Statistical mechanics of neocortical interactions: Path-integral evolution of short-term memory.

Previous papers in this series of statistical mechanics of neocortical interactions (SMNI) have detailed a development from the relatively microscopic scales of neurons up to the macroscopic scales as recorded by electroencephalography (EEG), requiring an intermediate mesocolumnar scale to be developed at the scale of minicolumns ($approx 10 sup 2$ neurons) and macrocolumns ($approx 10 sup 5$ neurons). Opportunity was taken to view SMNI as sets of statistical constraints, not necessarily describing specific synaptic or neuronal mechanisms, on neuronal interactions, on some aspects of short-term memory (STM), e.g., its capacity, stability, and duration. A recently developed C-language code, PATHINT, provides a non-Monte Carlo technique for calculating the dynamic evolution of arbitrary-dimension (subject to computer resources) nonlinear Lagrangians, such as derived for the two-variable SMNI problem. Here, PATHINT is used to explicitly detail the evolution of the SMNI constraints on STM.

[1]  Paul L. Nunez,et al.  Multiple scales of statistical physics of the neocortex: Application to electroencephalography , 1990 .

[2]  D. Ferster,et al.  Linearity of summation of synaptic potentials underlying direction selectivity in simple cells of the cat visual cortex. , 1993, Science.

[3]  H Eichenbaum,et al.  Thinking about brain cell assemblies. , 1993, Science.

[4]  E J Baier.  Editorial: Learning how to learn. , 1975, American Industrial Hygiene Association journal.

[5]  Bennet B. Murdock,et al.  A distributed memory model for serial-order information. , 1983 .

[6]  B. C. Motter,et al.  The influence of attentive fixation upon the excitability of the light- sensitive neurons of the posterior parietal cortex , 1981, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[7]  L. Ingber.  Statistical Mechanics of Neocortical Interactions. I. Basic Formulation , 2001 .

[8]  Michael F. Wehner,et al.  Mathematical comparison of combat computer models to exercise data , 1991 .

[9]  T. Wiesel,et al.  Functional organization of the visual cortex. , 1983, Progress in brain research.

[10]  J. Fermaglich.  Electric Fields of the Brain: The Neurophysics of EEG , 1982 .

[11]  Ingber,et al.  Statistical-mechanical aids to calculating term-structure models. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[12]  V. Mountcastle,et al.  An organizing principle for cerebral function : the unit module and the distributed system , 1978 .

[13]  Lester Ingber.  Elements of Advanced Karate , 1985 .

[14]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[15]  E. G. Jones,et al.  Intracortical connectivity of architectonic fields in the somatic sensory, motor and parietal cortex of monkeys , 1978, The Journal of comparative neurology.

[16]  Nunez Pl,et al.  Localization of brain activity with electroencephalography. , 1990 .

[17]  R. Reale,et al.  Patterns of cortico‐cortical connections related to tonotopic maps in cat auditory cortex , 1980, The Journal of comparative neurology.

[18]  Robert Graham,et al.  Covariant formulation of non-equilibrium statistical thermodynamics , 1977 .

[19]  Lester Ingberg,et al.  Theoretical issues of biological intelligence: Information and structure: Statistical mechanics of mesoscales in neocortex and in command, control and communications (C3) , 1988 .

[20]  G. S. Agarwal,et al.  Observability of hysteresis in first-order equilibrium and nonequilibrium phase transitions , 1981 .

[21]  Lester Ingber.  Applications of biological intelligence to Command, Control and Communications , 1988 .

[22]  Lester Ingber,et al.  Mesoscales in neocortex and in command, control and communications (C3) systems , 1988 .

[23]  W. Ebeling.  Stochastic Processes in Physics and Chemistry , 1995 .

[24]  L. Ingber.  Adaptive Simulated Annealing (ASA) , 1993 .

[25]  L. Ingber.  Statistical mechanics of multiple scales of neocortical interactions , 1995 .

[26]  Franklin A. Graybill,et al.  Introduction to The theory , 1974 .

[27]  E. Tirapegui,et al.  Functional Integration and Semiclassical Expansions , 1982 .

[28]  R. Dykes.  Parallel processing of somatosensory information: A theory , 1983, Brain Research Reviews.

[29]  L. Ingber,et al.  Application of statistical mechanics methodology to term-structure bond-pricing models , 1991 .

[30]  H. Pinsker,et al.  Information Processing in the Nervous System , 1980 .

[31]  R. Erickson,et al.  The Across-Fiber Pattern Theory: An Organizing Principle for Molar Neural Function , 1982 .

[32]  G. A. Miller.  THE PSYCHOLOGICAL REVIEW THE MAGICAL NUMBER SEVEN, PLUS OR MINUS TWO: SOME LIMITS ON OUR CAPACITY FOR PROCESSING INFORMATION 1 , 1956 .

[33]  Ingber,et al.  Statistical mechanics of neocortical interactions: A scaling paradigm applied to electroencephalography. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[34]  P. Nunez,et al.  Localization of brain activity with electroencephalography. , 1990, Advances in neurology.

[35]  D. Hubel,et al.  Receptive fields, binocular interaction and functional architecture in the cat's visual cortex , 1962, The Journal of physiology.

[36]  W G Chase,et al.  Exceptional memory. , 1982, American scientist.

[37]  L. Ingber.  Very fast simulated re-annealing , 1989 .

[38]  L. Ingber.  Statistical mechanics of neocortical interactions. Derivation of short-term-memory capacity , 1984 .

[39]  Ingber,et al.  Generic mesoscopic neural networks based on statistical mechanics of neocortical interactions. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[40]  H. Simon,et al.  STM capacity for Chinese words and idioms: Chunking and acoustical loop hypotheses , 1985, Memory & cognition.

[41]  Ingber,et al.  Statistical mechanics of neocortical interactions: Stability and duration of the 7+/-2 rule of short-term-memory capacity. , 1985, Physical review. A, General physics.

[42]  Michael F. Wehner,et al.  Numerical evaluation of path-integral solutions to Fokker-Planck equations. II. Restricted stochastic processes , 1983 .

[43]  Lester Ingber,et al.  Statistical Mechanics of Neocortical Interactions: EEG Dispersion Relations , 1985, IEEE Transactions on Biomedical Engineering.

[44]  W. G. Wolfer,et al.  Numerical evaluation of path-integral solutions to Fokker-Planck equations. III. Time and functionally dependent coefficients. , 1987, Physical review. A, General physics.

[45]  L Ingber,et al.  Statistical mechanics of neocortical interactions: multiple scales of EEG. , 1996, Electroencephalography and clinical neurophysiology. Supplement.

[46]  Lester Ingber.  Karate: Kinematics and Dynamics , 1981 .

[47]  W. Nauta,et al.  Columnar distribution of cortico-cortical fibers in the frontal association, limbic, and motor cortex of the developing rhesus monkey , 1977, Brain Research.

[48]  Lester Ingber,et al.  Towards a unified brain theory , 1981 .

[49]  Lester Ingber.  Towards clinical applications of statistical mechanics of neocortical interactions , 1985 .

[50]  N. Kampen,et al.  Stochastic processes in physics and chemistry , 1981 .

[51]  Lester Ingber,et al.  Statistical mechanics of neocortical interactions. Dynamics of synaptic modification , 1983 .