Statistical Data Assimilation: Formulation and Examples From Neurobiology

For the Research Topic Data Assimilation and Control: Theory and Applications in Life Sciences we first review the formulation of statistical data assimilation (SDA) and discuss algorithms for exploring variational approximations to the conditional expected values of biophysical aspects of functional neural circuits. Then we report on the application of SDA to (1) the exploration of properties of individual neurons in the HVC nucleus of the avian song system, and (2) characterizing individual neurons formulated as very large scale integration (VLSI) analog circuits with a goal of building functional, biophysically realistic, VLSI representations of functional nervous systems. Networks of neurons pose a substantially greater challenge, and we comment on formulating experiments to probe the properties, especially the functional connectivity, in song command circuits within HVC.

[1]  Henry D. I. Abarbanel,et al.  Predicting the Future: Completing Models of Observed Complex Systems , 2013 .

[2]  E. Lorenz.  Predictability of Weather and Climate: Predictability – a problem partly solved , 2006 .

[3]  Edward A. Stern,et al.  Birdbrains could teach basal ganglia research a new song , 2005, Trends in Neurosciences.

[4]  Gerald E. Hough,et al.  Avian brains and a new understanding of vertebrate brain evolution , 2005, Nature Reviews Neuroscience.

[5]  R. Mooney,et al.  The HVC Microcircuit: The Synaptic Basis for Interactions between Song Motor and Vocal Plasticity Pathways , 2005, The Journal of Neuroscience.

[6]  Katta G. Murty,et al.  Some NP-complete problems in quadratic and nonlinear programming , 1987, Math. Program..

[7]  Sharan K Bagal,et al.  Voltage gated sodium channels as drug discovery targets , 2015, Channels.

[8]  Alain Nogaret,et al.  Automatic Construction of Predictive Neuron Models through Large Scale Assimilation of Electrophysiological Data , 2016, Scientific reports.

[9]  Radford M. Neal.  MCMC Using Hamiltonian Dynamics , 2011, 1206.1901.

[10]  Teddy Seidenfeld.  [The Axioms of Subjective Probability]: Comment , 1986 .

[11]  C. Scharff,et al.  Twitter evolution: converging mechanisms in birdsong and human speech , 2010, Nature Reviews Neuroscience.

[12]  B. Horwitz,et al.  Dopamine regulation of human speech and bird song: A critical review , 2012, Brain and Language.

[13]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[14]  Aleksandra Shirman.  Strategic Monte Carlo and Variational Methods in Statistical Data Assimilation for Nonlinear Dynamical Systems , 2018 .

[15]  D. Margoliash,et al.  Parallel pathways and convergence onto HVc and adjacent neostriatum of adult zebra finches (Taeniopygia guttata) , 1995, The Journal of comparative neurology.

[16]  R. Frolov,et al.  Harnessing the Flow of Excitation: TRP, Voltage-Gated Na(+), and Voltage-Gated Ca(2+) Channels in Contemporary Medicine. , 2016, Advances in protein chemistry and structural biology.

[17]  Daniel Breen.  Characterizing Real World Neural Systems Using Variational Methods of Data Assimilation , 2017 .

[18]  Mark Kostuk,et al.  Dynamical estimation of neuron and network properties II: path integral Monte Carlo methods , 2012, Biological Cybernetics.

[19]  B. Sakmann,et al.  Improved patch-clamp techniques for high-resolution current recording from cells and cell-free membrane patches , 1981, Pflügers Archiv.

[20]  John C. Quinn.  A path integral approach to data assimilation in stochastic nonlinear systems , 2010 .

[21]  F. Nottebohm,et al.  Central control of song in the canary, Serinus canarius , 1976, The Journal of comparative neurology.

[22]  P. Kuhl,et al.  Birdsong and human speech: common themes and mechanisms. , 1999, Annual review of neuroscience.

[23]  Michale S Fee,et al.  The songbird as a model for the generation and learning of complex sequential behaviors. , 2010, ILAR journal.

[24]  S. Lakshmivarahan,et al.  Ensemble Kalman filter , 2009, IEEE Control Systems.

[25]  Erick O Hernández-Ochoa,et al.  Voltage clamp methods for the study of membrane currents and SR Ca(2+) release in adult skeletal muscle fibres. , 2012, Progress in biophysics and molecular biology.

[26]  Daniel Margoliash,et al.  Nonlinear statistical data assimilation for HVC$$_{\mathrm{RA}}$$RA neurons in the avian song system , 2016, Biological Cybernetics.

[27]  Richard Mooney,et al.  Neural mechanisms for learned birdsong. , 2009, Learning & memory.

[28]  J. Avery.  Critical review. , 2006, The Journal of the Arkansas Medical Society.

[29]  H. Abarbanel,et al.  Nonlinear Statistical Data Assimilation for HVC$_{\text{RA}}$ Neurons in the Avian Song System , 2016, 1608.04005.

[30]  Henry D. I. Abarbanel,et al.  Machine Learning: Deepest Learning as Statistical Data Assimilation Problems , 2017, Neural Computation.

[31]  J. C. Quinn,et al.  Systematic variational method for statistical nonlinear state and parameter estimation. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Jingxin Ye.  Systematic Annealing Approach for Statistical Data Assimilation , 2016 .

[34]  D. Perkel,et al.  Multiple cell types distinguished by physiological, pharmacological, and anatomic properties in nucleus HVc of the adult zebra finch. , 1998, Journal of neurophysiology.

[35]  G. Evensen.  Data Assimilation: The Ensemble Kalman Filter , 2006 .

[36]  R. Bertram,et al.  Electrophysiological characterization and computational models of HVC neurons in the zebra finch. , 2013, Journal of neurophysiology.

[37]  Michael S. Brainard,et al.  Auditory feedback in learning and maintenance of vocal behaviour , 2000, Nature Reviews Neuroscience.

[38]  Jeffrey S. Rosenthal,et al.  Optimal Proposal Distributions and Adaptive MCMC , 2011 .

[39]  M. Long,et al.  Interplay of Inhibition and Excitation Shapes a Premotor Neural Sequence , 2015, The Journal of Neuroscience.

[40]  William H. Press,et al.  Numerical Recipes: The Art of Scientific Computing , 1987 .

[41]  Nirag Kadakia,et al.  HVC I Neuron Properties from Statistical Data Assimilation , 2016 .

[42]  Henry D. I. Abarbanel,et al.  Predicting the Future , 2013 .

[43]  S. Brendle,et al.  Calculus of Variations , 1927, Nature.

[44]  J. C. Quinn,et al.  Improved variational methods in statistical data assimilation , 2015 .

[45]  P. Laplace.  Memoir on the Probability of the Causes of Events , 1986 .

[46]  R. Mooney.  Different Subthreshold Mechanisms Underlie Song Selectivity in Identified HVc Neurons of the Zebra Finch , 2000, The Journal of Neuroscience.

[47]  Gert Cauwenberghs,et al.  Assimilation of Biophysical Neuronal Dynamics in Neuromorphic VLSI , 2017, IEEE Transactions on Biomedical Circuits and Systems.

[48]  Richard A. Anthes,et al.  Data Assimilation and Initialization of Hurricane Prediction Models , 1974 .

[49]  G. A. Barnard,et al.  Transmission of Information: A Statistical Theory of Communications. , 1961 .

[50]  M. Kubota,et al.  Electrophysiological characteristics of classes of neuron in the HVc of the zebra finch. , 1998, Journal of neurophysiology.

[51]  D. E. Goldman.  POTENTIAL, IMPEDANCE, AND RECTIFICATION IN MEMBRANES , 1943, The Journal of general physiology.

[52]  R. Morris.  Foundations of cellular neurophysiology , 1996 .

[53]  Sarah E. London,et al.  Parallel FoxP1 and FoxP2 Expression in Songbird and Human Brain Predicts Functional Interaction , 2004, The Journal of Neuroscience.