate.%20We%20have%20validated%20the%20adaptation%20of%20stimulation%20to%20alterations%20in%20respiratory%20rate.%20We%20demonstrate%20that%20the%20hCPG%20is%20tuneable%20in%20terms%20of%20the%20depth%20and%20timing%20of%20the%20RSA%20relative%20to%20respiratory%20phase.%20These%20pioneering%20studies%20will%20now%20permit%20an%20analysis%20of%20the%20physiological%20role%20of%20RSA%20as%20well%20as%20its%20any%20potential%20therapeutic%20use%20in%20cardiac%20disease.%22%2C%22date%22%3A%222015%5C%2F02%22%2C%22language%22%3A%22%22%2C%22DOI%22%3A%2210.1113%5C%2Fjphysiol.2014.282723%22%2C%22ISSN%22%3A%220022-3751%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A08Z%22%7D%7D%2C%7B%22key%22%3A%22LD5WA7IW%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Ye%20et%20al.%22%2C%22parsedDate%22%3A%222015%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EYe%2C%20J.%2C%20Kadakia%2C%20N.%2C%20Rozdeba%2C%20P.%20J.%2C%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%2C%20%26amp%3B%20Quinn%2C%20J.%20C.%20%282015%29.%20Improved%20variational%20methods%20in%20statistical%20data%20assimilation.%20%3Ci%3ENonlinear%20Processes%20in%20Geophysics%3C%5C%2Fi%3E%2C%20%3Ci%3E22%3C%5C%2Fi%3E%282%29%2C%20205%26%23x2013%3B213.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.5194%5C%2Fnpg-22-205-2015%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.5194%5C%2Fnpg-22-205-2015%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Improved%20variational%20methods%20in%20statistical%20data%20assimilation%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%22%2C%22lastName%22%3A%22Ye%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22N.%22%2C%22lastName%22%3A%22Kadakia%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22P.%20J.%22%2C%22lastName%22%3A%22Rozdeba%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%20C.%22%2C%22lastName%22%3A%22Quinn%22%7D%5D%2C%22abstractNote%22%3A%22Data%20assimilation%20transfers%20information%20from%20an%20observed%20system%20to%20a%20physically%20based%20model%20system%20with%20state%20variables%20x%28t%29.%20The%20observations%20are%20typically%20noisy%2C%20the%20model%20has%20errors%2C%20and%20the%20initial%20state%20x%28t%280%29%29%20is%20uncertain%3A%20the%20data%20assimilation%20is%20statistical.%20One%20can%20ask%20about%20expected%20values%20of%20functions%20h%20%3C%20G%28X%29%3E%20on%20the%20path%20X%20%3D%20%7Bx%28t%280%29%29%2C%20...%2C%20x%28t%28m%29%29%7D%20of%20the%20model%20state%20through%20the%20observation%20window%20t%28n%29%20%3D%20%7Bt%280%29%2C...%2C%20t%28m%29%29.%20The%20conditional%20%28on%20the%20measurements%29%20probability%20distribution%20P%28X%29%20%3D%20exp%5B-A%280%29%28X%29%5D%20determines%20these%20expected%20values.%20Variational%20methods%20using%20saddle%20points%20of%20the%20%5C%22action%5C%22%20A%280%29%28X%29%2C%20known%20as%204DVar%20%28Talagrand%20and%20Courtier%2C%201987%3B%20Evensen%2C%202009%29%2C%20are%20utilized%20for%20estimating%20%3C%20G%28X%29%3E.%20In%20a%20path%20integral%20formulation%20of%20statistical%20data%20assimilation%2C%20we%20consider%20variational%20approximations%20in%20a%20realization%20of%20the%20action%20where%20measurement%20errors%20and%20model%20errors%20are%20Gaussian.%20We%20%28a%29%20discuss%20an%20annealing%20method%20for%20locating%20the%20path%20X-0%20giving%20a%20consistent%20minimum%20of%20the%20action%20A%280%29%28X-0%29%2C%20%28b%29%20consider%20the%20explicit%20role%20of%20the%20number%20of%20measurements%20at%20each%20t%20n%20in%20determining%20A%280%29%28X-0%29%2C%20and%20%28c%29%20identify%20a%20parameter%20regime%20for%20the%20scale%20of%20model%20errors%2C%20which%20allows%20X-0%20to%20give%20a%20precise%20estimate%20of%20%3C%20G%28X-0%29%3E%20with%20computable%2C%20small%20higher-order%20corrections.%22%2C%22date%22%3A%222015%22%2C%22language%22%3A%22%22%2C%22DOI%22%3A%2210.5194%5C%2Fnpg-22-205-2015%22%2C%22ISSN%22%3A%221023-5809%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A04Z%22%7D%7D%2C%7B%22key%22%3A%22MMLV84IW%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Rey%20et%20al.%22%2C%22parsedDate%22%3A%222014-12-22%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3ERey%2C%20D.%2C%20Eldridge%2C%20M.%2C%20Morone%2C%20U.%2C%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%2C%20Parlitz%2C%20U.%2C%20%26amp%3B%20Schumann-Bischoff%2C%20J.%20%282014%29.%20Using%20waveform%20information%20in%20nonlinear%20data%20assimilation.%20%3Ci%3EPhysical%20Review%20E%3C%5C%2Fi%3E%2C%20%3Ci%3E90%3C%5C%2Fi%3E%286%29.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1103%5C%2FPhysRevE.90.062916%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1103%5C%2FPhysRevE.90.062916%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Using%20waveform%20information%20in%20nonlinear%20data%20assimilation%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22Daniel%22%2C%22lastName%22%3A%22Rey%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22Michael%22%2C%22lastName%22%3A%22Eldridge%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22Uriel%22%2C%22lastName%22%3A%22Morone%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22Henry%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22Ulrich%22%2C%22lastName%22%3A%22Parlitz%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22Jan%22%2C%22lastName%22%3A%22Schumann-Bischoff%22%7D%5D%2C%22abstractNote%22%3A%22Information%20in%20measurements%20of%20a%20nonlinear%20dynamical%20system%20can%20be%20transferred%20to%20a%20quantitative%20model%20of%20the%20observed%20system%20to%20establish%20its%20fixed%20parameters%20and%20unobserved%20state%20variables.%20After%20this%20learning%20period%20is%20complete%2C%20one%20may%20predict%20the%20model%20response%20to%20new%20forces%20and%2C%20when%20successful%2C%20these%20predictions%20will%20match%20additional%20observations.%20This%20adjustment%20process%20encounters%20problems%20when%20the%20model%20is%20nonlinear%20and%20chaotic%20because%20dynamical%20instability%20impedes%20the%20transfer%20of%20information%20from%20the%20data%20to%20the%20model%20when%20the%20number%20of%20measurements%20at%20each%20observation%20time%20is%20insufficient.%20We%20discuss%20the%20use%20of%20information%20in%20the%20waveform%20of%20the%20data%2C%20realized%20through%20a%20time%20delayed%20collection%20of%20measurements%2C%20to%20provide%20additional%20stability%20and%20accuracy%20to%20this%20search%20procedure.%20Several%20examples%20are%20explored%2C%20including%20a%20few%20familiar%20nonlinear%20dynamical%20systems%20and%20small%20networks%20of%20Colpitts%20oscillators.%22%2C%22date%22%3A%22Dec%2022%202014%22%2C%22language%22%3A%22%22%2C%22DOI%22%3A%2210.1103%5C%2FPhysRevE.90.062916%22%2C%22ISSN%22%3A%221539-3755%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A10Z%22%7D%7D%2C%7B%22key%22%3A%22SW42J63A%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Meliza%20et%20al.%22%2C%22parsedDate%22%3A%222014-08%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EMeliza%2C%20C.%20D.%2C%20Kostuk%2C%20M.%2C%20Huang%2C%20H.%2C%20Nogaret%2C%20A.%2C%20Margoliash%2C%20D.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282014%29.%20Estimating%20parameters%20and%20predicting%20membrane%20voltages%20with%20conductance-based%20neuron%20models.%20%3Ci%3EBiological%20Cybernetics%3C%5C%2Fi%3E%2C%20%3Ci%3E108%3C%5C%2Fi%3E%284%29%2C%20495%26%23x2013%3B516.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1007%5C%2Fs00422-014-0615-5%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1007%5C%2Fs00422-014-0615-5%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Estimating%20parameters%20and%20predicting%20membrane%20voltages%20with%20conductance-based%20neuron%20models%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22C.%20D.%22%2C%22lastName%22%3A%22Meliza%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22M.%22%2C%22lastName%22%3A%22Kostuk%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%22%2C%22lastName%22%3A%22Huang%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22A.%22%2C%22lastName%22%3A%22Nogaret%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22D.%22%2C%22lastName%22%3A%22Margoliash%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22Recent%20results%20demonstrate%20techniques%20for%20fully%20quantitative%2C%20statistical%20inference%20of%20the%20dynamics%20of%20individual%20neurons%20under%20the%20Hodgkin-Huxley%20framework%20of%20voltage-gated%20conductances.%20Using%20a%20variational%20approximation%2C%20this%20approach%20has%20been%20successfully%20applied%20to%20simulated%20data%20from%20model%20neurons.%20Here%2C%20we%20use%20this%20method%20to%20analyze%20a%20population%20of%20real%20neurons%20recorded%20in%20a%20slice%20preparation%20of%20the%20zebra%20finch%20forebrain%20nucleus%20HVC.%20Our%20results%20demonstrate%20that%20using%20only%201%2C500%20ms%20of%20voltage%20recorded%20while%20injecting%20a%20complex%20current%20waveform%2C%20we%20can%20estimate%20the%20values%20of%2012%20state%20variables%20and%2072%20parameters%20in%20a%20dynamical%20model%2C%20such%20that%20the%20model%20accurately%20predicts%20the%20responses%20of%20the%20neuron%20to%20novel%20injected%20currents.%20A%20less%20complex%20model%20produced%20consistently%20worse%20predictions%2C%20indicating%20that%20the%20additional%20currents%20contribute%20significantly%20to%20the%20dynamics%20of%20these%20neurons.%20Preliminary%20results%20indicate%20some%20differences%20in%20the%20channel%20complement%20of%20the%20models%20for%20different%20classes%20of%20HVC%20neurons%2C%20which%20accords%20with%20expectations%20from%20the%20biology.%20Whereas%20the%20model%20for%20each%20cell%20is%20incomplete%20%28representing%20only%20the%20somatic%20compartment%2C%20and%20likely%20to%20be%20missing%20classes%20of%20channels%20that%20the%20real%20neurons%20possess%29%2C%20our%20approach%20opens%20the%20possibility%20to%20investigate%20in%20modeling%20the%20plausibility%20of%20additional%20classes%20of%20channels%20the%20cell%20might%20possess%2C%20thus%20improving%20the%20models%20over%20time.%20These%20results%20provide%20an%20important%20foundational%20basis%20for%20building%20biologically%20realistic%20network%20models%2C%20such%20as%20the%20one%20in%20HVC%20that%20contributes%20to%20the%20process%20of%20song%20production%20and%20developmental%20vocal%20learning%20in%20songbirds.%22%2C%22date%22%3A%222014%5C%2F08%22%2C%22language%22%3A%22%22%2C%22DOI%22%3A%2210.1007%5C%2Fs00422-014-0615-5%22%2C%22ISSN%22%3A%220340-1200%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A03Z%22%7D%7D%2C%7B%22key%22%3A%22ZV8VLCKR%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Ye%20et%20al.%22%2C%22parsedDate%22%3A%222014-06%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EYe%2C%20J.%20X.%2C%20Rozdeba%2C%20P.%20J.%2C%20Morone%2C%20U.%20I.%2C%20Daou%2C%20A.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282014%29.%20Estimating%20the%20biophysical%20properties%20of%20neurons%20with%20intracellular%20calcium%20dynamics.%20%3Ci%3EPhysical%20Review%20E%3C%5C%2Fi%3E%2C%20%3Ci%3E89%3C%5C%2Fi%3E%286%29.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1103%5C%2FPhysRevE.89.062714%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1103%5C%2FPhysRevE.89.062714%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Estimating%20the%20biophysical%20properties%20of%20neurons%20with%20intracellular%20calcium%20dynamics%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%20X.%22%2C%22lastName%22%3A%22Ye%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22P.%20J.%22%2C%22lastName%22%3A%22Rozdeba%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22U.%20I.%22%2C%22lastName%22%3A%22Morone%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22A.%22%2C%22lastName%22%3A%22Daou%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22We%20investigate%20the%20dynamics%20of%20a%20conductance-based%20neuron%20model%20coupled%20to%20a%20model%20of%20intracellular%20calcium%20uptake%20and%20release%20by%20the%20endoplasmic%20reticulum.%20The%20intracellular%20calcium%20dynamics%20occur%20on%20a%20time%20scale%20that%20is%20orders%20of%20magnitude%20slower%20than%20voltage%20spiking%20behavior.%20Coupling%20these%20mechanisms%20sets%20the%20stage%20for%20the%20appearance%20of%20chaotic%20dynamics%2C%20which%20we%20observe%20within%20certain%20ranges%20of%20model%20parameter%20values.%20We%20then%20explore%20the%20question%20of%20whether%20one%20can%2C%20using%20observed%20voltage%20data%20alone%2C%20estimate%20the%20states%20and%20parameters%20of%20the%20voltage%20plus%20calcium%20%28V%2BCa%29%20dynamics%20model.%20We%20find%20the%20answer%20is%20negative.%20Indeed%2C%20we%20show%20that%20voltage%20plus%20another%20observed%20quantity%20must%20be%20known%20to%20allow%20the%20estimation%20to%20be%20accurate.%20We%20show%20that%20observing%20both%20the%20voltage%20time%20course%20V%20%28t%29%20and%20the%20intracellular%20Ca%20time%20course%20will%20permit%20accurate%20estimation%2C%20and%20from%20the%20estimated%20model%20state%2C%20accurate%20prediction%20after%20observations%20are%20completed.%20This%20sets%20the%20stage%20for%20how%20one%20will%20be%20able%20to%20use%20a%20more%20detailed%20model%20of%20V%2BCa%20dynamics%20in%20neuron%20activity%20in%20the%20analysis%20of%20experimental%20data%20on%20individual%20neurons%20as%20well%20as%20functional%20networks%20in%20which%20the%20nodes%20%28neurons%29%20have%20these%20biophysical%20properties.%22%2C%22date%22%3A%222014%5C%2F06%22%2C%22language%22%3A%22%22%2C%22DOI%22%3A%2210.1103%5C%2FPhysRevE.89.062714%22%2C%22ISSN%22%3A%221539-3755%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A03Z%22%7D%7D%2C%7B%22key%22%3A%225FBQDDIG%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Knowlton%20et%20al.%22%2C%22parsedDate%22%3A%222014-06%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EKnowlton%2C%20C.%2C%20Meliza%2C%20C.%20D.%2C%20Margoliash%2C%20D.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282014%29.%20Dynamical%20estimation%20of%20neuron%20and%20network%20properties%20III%3A%20network%20analysis%20using%20neuron%20spike%20times.%20%3Ci%3EBiological%20Cybernetics%3C%5C%2Fi%3E%2C%20%3Ci%3E108%3C%5C%2Fi%3E%283%29%2C%20261%26%23x2013%3B273.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1007%5C%2Fs00422-014-0601-y%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1007%5C%2Fs00422-014-0601-y%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Dynamical%20estimation%20of%20neuron%20and%20network%20properties%20III%3A%20network%20analysis%20using%20neuron%20spike%20times%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22C.%22%2C%22lastName%22%3A%22Knowlton%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22C.%20D.%22%2C%22lastName%22%3A%22Meliza%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22D.%22%2C%22lastName%22%3A%22Margoliash%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22Estimating%20the%20behavior%20of%20a%20network%20of%20neurons%20requires%20accurate%20models%20of%20the%20individual%20neurons%20along%20with%20accurate%20characterizations%20of%20the%20connections%20among%20them.%20Whereas%20for%20a%20single%20cell%2C%20measurements%20of%20the%20intracellular%20voltage%20are%20technically%20feasible%20and%20sufficient%20to%20characterize%20a%20useful%20model%20of%20its%20behavior%2C%20making%20sufficient%20numbers%20of%20simultaneous%20intracellular%20measurements%20to%20characterize%20even%20small%20networks%20is%20infeasible.%20This%20paper%20builds%20on%20prior%20work%20on%20single%20neurons%20to%20explore%20whether%20knowledge%20of%20the%20time%20of%20spiking%20of%20neurons%20in%20a%20network%2C%20once%20the%20nodes%20%28neurons%29%20have%20been%20characterized%20biophysically%2C%20can%20provide%20enough%20information%20to%20usefully%20constrain%20the%20functional%20architecture%20of%20the%20network%3A%20the%20existence%20of%20synaptic%20links%20among%20neurons%20and%20their%20strength.%20Using%20standardized%20voltage%20and%20synaptic%20gating%20variable%20waveforms%20associated%20with%20a%20spike%2C%20we%20demonstrate%20that%20the%20functional%20architecture%20of%20a%20small%20network%20of%20model%20neurons%20can%20be%20established.%22%2C%22date%22%3A%222014%5C%2F06%22%2C%22language%22%3A%22%22%2C%22DOI%22%3A%2210.1007%5C%2Fs00422-014-0601-y%22%2C%22ISSN%22%3A%220340-1200%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A02Z%22%7D%7D%2C%7B%22key%22%3A%22LSWVGX7G%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Rey%20et%20al.%22%2C%22parsedDate%22%3A%222014-02%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3ERey%2C%20D.%2C%20Eldridge%2C%20M.%2C%20Kostuk%2C%20M.%2C%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%2C%20Schumann-Bischoff%2C%20J.%2C%20%26amp%3B%20Parlitz%2C%20U.%20%282014%29.%20Accurate%20state%20and%20parameter%20estimation%20in%20nonlinear%20systems%20with%20sparse%20observations.%20%3Ci%3EPhysics%20Letters%20A%3C%5C%2Fi%3E%2C%20%3Ci%3E378%3C%5C%2Fi%3E%2811%26%23x2013%3B12%29%2C%20869%26%23x2013%3B873.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1016%5C%2Fj.physleta.2014.01.027%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1016%5C%2Fj.physleta.2014.01.027%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Accurate%20state%20and%20parameter%20estimation%20in%20nonlinear%20systems%20with%20sparse%20observations%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22D.%22%2C%22lastName%22%3A%22Rey%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22M.%22%2C%22lastName%22%3A%22Eldridge%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22M.%22%2C%22lastName%22%3A%22Kostuk%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%22%2C%22lastName%22%3A%22Schumann-Bischoff%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22U.%22%2C%22lastName%22%3A%22Parlitz%22%7D%5D%2C%22abstractNote%22%3A%22Transferring%20information%20from%20observations%20to%20models%20of%20complex%20systems%20may%20meet%20impediments%20when%20the%20number%20of%20observations%20at%20any%20observation%20time%20is%20not%20sufficient.%20This%20is%20especially%20so%20when%20chaotic%20behavior%20is%20expressed.%20We%20show%20how%20to%20use%20time-delay%20embedding%2C%20familiar%20from%20nonlinear%20dynamics%2C%20to%20provide%20the%20information%20required%20to%20obtain%20accurate%20state%20and%20parameter%20estimates.%20Good%20estimates%20of%20parameters%20and%20unobserved%20states%20are%20necessary%20for%20good%20predictions%20of%20the%20future%20state%20of%20a%20model%20system.%20This%20method%20may%20be%20critical%20in%20allowing%20the%20understanding%20of%20prediction%20in%20complex%20systems%20as%20varied%20as%20nervous%20systems%20and%20weather%20prediction%20where%20insufficient%20measurements%20are%20typical.%20%28C%29%202014%20Elsevier%20B.V.%20All%20rights%20reserved.%22%2C%22date%22%3A%222014%5C%2F02%22%2C%22language%22%3A%22%22%2C%22DOI%22%3A%2210.1016%5C%2Fj.physleta.2014.01.027%22%2C%22ISSN%22%3A%220375-9601%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A00Z%22%7D%7D%2C%7B%22key%22%3A%227Y4V3SRR%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Whartenby%20et%20al.%22%2C%22parsedDate%22%3A%222013-07%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EWhartenby%2C%20W.%20G.%2C%20Quinn%2C%20J.%20C.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282013%29.%20The%20number%20of%20required%20observations%20in%20data%20assimilation%20for%20a%20shallow-water%20flow.%20%3Ci%3EMonthly%20Weather%20Review%3C%5C%2Fi%3E%2C%20%3Ci%3E141%3C%5C%2Fi%3E%287%29%2C%202502%26%23x2013%3B2518.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1175%5C%2Fmwr-d-12-00103.1%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1175%5C%2Fmwr-d-12-00103.1%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22The%20number%20of%20required%20observations%20in%20data%20assimilation%20for%20a%20shallow-water%20flow%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22W.%20G.%22%2C%22lastName%22%3A%22Whartenby%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%20C.%22%2C%22lastName%22%3A%22Quinn%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22The%20authors%20consider%20statistical%20ensemble%20data%20assimilation%20for%20a%20one-layer%20shallow-water%20equation%20in%20a%20twin%20experiment%3A%20data%20are%20generated%20by%20an%20N%20x%20N%20enstrophy-conserving%20grid%20integration%20scheme%20along%20with%20an%20Ekman%20vertical%20velocity%20at%20the%20bottom%20of%20an%20Ekman%20layer%20driving%20the%20flow%20and%20Rayleigh%20and%20eddy%20viscosity%20dissipation%20damping%20the%20flow.%20Data%20are%20generated%20for%20N%20%3D%2016%20and%20the%20chaotic%20flow%20that%20results%20is%20analyzed.%20This%20analysis%20is%20performed%20in%20a%20path-integral%20formulation%20of%20the%20data%20assimilation%20problem.%20These%20path%20integrals%20are%20estimated%20by%20a%20Monte%20Carlo%20method%20using%20a%20Metropolis%20Hastings%20algorithm.%20The%20authors%27%20concentration%20is%20on%20the%20number%20of%20measurements%20L-c%20that%20must%20be%20assimilated%20by%20the%20model%20to%20allow%20accurate%20estimation%20of%20the%20full%20state%20of%20the%20model%20at%20the%20end%20of%20an%20observation%20window.%20It%20is%20found%20that%20for%20this%20shallow-water%20flow%20approximately%2070%25%20of%20the%20full%20set%20of%20state%20variables%20must%20be%20observed%20to%20accomplish%20either%20goal.%20The%20number%20of%20required%20observations%20is%20determined%20by%20examining%20the%20number%20needed%20to%20synchronize%20the%20observed%20data%20L-c%20and%20the%20model%20output%20when%20L%20data%20streams%20are%20assimilated%20by%20the%20model.%20Synchronization%20occurs%20when%20L%20%3E%3D%20L-c%20and%20the%20correct%20selection%20of%20which%20L-c%20data%20are%20observed%20is%20made.%20If%20the%20number%20of%20observations%20is%20too%20small%2C%20so%20synchronization%20does%20not%20occur%2C%20or%20the%20selection%20of%20observations%20does%20not%20lead%20to%20synchronization%20of%20the%20data%20with%20the%20model%20output%2C%20state%20estimates%20during%20and%20at%20the%20end%20of%20the%20observation%20window%20and%20predictions%20beyond%20the%20observation%20window%20are%20inaccurate.%22%2C%22date%22%3A%222013%5C%2F07%22%2C%22language%22%3A%22%22%2C%22DOI%22%3A%2210.1175%5C%2Fmwr-d-12-00103.1%22%2C%22ISSN%22%3A%220027-0644%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A06Z%22%7D%7D%2C%7B%22key%22%3A%229EL2C6B7%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Neftci%20et%20al.%22%2C%22parsedDate%22%3A%222012-07%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3ENeftci%2C%20E.%20O.%2C%20Toth%2C%20B.%2C%20Indiveri%2C%20G.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282012%29.%20Dynamic%20State%20and%20Parameter%20Estimation%20Applied%20to%20Neuromorphic%20Systems.%20%3Ci%3ENeural%20Computation%3C%5C%2Fi%3E%2C%20%3Ci%3E24%3C%5C%2Fi%3E%287%29%2C%201669%26%23x2013%3B1694.%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Dynamic%20State%20and%20Parameter%20Estimation%20Applied%20to%20Neuromorphic%20Systems%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22E.%20O.%22%2C%22lastName%22%3A%22Neftci%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22B.%22%2C%22lastName%22%3A%22Toth%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22G.%22%2C%22lastName%22%3A%22Indiveri%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22Neuroscientists%20often%20propose%20detailed%20computational%20models%20to%20probe%20the%20properties%20of%20the%20neural%20systems%20they%20study.%20With%20the%20advent%20of%20neuromorphic%20engineering%2C%20there%20is%20an%20increasing%20number%20of%20hardware%20electronic%20analogs%20of%20biological%20neural%20systems%20being%20proposed%20as%20well.%20However%2C%20for%20both%20biological%20and%20hardware%20systems%2C%20it%20is%20often%20difficult%20to%20estimate%20the%20parameters%20of%20the%20model%20so%20that%20they%20are%20meaningful%20to%20the%20experimental%20system%20under%20study%2C%20especially%20when%20these%20models%20involve%20a%20large%20number%20of%20states%20and%20parameters%20that%20cannot%20be%20simultaneously%20measured.%20We%20have%20developed%20a%20procedure%20to%20solve%20this%20problem%20in%20the%20context%20of%20interacting%20neural%20populations%20using%20a%20recently%20developed%20dynamic%20state%20and%20parameter%20estimation%20%28DSPE%29%20technique.%20This%20technique%20uses%20synchronization%20as%20a%20tool%20for%20dynamically%20coupling%20experimentally%20measured%20data%20to%20its%20corresponding%20model%20to%20determine%20its%20parameters%20and%20internal%20state%20variables.%20Typically%20experimental%20data%20are%20obtained%20from%20the%20biological%20neural%20system%20and%20the%20model%20is%20simulated%20in%20software%3B%20here%20we%20show%20that%20this%20technique%20is%20also%20efficient%20in%20validating%20proposed%20network%20models%20for%20neuromorphic%20spike-based%20very%20large-scale%20integration%20%28VLSI%29%20chips%20and%20that%20it%20is%20able%20to%20systematically%20extract%20network%20parameters%20such%20as%20synaptic%20weights%2C%20time%20constants%2C%20and%20other%20variables%20that%20are%20not%20accessible%20by%20direct%20observation.%20Our%20results%20suggest%20that%20this%20method%20can%20become%20a%20very%20useful%20tool%20formodel-based%20identification%20and%20configuration%20of%20neuromorphic%20multichip%20VLSI%20systems.%22%2C%22date%22%3A%22Jul%202012%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%22%22%2C%22ISSN%22%3A%220899-7667%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A02Z%22%7D%7D%2C%7B%22key%22%3A%22WPEJ734I%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Kostuk%20et%20al.%22%2C%22parsedDate%22%3A%222012-03%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EKostuk%2C%20M.%2C%20Toth%2C%20B.%20A.%2C%20Meliza%2C%20C.%20D.%2C%20Margoliash%2C%20D.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282012%29.%20Dynamical%20estimation%20of%20neuron%20and%20network%20properties%20II%3A%20path%20integral%20Monte%20Carlo%20methods.%20%3Ci%3EBiological%20Cybernetics%3C%5C%2Fi%3E%2C%20%3Ci%3E106%3C%5C%2Fi%3E%283%29%2C%20155%26%23x2013%3B167.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1007%5C%2Fs00422-012-0487-5%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1007%5C%2Fs00422-012-0487-5%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Dynamical%20estimation%20of%20neuron%20and%20network%20properties%20II%3A%20path%20integral%20Monte%20Carlo%20methods%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22M.%22%2C%22lastName%22%3A%22Kostuk%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22B.%20A.%22%2C%22lastName%22%3A%22Toth%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22C.%20D.%22%2C%22lastName%22%3A%22Meliza%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22D.%22%2C%22lastName%22%3A%22Margoliash%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22Hodgkin-Huxley%20%28HH%29%20models%20of%20neuronal%20membrane%20dynamics%20consist%20of%20a%20set%20of%20nonlinear%20differential%20equations%20that%20describe%20the%20time-varying%20conductance%20of%20various%20ion%20channels.%20Using%20observations%20of%20voltage%20alone%20we%20show%20how%20to%20estimate%20the%20unknown%20parameters%20and%20unobserved%20state%20variables%20of%20an%20HH%20model%20in%20the%20expected%20circumstance%20that%20the%20measurements%20are%20noisy%2C%20the%20model%20has%20errors%2C%20and%20the%20state%20of%20the%20neuron%20is%20not%20known%20when%20observations%20commence.%20The%20joint%20probability%20distribution%20of%20the%20observed%20membrane%20voltage%20and%20the%20unobserved%20state%20variables%20and%20parameters%20of%20these%20models%20is%20a%20path%20integral%20through%20the%20model%20state%20space.%20The%20solution%20to%20this%20integral%20allows%20estimation%20of%20the%20parameters%20and%20thus%20a%20characterization%20of%20many%20biological%20properties%20of%20interest%2C%20including%20channel%20complement%20and%20density%2C%20that%20give%20rise%20to%20a%20neuron%27s%20electrophysiological%20behavior.%20This%20paper%20describes%20a%20method%20for%20directly%20evaluating%20the%20path%20integral%20using%20a%20Monte%20Carlo%20numerical%20approach.%20This%20provides%20estimates%20not%20only%20of%20the%20expected%20values%20of%20model%20parameters%20but%20also%20of%20their%20posterior%20uncertainty.%20Using%20test%20data%20simulated%20from%20neuronal%20models%20comprising%20several%20common%20channels%2C%20we%20show%20that%20short%20%28%3C%2050%20ms%29%20intracellular%20recordings%20from%20neurons%20stimulated%20with%20a%20complex%20time-varying%20current%20yield%20accurate%20and%20precise%20estimates%20of%20the%20model%20parameters%20as%20well%20as%20accurate%20predictions%20of%20the%20future%20behavior%20of%20the%20neuron.%20We%20also%20show%20that%20this%20method%20is%20robust%20to%20errors%20in%20model%20specification%2C%20supporting%20model%20development%20for%20biological%20preparations%20in%20which%20the%20channel%20expression%20and%20other%20biophysical%20properties%20of%20the%20neurons%20are%20not%20fully%20known.%22%2C%22date%22%3A%22Mar%202012%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1007%5C%2Fs00422-012-0487-5%22%2C%22ISSN%22%3A%220340-1200%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A02Z%22%7D%7D%2C%7B%22key%22%3A%22UCMGH3TK%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Toth%20et%20al.%22%2C%22parsedDate%22%3A%222011-10%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EToth%2C%20B.%20A.%2C%20Kostuk%2C%20M.%2C%20Meliza%2C%20C.%20D.%2C%20Margoliash%2C%20D.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282011%29.%20Dynamical%20estimation%20of%20neuron%20and%20network%20properties%20I%3A%20variational%20methods.%20%3Ci%3EBiological%20Cybernetics%3C%5C%2Fi%3E%2C%20%3Ci%3E105%3C%5C%2Fi%3E%283%26%23x2013%3B4%29%2C%20217%26%23x2013%3B237.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1007%5C%2Fs00422-011-0459-1%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1007%5C%2Fs00422-011-0459-1%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Dynamical%20estimation%20of%20neuron%20and%20network%20properties%20I%3A%20variational%20methods%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22B.%20A.%22%2C%22lastName%22%3A%22Toth%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22M.%22%2C%22lastName%22%3A%22Kostuk%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22C.%20D.%22%2C%22lastName%22%3A%22Meliza%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22D.%22%2C%22lastName%22%3A%22Margoliash%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22We%20present%20a%20method%20for%20using%20measurements%20of%20membrane%20voltage%20in%20individual%20neurons%20to%20estimate%20the%20parameters%20and%20states%20of%20the%20voltage-gated%20ion%20channels%20underlying%20the%20dynamics%20of%20the%20neuron%27s%20behavior.%20Short%20injections%20of%20a%20complex%20time-varying%20current%20provide%20sufficient%20data%20to%20determine%20the%20reversal%20potentials%2C%20maximal%20conductances%2C%20and%20kinetic%20parameters%20of%20a%20diverse%20range%20of%20channels%2C%20representing%20tens%20of%20unknown%20parameters%20and%20many%20gating%20variables%20in%20a%20model%20of%20the%20neuron%27s%20behavior.%20These%20estimates%20are%20used%20to%20predict%20the%20response%20of%20the%20model%20at%20times%20beyond%20the%20observation%20window.%20This%20method%20of%20data%20assimilation%20extends%20to%20the%20general%20problem%20of%20determining%20model%20parameters%20and%20unobserved%20state%20variables%20from%20a%20sparse%20set%20of%20observations%2C%20and%20may%20be%20applicable%20to%20networks%20of%20neurons.%20We%20describe%20an%20exact%20formulation%20of%20the%20tasks%20in%20nonlinear%20data%20assimilation%20when%20one%20has%20noisy%20data%2C%20errors%20in%20the%20models%2C%20and%20incomplete%20information%20about%20the%20state%20of%20the%20system%20when%20observations%20commence.%20This%20is%20a%20high%20dimensional%20integral%20along%20the%20path%20of%20the%20model%20state%20through%20the%20observation%20window.%20In%20this%20article%2C%20a%20stationary%20path%20approximation%20to%20this%20integral%2C%20using%20a%20variational%20method%2C%20is%20described%20and%20tested%20employing%20data%20generated%20using%20neuronal%20models%20comprising%20several%20common%20channels%20with%20Hodgkin-Huxley%20dynamics.%20These%20numerical%20experiments%20reveal%20a%20number%20of%20practical%20considerations%20in%20designing%20stimulus%20currents%20and%20in%20determining%20model%20consistency.%20The%20tools%20explored%20here%20are%20computationally%20efficient%20and%20have%20paths%20to%20parallelization%20that%20should%20allow%20large%20individual%20neuron%20and%20network%20problems%20to%20be%20addressed.%22%2C%22date%22%3A%22Oct%202011%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1007%5C%2Fs00422-011-0459-1%22%2C%22ISSN%22%3A%220340-1200%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A02Z%22%7D%7D%2C%7B%22key%22%3A%225HNE7LC9%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Quinn%20and%20Abarbanel%22%2C%22parsedDate%22%3A%222011-09%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EQuinn%2C%20J.%20C.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282011%29.%20Data%20assimilation%20using%20a%20GPU%20accelerated%20path%20integral%20Monte%20Carlo%20approach.%20%3Ci%3EJournal%20of%20Computational%20Physics%3C%5C%2Fi%3E%2C%20%3Ci%3E230%3C%5C%2Fi%3E%2822%29%2C%208168%26%23x2013%3B8178.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1016%5C%2Fj.jcp.2011.07.015%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1016%5C%2Fj.jcp.2011.07.015%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Data%20assimilation%20using%20a%20GPU%20accelerated%20path%20integral%20Monte%20Carlo%20approach%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%20C.%22%2C%22lastName%22%3A%22Quinn%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22The%20answers%20to%20data%20assimilation%20questions%20can%20be%20expressed%20as%20path%20integrals%20over%20all%20possible%20state%20and%20parameter%20histories.%20We%20show%20how%20these%20path%20integrals%20can%20be%20evaluated%20numerically%20using%20a%20Markov%20Chain%20Monte%20Carlo%20method%20designed%20to%20run%20in%20parallel%20on%20a%20graphics%20processing%20unit%20%28GPU%29.%20We%20demonstrate%20the%20application%20of%20the%20method%20to%20an%20example%20with%20a%20transmembrane%20voltage%20time%20series%20of%20a%20simulated%20neuron%20as%20an%20input%2C%20and%20using%20a%20Hodgkin-Huxley%20neuron%20model.%20By%20taking%20advantage%20of%20GPU%20computing%2C%20we%20gain%20a%20parallel%20speedup%20factor%20of%20up%20to%20about%20300%2C%20compared%20to%20an%20equivalent%20serial%20computation%20on%20a%20CPU%2C%20with%20performance%20increasing%20as%20the%20length%20of%20the%20observation%20time%20used%20for%20data%20assimilation%20increases.%20%28C%29%202011%20Elsevier%20Inc.%20All%20rights%20reserved.%22%2C%22date%22%3A%22Sep%202011%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1016%5C%2Fj.jcp.2011.07.015%22%2C%22ISSN%22%3A%220021-9991%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A01Z%22%7D%7D%2C%7B%22key%22%3A%223GRFGYNY%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Haas%20et%20al.%22%2C%22parsedDate%22%3A%222010-12%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EHaas%2C%20J.%20S.%2C%20Kreuz%2C%20T.%2C%20Torcini%2C%20A.%2C%20Politi%2C%20A.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282010%29.%20Rate%20maintenance%20and%20resonance%20in%20the%20entorhinal%20cortex.%20%3Ci%3EEuropean%20Journal%20of%20Neuroscience%3C%5C%2Fi%3E%2C%20%3Ci%3E32%3C%5C%2Fi%3E%2811%29%2C%201930%26%23x2013%3B1939.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1111%5C%2Fj.1460-9568.2010.07455.x%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1111%5C%2Fj.1460-9568.2010.07455.x%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Rate%20maintenance%20and%20resonance%20in%20the%20entorhinal%20cortex%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%20S.%22%2C%22lastName%22%3A%22Haas%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22T.%22%2C%22lastName%22%3A%22Kreuz%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22A.%22%2C%22lastName%22%3A%22Torcini%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22A.%22%2C%22lastName%22%3A%22Politi%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22Throughout%20the%20brain%2C%20neurons%20encode%20information%20in%20fundamental%20units%20of%20spikes.%20Each%20spike%20represents%20the%20combined%20thresholding%20of%20synaptic%20inputs%20and%20intrinsic%20neuronal%20dynamics.%20Here%2C%20we%20address%20a%20basic%20question%20of%20spike%20train%20formation%3A%20how%20do%20perithreshold%20synaptic%20inputs%20perturb%20the%20output%20of%20a%20spiking%20neuron%3F%20We%20recorded%20from%20single%20entorhinal%20principal%20cells%20in%20vitro%20and%20drove%20them%20to%20spike%20steadily%20at%20similar%20to%205%20Hz%20%28theta%20range%29%20with%20direct%20current%20injection%2C%20then%20used%20a%20dynamic-clamp%20to%20superimpose%20strong%20excitatory%20conductance%20inputs%20at%20varying%20rates.%20Neurons%20spiked%20most%20reliably%20when%20the%20input%20rate%20matched%20the%20intrinsic%20neuronal%20firing%20rate.%20We%20also%20found%20a%20striking%20tendency%20of%20neurons%20to%20preserve%20their%20rates%20and%20coefficients%20of%20variation%2C%20independently%20of%20input%20rates.%20As%20mechanisms%20for%20this%20rate%20maintenance%2C%20we%20show%20that%20the%20efficacy%20of%20the%20conductance%20inputs%20varied%20with%20the%20relationship%20of%20input%20rate%20to%20neuronal%20firing%20rate%2C%20and%20with%20the%20arrival%20time%20of%20the%20input%20within%20the%20natural%20period.%20Using%20a%20novel%20method%20of%20spike%20classification%2C%20we%20developed%20a%20minimal%20Markov%20model%20that%20reproduced%20the%20measured%20statistics%20of%20the%20output%20spike%20trains%20and%20thus%20allowed%20us%20to%20identify%20and%20compare%20contributions%20to%20the%20rate%20maintenance%20and%20resonance.%20We%20suggest%20that%20the%20strength%20of%20rate%20maintenance%20may%20be%20used%20as%20a%20new%20categorization%20scheme%20for%20neuronal%20response%20and%20note%20that%20individual%20intrinsic%20spiking%20mechanisms%20may%20play%20a%20significant%20role%20in%20forming%20the%20rhythmic%20spike%20trains%20of%20activated%20neurons%3B%20in%20the%20entorhinal%20cortex%2C%20individual%20pacemakers%20may%20dominate%20production%20of%20the%20regional%20theta%20rhythm.%22%2C%22date%22%3A%22Dec%202010%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1111%5C%2Fj.1460-9568.2010.07455.x%22%2C%22ISSN%22%3A%220953-816X%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A07Z%22%7D%7D%2C%7B%22key%22%3A%222FUWM5WM%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Quinn%20and%20Abarbanel%22%2C%22parsedDate%22%3A%222010-10%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EQuinn%2C%20J.%20C.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282010%29.%20State%20and%20parameter%20estimation%20using%20Monte%20Carlo%20evaluation%20of%20path%20integrals.%20%3Ci%3EQuarterly%20Journal%20of%20the%20Royal%20Meteorological%20Society%3C%5C%2Fi%3E%2C%20%3Ci%3E136%3C%5C%2Fi%3E%28652%29%2C%201855%26%23x2013%3B1867.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1002%5C%2Fqj.690%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1002%5C%2Fqj.690%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22State%20and%20parameter%20estimation%20using%20Monte%20Carlo%20evaluation%20of%20path%20integrals%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%20C.%22%2C%22lastName%22%3A%22Quinn%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22The%20process%20of%20transferring%20information%20from%20observations%20of%20a%20dynamical%20system%20to%20estimate%20the%20fixed%20parameters%20and%20unobserved%20states%20of%20a%20system%20model%20can%20be%20formulated%20as%20the%20evaluation%20of%20a%20discrete-time%20path%20integral%20in%20model%20state%20space.%20The%20observations%20serve%20as%20a%20guiding%20%27potential%27%20working%20with%20the%20dynamical%20rules%20of%20the%20model%20to%20direct%20system%20orbits%20in%20state%20space.%20The%20path-integral%20representation%20permits%20direct%20numerical%20evaluation%20of%20the%20conditional%20mean%20path%20through%20the%20state%20space%20as%20well%20as%20conditional%20moments%20about%20this%20mean.%20Using%20a%20Monte%20Carlo%20method%20for%20selecting%20paths%20through%20state%20space%2C%20we%20show%20how%20these%20moments%20can%20be%20evaluated%20and%20demonstrate%20in%20an%20interesting%20model%20system%20the%20explicit%20influence%20of%20the%20role%20of%20transfer%20of%20information%20from%20the%20observations.%20We%20address%20the%20question%20of%20how%20many%20observations%20are%20required%20to%20estimate%20the%20unobserved%20state%20variables%2C%20and%20we%20examine%20the%20assumptions%20of%20Gaussianity%20of%20the%20underlying%20conditional%20probability.%20Copyright%20%28C%29%202010%20Royal%20Meteorological%20Society%22%2C%22date%22%3A%22Oct%202010%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1002%5C%2Fqj.690%22%2C%22ISSN%22%3A%220035-9009%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A09Z%22%7D%7D%2C%7B%22key%22%3A%2238GVUJ5N%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Abarbanel%20et%20al.%22%2C%22parsedDate%22%3A%222010-04%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3E%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%2C%20Kostuk%2C%20M.%2C%20%26amp%3B%20Whartenby%2C%20W.%20%282010%29.%20Data%20assimilation%20with%20regularized%20nonlinear%20instabilities.%20%3Ci%3EQuarterly%20Journal%20of%20the%20Royal%20Meteorological%20Society%3C%5C%2Fi%3E%2C%20%3Ci%3E136%3C%5C%2Fi%3E%28648%29%2C%20769%26%23x2013%3B783.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1002%5C%2Fqj.600%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1002%5C%2Fqj.600%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Data%20assimilation%20with%20regularized%20nonlinear%20instabilities%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22M.%22%2C%22lastName%22%3A%22Kostuk%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22W.%22%2C%22lastName%22%3A%22Whartenby%22%7D%5D%2C%22abstractNote%22%3A%22In%20variational%20formulations%20of%20data%20assimilation%2C%20the%20estimation%20of%20parameters%20or%20initial%20state%20values%20by%20a%20search%20for%20a%20minimum%20of%20a%20cost%20function%20can%20be%20hindered%20by%20the%20numerous%20local%20minima%20in%20the%20dependence%20of%20the%20cost%20function%20on%20those%20quantities.%20We%20argue%20that%20this%20is%20a%20result%20of%20instability%20on%20the%20synchronization%20manifold%20where%20the%20observations%20are%20required%20to%20match%20the%20model%20outputs%20in%20the%20situation%20where%20the%20data%20and%20the%20model%20are%20chaotic.%20The%20solution%20to%20this%20impediment%20to%20estimation%20is%20given%20as%20controls%20moving%20the%20positive%20conditional%20Lyapunov%20exponents%20on%20the%20synchronization%20manifold%20to%20negative%20values%20and%20adding%20to%20the%20cost%20function%20a%20penalty%20that%20drives%20those%20controls%20to%20zero%20as%20a%20result%20of%20the%20optimization%20process%20implementing%20the%20assimilation.%20This%20is%20seen%20as%20the%20solution%20to%20the%20proper%20size%20of%20%27nudging%27%20terms%3A%20they%20are%20zero%20once%20the%20estimation%20has%20been%20completed%2C%20leaving%20only%20the%20physics%20of%20the%20problem%20to%20govern%20forecasts%20after%20the%20assimilation%20window.%20We%20show%20how%20this%20procedure%2C%20called%20Dynamical%20State%20and%20Parameter%20Estimation%20%28DSPE%29%2C%20works%20in%20the%20case%20of%20the%20Lorenz96%20model%20with%20nine%20dynamical%20variables.%20Using%20DSPE%2C%20we%20are%20able%20to%20accurately%20estimate%20the%20fixed%20parameter%20of%20this%20model%20and%20all%20of%20the%20state%20variables%2C%20observed%20and%20unobserved%2C%20over%20an%20assimilation%20time%20interval%20%5B0%2C%20T%5D.%20Using%20the%20state%20variables%20at%20T%20and%20the%20estimated%20fixed%20parameter%2C%20we%20are%20able%20to%20accurately%20forecast%20the%20state%20of%20the%20model%20for%20t%20%3E%20T%20to%20those%20times%20where%20the%20chaotic%20behaviour%20of%20the%20system%20interferes%20with%20forecast%20accuracy.%20Copyright%20%28C%29%202010%20Royal%20Meteorological%20Society%22%2C%22date%22%3A%22Apr%202010%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1002%5C%2Fqj.600%22%2C%22ISSN%22%3A%220035-9009%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A01Z%22%7D%7D%2C%7B%22key%22%3A%22GLQ86WUI%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Kreuz%20et%20al.%22%2C%22parsedDate%22%3A%222009-10%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EKreuz%2C%20T.%2C%20Chicharro%2C%20D.%2C%20Andrzejak%2C%20R.%20G.%2C%20Haas%2C%20J.%20S.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282009%29.%20Measuring%20multiple%20spike%20train%20synchrony.%20%3Ci%3EJournal%20of%20Neuroscience%20Methods%3C%5C%2Fi%3E%2C%20%3Ci%3E183%3C%5C%2Fi%3E%282%29%2C%20287%26%23x2013%3B299.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1016%5C%2Fj.jneumeth.2009.06.039%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1016%5C%2Fj.jneumeth.2009.06.039%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Measuring%20multiple%20spike%20train%20synchrony%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22T.%22%2C%22lastName%22%3A%22Kreuz%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22D.%22%2C%22lastName%22%3A%22Chicharro%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22R.%20G.%22%2C%22lastName%22%3A%22Andrzejak%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%20S.%22%2C%22lastName%22%3A%22Haas%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22Measures%20of%20multiple%20spike%20train%20synchrony%20are%20essential%20in%20order%20to%20study%20issues%20such%20as%20spike%20timing%20reliability%2C%20network%20synchronization%2C%20and%20neuronal%20coding.%20These%20measures%20can%20broadly%20be%20divided%20in%20multivariate%20measures%20and%20averages%20over%20bivariate%20measures.%20One%20of%20the%20most%20recent%20bivariate%20approaches%2C%20the%20ISI-distance%2C%20employs%20the%20ratio%20of%20instantaneous%20interspike%20intervals%20%28ISIs%29.%20In%20this%20study%20we%20propose%20two%20extensions%20of%20the%20ISI-distance%2C%20the%20straightforward%20averaged%20bivariate%20ISI-distance%20and%20the%20multivariate%20ISI-diversity%20based%20on%20the%20coefficient%20of%20variation.%20Like%20the%20original%20measure%20these%20extensions%20combine%20many%20properties%20desirable%20in%20applications%20to%20real%20data.%20In%20particular%2C%20they%20are%20parameter-free%2C%20time%20scale%20independent%2C%20and%20easy%20to%20visualize%20in%20a%20time-resolved%20manner%2C%20as%20we%20illustrate%20with%20in%20vitro%20recordings%20from%20a%20cortical%20neuron.%20Using%20a%20simulated%20network%20of%20Hindemarsh-Rose%20neurons%20as%20a%20controlled%20configuration%20we%20compare%20the%20performance%20of%20our%20methods%20in%20distinguishing%20different%20levels%20of%20multi-neuron%20spike%20train%20synchrony%20to%20the%20performance%20of%20six%20other%20previously%20published%20measures.%20We%20show%20and%20explain%20why%20the%20averaged%20bivariate%20measures%20perform%20better%20than%20the%20multivariate%20ones%20and%20why%20the%20multivariate%20ISI-diversity%20is%20the%20best%20performer%20among%20the%20multivariate%20methods.%20Finally%2C%20in%20a%20comparison%20against%20standard%20methods%20that%20rely%20on%20moving%20window%20estimates%2C%20we%20use%20single-unit%20monkey%20data%20to%20demonstrate%20the%20advantages%20of%20the%20instantaneous%20nature%20of%20our%20methods.%20%28C%29%202009%20Elsevier%20B.V.%20All%20rights%20reserved.%22%2C%22date%22%3A%22Oct%202009%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1016%5C%2Fj.jneumeth.2009.06.039%22%2C%22ISSN%22%3A%220165-0270%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A05Z%22%7D%7D%2C%7B%22key%22%3A%22EZ3PD3K2%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Abarbanel%22%2C%22parsedDate%22%3A%222009-10%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3E%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282009%29.%20Effective%20actions%20for%20statistical%20data%20assimilation.%20%3Ci%3EPhysics%20Letters%20A%3C%5C%2Fi%3E%2C%20%3Ci%3E373%3C%5C%2Fi%3E%2844%29%2C%204044%26%23x2013%3B4048.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1016%5C%2Fj.physleta.2009.08.072%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1016%5C%2Fj.physleta.2009.08.072%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Effective%20actions%20for%20statistical%20data%20assimilation%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22Data%20assimilation%20is%20a%20problem%20in%20estimating%20the%20fixed%20parameters%20and%20state%20of%20a%20model%20of%20an%20observed%20dynamical%20system%20as%20it%20receives%20inputs%20from%20measurements%20passing%20information%20to%20the%20model.%20Using%20methods%20developed%20in%20statistical%20physics%2C%20we%20present%20effective%20actions%20and%20equations%20of%20motion%20for%20the%20mean%20orbits%20associated%20with%20the%20temporal%20development%20of%20a%20dynamical%20model%20when%20it%20has%20errors%2C%20there%20is%20uncertainty%20in%20its%20initial%20state%2C%20and%20it%20receives%20information%20from%20noisy%20measurements.%20If%20there%20are%20statistical%20dependences%20among%20errors%20in%20the%20measurements%20they%20can%20be%20included%20in%20this%20approach.%20%28C%29%202009%20Elsevier%20B.V.%20All%20rights%20reserved.%22%2C%22date%22%3A%22Oct%202009%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1016%5C%2Fj.physleta.2009.08.072%22%2C%22ISSN%22%3A%220375-9601%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A03Z%22%7D%7D%2C%7B%22key%22%3A%22W7SA973R%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Gibb%20et%20al.%22%2C%22parsedDate%22%3A%222009-09%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EGibb%2C%20L.%2C%20Gentner%2C%20T.%20Q.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282009%29.%20Inhibition%20and%20recurrent%20excitation%20in%20a%20computational%20model%20of%20sparse%20bursting%20in%20song%20nucleus%20HVC.%20%3Ci%3EJournal%20of%20Neurophysiology%3C%5C%2Fi%3E%2C%20%3Ci%3E102%3C%5C%2Fi%3E%283%29%2C%201748%26%23x2013%3B1762.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1152%5C%2Fjn.00670.2007%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1152%5C%2Fjn.00670.2007%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Inhibition%20and%20recurrent%20excitation%20in%20a%20computational%20model%20of%20sparse%20bursting%20in%20song%20nucleus%20HVC%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22L.%22%2C%22lastName%22%3A%22Gibb%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22T.%20Q.%22%2C%22lastName%22%3A%22Gentner%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22Gibb%20L%2C%20Gentner%20TQ%2C%20Abarbanel%20HDI.%20Inhibition%20and%20recurrent%20excitation%20in%20a%20computational%20model%20of%20sparse%20bursting%20in%20song%20nucleus%20HVC.%20J%20Neurophysiol%20102%3A%201748-1762%2C%202009.%20First%20published%20June%2010%2C%202009%3B%20doi%3A10.1152%5C%2Fjn.00670.2007.%20The%20telencephalic%20premotor%20nucleus%20HVC%20is%20situated%20at%20a%20critical%20point%20in%20the%20pattern-generating%20premotor%20circuitry%20of%20oscine%20songbirds.%20A%20striking%20feature%20of%20HVC%27s%20premotor%20activity%20is%20that%20its%20projection%20neurons%20burst%20extremely%20sparsely.%20Here%20we%20present%20a%20computational%20model%20of%20HVC%20embodying%20several%20central%20hypotheses%3A%201%29%20sparse%20bursting%20is%20generated%20in%20bistable%20groups%20of%20recurrently%20connected%20robust%20nucleus%20of%20the%20arcopallium%20%28RA%29-%20projecting%20%28HVC%28RA%29%29%20neurons%3B%202%29%20inhibitory%20interneurons%20terminate%20bursts%20in%20the%20HVC%28RA%29%20groups%3B%20and%203%29%20sparse%20sequences%20of%20bursts%20are%20generated%20by%20the%20propagation%20of%20waves%20of%20bursting%20activity%20along%20networks%20of%20HVC%28RA%29%20neurons.%20Our%20model%20of%20sparse%20bursting%20places%20HVC%20in%20the%20context%20of%20central%20pattern%20generators%20and%20cortical%20networks%20using%20inhibition%2C%20recurrent%20excitation%2C%20and%20bistability.%20Importantly%2C%20the%20unintuitive%20result%20that%20inhibitory%20interneurons%20can%20precisely%20terminate%20the%20bursts%20of%20HVC%28RA%29%20groups%20while%20showing%20relatively%20sustained%20activity%20throughout%20the%20song%20is%20made%20possible%20by%20a%20specific%20constraint%20on%20their%20connectivity.%20We%20use%20the%20model%20to%20make%20novel%20predictions%20that%20can%20be%20tested%20experimentally.%22%2C%22date%22%3A%22Sep%202009%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1152%5C%2Fjn.00670.2007%22%2C%22ISSN%22%3A%220022-3077%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A04Z%22%7D%7D%2C%7B%22key%22%3A%228TF7248P%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Gibb%20et%20al.%22%2C%22parsedDate%22%3A%222009-09%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EGibb%2C%20L.%2C%20Gentner%2C%20T.%20Q.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282009%29.%20Brain%20stem%20feedback%20in%20a%20computational%20model%20of%20birdsong%20sequencing.%20%3Ci%3EJournal%20of%20Neurophysiology%3C%5C%2Fi%3E%2C%20%3Ci%3E102%3C%5C%2Fi%3E%283%29%2C%201763%26%23x2013%3B1778.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1152%5C%2Fjn.91154.2008%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1152%5C%2Fjn.91154.2008%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Brain%20stem%20feedback%20in%20a%20computational%20model%20of%20birdsong%20sequencing%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22L.%22%2C%22lastName%22%3A%22Gibb%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22T.%20Q.%22%2C%22lastName%22%3A%22Gentner%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22Gibb%20L%2C%20Gentner%20TQ%2C%20Abarbanel%20HDI.%20Brain%20stem%20feedback%20in%20a%20computational%20model%20of%20birdsong%20sequencing.%20J%20Neurophysiol%20102%3A%201763-1778%2C%202009.%20First%20published%20June%2024%2C%202009%3B%20doi%3A10.1152%5C%2Fjn.91154.2008.%20Uncovering%20the%20roles%20of%20neural%20feedback%20in%20the%20brain%20is%20an%20active%20area%20of%20experimental%20research.%20In%20songbirds%2C%20the%20telencephalic%20premotor%20nucleus%20HVC%20receives%20neural%20feedback%20from%20both%20forebrain%20and%20brain%20stem%20areas.%20Here%20we%20present%20a%20computational%20model%20of%20birdsong%20sequencing%20that%20incorporates%20HVC%20and%20associated%20nuclei%20and%20builds%20on%20the%20model%20of%20sparse%20bursting%20presented%20in%20our%20preceding%20companion%20paper.%20Our%20model%20embodies%20the%20hypotheses%20that%201%29%20different%20networks%20in%20HVC%20control%20different%20syllables%20or%20notes%20of%20birdsong%2C%202%29%20interneurons%20in%20HVC%20not%20only%20participate%20in%20sparse%20bursting%20but%20also%20provide%20mutual%20inhibition%20between%20networks%20controlling%20syllables%20or%20notes%2C%20and%203%29%20these%20syllable%20networks%20are%20sequentially%20excited%20by%20neural%20feedback%20via%20the%20brain%20stem%20and%20the%20afferent%20thalamic%20nucleus%20Uva%2C%20or%20a%20similar%20feedback%20pathway.%20We%20discuss%20the%20model%27s%20ability%20to%20unify%20physiological%2C%20behavioral%2C%20and%20lesion%20results%20and%20we%20use%20it%20to%20make%20novel%20predictions%20that%20can%20be%20tested%20experimentally.%20The%20model%20suggests%20a%20neural%20basis%20for%20sequence%20variations%2C%20shows%20that%20stimulation%20in%20the%20feedback%20pathway%20may%20have%20different%20effects%20depending%20on%20the%20balance%20of%20excitation%20and%20inhibition%20at%20the%20input%20to%20HVC%20from%20Uva%2C%20and%20predicts%20deviations%20from%20uniform%20expansion%20of%20syllables%20and%20gaps%20during%20HVC%20cooling.%22%2C%22date%22%3A%22Sep%202009%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1152%5C%2Fjn.91154.2008%22%2C%22ISSN%22%3A%220022-3077%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A01Z%22%7D%7D%2C%7B%22key%22%3A%22ZDY9T49J%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Quinn%20et%20al.%22%2C%22parsedDate%22%3A%222009-07%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EQuinn%2C%20J.%20C.%2C%20Bryant%2C%20P.%20H.%2C%20Creveling%2C%20D.%20R.%2C%20Klein%2C%20S.%20R.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282009%29.%20Parameter%20and%20state%20estimation%20of%20experimental%20chaotic%20systems%20using%20synchronization.%20%3Ci%3EPhysical%20Review%20E%3C%5C%2Fi%3E%2C%20%3Ci%3E80%3C%5C%2Fi%3E%281%29.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1103%5C%2FPhysRevE.80.016201%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1103%5C%2FPhysRevE.80.016201%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Parameter%20and%20state%20estimation%20of%20experimental%20chaotic%20systems%20using%20synchronization%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%20C.%22%2C%22lastName%22%3A%22Quinn%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22P.%20H.%22%2C%22lastName%22%3A%22Bryant%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22D.%20R.%22%2C%22lastName%22%3A%22Creveling%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22S.%20R.%22%2C%22lastName%22%3A%22Klein%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22We%20examine%20the%20use%20of%20synchronization%20as%20a%20mechanism%20for%20extracting%20parameter%20and%20state%20information%20from%20experimental%20systems.%20We%20focus%20on%20important%20aspects%20of%20this%20problem%20that%20have%20received%20little%20attention%20previously%20and%20we%20explore%20them%20using%20experiments%20and%20simulations%20with%20the%20chaotic%20Colpitts%20oscillator%20as%20an%20example%20system.%20We%20explore%20the%20impact%20of%20model%20imperfection%20on%20the%20ability%20to%20extract%20valid%20information%20from%20an%20experimental%20system.%20We%20compare%20two%20optimization%20methods%3A%20an%20initial%20value%20method%20and%20a%20constrained%20method.%20Each%20of%20these%20involves%20coupling%20the%20model%20equations%20to%20the%20experimental%20data%20in%20order%20to%20regularize%20the%20chaotic%20motions%20on%20the%20synchronization%20manifold.%20We%20explore%20both%20time-dependent%20and%20time-independent%20coupling%20and%20discuss%20the%20use%20of%20periodic%20impulse%20coupling.%20We%20also%20examine%20both%20optimized%20and%20fixed%20%28or%20manually%20adjusted%29%20coupling.%20For%20the%20case%20of%20an%20optimized%20time-dependent%20coupling%20function%20u%28t%29%20we%20find%20a%20robust%20structure%20which%20includes%20sharp%20peaks%20and%20intervals%20where%20it%20is%20zero.%20This%20structure%20shows%20a%20strong%20correlation%20with%20the%20location%20in%20phase%20space%20and%20appears%20to%20depend%20on%20noise%2C%20imperfections%20of%20the%20model%2C%20and%20the%20Lyapunov%20direction%20vectors.%20For%20time-independent%20coupling%20we%20find%20the%20counterintuitive%20result%20that%20often%20the%20optimal%20rms%20error%20in%20fitting%20the%20model%20to%20the%20data%20initially%20increases%20with%20coupling%20strength.%20Comparison%20of%20this%20result%20with%20that%20obtained%20using%20simulated%20data%20may%20provide%20one%20measure%20of%20model%20imperfection.%20The%20constrained%20method%20with%20time-dependent%20coupling%20appears%20to%20have%20benefits%20in%20synchronizing%20long%20data%20sets%20with%20minimal%20impact%2C%20while%20the%20initial%20value%20method%20with%20time-independent%20coupling%20tends%20to%20be%20substantially%20faster%2C%20more%20flexible%2C%20and%20easier%20to%20use.%20We%20also%20describe%20a%20method%20of%20coupling%20which%20is%20useful%20for%20sparse%20experimental%20data%20sets.%20Our%20use%20of%20the%20Colpitts%20oscillator%20allows%20us%20to%20explore%20in%20detail%20the%20case%20of%20a%20system%20with%20one%20positive%20Lyapunov%20exponent.%20The%20methods%20we%20explored%20are%20easily%20extended%20to%20driven%20systems%20such%20as%20neurons%20with%20time-dependent%20injected%20current.%20They%20are%20expected%20to%20be%20of%20value%20in%20nonchaotic%20systems%20as%20well.%20Software%20is%20available%20on%20request.%22%2C%22date%22%3A%22Jul%202009%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1103%5C%2FPhysRevE.80.016201%22%2C%22ISSN%22%3A%221539-3755%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A07Z%22%7D%7D%2C%7B%22key%22%3A%223297BR3B%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Muezzinoglu%20et%20al.%22%2C%22parsedDate%22%3A%222009-04%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EMuezzinoglu%2C%20M.%20K.%2C%20Huerta%2C%20R.%2C%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%2C%20Ryan%2C%20M.%20A.%2C%20%26amp%3B%20Rabinovich%2C%20M.%20I.%20%282009%29.%20Chemosensor-driven%20artificial%20antennal%20lobe%20transient%20dynamics%20enable%20fast%20recognition%20and%20working%20memory.%20%3Ci%3ENeural%20Computation%3C%5C%2Fi%3E%2C%20%3Ci%3E21%3C%5C%2Fi%3E%284%29%2C%201018%26%23x2013%3B1037.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1162%5C%2Fneco.2008.05-08-780%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1162%5C%2Fneco.2008.05-08-780%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Chemosensor-driven%20artificial%20antennal%20lobe%20transient%20dynamics%20enable%20fast%20recognition%20and%20working%20memory%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22M.%20K.%22%2C%22lastName%22%3A%22Muezzinoglu%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22R.%22%2C%22lastName%22%3A%22Huerta%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22M.%20A.%22%2C%22lastName%22%3A%22Ryan%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22M.%20I.%22%2C%22lastName%22%3A%22Rabinovich%22%7D%5D%2C%22abstractNote%22%3A%22The%20speed%20and%20accuracy%20of%20odor%20recognition%20in%20insects%20can%20hardly%20be%20resolved%20by%20the%20raw%20descriptors%20provided%20by%20olfactory%20receptors%20alone%20due%20to%20their%20slow%20time%20constant%20and%20high%20variability.%20The%20animal%20overcomes%20these%20barriers%20by%20means%20of%20the%20antennal%20lobe%20%28AL%29%20dynamics%2C%20which%20consolidates%20the%20classificatory%20information%20in%20receptor%20signal%20with%20a%20spatiotemporal%20code%20that%20is%20enriched%20in%20odor%20sensitivity%2C%20particularly%20in%20its%20transient.%20Inspired%20by%20this%20fact%2C%20we%20propose%20an%20easily%20implementable%20AL-like%20network%20and%20show%20that%20it%20significantly%20expedites%20and%20enhances%20the%20identification%20of%20odors%20from%20slow%20and%20noisy%20artificial%20polymer%20sensor%20responses.%20The%20device%20owes%20its%20efficiency%20to%20two%20intrinsic%20mechanisms%3A%20inhibition%20%28%20which%20triggers%20a%20competition%29%20and%20integration%20%28%20due%20to%20the%20dynamical%20nature%20of%20the%20network%29.%20The%20former%20functions%20as%20a%20sharpening%20filter%20extracting%20the%20features%20of%20receptor%20signal%20that%20favor%20odor%20separation%2C%20whereas%20the%20latter%20implements%20a%20working%20memory%20by%20accumulating%20the%20extracted%20features%20in%20trajectories.%20This%20cooperation%20boosts%20the%20odor%20specificity%20during%20the%20receptor%20transient%2C%20which%20is%20essential%20for%20fast%20odor%20recognition.%22%2C%22date%22%3A%22Apr%202009%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1162%5C%2Fneco.2008.05-08-780%22%2C%22ISSN%22%3A%220899-7667%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A01Z%22%7D%7D%2C%7B%22key%22%3A%22C5H2HG9E%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Muezzinoglu%20et%20al.%22%2C%22parsedDate%22%3A%222009-04%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EMuezzinoglu%2C%20M.%20K.%2C%20Vergara%2C%20A.%2C%20Huerta%2C%20R.%2C%20Rulkov%2C%20N.%2C%20Rabinovich%2C%20M.%20I.%2C%20Selverston%2C%20A.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282009%29.%20Acceleration%20of%20chemo-sensory%20information%20processing%20using%20transient%20features.%20%3Ci%3ESensors%20and%20Actuators%20B-Chemical%3C%5C%2Fi%3E%2C%20%3Ci%3E137%3C%5C%2Fi%3E%282%29%2C%20507%26%23x2013%3B512.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1016%5C%2Fj.snb.2008.10.065%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1016%5C%2Fj.snb.2008.10.065%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Acceleration%20of%20chemo-sensory%20information%20processing%20using%20transient%20features%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22M.%20K.%22%2C%22lastName%22%3A%22Muezzinoglu%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22A.%22%2C%22lastName%22%3A%22Vergara%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22R.%22%2C%22lastName%22%3A%22Huerta%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22N.%22%2C%22lastName%22%3A%22Rulkov%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22M.%20I.%22%2C%22lastName%22%3A%22Rabinovich%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22A.%22%2C%22lastName%22%3A%22Selverston%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22A%20snapshot%20from%20the%20steady-state%20response%20of%20chemical%20sensors%20conveys%2C%20on%20average%2C%20more%20mature%20and%20relevant%20information%20regarding%20the%20analyte%20than%20a%20snapshot%20from%20the%20transient%20can%20provide.%20Nevertheless%2C%20time%20constraints%20in%20many%20applications%20make%20it%20infeasible%20to%20wait%20for%20and%20extract%20steady-state%20features.%20Substituting%20them%20by%20transient%20ones%20is%20the%20only%20viable%20solution%20to%20accelerate%20odor%20processing.%20Based%20on%20measurements%20recorded%20from%20metal-oxide%20sensors%2C%20we%20point%20to%20a%20correlation%20between%20a%20transient%20feature%20and%20the%20steady-state%20resistance%20that%20are%20observed%20in%20response%20to%20fixed%20analyte%20concentration.%20We%20utilize%20this%20correlation%20to%20expedite%20standard%20quantification%20and%20classification%20substantially%20while%20ensuring%20the%20performance%20that%20the%20steady-state%20feature%20can%20provide.%20%28C%29%202008%20Elsevier%20B.V.%20All%20rights%20reserved.%22%2C%22date%22%3A%22Apr%202009%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1016%5C%2Fj.snb.2008.10.065%22%2C%22ISSN%22%3A%220925-4005%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A00Z%22%7D%7D%2C%7B%22key%22%3A%22LNUS7TFL%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Abarbanel%20et%20al.%22%2C%22parsedDate%22%3A%222009%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3E%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%2C%20Creveling%2C%20D.%20R.%2C%20Farsian%2C%20R.%2C%20%26amp%3B%20Kostuk%2C%20M.%20%282009%29.%20Dynamical%20state%20and%20parameter%20estimation.%20%3Ci%3ESIAM%20Journal%20on%20Applied%20Dynamical%20Systems%3C%5C%2Fi%3E%2C%20%3Ci%3E8%3C%5C%2Fi%3E%284%29%2C%201341%26%23x2013%3B1381.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1137%5C%2F090749761%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1137%5C%2F090749761%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Dynamical%20state%20and%20parameter%20estimation%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22D.%20R.%22%2C%22lastName%22%3A%22Creveling%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22R.%22%2C%22lastName%22%3A%22Farsian%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22M.%22%2C%22lastName%22%3A%22Kostuk%22%7D%5D%2C%22abstractNote%22%3A%22We%20discuss%20the%20problem%20of%20determining%20unknown%20fixed%20parameters%20and%20unobserved%20state%20variables%20in%20nonlinear%20models%20of%20a%20dynamical%20system%20using%20observed%20time%20series%20data%20from%20that%20system.%20In%20dynamical%20terms%20this%20requires%20synchronization%20of%20the%20experimental%20data%20with%20time%20series%20output%20from%20a%20model.%20If%20the%20model%20and%20the%20experimental%20system%20are%20chaotic%2C%20the%20synchronization%20manifold%2C%20where%20the%20data%20time%20series%20is%20equal%20to%20the%20model%20time%20series%2C%20may%20be%20unstable.%20If%20this%20occurs%2C%20then%20small%20perturbations%20in%20parameters%20or%20state%20variables%20can%20lead%20to%20large%20excursions%20near%20the%20synchronization%20manifold%20and%20produce%20a%20very%20complex%20surface%20in%20any%20estimation%20metric%20for%20those%20quantities.%20Coupling%20the%20experimental%20information%20to%20the%20model%20dynamics%20can%20lead%20to%20a%20stabilization%20of%20this%20manifold%20by%20reducing%20a%20positive%20conditional%20Lyapunov%20exponent%20%28CLE%29%20to%20a%20negative%20value.%20An%20approach%20called%20dynamical%20parameter%20estimation%20%28DPE%29%20addresses%20these%20instabilities%20and%20regularizes%20them%2C%20allowing%20for%20smooth%20surfaces%20in%20the%20space%20of%20parameters%20and%20initial%20conditions.%20DPE%20acts%20as%20an%20observer%20in%20the%20control%20systems%20sense%2C%20and%20because%20the%20control%20is%20systematically%20removed%20through%20an%20optimization%20process%2C%20it%20acts%20as%20an%20estimator%20of%20the%20unknown%20model%20parameters%20for%20the%20desired%20physical%20model%20without%20external%20control.%20Examples%20are%20given%20from%20several%20systems%20including%20an%20electronic%20oscillator%2C%20a%20neuron%20model%2C%20and%20a%20very%20simple%20geophysical%20model.%20In%20networks%20and%20larger%20dynamical%20models%20one%20may%20encounter%20many%20positive%20CLEs%2C%20and%20we%20investigate%20a%20general%20approach%20for%20estimating%20fixed%20model%20parameters%20and%20unobserved%20system%20states%20in%20this%20situation.%22%2C%22date%22%3A%222009%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1137%5C%2F090749761%22%2C%22ISSN%22%3A%221536-0040%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A03Z%22%7D%7D%2C%7B%22key%22%3A%22NRBZL5EZ%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Talathi%20et%20al.%22%2C%22parsedDate%22%3A%222008-09%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3ETalathi%2C%20S.%20S.%2C%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%2C%20%26amp%3B%20Ditto%2C%20W.%20L.%20%282008%29.%20Temporal%20spike%20pattern%20learning.%20%3Ci%3EPhysical%20Review%20E%3C%5C%2Fi%3E%2C%20%3Ci%3E78%3C%5C%2Fi%3E%283%29.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1103%5C%2FPhysRevE.78.031918%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1103%5C%2FPhysRevE.78.031918%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Temporal%20spike%20pattern%20learning%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22S.%20S.%22%2C%22lastName%22%3A%22Talathi%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22W.%20L.%22%2C%22lastName%22%3A%22Ditto%22%7D%5D%2C%22abstractNote%22%3A%22Sensory%20systems%20pass%20information%20about%20an%20animal%27s%20environment%20to%20higher%20nervous%20system%20units%20through%20sequences%20of%20action%20potentials.%20When%20these%20action%20potentials%20have%20essentially%20equivalent%20wave%20forms%2C%20all%20information%20is%20contained%20in%20the%20interspike%20intervals%20%28ISIs%29%20of%20the%20spike%20sequence.%20How%20do%20neural%20circuits%20recognize%20and%20read%20these%20ISI%20sequences%3F%20We%20address%20this%20issue%20of%20temporal%20sequence%20learning%20by%20a%20neuronal%20system%20utilizing%20spike%20timing%20dependent%20plasticity%20%28STDP%29.%20We%20present%20a%20general%20architecture%20of%20neural%20circuitry%20that%20can%20perform%20the%20task%20of%20ISI%20recognition.%20The%20essential%20ingredients%20of%20this%20neural%20circuit%2C%20which%20we%20refer%20to%20as%20%5C%22interspike%20interval%20recognition%20unit%5C%22%20%28IRU%29%20are%20%28i%29%20a%20spike%20selection%20unit%2C%20the%20function%20of%20which%20is%20to%20selectively%20distribute%20input%20spikes%20to%20downstream%20IRU%20circuitry%3B%20%28ii%29%20a%20time-delay%20unit%20that%20can%20be%20tuned%20by%20STDP%3B%20and%20%28iii%29%20a%20detection%20unit%2C%20which%20is%20the%20output%20of%20the%20IRU%20and%20a%20spike%20from%20which%20indicates%20successful%20ISI%20recognition%20by%20the%20IRU.%20We%20present%20two%20distinct%20configurations%20for%20the%20time-delay%20circuit%20within%20the%20IRU%20using%20excitatory%20and%20inhibitory%20synapses%2C%20respectively%2C%20to%20produce%20a%20delayed%20output%20spike%20at%20time%20t%280%29%2Btau%28R%29%20in%20response%20to%20the%20input%20spike%20received%20at%20time%20t%280%29.%20R%20is%20the%20tunable%20parameter%20of%20the%20time-delay%20circuit%20that%20controls%20the%20timing%20of%20the%20delayed%20output%20spike.%20We%20discuss%20the%20forms%20of%20STDP%20rules%20for%20excitatory%20and%20inhibitory%20synapses%2C%20respectively%2C%20that%20allow%20for%20modulation%20of%20R%20for%20the%20IRU%20to%20perform%20its%20task%20of%20ISI%20recognition.%20We%20then%20present%20two%20specific%20implementations%20for%20the%20IRU%20circuitry%2C%20derived%20from%20the%20general%20architecture%20that%20can%20both%20learn%20the%20ISIs%20of%20a%20training%20sequence%20and%20then%20recognize%20the%20same%20ISI%20sequence%20when%20it%20is%20presented%20on%20subsequent%20occasions.%22%2C%22date%22%3A%22Sep%202008%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1103%5C%2FPhysRevE.78.031918%22%2C%22ISSN%22%3A%221539-3755%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A10Z%22%7D%7D%2C%7B%22key%22%3A%22GLWCIJKZ%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Creveling%20et%20al.%22%2C%22parsedDate%22%3A%222008-04%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3ECreveling%2C%20D.%20R.%2C%20Gill%2C%20P.%20E.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282008%29.%20State%20and%20parameter%20estimation%20in%20nonlinear%20systems%20as%20an%20optimal%20tracking%20problem.%20%3Ci%3EPhysics%20Letters%20A%3C%5C%2Fi%3E%2C%20%3Ci%3E372%3C%5C%2Fi%3E%2815%29%2C%202640%26%23x2013%3B2644.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1016%5C%2Fj.physleta.2007.12.051%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1016%5C%2Fj.physleta.2007.12.051%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22State%20and%20parameter%20estimation%20in%20nonlinear%20systems%20as%20an%20optimal%20tracking%20problem%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22D.%20R.%22%2C%22lastName%22%3A%22Creveling%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22P.%20E.%22%2C%22lastName%22%3A%22Gill%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22In%20verifying%20and%20validating%20models%20of%20nonlinear%20processes%20it%20is%20important%20to%20incorporate%20information%20from%20observations%20in%20an%20efficient%20manner.%20Using%20the%20idea%20of%20synchronization%20of%20nonlinear%20dynamical%20systems%2C%20we%20present%20a%20framework%20for%20connecting%20a%20data%20signal%20with%20a%20model%20in%20a%20way%20that%20minimizes%20the%20required%20coupling%20yet%20allows%20the%20estimation%20of%20unknown%20parameters%20in%20the%20model.%20The%20need%20to%20evaluate%20unknown%20parameters%20in%20models%20of%20nonlinear%20physical%2C%20biophysical%2C%20and%20engineering%20systems%20occurs%20throughout%20the%20development%20of%20phenomenological%20or%20reduced%20models%20of%20dynamics.%20Our%20approach%20builds%20on%20existing%20work%20that%20uses%20synchronization%20as%20a%20tool%20for%20parameter%20estimation.%20We%20address%20some%20of%20the%20critical%20issues%20in%20that%20work%20and%20provide%20a%20practical%20framework%20for%20finding%20an%20accurate%20solution.%20In%20particular%2C%20we%20show%20the%20equivalence%20of%20this%20problem%20to%20that%20of%20tracking%20within%20an%20optimal%20control%20framework.%20This%20equivalence%20allows%20the%20application%20of%20powerful%20numerical%20methods%20that%20provide%20robust%20practical%20tools%20for%20model%20development%20and%20validation.%20%28c%29%202007%20Elsevier%20B.V%20All%20rights%20reserved.%22%2C%22date%22%3A%22Apr%202008%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1016%5C%2Fj.physleta.2007.12.051%22%2C%22ISSN%22%3A%220375-9601%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A09Z%22%7D%7D%2C%7B%22key%22%3A%22XMC3RXMA%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Creveling%20et%20al.%22%2C%22parsedDate%22%3A%222008-03%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3ECreveling%2C%20D.%20R.%2C%20Jeanne%2C%20J.%20M.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282008%29.%20Parameter%20estimation%20using%20balanced%20synchronization.%20%3Ci%3EPhysics%20Letters%20A%3C%5C%2Fi%3E%2C%20%3Ci%3E372%3C%5C%2Fi%3E%2812%29%2C%202043%26%23x2013%3B2047.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1016%5C%2Fj.physleta.2007.10.097%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1016%5C%2Fj.physleta.2007.10.097%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Parameter%20estimation%20using%20balanced%20synchronization%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22D.%20R.%22%2C%22lastName%22%3A%22Creveling%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%20M.%22%2C%22lastName%22%3A%22Jeanne%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22Synchronization%20between%20experimental%20observations%20and%20a%20dynamical%20model%20with%20undetermined%20parameters%20can%20assist%20in%20completing%20the%20specification%20of%20the%20model%20parameters.%20The%20quality%20of%20the%20synchronization%2C%20a%20cost%20function%20to%20be%20minimized%2C%20typically%20depends%20on%20the%20difference%20between%20the%20data%20time%20series%20and%20the%20model%20time%20series.%20If%20the%20coupling%20between%20the%20data%20and%20the%20model%20is%20too%20strong%2C%20this%20cost%20function%20is%20small%20for%20any%20data%20and%20any%20model%2C%20and%20the%20variation%20of%20the%20cost%20function%20with%20respect%20to%20the%20parameters%20of%20interest%20is%20too%20small%20to%20permit%20selection%20of%20a%20value%20of%20the%20parameters.%20If%20the%20coupling%20is%20too%20small%2C%20synchronization%20is%20lost.%20We%20introduce%20two%20methods%20for%20balancing%20the%20competing%20desires%20of%20a%20small%20cost%20function%20and%20the%20numerical%20ability%20to%20determine%20parameters%20accurately.%20One%20method%20of%20%27balanced%27%20synchronization%20adds%20a%20requirement%20that%20the%20conditional%20Lyapunov%20exponent%20of%20the%20model%20system%2C%20conditioned%20on%20being%20driven%20by%20the%20data%2C%20remain%20negative%20but%20small.%20The%20other%20method%20allows%20the%20coupling%20to%20vary%20in%20time%20according%20to%20the%20error%20in%20synchronization.%20This%20second%20method%20succeeds%20because%20the%20data%20and%20the%20model%20exhibit%20generalized%20synchronization%20in%20the%20region%20where%20the%20parameters%20of%20the%20model%20are%20well%20determined.%20%28c%29%202007%20Elsevier%20B.V.%20All%20rights%20reserved.%22%2C%22date%22%3A%22Mar%202008%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1016%5C%2Fj.physleta.2007.10.097%22%2C%22ISSN%22%3A%220375-9601%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A07Z%22%7D%7D%2C%7B%22key%22%3A%22SJ5NXRDD%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Abarbanel%20et%20al.%22%2C%22parsedDate%22%3A%222008-01%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3E%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%2C%20Creveling%2C%20D.%20R.%2C%20%26amp%3B%20Jeanne%2C%20J.%20M.%20%282008%29.%20Estimation%20of%20parameters%20in%20nonlinear%20systems%20using%20balanced%20synchronization.%20%3Ci%3EPhysical%20Review%20E%3C%5C%2Fi%3E%2C%20%3Ci%3E77%3C%5C%2Fi%3E%281%29.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1103%5C%2FPhysRevE.77.016208%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1103%5C%2FPhysRevE.77.016208%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Estimation%20of%20parameters%20in%20nonlinear%20systems%20using%20balanced%20synchronization%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22D.%20R.%22%2C%22lastName%22%3A%22Creveling%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%20M.%22%2C%22lastName%22%3A%22Jeanne%22%7D%5D%2C%22abstractNote%22%3A%22Using%20synchronization%20between%20observations%20and%20a%20model%20with%20undetermined%20parameters%20is%20a%20natural%20way%20to%20complete%20the%20specification%20of%20the%20model.%20The%20quality%20of%20the%20synchronization%2C%20a%20cost%20function%20to%20be%20minimized%2C%20typically%20is%20evaluated%20by%20a%20least%20squares%20difference%20between%20the%20data%20time%20series%20and%20the%20model%20time%20series.%20If%20the%20coupling%20between%20the%20data%20and%20the%20model%20is%20too%20strong%2C%20this%20cost%20function%20is%20small%20for%20any%20data%20and%20any%20model%20and%20the%20variation%20of%20the%20cost%20function%20with%20respect%20to%20the%20parameters%20of%20interest%20is%20too%20small%20to%20permit%20selection%20of%20an%20optimal%20value%20of%20the%20parameters.%20We%20introduce%20two%20methods%20for%20balancing%20the%20competing%20desires%20of%20a%20small%20cost%20function%20for%20the%20quality%20of%20the%20synchronization%20and%20the%20numerical%20ability%20to%20determine%20parameters%20accurately.%20One%20method%20of%20%5C%22balanced%5C%22%20synchronization%20adds%20to%20the%20synchronization%20cost%20function%20a%20requirement%20that%20the%20conditional%20Lyapunov%20exponent%20of%20the%20model%20system%2C%20conditioned%20on%20being%20driven%20by%20the%20data%20remain%20negative%20but%20small%20in%20magnitude.%20The%20other%20method%20allows%20the%20coupling%20between%20the%20data%20and%20the%20model%20to%20vary%20in%20time%20according%20to%20the%20error%20in%20synchronization.%20This%20method%20succeeds%20because%20the%20data%20and%20the%20model%20exhibit%20generalized%20synchronization%20in%20the%20region%20where%20the%20parameters%20of%20the%20model%20are%20well%20determined.%20Examples%20are%20explored%20which%20have%20deterministic%20chaos%20with%20and%20without%20noise%20in%20the%20data%20signal.%22%2C%22date%22%3A%22Jan%202008%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1103%5C%2FPhysRevE.77.016208%22%2C%22ISSN%22%3A%221539-3755%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A03Z%22%7D%7D%2C%7B%22key%22%3A%22FI4JEHAS%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Kreuz%20et%20al.%22%2C%22parsedDate%22%3A%222007-09%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EKreuz%2C%20T.%2C%20Haas%2C%20J.%20S.%2C%20Morelli%2C%20A.%2C%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%2C%20%26amp%3B%20Politi%2C%20A.%20%282007%29.%20Measuring%20spike%20train%20synchrony.%20%3Ci%3EJournal%20of%20Neuroscience%20Methods%3C%5C%2Fi%3E%2C%20%3Ci%3E165%3C%5C%2Fi%3E%281%29%2C%20151%26%23x2013%3B161.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1016%5C%2Fj.jneumeth.2007.05.031%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1016%5C%2Fj.jneumeth.2007.05.031%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Measuring%20spike%20train%20synchrony%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22T.%22%2C%22lastName%22%3A%22Kreuz%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%20S.%22%2C%22lastName%22%3A%22Haas%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22A.%22%2C%22lastName%22%3A%22Morelli%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22A.%22%2C%22lastName%22%3A%22Politi%22%7D%5D%2C%22abstractNote%22%3A%22Estimating%20the%20degree%20of%20synchrony%20or%20reliability%20between%20two%20or%20more%20spike%20trains%20is%20a%20frequent%20task%20in%20both%20experimental%20and%20computational%20neuroscience.%20In%20recent%20years%2C%20many%20different%20methods%20have%20been%20proposed%20that%20typically%20compare%20the%20timing%20of%20spikes%20on%20a%20certain%20time%20scale%20to%20be%20optimized%20by%20the%20analyst.%20Here%2C%20we%20propose%20the%20ISI-distance%2C%20a%20simple%20complementary%20approach%20that%20extracts%20information%20from%20the%20interspike%20intervals%20by%20evaluating%20the%20ratio%20of%20the%20instantaneous%20firing%20rates.%20The%20method%20is%20parameter%20free%2C%20time%20scale%20independent%20and%20easy%20to%20visualize%20as%20illustrated%20by%20an%20application%20to%20real%20neuronal%20spike%20trains%20obtained%20in%20vitro%20from%20rat%20slices.%20In%20a%20comparison%20with%20existing%20approaches%20on%20spike%20trains%20extracted%20from%20a%20simulated%20Hindemarsh-Rose%20network%2C%20the%20ISI-distance%20performs%20as%20well%20as%20the%20best%20time-scale-optimized%20measure%20based%20on%20spike%20timing.%20%28c%29%202007%20Elsevier%20B.V.%20All%20rights%20reserved.%22%2C%22date%22%3A%22Sep%202007%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1016%5C%2Fj.jneumeth.2007.05.031%22%2C%22ISSN%22%3A%220165-0270%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A05Z%22%7D%7D%2C%7B%22key%22%3A%22Z2UX8RMY%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Shlens%20et%20al.%22%2C%22parsedDate%22%3A%222007-07%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EShlens%2C%20J.%2C%20Kennel%2C%20M.%20B.%2C%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%2C%20%26amp%3B%20Chichilnisky%2C%20E.%20J.%20%282007%29.%20Estimating%20information%20rates%20with%20confidence%20intervals%20in%20neural%20spike%20trains.%20%3Ci%3ENeural%20Computation%3C%5C%2Fi%3E%2C%20%3Ci%3E19%3C%5C%2Fi%3E%287%29%2C%201683%26%23x2013%3B1719.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1162%5C%2Fneco.2007.19.7.1683%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1162%5C%2Fneco.2007.19.7.1683%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Estimating%20information%20rates%20with%20confidence%20intervals%20in%20neural%20spike%20trains%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%22%2C%22lastName%22%3A%22Shlens%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22M.%20B.%22%2C%22lastName%22%3A%22Kennel%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22E.%20J.%22%2C%22lastName%22%3A%22Chichilnisky%22%7D%5D%2C%22abstractNote%22%3A%22Information%20theory%20provides%20a%20natural%20set%20of%20statistics%20to%20quantify%20the%20amount%20of%20knowledge%20a%20neuron%20conveys%20about%20a%20stimulus.%20A%20related%20work%20%28Kennel%2C%20Shlens%2C%20Abarbanel%2C%20%26%20Chichilnisky%2C%202005%29%20demonstrated%20how%20to%20reliably%20estimate%2C%20with%20a%20Bayesian%20confidence%20interval%2C%20the%20entropy%20rate%20from%20a%20discrete%2C%20observed%20time%20series.%20We%20extend%20this%20method%20to%20measure%20the%20rate%20of%20novel%20information%20that%20a%20neural%20spike%20train%20encodes%20about%20a%20stimulus-the%20average%20and%20specific%20mutual%20information%20rates.%20Our%20estimator%20makes%20few%20assumptions%20about%20the%20underlying%20neural%20dynamics%2C%20shows%20excellent%20performance%20in%20experimentally%20relevant%20regimes%2C%20and%20uniquely%20provides%20confidence%20intervals%20bounding%20the%20range%20of%20information%20rates%20compatible%20with%20the%20observed%20spike%20train.%20We%20validate%20this%20estimator%20with%20simulations%20of%20spike%20trains%20and%20highlight%20how%20stimulus%20parameters%20affect%20its%20convergence%20in%20bias%20and%20variance.%20Finally%2C%20we%20apply%20these%20ideas%20to%20a%20recording%20from%20a%20guinea%20pig%20retinal%20ganglion%20cell%20and%20compare%20results%20to%20a%20simple%20linear%20decoder.%22%2C%22date%22%3A%22Jul%202007%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1162%5C%2Fneco.2007.19.7.1683%22%2C%22ISSN%22%3A%220899-7667%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A03Z%22%7D%7D%2C%7B%22key%22%3A%227WGV8BGM%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Borst%20and%20Abarbanel%22%2C%22parsedDate%22%3A%222007%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EBorst%2C%20A.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282007%29.%20Relating%20a%20calcium%20indicator%20signal%20to%20the%20unperturbed%20calcium%20concentration%20time-course.%20%3Ci%3ETheoretical%20Biology%20and%20Medical%20Modelling%3C%5C%2Fi%3E%2C%20%3Ci%3E4%3C%5C%2Fi%3E.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1186%5C%2F1742-4682-4-7%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1186%5C%2F1742-4682-4-7%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Relating%20a%20calcium%20indicator%20signal%20to%20the%20unperturbed%20calcium%20concentration%20time-course%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22A.%22%2C%22lastName%22%3A%22Borst%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22Background%3A%20Optical%20indicators%20of%20cytosolic%20calcium%20levels%20have%20become%20important%20experimental%20tools%20in%20systems%20and%20cellular%20neuroscience.%20Indicators%20are%20known%20to%20interfere%20with%20intracellular%20calcium%20levels%20by%20acting%20as%20additional%20buffers%2C%20and%20this%20may%20strongly%20alter%20the%20time-course%20of%20various%20dynamical%20variables%20to%20be%20measured.%20Results%3A%20By%20investigating%20the%20underlying%20reaction%20kinetics%2C%20we%20show%20that%20in%20some%20ranges%20of%20kinetic%20parameters%20one%20can%20explicitly%20link%20the%20time%20dependent%20indicator%20signal%20to%20the%20time-course%20of%20the%20calcium%20influx%2C%20and%20thus%2C%20to%20the%20unperturbed%20calcium%20level%20had%20there%20been%20no%20indicator%20in%20the%20cell.%22%2C%22date%22%3A%222007%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1186%5C%2F1742-4682-4-7%22%2C%22ISSN%22%3A%221742-4682%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A07Z%22%7D%7D%2C%7B%22key%22%3A%22CBUGIQ4X%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Rabinovich%20et%20al.%22%2C%22parsedDate%22%3A%222006-12%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3ERabinovich%2C%20M.%20I.%2C%20Varona%2C%20P.%2C%20Selverston%2C%20A.%20I.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282006%29.%20Dynamical%20principles%20in%20neuroscience.%20%3Ci%3EReviews%20of%20Modern%20Physics%3C%5C%2Fi%3E%2C%20%3Ci%3E78%3C%5C%2Fi%3E%284%29%2C%201213%26%23x2013%3B1265.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1103%5C%2FRevModPhys.78.1213%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1103%5C%2FRevModPhys.78.1213%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Dynamical%20principles%20in%20neuroscience%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22M.%20I.%22%2C%22lastName%22%3A%22Rabinovich%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22P.%22%2C%22lastName%22%3A%22Varona%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22A.%20I.%22%2C%22lastName%22%3A%22Selverston%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22Dynamical%20modeling%20of%20neural%20systems%20and%20brain%20functions%20has%20a%20history%20of%20success%20over%20the%20last%20half%20century.%20This%20includes%2C%20for%20example%2C%20the%20explanation%20and%20prediction%20of%20some%20features%20of%20neural%20rhythmic%20behaviors.%20Many%20interesting%20dynamical%20models%20of%20learning%20and%20memory%20based%20on%20physiological%20experiments%20have%20been%20suggested%20over%20the%20last%20two%20decades.%20Dynamical%20models%20even%20of%20consciousness%20now%20exist.%20Usually%20these%20models%20and%20results%20are%20based%20on%20traditional%20approaches%20and%20paradigms%20of%20nonlinear%20dynamics%20including%20dynamical%20chaos.%20Neural%20systems%20are%2C%20however%2C%20an%20unusual%20subject%20for%20nonlinear%20dynamics%20for%20several%20reasons%3A%20%28i%29%20Even%20the%20simplest%20neural%20network%2C%20with%20only%20a%20few%20neurons%20and%20synaptic%20connections%2C%20has%20an%20enormous%20number%20of%20variables%20and%20control%20parameters.%20These%20make%20neural%20systems%20adaptive%20and%20flexible%2C%20and%20are%20critical%20to%20their%20biological%20function.%20%28ii%29%20In%20contrast%20to%20traditional%20physical%20systems%20described%20by%20well-known%20basic%20principles%2C%20first%20principles%20governing%20the%20dynamics%20of%20neural%20systems%20are%20unknown.%20%28iii%29%20Many%20different%20neural%20systems%20exhibit%20similar%20dynamics%20despite%20having%20different%20architectures%20and%20different%20levels%20of%20complexity.%20%28iv%29%20The%20network%20architecture%20and%20connection%20strengths%20are%20usually%20not%20known%20in%20detail%20and%20therefore%20the%20dynamical%20analysis%20must%2C%20in%20some%20sense%2C%20be%20probabilistic.%20%28v%29%20Since%20nervous%20systems%20are%20able%20to%20organize%20behavior%20based%20on%20sensory%20inputs%2C%20the%20dynamical%20modeling%20of%20these%20systems%20has%20to%20explain%20the%20transformation%20of%20temporal%20information%20into%20combinatorial%20or%20combinatorial-temporal%20codes%2C%20and%20vice%20versa%2C%20for%20memory%20and%20recognition.%20In%20this%20review%20these%20problems%20are%20discussed%20in%20the%20context%20of%20addressing%20the%20stimulating%20questions%3A%20What%20can%20neuroscience%20learn%20from%20nonlinear%20dynamics%2C%20and%20what%20can%20nonlinear%20dynamics%20learn%20from%20neuroscience%3F%22%2C%22date%22%3A%22Oct-Dec%202006%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1103%5C%2FRevModPhys.78.1213%22%2C%22ISSN%22%3A%220034-6861%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A03Z%22%7D%7D%2C%7B%22key%22%3A%22APLRM9N3%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Haas%20et%20al.%22%2C%22parsedDate%22%3A%222006-12%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EHaas%2C%20J.%20S.%2C%20Nowotny%2C%20T.%2C%20%26amp%3B%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%20%282006%29.%20Spike-timing-dependent%20plasticity%20of%20inhibitory%20synapses%20in%20the%20entorhinal%20cortex.%20%3Ci%3EJournal%20of%20Neurophysiology%3C%5C%2Fi%3E%2C%20%3Ci%3E96%3C%5C%2Fi%3E%286%29%2C%203305%26%23x2013%3B3313.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1152%5C%2Fjn.00551.2006%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1152%5C%2Fjn.00551.2006%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Spike-timing-dependent%20plasticity%20of%20inhibitory%20synapses%20in%20the%20entorhinal%20cortex%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%20S.%22%2C%22lastName%22%3A%22Haas%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22T.%22%2C%22lastName%22%3A%22Nowotny%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%5D%2C%22abstractNote%22%3A%22Actions%20of%20inhibitory%20interneurons%20organize%20and%20modulate%20many%20neuronal%20processes%2C%20yet%20the%20mechanisms%20and%20consequences%20of%20plasticity%20of%20inhibitory%20synapses%20remain%20poorly%20understood.%20We%20report%20on%20spike-timing-dependent%20plasticity%20of%20inhibitory%20synapses%20in%20the%20entorhinal%20cortex.%20After%20pairing%20presynaptic%20stimulations%20at%20time%20t%28pre%29%20with%20evoked%20postsynaptic%20spikes%20at%20time%20t%28post%29%20under%20pharmacological%20blockade%20of%20excitation%20we%20found%2C%20via%20whole%20cell%20recordings%2C%20an%20asymmetrical%20timing%20rule%20for%20plasticity%20of%20the%20remaining%20inhibitory%20responses.%20Strength%20of%20response%20varied%20as%20a%20function%20of%20the%20time%20interval%20Delta%20t%20%3D%20t%28post%29%20-%20t%28pre%29%3A%20for%20Delta%20t%20%3E%200%20inhibitory%20responses%20potentiated%2C%20peaking%20at%20a%20delay%20of%2010%20ms.%20For%20Delta%20t%20%3C%200%2C%20the%20synaptic%20coupling%20depressed%2C%20again%20with%20a%20maximal%20effect%20near%2010%20ms%20of%20delay.%20We%20also%20show%20that%20changes%20in%20synaptic%20strength%20depend%20on%20changes%20in%20intracellular%20calcium%20concentrations%20and%20demonstrate%20that%20the%20calcium%20enters%20the%20postsynaptic%20cell%20through%20voltage-gated%20channels.%20Using%20network%20models%2C%20we%20demonstrate%20how%20this%20novel%20form%20of%20plasticity%20can%20sculpt%20network%20behavior%20efficiently%20and%20with%20remarkable%20flexibility.%22%2C%22date%22%3A%22Dec%202006%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1152%5C%2Fjn.00551.2006%22%2C%22ISSN%22%3A%220022-3077%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A09Z%22%7D%7D%2C%7B%22key%22%3A%22AAM8A3AQ%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Abarbanel%20and%20Talathi%22%2C%22parsedDate%22%3A%222006-04%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3E%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%2C%20%26amp%3B%20Talathi%2C%20S.%20S.%20%282006%29.%20Neural%20circuitry%20for%20recognizing%20interspike%20interval%20sequences.%20%3Ci%3EPhysical%20Review%20Letters%3C%5C%2Fi%3E%2C%20%3Ci%3E96%3C%5C%2Fi%3E%2814%29.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1103%5C%2FPhysRevLett.96.148104%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1103%5C%2FPhysRevLett.96.148104%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Neural%20circuitry%20for%20recognizing%20interspike%20interval%20sequences%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22S.%20S.%22%2C%22lastName%22%3A%22Talathi%22%7D%5D%2C%22abstractNote%22%3A%22Sensory%20systems%20present%20environmental%20information%20to%20central%20nervous%20system%20as%20sequences%20of%20action%20potentials%20or%20spikes.%20How%20do%20animals%20recognize%20these%20sequences%20carrying%20information%20about%20their%20world%3F%20We%20present%20a%20biologically%20inspired%20neural%20circuit%20designed%20to%20enable%20spike%20pattern%20recognition.%20This%20circuit%20is%20capable%20of%20training%20itself%20on%20a%20given%20interspike%20interval%20%28ISI%29%20sequence%20and%20is%20then%20able%20to%20respond%20to%20presentations%20of%20the%20same%20sequence.%20The%20essential%20ingredients%20of%20the%20recognition%20circuit%20are%20%28a%29%20a%20tunable%20time%20delay%20circuit%2C%20%28b%29%20a%20spike%20selection%20unit%2C%20and%20%28c%29%20a%20tuning%20mechanism%20using%20spike%20timing%20dependent%20plasticity%20of%20inhibitory%20synapses.%20We%20have%20investigated%20this%20circuit%20using%20Hodgkin-Huxley%20neuron%20models%20connected%20by%20realistic%20excitatory%20and%20inhibitory%20synapses.%20It%20is%20robust%20in%20the%20presence%20of%20noise%20represented%20as%20jitter%20in%20the%20spike%20times%20of%20the%20ISI%20sequence.%22%2C%22date%22%3A%22Apr%202006%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1103%5C%2FPhysRevLett.96.148104%22%2C%22ISSN%22%3A%220031-9007%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A05Z%22%7D%7D%2C%7B%22key%22%3A%229BXFFVIV%22%2C%22library%22%3A%7B%22id%22%3A9129767%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Briggman%20et%20al.%22%2C%22parsedDate%22%3A%222006-04%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%202%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EBriggman%2C%20K.%20L.%2C%20%3Cstrong%3EAbarbanel%3C%5C%2Fstrong%3E%2C%20H.%20D.%20I.%2C%20%26amp%3B%20Kristan%2C%20W.%20B.%20%282006%29.%20From%20crawling%20to%20cognition%3A%20analyzing%20the%20dynamical%20interactions%20among%20populations%20of%20neurons.%20%3Ci%3ECurrent%20Opinion%20in%20Neurobiology%3C%5C%2Fi%3E%2C%20%3Ci%3E16%3C%5C%2Fi%3E%282%29%2C%20135%26%23x2013%3B144.%20%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1016%5C%2Fj.conb.2006.03.014%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1016%5C%2Fj.conb.2006.03.014%3C%5C%2Fa%3E%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22From%20crawling%20to%20cognition%3A%20analyzing%20the%20dynamical%20interactions%20among%20populations%20of%20neurons%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22K.%20L.%22%2C%22lastName%22%3A%22Briggman%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22H.%20D.%20I.%22%2C%22lastName%22%3A%22Abarbanel%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22W.%20B.%22%2C%22lastName%22%3A%22Kristan%22%7D%5D%2C%22abstractNote%22%3A%22By%20using%20multi-electrode%20arrays%20or%20optical%20imaging%2C%20investigators%20can%20now%20record%20from%20many%20individual%20neurons%20in%20various%20parts%20of%20nervous%20systems%20simultaneously%20while%20an%20animal%20performs%20sensory%2C%20motor%20or%20cognitive%20tasks.%20Given%20the%20large%20multidimensional%20datasets%20that%20are%20now%20routinely%20generated%2C%20it%20is%20often%20not%20obvious%20how%20to%20find%20meaningful%20results%20within%20the%20data.%20The%20analysis%20of%20neuronal-population%20recordings%20typically%20involves%20two%20steps%3A%20the%20extraction%20of%20relevant%20dynamics%20from%20neural%20data%2C%20and%20then%20use%20of%20the%20dynamics%20to%20classify%20and%20discriminate%20features%20of%20a%20stimulus%20or%20behavior.%20We%20focus%20on%20the%20application%20of%20techniques%20that%20emphasize%20interactions%20among%20the%20recorded%20neurons%20rather%20than%20using%20just%20the%20correlations%20between%20individual%20neurons%20and%20a%20perception%20or%20a%20behavior.%20An%20understanding%20of%20modern%20analysis%20techniques%20is%20crucially%20important%20for%20researchers%20interested%20in%20the%20co-varying%20activity%20among%20populations%20of%20neurons%20or%20even%20brain%20regions.%22%2C%22date%22%3A%22Apr%202006%22%2C%22language%22%3A%22English%22%2C%22DOI%22%3A%2210.1016%5C%2Fj.conb.2006.03.014%22%2C%22ISSN%22%3A%220959-4388%22%2C%22url%22%3A%22%22%2C%22collections%22%3A%5B%22UWS2UD76%22%5D%2C%22dateModified%22%3A%222022-04-27T22%3A54%3A03Z%22%7D%7D%5D%7D
Clark, R., Fuller, L., Platt, J. A., & Abarbanel, H. D. I. (2022). Reduced-Dimension, Biophysical Neuron Models Constructed From Observed Data. Neural Computation, 34(7), 1545–1587. https://doi.org/10.1162/neco_a_01515
Penny, S. G., Smith, T. A., Chen, T. C., Platt, J. A., Lin, H. Y., Goodliff, M., & Abarbanel, H. D. I. (2022). Integrating recurrent neural networks with data assimilation for scalable data-driven state estimation. Journal of Advances in Modeling Earth Systems, 14(3), 25. https://doi.org/10.1029/2021ms002843
Platt, J. A., Penny, S. G., Smith, T. A., Chen, T.-C., & Abarbanel, H. D. I. (2022). A systematic exploration of reservoir computing for forecasting complex spatiotemporal dynamics. Neural Networks, 153, 530–552. https://doi.org/10.1016/j.neunet.2022.06.025
Platt, J. A., Wong, A. D., Clark, R., Penny, S. G., & Abarbanel, H. D. I. (2021). Robust forecasting using predictive generalized synchronization in reservoir computing. Chaos, 31(12), 16. https://doi.org/10.1063/5.0066013
Abarbanel, H. D. I. (2021). A personal retrospective on the 60th anniversary of the journal Biological Cybernetics. Biological Cybernetics, 2. https://doi.org/10.1007/s00422-021-00878-6
Ty, A. J. A., Fang, Z., Gonzalez, R. A., Rozdeba, P. J., & Abarbanel, H. D. I. (2019). Machine learning of time series using time-delay embedding and precision annealing. Neural Computation, 31(10), 2004–2024. https://doi.org/10.1162/neco_a_01224
Abarbanel, H. D. I., Rozdeba, P. J., & Shirman, S. (2018). Machine learning: Deepest learning as statistical data assimilation problems. Neural Computation, 30(8), 2025–2055. https://doi.org/10.1162/neco_a_01094
Abarbanel, H. D. I., Shirman, S., Breen, D., Kadakia, N., Rey, D., Armstrong, E., & Margoliash, D. (2017). A unifying view of synchronization for data assimilation in complex nonlinear networks. Chaos, 27(12). https://doi.org/10.1063/1.5001816
Armstrong, E., Patwardhan, A. V., Johns, L., Kishimoto, C. T., Abarbanel, H. D. I., & Fuller, G. M. (2017). An optimization-based approach to calculating neutrino flavor evolution. Physical Review D, 96(8). https://doi.org/10.1103/PhysRevD.96.083008
Kadakia, N., Rey, D., Ye, J., & Abarbanel, H. D. I. (2017). Symplectic Structure Of Statistical Variational Data Assimilation. Quarterly Journal of the Royal Meteorological Society, 143(703), 756–771. https://doi.org/10.1002/qj.2962
An, Z., Rey, D., Ye, J. X., & Abarbanel, H. D. I. (2017). Estimating the state of a geophysical system with sparse observations: time delay methods to achieve accurate initial states for prediction. Nonlinear Processes in Geophysics, 24(1), 9–22. https://doi.org/10.5194/npg-24-9-2017
Kadakia, N., Armstrong, E., Breen, D., Morone, U., Daou, A., Margoliash, D., & Abarbanel, H. D. I. (2016). Nonlinear statistical data assimilation for HVCRA neurons in the avian song system. Biological Cybernetics, 110(6), 417–434. https://doi.org/10.1007/s00422-016-0697-3
Armstrong, E., & Abarbanel, H. D. I. (2016). Model of the songbird nucleus HVC as a network of central pattern generators. Journal of Neurophysiology, 116(5), 2405–2419. https://doi.org/10.1152/jn.00438.2016
Nogaret, A., Meliza, C. D., Margoliash, D., & Abarbanel, H. D. I. (2016). Automatic construction of predictive neuron models through large scale assimilation of electrophysiological data. Scientific Reports, 6. https://doi.org/10.1038/srep32749
Ye, J. X., Rey, D., Kadakia, N., Eldridge, M., Morone, U. I., Rozdeba, P., Abarbanel, H. D. I., & Quinn, J. C. (2015). Systematic variational method for statistical nonlinear state and parameter estimation. Physical Review E, 92(5). https://doi.org/10.1103/PhysRevE.92.052901
Schumann-Bischoff, J., Parlitz, U., Abarbanel, H. D. I., Kostuk, M., Rey, D., Eldridge, M., & Luther, S. (2015). Basin structure of optimization based state and parameter estimation. Chaos, 25(5). https://doi.org/10.1063/1.4920942
Nogaret, A., O’Callaghan, E. L., Lataro, R. M., Salgado, H. C., Meliza, C. D., Duncan, E., Abarbanel, H. D. I., & Paton, J. F. R. (2015). Silicon central pattern generators for cardiac diseases. Journal of Physiology-London, 593(4), 763–774. https://doi.org/10.1113/jphysiol.2014.282723
Ye, J., Kadakia, N., Rozdeba, P. J., Abarbanel, H. D. I., & Quinn, J. C. (2015). Improved variational methods in statistical data assimilation. Nonlinear Processes in Geophysics, 22(2), 205–213. https://doi.org/10.5194/npg-22-205-2015
Rey, D., Eldridge, M., Morone, U., Abarbanel, H. D. I., Parlitz, U., & Schumann-Bischoff, J. (2014). Using waveform information in nonlinear data assimilation. Physical Review E, 90(6). https://doi.org/10.1103/PhysRevE.90.062916
Meliza, C. D., Kostuk, M., Huang, H., Nogaret, A., Margoliash, D., & Abarbanel, H. D. I. (2014). Estimating parameters and predicting membrane voltages with conductance-based neuron models. Biological Cybernetics, 108(4), 495–516. https://doi.org/10.1007/s00422-014-0615-5
Ye, J. X., Rozdeba, P. J., Morone, U. I., Daou, A., & Abarbanel, H. D. I. (2014). Estimating the biophysical properties of neurons with intracellular calcium dynamics. Physical Review E, 89(6). https://doi.org/10.1103/PhysRevE.89.062714
Knowlton, C., Meliza, C. D., Margoliash, D., & Abarbanel, H. D. I. (2014). Dynamical estimation of neuron and network properties III: network analysis using neuron spike times. Biological Cybernetics, 108(3), 261–273. https://doi.org/10.1007/s00422-014-0601-y
Rey, D., Eldridge, M., Kostuk, M., Abarbanel, H. D. I., Schumann-Bischoff, J., & Parlitz, U. (2014). Accurate state and parameter estimation in nonlinear systems with sparse observations. Physics Letters A, 378(11–12), 869–873. https://doi.org/10.1016/j.physleta.2014.01.027
Whartenby, W. G., Quinn, J. C., & Abarbanel, H. D. I. (2013). The number of required observations in data assimilation for a shallow-water flow. Monthly Weather Review, 141(7), 2502–2518. https://doi.org/10.1175/mwr-d-12-00103.1
Neftci, E. O., Toth, B., Indiveri, G., & Abarbanel, H. D. I. (2012). Dynamic State and Parameter Estimation Applied to Neuromorphic Systems. Neural Computation, 24(7), 1669–1694.
Kostuk, M., Toth, B. A., Meliza, C. D., Margoliash, D., & Abarbanel, H. D. I. (2012). Dynamical estimation of neuron and network properties II: path integral Monte Carlo methods. Biological Cybernetics, 106(3), 155–167. https://doi.org/10.1007/s00422-012-0487-5
Toth, B. A., Kostuk, M., Meliza, C. D., Margoliash, D., & Abarbanel, H. D. I. (2011). Dynamical estimation of neuron and network properties I: variational methods. Biological Cybernetics, 105(3–4), 217–237. https://doi.org/10.1007/s00422-011-0459-1
Quinn, J. C., & Abarbanel, H. D. I. (2011). Data assimilation using a GPU accelerated path integral Monte Carlo approach. Journal of Computational Physics, 230(22), 8168–8178. https://doi.org/10.1016/j.jcp.2011.07.015
Haas, J. S., Kreuz, T., Torcini, A., Politi, A., & Abarbanel, H. D. I. (2010). Rate maintenance and resonance in the entorhinal cortex. European Journal of Neuroscience, 32(11), 1930–1939. https://doi.org/10.1111/j.1460-9568.2010.07455.x
Quinn, J. C., & Abarbanel, H. D. I. (2010). State and parameter estimation using Monte Carlo evaluation of path integrals. Quarterly Journal of the Royal Meteorological Society, 136(652), 1855–1867. https://doi.org/10.1002/qj.690
Abarbanel, H. D. I., Kostuk, M., & Whartenby, W. (2010). Data assimilation with regularized nonlinear instabilities. Quarterly Journal of the Royal Meteorological Society, 136(648), 769–783. https://doi.org/10.1002/qj.600
Kreuz, T., Chicharro, D., Andrzejak, R. G., Haas, J. S., & Abarbanel, H. D. I. (2009). Measuring multiple spike train synchrony. Journal of Neuroscience Methods, 183(2), 287–299. https://doi.org/10.1016/j.jneumeth.2009.06.039
Abarbanel, H. D. I. (2009). Effective actions for statistical data assimilation. Physics Letters A, 373(44), 4044–4048. https://doi.org/10.1016/j.physleta.2009.08.072
Gibb, L., Gentner, T. Q., & Abarbanel, H. D. I. (2009). Inhibition and recurrent excitation in a computational model of sparse bursting in song nucleus HVC. Journal of Neurophysiology, 102(3), 1748–1762. https://doi.org/10.1152/jn.00670.2007
Gibb, L., Gentner, T. Q., & Abarbanel, H. D. I. (2009). Brain stem feedback in a computational model of birdsong sequencing. Journal of Neurophysiology, 102(3), 1763–1778. https://doi.org/10.1152/jn.91154.2008
Quinn, J. C., Bryant, P. H., Creveling, D. R., Klein, S. R., & Abarbanel, H. D. I. (2009). Parameter and state estimation of experimental chaotic systems using synchronization. Physical Review E, 80(1). https://doi.org/10.1103/PhysRevE.80.016201
Muezzinoglu, M. K., Huerta, R., Abarbanel, H. D. I., Ryan, M. A., & Rabinovich, M. I. (2009). Chemosensor-driven artificial antennal lobe transient dynamics enable fast recognition and working memory. Neural Computation, 21(4), 1018–1037. https://doi.org/10.1162/neco.2008.05-08-780
Muezzinoglu, M. K., Vergara, A., Huerta, R., Rulkov, N., Rabinovich, M. I., Selverston, A., & Abarbanel, H. D. I. (2009). Acceleration of chemo-sensory information processing using transient features. Sensors and Actuators B-Chemical, 137(2), 507–512. https://doi.org/10.1016/j.snb.2008.10.065
Abarbanel, H. D. I., Creveling, D. R., Farsian, R., & Kostuk, M. (2009). Dynamical state and parameter estimation. SIAM Journal on Applied Dynamical Systems, 8(4), 1341–1381. https://doi.org/10.1137/090749761
Talathi, S. S., Abarbanel, H. D. I., & Ditto, W. L. (2008). Temporal spike pattern learning. Physical Review E, 78(3). https://doi.org/10.1103/PhysRevE.78.031918
Creveling, D. R., Gill, P. E., & Abarbanel, H. D. I. (2008). State and parameter estimation in nonlinear systems as an optimal tracking problem. Physics Letters A, 372(15), 2640–2644. https://doi.org/10.1016/j.physleta.2007.12.051
Creveling, D. R., Jeanne, J. M., & Abarbanel, H. D. I. (2008). Parameter estimation using balanced synchronization. Physics Letters A, 372(12), 2043–2047. https://doi.org/10.1016/j.physleta.2007.10.097
Abarbanel, H. D. I., Creveling, D. R., & Jeanne, J. M. (2008). Estimation of parameters in nonlinear systems using balanced synchronization. Physical Review E, 77(1). https://doi.org/10.1103/PhysRevE.77.016208
Kreuz, T., Haas, J. S., Morelli, A., Abarbanel, H. D. I., & Politi, A. (2007). Measuring spike train synchrony. Journal of Neuroscience Methods, 165(1), 151–161. https://doi.org/10.1016/j.jneumeth.2007.05.031
Shlens, J., Kennel, M. B., Abarbanel, H. D. I., & Chichilnisky, E. J. (2007). Estimating information rates with confidence intervals in neural spike trains. Neural Computation, 19(7), 1683–1719. https://doi.org/10.1162/neco.2007.19.7.1683
Borst, A., & Abarbanel, H. D. I. (2007). Relating a calcium indicator signal to the unperturbed calcium concentration time-course. Theoretical Biology and Medical Modelling, 4. https://doi.org/10.1186/1742-4682-4-7
Rabinovich, M. I., Varona, P., Selverston, A. I., & Abarbanel, H. D. I. (2006). Dynamical principles in neuroscience. Reviews of Modern Physics, 78(4), 1213–1265. https://doi.org/10.1103/RevModPhys.78.1213
Haas, J. S., Nowotny, T., & Abarbanel, H. D. I. (2006). Spike-timing-dependent plasticity of inhibitory synapses in the entorhinal cortex. Journal of Neurophysiology, 96(6), 3305–3313. https://doi.org/10.1152/jn.00551.2006
Abarbanel, H. D. I., & Talathi, S. S. (2006). Neural circuitry for recognizing interspike interval sequences. Physical Review Letters, 96(14). https://doi.org/10.1103/PhysRevLett.96.148104
Briggman, K. L., Abarbanel, H. D. I., & Kristan, W. B. (2006). From crawling to cognition: analyzing the dynamical interactions among populations of neurons. Current Opinion in Neurobiology, 16(2), 135–144. https://doi.org/10.1016/j.conb.2006.03.014