Interpreting neurodynamics: concepts and facts

The dynamics of neuronal systems, briefly neurodynamics, has developed into an attractive and influential research branch within neuroscience. In this paper, we discuss a number of conceptual issues in neurodynamics that are important for an appropriate interpretation and evaluation of its results. We demonstrate their relevance for selected topics of theoretical and empirical work. In particular, we refer to the notions of determinacy and stochasticity in neurodynamics across levels of microscopic, mesoscopic and macroscopic descriptions. The issue of correlations between neural, mental and behavioral states is also addressed in some detail. We propose an informed discussion of conceptual foundations with respect to neurobiological results as a viable step to a fruitful future philosophy of neuroscience.

[1]  Stephen D. Collins Neurocomputing 2 , 1992, Neurology.

[2]  Walter J. Freeman,et al.  Consciousness, Intentionality, and Causality , 2001 .

[3]  Arvind Kumar,et al.  The High-Conductance State of Cortical Networks , 2008, Neural Computation.

[4]  M. Carandini Amplification of Trial-to-Trial Response Variability by Neurons in Visual Cortex , 2004, PLoS biology.

[5]  Nicolas Brunel,et al.  Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons , 2000, Journal of Computational Neuroscience.

[6]  Günther Palm,et al.  Detecting higher-order interactions among the spiking events in a group of neurons , 1995, Biological Cybernetics.

[7]  J.A. Anderson,et al.  Foundations of research , 1988 .

[8]  A. Kolmogoroff Grundbegriffe der Wahrscheinlichkeitsrechnung , 1933 .

[9]  W. Quine Ontological Relativity and Other Essays , 1969 .

[10]  H. L. Bryant,et al.  Spike initiation by transmembrane current: a white‐noise analysis. , 1976, The Journal of physiology.

[12]  Stefan Rotter,et al.  Statistical analysis of spatially embedded networks: From grid to random node positions , 2007, Neurocomputing.

[13]  Ray J. Solomonoff,et al.  A Formal Theory of Inductive Inference. Part I , 1964, Inf. Control..

[14]  Harald Atmanspacher,et al.  From the Dynamics of Coupled Map Lattices to the Psychological Arrow of Time , 2006 .

[15]  Paul R. Halmos,et al.  I Want to be a Mathematician , 1985 .

[16]  James A. Anderson,et al.  Neurocomputing: Foundations of Research , 1988 .

[17]  Peter J. Huber Zufall oder Unordnung , 1995 .

[18]  A. Aertsen,et al.  Spike synchronization and rate modulation differentially involved in motor cortical function. , 1997, Science.

[19]  Karl Gustafson,et al.  Lectures on Computational Fluid Dynamics, Mathematical Physics and Linear Algebra , 1997 .

[20]  N. Logothetis,et al.  Very slow activity fluctuations in monkey visual cortex: implications for functional brain imaging. , 2003, Cerebral cortex.

[21]  David L Hurd The Logical Analysis of Quantum Mechanics , 1974 .

[22]  B. Mandelbrot,et al.  RANDOM WALK MODELS FOR THE SPIKE ACTIVITY OF A SINGLE NEURON. , 1964, Biophysical journal.

[23]  T. Sejnowski,et al.  Impact of Correlated Synaptic Input on Output Firing Rate and Variability in Simple Neuronal Models , 2000, The Journal of Neuroscience.

[24]  W. Newsome,et al.  Neural basis of a perceptual decision in the parietal cortex (area LIP) of the rhesus monkey. , 2001, Journal of neurophysiology.

[25]  E. Vaadia,et al.  Spatiotemporal structure of cortical activity: properties and behavioral relevance. , 1998, Journal of neurophysiology.

[26]  S. Nelson,et al.  Homeostatic plasticity in the developing nervous system , 2004, Nature Reviews Neuroscience.

[27]  H. Price Time's arrow and Archimedes' point new directions for the physics of time , 1997 .

[28]  Harald Atmanspacher,et al.  Stability Conditions in Contextual Emergence , 2007 .

[29]  T. Gelder,et al.  The dynamical hypothesis in cognitive science , 1998, Behavioral and Brain Sciences.

[30]  A. Destexhe,et al.  The high-conductance state of neocortical neurons in vivo , 2003, Nature Reviews Neuroscience.

[31]  B. Sakmann,et al.  Single-Channel Recording , 1995, Springer US.

[32]  A. Aertsen,et al.  Conditions for Propagating Synchronous Spiking and Asynchronous Firing Rates in a Cortical Network Model , 2008, The Journal of Neuroscience.

[33]  B. Sakmann,et al.  Whisker movements evoked by stimulation of single pyramidal cells in rat motor cortex , 2004, Nature.

[34]  S. Bressler,et al.  Granger Causality: Basic Theory and Application to Neuroscience , 2006, q-bio/0608035.

[35]  A Bastian,et al.  Prior information preshapes the population representation of movement direction in motor cortex , 1998, Neuroreport.

[36]  Harald Atmanspacher,et al.  Ontic and epistemic descriptions of chaotic systems , 2001 .

[37]  Ernest Sosa,et al.  Supervenience and Mind: Selected Philosophical Essays , 1993 .

[38]  Sonja Grün,et al.  Unitary Events in Multiple Single-Neuron Spiking Activity: II. Nonstationary Data , 2002, Neural Computation.

[39]  B. Gaveau,et al.  Coarse Grains: The Emergence of Space and Order , 2001 .

[40]  Michael N. Shadlen,et al.  Noise, neural codes and cortical organization , 1994, Current Opinion in Neurobiology.

[41]  F. Attneave,et al.  The Organization of Behavior: A Neuropsychological Theory , 1949 .

[42]  Gregory J. Chaitin,et al.  On the Length of Programs for Computing Finite Binary Sequences , 1966, JACM.

[43]  T. Sejnowski,et al.  Correlated neuronal activity and the flow of neural information , 2001, Nature Reviews Neuroscience.

[44]  J. Szentágothai Downward causation? , 1984, Annual review of neuroscience.

[45]  H. Kantz,et al.  Nonlinear time series analysis , 1997 .

[46]  Shun-ichi Amari,et al.  A method of statistical neurodynamics , 1974, Kybernetik.

[47]  F. Varela,et al.  Radical embodiment: neural dynamics and consciousness , 2001, Trends in Cognitive Sciences.

[48]  Lewis Campbell,et al.  The Life of James Clerk Maxwell , .

[49]  R. Ellis,et al.  Entropy, large deviations, and statistical mechanics , 1985 .

[50]  Bruno Cessac,et al.  On Dynamics of Integrate-and-Fire Neural Networks with Conductance Based Synapses , 2007, Frontiers Comput. Neurosci..

[51]  Michael C. Mackey,et al.  Chaos, Fractals, and Noise , 1994 .

[52]  Masamichi Takesaki Disjointness of the KMS-states of different temperatures , 1970 .

[53]  DiesmannMarkus,et al.  Unitary events in multiple single-neuron spiking activity , 2002 .

[54]  R. Kass,et al.  Multiple neural spike train data analysis: state-of-the-art and future challenges , 2004, Nature Neuroscience.

[55]  Hans Primas,et al.  Emergence in exact natural science , 1998 .

[56]  L. Arnold Random Dynamical Systems , 2003 .

[57]  Christof Koch,et al.  Biophysics of Computation: Information Processing in Single Neurons (Computational Neuroscience Series) , 1998 .

[58]  C. Koch,et al.  Synaptic background activity influences spatiotemporal integration in single pyramidal cells. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[59]  Wolfgang Kliemann,et al.  Qualitative Theory of Stochastic Systems , 1983 .

[60]  R. Beer Dynamical approaches to cognitive science , 2000, Trends in Cognitive Sciences.

[61]  Prof. Dr. Dr. Valentino Braitenberg,et al.  Cortex: Statistics and Geometry of Neuronal Connectivity , 1998, Springer Berlin Heidelberg.

[62]  William R. Softky,et al.  Comparison of discharge variability in vitro and in vivo in cat visual cortex neurons. , 1996, Journal of neurophysiology.

[63]  A. Aertsen,et al.  Neuronal Integration of Synaptic Input in the Fluctuation-Driven Regime , 2004, The Journal of Neuroscience.

[64]  W. Newsome,et al.  What electrical microstimulation has revealed about the neural basis of cognition , 2004, Current Opinion in Neurobiology.

[65]  Kelvin E. Jones,et al.  Neuronal variability: noise or part of the signal? , 2005, Nature Reviews Neuroscience.

[66]  Stefan Rotter,et al.  Higher-Order Statistics of Input Ensembles and the Response of Simple Model Neurons , 2003, Neural Computation.

[67]  L. Elton,et al.  THE DIRECTION OF TIME , 1978 .

[68]  P. Laplace A Philosophical Essay On Probabilities , 1902 .

[69]  Henry C. Tuckwell,et al.  Introduction to theoretical neurobiology , 1988 .

[70]  Harald Atmanspacher,et al.  Contextual Emergence in the Description of Properties , 2006 .

[71]  James H. Moor,et al.  Knowledge and the Flow of Information. , 1982 .

[72]  H. Sompolinsky,et al.  Chaos in Neuronal Networks with Balanced Excitatory and Inhibitory Activity , 1996, Science.

[73]  Stefan Rotter,et al.  Correlations and Population Dynamics in Cortical Networks , 2008, Neural Computation.

[74]  W. Freeman Nonlinear dynamics of paleocortex manifested in the olfactory EEG , 1979, Biological Cybernetics.

[75]  C. W. Gardiner,et al.  Handbook of stochastic methods - for physics, chemistry and the natural sciences, Second Edition , 1986, Springer series in synergetics.

[76]  W. Newsome,et al.  The Variable Discharge of Cortical Neurons: Implications for Connectivity, Computation, and Information Coding , 1998, The Journal of Neuroscience.

[77]  H. Haken,et al.  Synergetics , 1988, IEEE Circuits and Devices Magazine.

[78]  William R. Softky,et al.  The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs , 1993, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[79]  R. Triendl A clash of two cultures , 2002, Nature.

[80]  Huw Price,et al.  Time's Arrow and Archimedes’ Point , 1997 .

[81]  I. Fried,et al.  Coupling between Neuronal Firing Rate, Gamma LFP, and BOLD fMRI Is Related to Interneuronal Correlations , 2007, Current Biology.

[82]  A. Aertsen,et al.  Controlling synaptic input patterns in vitro by dynamic photo stimulation. , 2005, Journal of neurophysiology.

[83]  R. Keynes The ionic channels in excitable membranes. , 1975, Ciba Foundation symposium.

[84]  Stefan Rotter,et al.  Measurement of variability dynamics in cortical spike trains , 2008, Journal of Neuroscience Methods.

[85]  Y. Dan,et al.  Spike timing-dependent plasticity: from synapse to perception. , 2006, Physiological reviews.

[86]  Hans Primas,et al.  Hidden Determinism, Probability, and Time's Arrow , 2002 .

[87]  L. M. M.-T. Theory of Probability , 1929, Nature.

[88]  Ray J. Solomonoff,et al.  A Formal Theory of Inductive Inference. Part II , 1964, Inf. Control..

[89]  D. Perkel,et al.  Nerve-impulse patterns: A quantitative display technique for three neurons , 1975, Brain Research.

[90]  Rolf Pfeifer,et al.  Understanding intelligence , 2020, Inequality by Design.

[91]  Vivien A. Casagrande,et al.  Biophysics of Computation: Information Processing in Single Neurons , 1999 .

[92]  I. Fried,et al.  Coupling Between Neuronal Firing, Field Potentials, and fMRI in Human Auditory Cortex , 2005, Science.

[93]  K. Vahala Handbook of stochastic methods for physics, chemistry and the natural sciences , 1986, IEEE Journal of Quantum Electronics.

[94]  Shun-ichi Amari,et al.  Information-Geometric Measure for Neural Spikes , 2002, Neural Computation.

[95]  Stefan Rotter,et al.  Statistical Significance of Coincident Spikes: Count-Based Versus Rate-Based Statistics , 2002, Neural Computation.

[96]  C. Granger Investigating Causal Relations by Econometric Models and Cross-Spectral Methods , 1969 .

[97]  L. Abbott,et al.  Synaptic plasticity: taming the beast , 2000, Nature Neuroscience.

[98]  Naama Brenner,et al.  History-Dependent Multiple-Time-Scale Dynamics in a Single-Neuron Model , 2005, The Journal of Neuroscience.

[99]  Bernhard Rüger,et al.  Grundlagen der Statistik und ihre Anwendungen , 1995 .

[100]  Kathryn B. Laskey,et al.  Neural Coding: Higher-Order Temporal Patterns in the Neurostatistics of Cell Assemblies , 2000, Neural Computation.

[101]  Markus Diesmann,et al.  Spike-Timing-Dependent Plasticity in Balanced Random Networks , 2007, Neural Computation.

[102]  Mario Dal Cin,et al.  Physics and Mathematics of the Nervous System , 1975 .

[103]  D. Chklovskii,et al.  Geometry and Structural Plasticity of Synaptic Connectivity , 2002, Neuron.

[104]  E. Bienenstock A model of neocortex , 1995 .

[105]  Daniel J. Amit,et al.  Modeling brain function: the world of attractor neural networks, 1st Edition , 1989 .

[106]  Stefan Rotter,et al.  Analysis of higher-order neuronal interactions based on conditional inference , 2003, Biological Cybernetics.

[107]  Anil K. Seth,et al.  Causal networks in simulated neural systems , 2008, Cognitive Neurodynamics.

[108]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1990 .

[109]  James A. Anderson,et al.  Neurocomputing (vol. 2): directions for research , 1990 .

[110]  Douglas Lind,et al.  An Introduction to Symbolic Dynamics and Coding , 1995 .

[111]  Haim Sompolinsky,et al.  Chaotic Balanced State in a Model of Cortical Circuits , 1998, Neural Computation.

[112]  Hans V. Westerhoff,et al.  Emergence and Its Place in Nature: A Case Study of Biochemical Networks , 2005, Synthese.

[113]  O. Prospero-Garcia,et al.  Reliability of Spike Timing in Neocortical Neurons , 1995 .

[114]  Henry P. Stapp,et al.  Attention, Intention, and Will in Quantum Physics , 1999, quant-ph/9905054.

[115]  C. Malsburg Binding in models of perception and brain function , 1995, Current Opinion in Neurobiology.

[116]  J. Rothwell Principles of Neural Science , 1982 .

[117]  Christian E Elger,et al.  Do neural correlates of consciousness cause conscious states? , 2004, Medical hypotheses.

[118]  William P. Alston,et al.  Knowledge and the Flow of Information , 1985 .

[119]  P. Érdi,et al.  Mesoscopic neurodynamics. , 2002, Bio Systems.

[120]  Hans Primas,et al.  Time-Entanglement Between Mind and Matter , 2003 .

[121]  Nicholas R Wall,et al.  Regulation of Dendritic Protein Synthesis by Miniature Synaptic Events , 2004, Science.

[122]  Agustín Vicente,et al.  Supervenience and Mind , 1996 .

[123]  Holk Cruse,et al.  The evolution of cognition - a hypothesis , 2003, Cogn. Sci..

[124]  Kunihiko Kaneko,et al.  Supertransients, spatiotemporal intermittency and stability of fully developed spatiotemporal chaos , 1990 .

[125]  Ad Aertsen,et al.  Stable propagation of synchronous spiking in cortical neural networks , 1999, Nature.

[126]  B. M. Hill,et al.  Theory of Probability , 1990 .

[127]  M. Timme,et al.  Long chaotic transients in complex networks. , 2004, Physical review letters.

[128]  Jens Timmer,et al.  Handbook of Time Series Analysis , 2006 .

[129]  Klaas Enno Stephan,et al.  On the role of general system theory for functional neuroimaging , 2004, Journal of anatomy.

[130]  Gregory J. Chaitin,et al.  On the Length of Programs for Computing Finite Binary Sequences: statistical considerations , 1969, JACM.

[131]  J. H. Williamson,et al.  Functional Analysis and its Applications , 1974 .

[132]  Harald Atmanspacher,et al.  Epistemic and Ontic Quantum Realities , 2003 .

[133]  D. Chalmers What is a Neural Correlate of Consciousness , 2000 .

[134]  C. Gray,et al.  Cellular Mechanisms Contributing to Response Variability of Cortical Neurons In Vivo , 1999, The Journal of Neuroscience.

[135]  J. Movshon,et al.  The analysis of visual motion: a comparison of neuronal and psychophysical performance , 1992, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[136]  R. Pfeifer,et al.  Self-Organization, Embodiment, and Biologically Inspired Robotics , 2007, Science.

[137]  Henri Poincaré,et al.  Science et méthode , 1934 .

[138]  R. Malach,et al.  Intersubject Synchronization of Cortical Activity During Natural Vision , 2004, Science.

[139]  Haim Sompolinsky,et al.  Learning Input Correlations through Nonlinear Temporally Asymmetric Hebbian Plasticity , 2003, The Journal of Neuroscience.

[140]  B. Hille Ionic channels of excitable membranes , 2001 .

[141]  V. Braitenberg Vehicles, Experiments in Synthetic Psychology , 1984 .

[142]  S. Rotter,et al.  Decomposition of neuronal assembly activity via empirical de-Poissonization , 2007, 0711.1965.

[143]  D. Cox Some Statistical Methods Connected with Series of Events , 1955 .

[144]  C. Stevens,et al.  Input synchrony and the irregular firing of cortical neurons , 1998, Nature Neuroscience.

[145]  Stefan Rotter,et al.  Correlated input spike trains and their effects on the response of the leaky integrate-and-fire neuron , 2002, Neurocomputing.

[146]  H. Atmanspacher,et al.  Contextual Emergence of Mental States from Neurodynamics , 2005, q-bio/0512034.

[147]  I. Tsuda Toward an interpretation of dynamic neural activity in terms of chaotic dynamical systems. , 2001, The Behavioral and brain sciences.

[148]  Sonja Grün,et al.  Unitary Events in Multiple Single-Neuron Spiking Activity: I. Detection and Significance , 2002, Neural Computation.

[149]  Conrad,et al.  On the representation of objects and their relations in the brain , 1974 .

[150]  J.A. Anderson,et al.  Directions for research , 1990 .

[151]  Walter Senn,et al.  Modulating the Granularity of Category Formation by Global Cortical States , 2008, Frontiers Comput. Neurosci..

[152]  M. Bennett,et al.  Philosophical Foundations of Neuroscience , 2006, History & Philosophy of Psychology.

[153]  M. Jammer The philosophy of quantum mechanics , 1974 .

[154]  Nicolas Brunel,et al.  Fast Global Oscillations in Networks of Integrate-and-Fire Neurons with Low Firing Rates , 1999, Neural Computation.

[155]  A. Grinvald,et al.  Dynamics of Ongoing Activity: Explanation of the Large Variability in Evoked Cortical Responses , 1996, Science.

[156]  Otfried Ischebeck,et al.  Time, quantum and information , 2003 .

[157]  William T Newsome,et al.  Is there a signal in the noise? , 1995, Current Opinion in Neurobiology.

[158]  Dennis J. Aigner,et al.  ERRORS OF MEASUREMENT AND LEAST SQUARES ESTIMATION IN A SIMPLE RECURSIVE MODEL OF DYNAMIC EQUILIBRIUM , 1966 .

[159]  Moshe Abeles,et al.  Corticonics: Neural Circuits of Cerebral Cortex , 1991 .

[160]  H. Pashler The Psychology of Attention , 1997 .

[161]  C. Granger Investigating causal relations by econometric models and cross-spectral methods , 1969 .

[162]  Ioannis Antoniou,et al.  From irreversible Markov semigroups to chaotic dynamics , 1997 .

[163]  Hans Primas,et al.  EMERGENCE IN EXACT NATURAL SCIENCES , 1998 .

[164]  Peter König,et al.  Dynamical features of higher-order correlation events: impact on cortical cells , 2007, Cognitive neurodynamics.

[165]  William T Newsome,et al.  Middle Temporal Visual Area Microstimulation Influences Veridical Judgments of Motion Direction , 2002, The Journal of Neuroscience.