Mathematical Models of Memory

ingber at umiacs.umd.edu ingber at umiacs.umd.edu
Tue Aug 6 17:58:10 EST 1991






               Back in April, I posted the abstract below of a paper I sub-
          mitted to Physical Review A, stating that I'd be glad to e-mail a
          uuencoded compressed PostScript draft to interested people.   The
          paper  is  scheduled  to appear in the 15 September issue of that
          journal.

               In the  context  of  mathematical  models  of  memory  being
          queried  currently in this forum, this paper, in part, deals with
          statistical constraints imposed on short-term memory by the  phy-
          sics   of  interactions  at  the  underlying  scale  of  neuronal
          activity.
                      ========================================

                 Statistical mechanics of neocortical interactions:
                A scaling paradigm applied to electroencephalography

               A series of papers has developed a statistical mechanics  of
          neocortical  interactions  (SMNI), deriving aggregate behavior of
          experimentally  observed  columns  of  neurons  from  statistical
          electrical-chemical  properties  of synaptic interactions.  While
          not useful to yield insights at the single neuron level, SMNI has
          demonstrated  its capability in describing large-scale properties
          of short-term memory and electroencephalographic (EEG)  systemat-
          ics.   The necessity of including nonlinear and stochastic struc-
          tures in this development has been stressed.  In  this  paper,  a
          more  stringent test is placed on SMNI: The algebraic and numeri-
          cal algorithms previously developed in this and  similar  systems
          are  brought  to  bear  to fit large sets of EEG/evoked potential
          data being collected to investigate  genetic  predispositions  to
          alcoholism  and  to  extract  brain  "signatures"  of  short-term
          memory.  Using the numerical algorithm  of  Very  Fast  Simulated
          Re-Annealing,  it  is  demonstrated that SMNI can indeed fit this
          data within experimentally  observed  ranges  of  its  underlying
          neuronal-synaptic  parameters,  and use the quantitative modeling
          results to examine physical neocortical  mechanisms  to  discrim-
          inate  between  high-risk  and  low-risk  populations genetically
          predisposed to alcoholism.  Since this first study is  a  control
          to  span relatively long time epochs, similar to earlier attempts
          to establish such correlations,  this  discrimination  is  incon-
          clusive  because  of  other neuronal activity which can mask such
          effects.  However, the SMNI model is shown to be consistent  with
          EEG  data  during  selective attention tasks and with neocortical
          mechanisms describing short-term  memory  (STM)  previously  pub-
          lished  using  this  approach.   This paper explicitly identifies
          similar nonlinear stochastic mechanisms  of  interaction  at  the
          microscopic-neuronal,    mesoscopic-columnar   and   macroscopic-
          regional scales of neocortical interactions.  These results  give
          strong  quantitative  support  for an accurate intuitive picture,
          portraying   neocortical   interactions    as    having    common
          algebraic/physics  mechanisms  that  scale across quite disparate
          spatial  scales  and   functional/behavioral   phenomena,   i.e.,
          describing  interactions  among  neurons, columns of neurons, and
          regional masses of neurons.









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