STATISTICAL MECHANICS OF NEOCORTICAL INTERACTIONS:

1. Introduction
1.1. Context of Review
1.2. Errors In Simple Statistical Approaches
2.1. Statistical Aggregation
2.4. Complexity in EEG
3.3. Hick's Law -- Linearity of RT vs STM Information
REFERENCES


Lester Ingber

Lester Ingber Research

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and

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ingber@ingber.com, ingber@alumni.caltech.edu

http://www.ingber.com/

Psycholoquy Commentary on




by Arthur Jensen



theory of short-term memory (STM) and a model of electroencephalography (EEG) are key to providing this



KEYWORDS: short term memory; nonlinear; statistical

Basis for the g factor - 2 - Lester Ingber

1. Introduction

1.1. Context of Review



factor.

From circa 1978 through the present, a series of papers on the statistical mechanics of neocortical interactions (SMNI) has been developed to model columns and regions of neocortex, spanning mm to cm of tissue. Most of these papers have dealt explicitly with calculating properties of short-term memory (STM) and scalp EEG in order to test the basic formulation of this approach. SMNI derives 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) systematics (Ingber, 1982; Ingber, 1983; Ingber, 1984; Ingber, 1991; Ingber, 1994; Ingber, 1995a; Ingber & Nunez, 1995; Ingber, 1996a; Ingber, 1997).

1.2. Errors In Simple Statistical Approaches

I must assume that AJ faced very difficult problems in choosing just how much technical details to give in his



factor. However, I do see reason to criticize some general features of the simple statistical algorithms presented, especially those that overlap with my own mathematical and physics expertise.

The simple approach to factor analysis initiated on page 23,



(1)



Basis for the g factor - 3 - Lester Ingber evidence at each spatial-temporal scale purported to be modeled.

It must be understood that there is a quite explicit model being assumed here of the real world -- that of a simple normal Gaussian process. The real issue in many physical/biological systems is that most often the real multivariable world is much more aptly described by something like



(2.a)




(2.b)



Basis for the g factor - 4 - Lester Ingber have dealt explicitly with calculating properties of short-term memory (STM) and scalp EEG in order to test the basic formulation of this approach (Ingber, 1981; Ingber, 1982; Ingber, 1983; Ingber, 1984; Ingber, 1985a; Ingber, 1985b; Ingber, 1986; Ingber & Nunez, 1990; Ingber, 1991; Ingber, 1992; Ingber, 1994; Ingber & Nunez, 1995; Ingber, 1995a; Ingber, 1995b; Ingber, 1996b; Ingber, 1997; Ingber, 1998). This model was the first physical application of a nonlinear multivariate calculus developed by other mathematical physicists in the late 1970's (Graham, 1977; Langouche et al, 1982).

2.1. Statistical Aggregation

SMNI studies have detailed a physics of short-term memory and of (short-fiber contribution to) EEG



Basis for the g factor - 5 - Lester Ingber learned items still more error-free than those in the middle (Murdock, 1983). The basic assumption is that a



Basis for the g factor - 6 - Lester Ingber mesocolumnar scale, whereas the top-down eigenfunctions are at the global regional scale. However, these approaches have regions of substantial overlap (Ingber & Nunez, 1990; Ingber, 1995a), and future studies may expand top-down eigenfunctions into the bottom-up eigenfunctions, yielding a model of scalp EEG that is ultimately expressed in terms of columnar states of neocortical processing of attention and short-term memory.

An optimistic outcome of future work might be that these EEG eigenfunctions, baselined to specific STM



2.4. Complexity in EEG


First, psychometric tests were never intended or devised to measure anything other than behavioral

variables. ... at this point most explanations are still conjectural.

However, most of the chapter falls back to similar too-simple statistical models of correlations between measured variables and behavioral characteristics.



superficial relative most of the other parts of the book. The introduction of ``complexity'' as a possible correlate to IQ is based on faddish studies that do not have any theoretical or experimental support (Nunez, 1995). If such support does transpire, most likely it will be developed on the shoulders of more complete stochastic models and much better EEG recordings.














This seems to be a similar correlation as that drawn by Spearman, as described by AJ, in having ``education



of experience.''

Basis for the g factor - 7 - Lester Ingber




From the SMNI perspective, control of selective attention generally is highly correlated with high utilization of STM, e.g., to tune the ``centering mechanism.'' This seems similar to Spearman's correlation of ``mental





tasks. The ability to control the ``centering mechanism'' is required to sustain a high degree of statistical processes of multiple most probable states of information. The particular balance of general chemical-electrical activity directly shapes the distribution of most probable states. For some tasks, processing across relatively more most probable states might be required; for other tasks processing among larger focussed peaks of most probable states might be more important.

3.3. Hick's Law -- Linearity of RT vs STM Information

Th SMNI approach to STM gives a reasonable foundation to discuss RT to items in STM storage. Previous calculations give detailed support to items in STM storage as being represented as peaks in the short-time (10 msec) (Ingber, 1984; Ingber, 1985b) as well as the long-time (several secs) (Ingber, 1994; Ingber & Nunez, 1995) conditional probability distribution of correlated mesocolumnar firings of columns of neurons, correlated to STM tasks also correlated to EEG observations of evoked potential activities (Ingber, 1997; Ingber, 1998). This distribution is explicitly calculated by respecting the nonlinear synaptic interactions among all possible combinatoric aggregates of columnar firing states (Ingber, 1982; Ingber, 1983).

The RT necessary to ``visit'' the states under control during the span of STM can be calculated as the mean



Basis for the g factor - 8 - Lester Ingber




Basis for the g factor - 9 - Lester Ingber

REFERENCES

Graham, R. (1977) Covariant formulation of non-equilibrium statistical thermodynamics. Z. Physik B26:397-405. Ingber, L. (1981) Towards a unified brain theory. J. Social Biol. Struct. 4:211-224.

Ingber, L. (1982) Statistical mechanics of neocortical interactions. I. Basic formulation. Physica D 5:83-107.

[URL http://www.ingber.com/smni82_basic.ps.gz]

Ingber, L. (1983) Statistical mechanics of neocortical interactions. Dynamics of synaptic modification. Phys. Rev.

A 28:395-416. [URL http://www.ingber.com/smni83_dynamics.ps.gz]

Ingber, L. (1984) Statistical mechanics of neocortical interactions. Derivation of short-term-memory capacity.

Phys. Rev. A 29:3346-3358. [URL http://www.ingber.com/smni84_stm.ps.gz]

Ingber, L. (1985a) Statistical mechanics of neocortical interactions. EEG dispersion relations. IEEE Trans.

Biomed. Eng. 32:91-94. [URL http://www.ingber.com/smni85_eeg.ps.gz]

Ingber, L. (1985b) Statistical mechanics of neocortical interactions: Stability and duration of the 7+-2 rule of

short-term-memory capacity. Phys. Rev. A 31:1183-1186. [URL

http://www.ingber.com/smni85_stm.ps.gz]

Ingber, L. (1986) Statistical mechanics of neocortical interactions. Bull. Am. Phys. Soc. 31:868.

Ingber, L. (1991) Statistical mechanics of neocortical interactions: A scaling paradigm applied to

electroencephalography. Phys. Rev. A 44:4017-4060. [URL http://www.ingber.com/smni91_eeg.ps.gz]

Ingber, L. (1992) Generic mesoscopic neural networks based on statistical mechanics of neocortical interactions.

Phys. Rev. A 45:R2183-R2186. [URL http://www.ingber.com/smni92_mnn.ps.gz]

Ingber, L. (1994) Statistical mechanics of neocortical interactions: Path-integral evolution of short-term memory.

Phys. Rev. E 49:4652-4664. [URL http://www.ingber.com/smni94_stm.ps.gz]

Ingber, L. (1995a) Statistical mechanics of multiple scales of neocortical interactions, In: Neocortical Dynamics

and Human EEG Rhythms, ed. P.L. Nunez. Oxford University Press, 628-681. [ISBN 0-19-505728-7. URL

http://www.ingber.com/smni95_scales.ps.gz]

Ingber, L. (1995b) Statistical mechanics of neocortical interactions: Constraints on 40 Hz models of short-term

memory. Phys. Rev. E 52:4561-4563. [URL http://www.ingber.com/smni95_stm40hz.ps.gz]

Ingber, L. (1996a) Nonlinear nonequilibrium nonquantum nonchaotic statistical mechanics of neocortical

interactions. Behavioral and Brain Sci. 19:300-301. [Invited commentary on Dynamics of the brain at global

and microscopic scales: Neural networks and the EEG, by J.J. Wright and D.T.J. Liley. URL

http://www.ingber.com/smni96_nonlinear.ps.gz]

Basis for the g factor - 10 - Lester Ingber Ingber, L. (1996b) Statistical mechanics of neocortical interactions: Multiple scales of EEG, In: Frontier Science

in EEG: Continuous Waveform Analysis (Electroencephal. clin. Neurophysiol. Suppl. 45), ed. R.M. Dasheiff

& D.J. Vincent. Elsevier, 79-112. [Invited talk to Frontier Science in EEG Symposium, New Orleans, 9 Oct

1993. ISBN 0-444-82429-4. URL http://www.ingber.com/smni96_eeg.ps.gz]

Ingber, L. (1997) Statistical mechanics of neocortical interactions: Applications of canonical momenta indicators

to electroencephalography. Phys. Rev. E 55:4578-4593. [URL http://www.ingber.com/smni97_cmi.ps.gz]

Ingber, L. (1998) Statistical mechanics of neocortical interactions: Training and testing canonical momenta

indicators of EEG. Mathl. Computer Modelling 27:33-64. [URL

http://www.ingber.com/smni98_cmi_test.ps.gz]

Ingber, L. (2000) Statistical mechanics of neocortical interactions: EEG eigenfunctions of short-term memory.

Behavioral and Brain Sci. (to be published). [Invited commentary on Toward a Quantitative Description of

Large-Scale Neo-Cortical Dynamic Function and EEG, by P.L. Nunez. URL

http://www.ingber.com/smni00_eeg_stm.ps.gz]

Ingber, L. & Nunez, P.L. (1990) Multiple scales of statistical physics of neocortex: Application to

electroencephalography. Mathl. Comput. Modelling 13:83-95.

Ingber, L. & Nunez, P.L. (1995) Statistical mechanics of neocortical interactions: High resolution path-integral

calculation of short-term memory. Phys. Rev. E 51:5074-5083. [URL

http://www.ingber.com/smni95_stm.ps.gz]

Langouche, F., Roekaerts, D. & Tirapegui, E. (1982) Functional Integration and Semiclassical Expansions.

Reidel, Dordrecht, The Netherlands.

Miller, G.A. (1956) The magical number seven, plus or minus two. Psychol. Rev. 63:81-97.

Mountcastle, V.B., Andersen, R.A. & Motter, B.C. (1981) The influence of attentive fixation upon the

excitability of the light-sensitive neurons of the posterior parietal cortex. J. Neurosci. 1:1218-1235.

Murdock, B.B., Jr. (1983) A distributed memory model for serial-order information. Psychol. Rev. 90:316-338.

Nunez, P.L. (1981) Electric Fields of the Brain: The Neurophysics of EEG. Oxford University Press, London.

Nunez, P.L. (1989) Towards a physics of neocortex, Vol. 2, In: Advanced Methods of Physiological System

Modeling, ed. V.Z. Marmarelis. Plenum, 241-259.

Nunez, P.L. (1995) Neocortical Dynamics and Human EEG Rhythms. Oxford University Press, New York, NY.

Nunez, P.L. & Srinivasan, R. (1993) Implications of recording strategy for estimates of neocortical dynamics with

electroencephalography. Chaos 3:257-266.

Risken, H. (1989) The Fokker-Planck Equation: Methods of Solution and Applications. Springer-Verlag, Berlin.

Basis for the g factor - 11 - Lester Ingber Zhang, G. & Simon, H.A. (1985) STM capacity for Chinese words and idioms: Chunking and acoustical loop

hypotheses. Memory & Cognition 13:193-201.