## Statistical mechanics of neocortical interactions: A scaling paradigm applied to electroencephalography (1991)

Venue: | PHYS. REV. A |

Citations: | 47 - 41 self |

### BibTeX

@ARTICLE{Ingber91statisticalmechanics,

author = {Lester Ingber},

title = {Statistical mechanics of neocortical interactions: A scaling paradigm applied to electroencephalography},

journal = {PHYS. REV. A},

year = {1991},

volume = {44},

number = {6},

pages = {4017--4060}

}

### Years of Citing Articles

### OpenURL

### Abstract

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) systematics. The necessity of including nonlinear and stochastic structures in this development has been stressed. In this paper, a more stringent test is placed on SMNI: The algebraic and numerical algorithms previously developed in this and similar systems are brought to bear to fit large sets of EEG and 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 discriminate 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 inconclusive because of other neuronal activity which can mask such effects. However, the SMNI model is shown to be consistent

### Citations

3527 | Optimization by Simulated Annealing
- Kirkpatrick, Gelatt, et al.
- 1989
(Show Context)
Citation Context ... T i0 exp(−c ik 1/D ). Heuristic arguments have been developed to demonstrate that this algorithm is faster than the fast Cauchy annealing [174], T i = T 0/k, and much faster than Boltzmann annealin=-=g [175], T i = -=-T 0/lnk. To be more specific, the k th estimate of parameter α i , α i k ∈[A i, B i] , (117) is used with the random variable x i to get the (k + 1)th estimate, α i k+1 = α i k + x i (B i − A ... |

1220 |
Gravitation and Cosmology
- Weinberg
- 1972
(Show Context)
Citation Context ...are still two viable camps of opinions, considering this geometry itself as a basic foundation [117], or considering the physical entities on which its transformations operate as the basic foundation =-=[118]-=-. However, there is unanimous agreement that Riemannian geometry is an essential theoretical construct to explain some observed physical phenomena. The existence of Riemannian geometry also is a natur... |

962 |
The Organization of Behavior
- Hebb
- 1949
(Show Context)
Citation Context ...eds to search for collective behavior, limit cycles, and oscillatory behavior [81-86]. Mechanisms are sought to explain varied phenomena such as hysteresis in perception [84], perception and learning =-=[87,88]-=-, and ontogenesis of columnar formation [88,89]. Comparisons with applications of these techniques to those used in other physical systems [1], illustrates that the pioneering application of these app... |

818 |
Receptive fields, binocular interaction and functiond architecture in the cat's visual cortex
- Hubel, Wiesel
- 1962
(Show Context)
Citation Context ...110 neurons (about 220 in the visual cortex) comprise modular units vertically oriented relative to the warped and convoluted neocortical surface throughout most, if not all, regions of the neocortex =-=[59,61,62,64,103,104]. -=-Clusters of about 100 neurons have been deduced to be reasonable from other considerations as well [43]. Since the short-ranged interactions between neurons take place within ∼1 mm, which is the ext... |

715 |
A logical calculus of the ideas immanent in nervous activity
- McCulloch, Pitts
- 1943
(Show Context)
Citation Context ... mesoscopic cells. These spatially ordered mesoscopic domains respect the observed anatomy and physiology of the neocortex [67,68], complementing earlier theories hypothesizing random neural networks =-=[76,77]-=-. iii. Dynamics. A viable formalism must be adopted to describe the statistical time evolution of the macroscopic nonequilibrium system over scales of 10 2 to 10 4 msec. Although cooperativity between... |

615 | Handbook of Stochastic Methods - Gardiner - 1985 |

314 | Excitatory and inhibitory interactions in localized populations of model neurons - Wilson, Cowan - 1972 |

266 | The Feynman Lectures on - Feynman, Leighton, et al. - 1963 |

257 |
Introduction to the theory of quantized fields
- Bogoliubov, Shirkov
- 1980
(Show Context)
Citation Context ... where Ω is the area of the region considered, and ΛΩ −1 ρ→0 dx dy = lim Λ Σ . (68) ∫ d2r =ΛΩ −1 ∫ Λ→∞ ν =1 The Euler-Lagrange (EL) equations, giving the extrema << M G >>, =-=are obtained from δ ˜S = 0 [111]. Th-=-e Einstein convention is used to designate summation over repeated indices, and the following notation for derivatives is used: (...) :z = d(...)/dz, z = { x, y } , (...), G =∂(...)/∂M G , (...), ... |

252 |
Measuring the strangeness of strange attractors
- Grassberger, Procaccia
- 1983
(Show Context)
Citation Context ...pt, e.g., since the EEG of event-related potentials is likely nonstationary and very much context and subject dependent [141]. Its calculation, e.g., using the popular Grassberger-Procaccia algorithm =-=[142]-=-, even when supplemented with finer statistical tests [143] and noise reduction techniques [144], may prove fruitful, but likely only as a sensitivity index relative to shifting contexts and complemen... |

226 |
Techniques and Applications of path integration
- Schulman
- 1981
(Show Context)
Citation Context ...bing some systems. The introduction of a nonconstant coefficient of even the first-derivative term requires careful treatment. Such a problem arises for a charged particle in an electromagnetic field =-=[29], which or-=-iginally was treated by physical arguments to enforce ‘‘minimal coupling,’’ whereby the momentum p is simply replaced by p − Ae/c, where A is the electromagnetic potential, e is the electric... |

188 | A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue, Kybernetik 13(2): 55–80 - Wilson, Cowan - 1973 |

187 |
T.: Functional architecture of macaque monkey visual cortex. Proceedings of Royal Society on Biology 198
- Hubel, Wiesel
- 1978
(Show Context)
Citation Context ...bserved columnar structure to first attempt to analytically scale the neuronal system into mesoscopic domains that are still relatively microscopic compared to the macroscopic regions to be described =-=[59-61,63,64,88]-=-. For purposes of macroscopic description, the minicolumnar structure effectively spatially averages the neuronal interactions within one to several firing periods. The following development is propos... |

181 | Very fast simulated re-annealing
- Ingber
- 1989
(Show Context)
Citation Context ...determine the degree to which this can be accomplished. As reported here, the solutions are being tested by their goodness of fit to existing EEG data using methods of very fast simulated reannealing =-=[58]. III. S-=-MNI MODEL A. Rationale We begin our ‘‘bottom-up’’ approach by taking the viewpoint that, since there has been much progress made in mathematically describing the physics at finer spatial-tempo... |

152 |
Electric Fields of the Brain: The Neurophysics of EEG
- NUNEZ, SRINIVASAN
- 2005
(Show Context)
Citation Context ...) of average length less than 1 mm, and the long-range cortico-cortical fibers (exclusively excitatory) which form most of the white matter in humans and have an average length of several centimeters =-=[45,46]-=-. There are several noninvasive experimental or clinical methods of recording brain activity, e.g., EEG, magnetoencephalography (MEG), magnetic resonance imaging (MRI), positron-emission tomography (P... |

140 |
Extracting Qualitative Dynamics from Experimental Data
- Broomhead, King
(Show Context)
Citation Context ...t and subject dependent [141]. Its calculation, e.g., using the popular Grassberger-Procaccia algorithm [142], even when supplemented with finer statistical tests [143] and noise reduction techniques =-=[144]-=-, may prove fruitful, but likely only as a sensitivity index relative to shifting contexts and complementary to other models of EEG data. IV. VERIFICATION OF SMNI A. Short-term memory 1. General descr... |

136 |
The Philosophy of Quantum Mechanics
- Jammer
- 1974
(Show Context)
Citation Context ...mplex systems, we inevitably must form functional models to represent huge sets of data. Indeed, modeling phenomena is as much a cornerstone of 20th century science as is collection of empirical data =-=[179]-=-. We hav e been able to fit these sets of EEG data taken during selective attention tasks, using parameters either set to experimentally observed values, or being fitted within experimentally observed... |

120 |
The Magic Number Seven Plus or Minus Two
- Miller
- 1956
(Show Context)
Citation Context ...c bounds for the phenomena of human STM capacity during focused selective attention [16,18,145-147], transpiring on the order of tenths of a second to seconds, limited to the retention of 7 ± 2 items=-= [148]. This i-=-s true even for apparently exceptional memory performers who, while they may be capable of more efficient encoding and retrieval of STM, and while they may be more efficient in ‘‘chunking’’ la... |

119 |
Classical Mechanics 2nd ed
- Goldstein
- 1981
(Show Context)
Citation Context ...of ˆϒ with respect to ˜P, with ˜M constrained to its (possibly multivalued) mean trajectory < ˜M >, is formalized by the use of Lagrange parameters JG. This results in the Legendre transform of l=-=n ˜P [131],-=- and is equivalent to the generating functional ϒ defined in the presence of extrinsic sources JG [121,130]. In the neocortex, some of these JG sources were used to specify firing constraints imposed... |

99 |
Theory of dynamic critical phenomena
- Hohenberg, Halperin
- 1977
(Show Context)
Citation Context ...hese fluctuations are physically important for various excitations and possible critical behavior of second-order phase transitions between ordered and disordered states, e.g., as in magnetic systems =-=[4,108]. Figu-=-res 1(c) and 1(c’) illustrate how the mesocolumnar structure is a substrate for activity persisting for hundreds of milliseconds over a spatial region containing Λ≈5 × 10 5 mesocolumns, spanning... |

92 |
in The Principle of Relativity
- Lorentz
- 1923
(Show Context)
Citation Context ...ractions, i.e., most specifically in the cerebellum, and they hav e gone further to postulate this geometry as the essential component of their theory [113-115]. As developed most notably by Einstein =-=[116]-=-, Riemannian geometry has been firmly established as a necessary component of the foundations of physics. There are still two viable camps of opinions, considering this geometry itself as a basic foun... |

84 | Simulation of chaotic EEG patterns with a dynamic model of the olfactory system - Freeman - 1987 |

62 |
A test for independence based on the correlation dimension
- Brock, Dechert, et al.
- 1996
(Show Context)
Citation Context ...ly nonstationary and very much context and subject dependent [141]. Its calculation, e.g., using the popular Grassberger-Procaccia algorithm [142], even when supplemented with finer statistical tests =-=[143]-=- and noise reduction techniques [144], may prove fruitful, but likely only as a sensitivity index relative to shifting contexts and complementary to other models of EEG data. IV. VERIFICATION OF SMNI ... |

60 |
Movements of attention across the visual field
- Tsal
- 1983
(Show Context)
Citation Context ...e processed simultaneously, possibly giving feedback to the primary sensory regions. The propagation velocities calculated by SMNI, ∼1 cm/sec, also are consistent with observed movements of attentio=-=n [160]-=- and of hallucinations [161] across the visual field. This strongly suggests that nearest-neighbor mesocolumnar interactions as developed here are an important mechanism in these movements. These velo... |

55 |
Information and self-organization: A Macroscopic Approach to Complex Systems
- Haken
- 2000
(Show Context)
Citation Context ...s that many collective aspects of this system may be fruitfully studied similarly to other collective systems, e.g., including magnetic systems, lasers, and more general information-theoretic systems =-=[8,66]. Collec-=-tive effects, from clustering [67,68] or from statistical interactions [69], are proposed to be mechanisms of information processing, in addition to the ‘‘hard-wiring’’ mechanisms also possess... |

47 |
A distributed memory model for serial-order information
- Murdock
- 1983
(Show Context)
Citation Context ... theory is the primacy versus recency effect in STM serial processing, wherein first-learned items are recalled most error-free, with last-learned items still more error-free than those in the middle =-=[153]. The bas-=-ic assumption being made is that a pattern of neuronal firing that persists for many τ cycles is a candidate to store the ‘‘memory’’ of activity that gav e rise to this pattern. If several fi... |

44 |
Stochatic Models in Biology
- Goel, Richter-Dyn
- 1974
(Show Context)
Citation Context ...ics calculations with mesoscopic diffusion equations to study angular winding [10]. These approaches have been directed to study electroencephalography (EEG) [11], as well as other biological systems =-=[12]-=-. Therefore, it should not be surprising that the complex human brain supports many phenomena arising at different spatial-temporal scales. What is perhaps surprising is that it seems possible to stud... |

41 | Statistical mechanics of nonlinear nonequilibrium financial markets - Ingber - 1984 |

40 |
The influence of attentive fixation upon the excitability of the light-sensitive neurons of the posterior parietal cortex
- MOUNTCASTLE, ANDERSEN, et al.
(Show Context)
Citation Context ...text, it is experimentally observed that the synaptic sensitivity of neurons engaged in selective attention is altered, presumably by the influence of chemical neuromodulators on postsynaptic neurons =-=[159]. By this c-=-entering mechanism, B′ E E = 1. 38 and B′ I I = 15. 3, and F G IC is transformed to F G IC′ ,sStatistical Mechanics of Neocortical ... -33- Lester Ingber F E IC′ = 0. 5M I − 0. 25M E π 1/2 ... |

39 |
The ‘module-concept’ in cerebral cortex architecture. Brain Res. 95(2--3):475--496
- Szenta´gothai
- 1975
(Show Context)
Citation Context ...m may be fruitfully studied similarly to other collective systems, e.g., including magnetic systems, lasers, and more general information-theoretic systems [8,66]. Collective effects, from clustering =-=[67,68] or from-=- statistical interactions [69], are proposed to be mechanisms of information processing, in addition to the ‘‘hard-wiring’’ mechanisms also possessed by other more ordered cortical entities [7... |

38 | Statistical mechanics of neocortical interactions: Stability and duration of the 7+-2 rule of short-term-memory capacity,’’ Phys - Ingber - 1985 |

37 | Statistical mechanics of neocortical interactions. Dynamics of synaptic modification. Physical Review A. 28, 395-416. [URL http://www.ingber.com/smni83_dynamics.pdf
- Ingber
- 1983
(Show Context)
Citation Context ...is expanded about L, treating dF G as perturbations. This yields Eq. (41) in terms of V ′, the nearest-neighbor potential. 4. Further development of mesocolumn model As pointed out in this derivatio=-=n [14,15], th-=-is microscopic scale itself represents a high aggregation of submicroscopic scales, aggregating effects of tens of thousands of quanta of chemical transmitters as they influence the 5 × 10 −3 µm s... |

36 | Statistical mechanics of multiple scales of neocortical interactions - Ingber - 1995 |

35 | Mathematical comparison of combat computer models to exercise data
- Ingber, Fujio, et al.
- 1991
(Show Context)
Citation Context ...ation has a utility beyond its deterministic Euler-Lagrange limit. We hav e utilized this to explicitly examine the long-time evolution of systems, to compare models to long-time correlations in data =-=[36,37]-=-. This use is being extended to other systems, in finance [41,42] and in EEG modeling as described here.sStatistical Mechanics of Neocortical ... -8- Lester Ingber D. Macroscopic coarse graining and r... |

35 |
Distinguishing Random and Deterministic System
- Brock
- 1986
(Show Context)
Citation Context ...riances did increase somewhat during the middle of the battle. In summary, this battalion-regiment scale of battle does not seem to possess chaos. Similar to serious work undertaken in several fields =-=[135,136], here t-=-oo, the impulse to identify ‘‘chaos’’ in a complex system has been premature. It is not supported by the facts, tentative as they are because of sparse data. Of course, some other combat condi... |

34 | The existence of persistent states in the brain - Little - 1974 |

34 |
Fast simulated annealing,” Phys
- Szu, Harley
- 1987
(Show Context)
Citation Context ...n ‘‘time’’ (cycle number of iterative process) k, i.e., T i = T i0 exp(−c ik 1/D ). Heuristic arguments have been developed to demonstrate that this algorithm is faster than the fast Cauchy =-=annealing [174], T -=-i = T 0/k, and much faster than Boltzmann annealing [175], T i = T 0/lnk. To be more specific, the k th estimate of parameter α i , α i k ∈[A i, B i] , (117) is used with the random variable x i t... |

33 |
Statistical Mechanics (World Scientific
- Ma
- 1985
(Show Context)
Citation Context ...ems are in nonequilibrium, being driven by nonlinear and stochastic interactions of many external and internal degrees of freedom. For these systems, classical thermodynamics typically does not apply =-=[3]-=-. For example, the description of weather and ocean patterns, which attempt to include important features such as turbulence, rely on semiphenomenological mesoscopic models, those in agreement with mo... |

33 |
Statistical mechanics of neocortical interactions. Derivation of short-term-memory capacity. Physical Review A.29, 3346-3358. [URL http://www.ingber.com/smni84_stm.pdf
- Ingber
- 1984
(Show Context)
Citation Context ...es M G are fields which themselves may depend on space and time coordinates. The above equation is derived in the nearest-neighbor approximation from the general equation using functional derivatives =-=[16], ∂(...)/∂M G ��-=-� δ (...)/δ M G , δ (...)/δ M G = (...) ,G −∇i(...) ,∇iG +∇ 2 i (...) ,∇2 i G , (89) where we have used the compacted notation introduced previously [16]. An estimate of a stationary sol... |

33 | Draft of Statistical Mechanical Aids to Calculating Term Structure Models
- Ingber, L
- 1990
(Show Context)
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32 |
Statistical mechanics of neocortical interactions
- Ingber
- 1986
(Show Context)
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32 | Application of statistical mechanics methodology to term-structure bond-pricing models
- Ingber, Wehner, et al.
- 1991
(Show Context)
Citation Context .... We hav e utilized this to explicitly examine the long-time evolution of systems, to compare models to long-time correlations in data [36,37]. This use is being extended to other systems, in finance =-=[41,42]-=- and in EEG modeling as described here.sStatistical Mechanics of Neocortical ... -8- Lester Ingber D. Macroscopic coarse graining and renormalization We now are in a position to address the issue pose... |

32 |
Theory, the Renormalization Group
- Amit, “Field
- 1984
(Show Context)
Citation Context ...,24]. ϒJ=0 is a proper potential, i.e., it possesses free-energy-like properties, having a true minimum about (< ˜M > J − << ˜M >>), where << ˜M >> is the extremum of L obtained by maximizing ˜=-=P( ˜M) [133]. Its lowest-=--order approximate ϒ (0) gives the mean-field approximation: ϒ (0) = ˜S(< ˜M >). (82) T , defined as the ‘‘kinetic-energy’’ dF-independent part of L, is scale independent of N. Therefore, ... |

31 | Problems in Physics with Many Scales of Length," Scienti c - Wilson - 1979 |

30 |
Covariant formulation of non-equilibrium statistical thermodynamics. Zeitschrift für Physik
- Graham
- 1977
(Show Context)
Citation Context ...t to the mathematics of the neocortex. The first real breakthrough was achieved by noting how these issues should be treated in the context of classical nonlinear nonequilibrium statistical mechanics =-=[30,31]-=-. While application has been made of these new mathematical physics techniques in quantum and classical statistical mechanics [32-34], we are not merely bringing over techniques to neuroscience from o... |

29 | Tow ards a unified brain theory - Ingber - 1981 |

29 | Statistical mechanics of neocortical interactions. EEG dispersion relations
- Ingber
- 1985
(Show Context)
Citation Context ...r activity of columns of neurons, to finally achieve a reasonable macroscopic description of EEG activity. The confluence of these approaches is expected to yield a tractable approach to EEG analyses =-=[17,24,44]-=-. Section II presents the current dipole string model as a top-down approach to give a rationale for incorporating several scales of neuronal interactions in order to understand macroscopic EEG phenom... |

29 |
Numerical evaluation of path–integral solutions to Fokker–Planck equations. II. Restricted stochastic processes, Phys
- Wehner, Wolfer
- 1983
(Show Context)
Citation Context ...and the ‘‘action’’ NL, such that θ NL ≤ 1. By considering the contributions to the first and second moments of ∆M G for small time slices θ , conditions on the time and variable meshes c=-=an be derived [123]. The-=- time slice is determined by θ ≤ (NL) −1 throughout the ranges of M G giving the most important contributions to the probability distribution P. The variable mesh, a function of M G , is optimall... |

29 | Spatial properties of an EEG event in the olfactory bulb and cortex - Freeman - 1978 |

28 |
Multiple scales of statistical physics of neocortex: Application to electroencephalography
- Ingber, Nunez
- 1990
(Show Context)
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