## Statistical mechanics of multiple scales of neocortical interactions (1995)

Venue: | in Neocortical Dynamics and Human EEG Rhythms, (Edited by P.L. Nunez |

Citations: | 36 - 18 self |

### BibTeX

@INPROCEEDINGS{Ingber95statisticalmechanics,

author = {Lester Ingber},

title = {Statistical mechanics of multiple scales of neocortical interactions},

booktitle = {in Neocortical Dynamics and Human EEG Rhythms, (Edited by P.L. Nunez},

year = {1995},

pages = {628--681},

publisher = {University Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

14. Statistical mechanics of multiple scales of neocortical interactions

### Citations

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Citation Context ...able camps of opinions, considering this geometry itself as a basic foundation (Misner et al, 1973), or considering the physical entities on which its transformations operate as the basic foundation (=-=Weinberg, 1972-=-). 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 natu... |

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Citation Context ...lson, 1977; H.R. Wilson and Cowan, 1972; H.R. Wilson and Cowan, 1973). Mechanisms are sought to explain varied phenomena such as hysteresis in perception (H.R. Wilson, 1977), perception and learning (=-=Hebb, 1949-=-; Takeuchi and Amari, 1979), and ontogenesis of columnar formation (Takeuchi and Amari, 1979; von der Marlsburg, 1979). Comparisons with applications of these techniques to those used in other physica... |

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Citation Context ...anatomical minicolumn out to a macrocolumnar extent. Calculations support observations of periodically alternating firings of columnar structures (Fitzpatrick and Imig, 1980; Goldman and Nauta, 1977; =-=Hubel and Wiesel, 1962-=-; Hubel and Wiesel, 1977; Jones et al, 1978). As pictured in Fig. 14-1, this microscopic scale is orders of magnitude larger than the molecular scale of membrane biophysics. Also note that “macrocolum... |

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A logical calculus of the ideas immanent in nervous activity
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Citation Context ...s respect the observed anatomy and physiology of the neocortex (Szentágothai, 1975; Szentágothai and Arbib, 1974), complementing earlier theories hypothesizing random neural networks (Griffith, 1971; =-=McCulloch and Pitts, 1943-=-). 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 betwee... |

617 |
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Citation Context ... general theory of nonequilibrium nonlinear process, there are several overlapping approaches, typically geared to classes of systems, usually expanding on nonlinear treatments of stochastic systems (=-=Gardiner, 1983-=-; Haken, 1983; Kubo et al, 1973; Nicolis and Prigogine, 1973; van Kampen, 1981). Many biological systems give rise to phenomena at overlapping spatial-temporal scales. For example, the coiling of DNA ... |

314 | Excitatory and inhibitory interactions in localized populations of model neurons
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Citation Context ...gs, and then proceeds to search for collective behavior, limit cycles, and oscillatory behavior (Babloyantz and Kaczmarek, 1979; Freeman, 1975; Kaczmarek and Babloyantz, 1977; H.R. Wilson, 1977; H.R. =-=Wilson and Cowan, 1972-=-; H.R. Wilson and Cowan, 1973). Mechanisms are sought to explain varied phenomena such as hysteresis in perception (H.R. Wilson, 1977), perception and learning (Hebb, 1949; Takeuchi and Amari, 1979), ... |

266 |
The Feynman Lectures on
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Citation Context ...st order in an expansion about the most likely state of a quantum or stochastic system, gives a global formulation and generalization of the well-known relation, force equals mass times acceleration (=-=Feynman et al, 1963-=-). In the neocortex, the velocity corresponds to the rate of firing of a column of neurons, and a potential is derived which includes nearest-neighbor interactions between columns. The Lagrangian form... |

226 |
Techniques and Applications of path integration
- Schulman
- 1981
(Show Context)
Citation Context ...ing 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 (=-=Schulman, 1981-=-), which originally 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 |
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Citation Context ...ch for collective behavior, limit cycles, and oscillatory behavior (Babloyantz and Kaczmarek, 1979; Freeman, 1975; Kaczmarek and Babloyantz, 1977; H.R. Wilson, 1977; H.R. Wilson and Cowan, 1972; H.R. =-=Wilson and Cowan, 1973-=-). Mechanisms are sought to explain varied phenomena such as hysteresis in perception (H.R. Wilson, 1977), perception and learning (Hebb, 1949; Takeuchi and Amari, 1979), and ontogenesis of columnar f... |

187 |
T.: Functional architecture of macaque monkey visual cortex. Proceedings of Royal Society on Biology 198
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Citation Context ...t to a macrocolumnar extent. Calculations support observations of periodically alternating firings of columnar structures (Fitzpatrick and Imig, 1980; Goldman and Nauta, 1977; Hubel and Wiesel, 1962; =-=Hubel and Wiesel, 1977-=-; Jones et al, 1978). As pictured in Fig. 14-1, this microscopic scale is orders of magnitude larger than the molecular scale of membrane biophysics. Also note that “macrocolumns” spanning roughly 7 ×... |

181 | Very fast simulated re-annealing
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- 1989
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Citation Context ...e 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 (VFSR) (=-=Ingber, 1989-=-; Ingber, 1993b; Ingber and Rosen, 1992), the precursor to a more powerful code, adaptive simulated annealing (ASA) (Ingber, 1993a). 3. BOTTOM-UP SMNI MODEL 3.1. Rationale We begin our “bottom-up” app... |

158 | Simulated annealing: Practice versus theory
- Ingber
- 1993
(Show Context)
Citation Context ... useful pedagogically. The mathematical approach presented here also has been useful to describe phenomena in social systems, ranging from military command, control and communications (Ingber, 1991a; =-=Ingber, 1993-=-c; Ingber, Fujio, and Wehner, 1991; Ingber and Sworder, 1991), to political systems (Weidlich and Haag, 1983), to pricing bonds on financial markets (Ingber, 1984c; Ingber, 1990; Ingber, Wehner et al,... |

152 |
Electric Fields of the Brain: The Neurophysics of EEG
- NUNEZ, SRINIVASAN
- 2005
(Show Context)
Citation Context ...stion: What can we say about ˆΦ(x, t), the macroscopic observable displacement potential on the scalp or cortical surface? On the basis of previous studies of EEG dispersion relations (Ingber, 1985c; =-=Nunez, 1981-=-a), it would seem that we should be able to describe ˆΦ as a linear or quasilinear variable, but influenced by the local nonlinear behavior that crosses the hierarchical level from mesoscopic to macro... |

136 |
The Philosophy of Quantum Mechanics
- Jammer
- 1974
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Citation Context ...plex 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 (=-=Jammer, 1974-=-). The ability to fit data to these particular SMNI functional forms goes beyond nonlinear statistical modeling of data. The plausibility of the SMNI model, as emphasized in this and previous SMNI pap... |

120 |
The Magic Number Seven Plus or Minus Two
- Miller
- 1956
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Citation Context ...sed selective attention (Ingber, 1972; Ingber, 1981b; Ingber, 1984b; Ingber, 1985a; Ingber, 1985d), transpiring on the order of tenths of a second to seconds, limited to the retention of 7 ± 2 items (=-=Miller, 1956-=-). This is 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” lar... |

93 |
An Organizing Principle for Cerebral Function: The Unit Model and the Distributed System
- Mountcastle
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Citation Context ...l be used to support the “top-down” development described above.sStatistical mechanics of multiple scales ... -11- Lester Ingber A major contribution of SMNI is its analytic treatment of minicolumns (=-=Mountcastle, 1978-=-). Minicolumns are observed to span approximately 7 × 10 2 µm 2 , as discussed in Chapter 2. Mesocolumnar domains are defined here as physiological (functional) units, with input converging from an an... |

92 |
in The Principle of Relativity
- Lorentz
- 1923
(Show Context)
Citation Context ... theory (A. Pellionisz and Llinás, 1979; A. Pellionisz and Llinás, 1980; A.J. Pellionisz, 1984).sStatistical mechanics of multiple scales ... -28- Lester Ingber As developed most notably by Einstein (=-=Einstein et al, 1923-=-), 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 fou... |

55 |
Information and self-organization: A Macroscopic Approach to Complex Systems
- Haken
- 2000
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Citation Context ...such that all intermediate-time values of ˜M appearing in the folded short-time distributions ˜P are integrated over. This is quite general for any system that can be described as Gaussian-Markovian (=-=Haken, 1988-=-), even if only in the short-time limit, e.g., the SMNI theory. (As time evolves, the distribution likely no longer behaves in a Gaussian manner, and the apparent simplicity of the short-time distribu... |

47 | Statistical mechanics of neocortical interactions: A scaling paradigm applied to electroencephalography
- Ingber
- 1991
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Citation Context ...M G /∂t)∂(∂M G′ /∂t) F = ma δ LF = 0 = ∂L F ∂ − ∂M G ∂t ∂L F ∂(∂M G /∂t) (14.28) These physical entities provide another form of intuitive, but quantitatively precise, presentation of these analyses (=-=Ingber, 1991-=-a). The key issue is that Riemannian geometry is not required to derive the mathematics of multiplicative Gaussian-Markovian systems. More interestingly, after this derivation, it can be demonstrated ... |

47 |
A distributed memory model for serial-order information
- Murdock
- 1983
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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 (=-=Murdock, 1983-=-). The basic 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 fir... |

44 |
Stochatic Models in Biology
- Goel, Richter-Dyn
- 1974
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Citation Context ...mesoscopic diffusion equations to study angular winding (Cartling, 1989). These approaches have been directed to study electroencephalography (EEG) (Basar, 1980), as well as other biological systems (=-=Goel and Richter-Dyn, 1974-=-).sStatistical mechanics of multiple scales ... -3- Lester Ingber Therefore, it should not be surprising that the complex human brain supports many phenomena arising at different spatial-temporal scal... |

41 | Statistical mechanics of nonlinear nonequilibrium financial markets: Applications to optimized trading
- Ingber
- 1996
(Show Context)
Citation Context ...defined in terms of electrical-chemical synaptic and neuronal parameters all lying within their experimentally observed ranges. 4.1.2. STM calculation Three cases of neuronal firings were considered (=-=Ingber, 1984-=-b). That reference is recommended for several figures that exhibit the minima structures algebraically described below. Since STM duration is still long relative to τ ,stationary solutions of L, deriv... |

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 ...ext, 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 (=-=Mountcastle et al, 1981-=-). By this centering mechanism, B′ E E = 1. 38 and B′ I I = 15. 3, and F G IC is transformed to F G IC′ , F E IC′ = F I IC′ = 0. 5M I − 0. 25M E π 1/2 (0. 1M I + 0. 05M E , + 10. 4) 1/2 0. 005M I − 0.... |

39 |
The ‘module-concept’ in cerebral cortex architecture. Brain Res. 95(2--3):475--496
- Szenta´gothai
- 1975
(Show Context)
Citation Context ...d similarly to other collective systems, e.g., including magnetic systems, lasers, and more general information-theoretic systems (Haken, 1988; van Kampen, 1981). Collective effects, from clustering (=-=Szentágothai, 1975-=-; Szentágothai and Arbib, 1974) or from statistical interactions (Katchalsky et al, 1974), are proposed to be mechanisms of information processing, in addition to the “hard-wiring” mechanisms also pos... |

38 |
Statistical mechanics of neocortical interactions: Stability and duration of the 7+-2 rule of short-term-memory capacity,’’ Phys
- Ingber
- 1985
(Show Context)
Citation Context ...erlapping microscopic and mesoscopic scales. A series of papers has developed this statistical mechanics of neocortical interactions (SMNI) (Ingber, 1981c; Ingber, 1982; Ingber, 1983b; Ingber, 1984b; =-=Ingber, 1985-=-c; Ingber, 1985d; Ingber, 1985e; Ingber, 1986b; Ingber, 1988a; Ingber, 1988b; Ingber, 1988c; Ingber, 1991b; Ingber, 1992; Ingber, 1996; Ingber and Nunez, 1990). This approach permits us to find models... |

35 | Mathematical comparison of combat computer models to exercise data
- Ingber, Fujio, et al.
- 1991
(Show Context)
Citation Context ...ically. The mathematical approach presented here also has been useful to describe phenomena in social systems, ranging from military command, control and communications (Ingber, 1991a; Ingber, 1993c; =-=Ingber, Fujio, and Wehner, 1991-=-; Ingber and Sworder, 1991), to political systems (Weidlich and Haag, 1983), to pricing bonds on financial markets (Ingber, 1984c; Ingber, 1990; Ingber, Wehner et al, 1991). In this context, it has be... |

34 |
Statistical Mechanics; World Scientific
- Ma
- 1985
(Show Context)
Citation Context ...ms 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 (=-=Ma, 1985-=-). 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 m... |

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 ...f we consider the area of influence of a minicolumn as extending out to a macrocolumn’s reach, then the area of interactions engaged by nearest-neighbor minicolumns has an offset circle of influence (=-=Ingber, 1984-=-b). (See Fig. 14-3.) Therefore, within one or two epochs spanning the refractory periods of a typical neuron, interactions engaged by a given minicolumn can be extended out to areas of influence engag... |

33 | Statistical mechanical aids to calculating term structure models
- Ingber
- 1990
(Show Context)
Citation Context ...ations (Ingber, 1991a; Ingber, 1993c; Ingber, Fujio, and Wehner, 1991; Ingber and Sworder, 1991), to political systems (Weidlich and Haag, 1983), to pricing bonds on financial markets (Ingber, 1984c; =-=Ingber, 1990-=-; Ingber, Wehner et al, 1991). In this context, it has been noted that the activity of neurons may resemble the activity of a throng of people, in which interactions take place at multiple hierarchica... |

32 |
Statistical mechanics of neocortical interactions
- Ingber
- 1986
(Show Context)
Citation Context ...ling to a chain of arguments dealing with overlapping microscopic and mesoscopic scales. A series of papers has developed this statistical mechanics of neocortical interactions (SMNI) (Ingber, 1981c; =-=Ingber, 1982-=-; Ingber, 1983b; Ingber, 1984b; Ingber, 1985c; Ingber, 1985d; Ingber, 1985e; Ingber, 1986b; Ingber, 1988a; Ingber, 1988b; Ingber, 1988c; Ingber, 1991b; Ingber, 1992; Ingber, 1996; Ingber and Nunez, 19... |

32 | Application of statistical mechanics methodology to term-structure bond-pricing models - Ingber, Wehner, et al. - 1991 |

30 |
Covariant formulation of non-equilibrium statistical thermodynamics. Zeitschrift für Physik
- Graham
- 1977
(Show Context)
Citation Context ... 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 (=-=Graham, 1977-=-a; Graham, 1977b). While application has been made of these new mathematical physics techniques in quantum and classical statistical mechanics (Ingber, 1983a; Ingber, 1984a; Ingber, 1986a), we are not... |

29 |
Spatial properties of an EEG event in the olfactory bulb and cortex
- Freeman
- 1978
(Show Context)
Citation Context ...might fundamentally be responsible for macroscopic activity, other than those proposed here which detail synaptic dynamics of mesocolumnar interactions (Amari, 1983; Anninos et al, 1983; Basar, 1980; =-=Freeman, 1978-=-; Klemm and Sherry, 1981; Steriade, 1981; Traub and Llinás, 1979). For example, given the present lack of experimental knowledge, it is possible to formulate macroscopic neocortical activity in terms ... |

29 | Tow ards a unified brain theory
- Ingber
- 1981
(Show Context)
Citation Context ...as EEG by appealing to a chain of arguments dealing with overlapping microscopic and mesoscopic scales. A series of papers has developed this statistical mechanics of neocortical interactions (SMNI) (=-=Ingber, 1981-=-c; Ingber, 1982; Ingber, 1983b; Ingber, 1984b; Ingber, 1985c; Ingber, 1985d; Ingber, 1985e; Ingber, 1986b; Ingber, 1988a; Ingber, 1988b; Ingber, 1988c; Ingber, 1991b; Ingber, 1992; Ingber, 1996; Ingbe... |

29 |
Numerical evaluation of path–integral solutions to Fokker–Planck equations. II. Restricted stochastic processes, Phys
- Wehner, Wolfer
- 1983
(Show Context)
Citation Context ...ar systems to data using methods of ASA (Ingber, 1989; Ingber, 1993a; Ingber, 1993b), and then integrating the path integral using a non-Monte Carlo technique especially suited for nonlinear systems (=-=Wehner and Wolfer, 1983-=-a; Wehner and Wolfer, 1983b; Wehner and Wolfer, 1987). This numerical methodology has been applied with success to military modeling (Ingber, Fujio, and Wehner, 1991; Ingber and Sworder, 1991) and to ... |

28 | Generic mesoscopic neural networks based on statistical mechanics of neocortical interactions
- Ingber
- 1992
(Show Context)
Citation Context ...interactions (SMNI) (Ingber, 1981c; Ingber, 1982; Ingber, 1983b; Ingber, 1984b; Ingber, 1985c; Ingber, 1985d; Ingber, 1985e; Ingber, 1986b; Ingber, 1988a; Ingber, 1988b; Ingber, 1988c; Ingber, 1991b; =-=Ingber, 1992-=-; Ingber, 1996; Ingber and Nunez, 1990). This approach permits us to find models of EEG whose variables and parameters are reasonably identified with ensembles of synaptic and neuronal interactions. T... |

28 |
STM capacity for Chinese words and idioms: Chunking and acoustical loop hypothesis. Memory and Cognition, 13, 193-201. 24, 2007 27 Authors' note Preparation of this article was supported by grant no 8210-30606 from the Swiss National Funds of Scientific R
- Zhang, Simon
- 1985
(Show Context)
Citation Context ...al STM, but for visual or semantic STM, which typically require longer times for rehearsal in an hypothesized articulatory loop of individual items, STM capacity appears to be limited to two to four (=-=Zhang and Simon, 1985-=-). This STM capacity-limited chunking phenomenon also has been noted with items requiring varying depths and breadths of processing (Ingber, 1972; Ingber, 1976; Ingber, 1981a; Ingber, 1981b; Ingber, 1... |

26 |
Path-integral methods in nonequilibrium thermodynamics and statistics
- Graham
- 1978
(Show Context)
Citation Context ...ure to compare different subjects within certain categories. With reference to a steady state P( ˜M), when it exists, an analytic definition of the information gain ˆϒ in state ˜P( ˜M) is defined by (=-=Graham, 1978-=-; Haken, 1983) ˆϒ[ ˜P] = ∫ ... ∫ D ˜M ˜P ln( ˜P/P), (14.29)sStatistical mechanics of multiple scales ... -31- Lester Ingber where again a path integral is defined such that all intermediate-time value... |

25 |
The neuron network of the cerebral cortex: a functional interpretation
- Szentágothai
- 1978
(Show Context)
Citation Context ...ribution of firings in a minicolumn, composed of ∼ 10 2 neurons (Gilbert and Wiesel, 1983; Goldman and Nauta, 1977; Hubel and Wiesel, 1962; Imig and Reale, 1980; Jones et al, 1978; Mountcastle, 1978; =-=Szentágothai, 1978-=-), given its just previous interactions with all other neurons in its macrocolumnar surround. P = G Π P G [M G (r; t + τ )|M G (r′; t)] ⎛ Σ δ ⎜ ⎝ jEΣ σ j − M E ⎞ ⎛ (r; t + τ ) ⎟ δ ⎜ ⎠ ⎝ jI Σ σ j − M I... |

24 |
Concepts and Models of a Quantitative Sociology
- Weidlich, Haag
- 1983
(Show Context)
Citation Context ...phenomena in social systems, ranging from military command, control and communications (Ingber, 1991a; Ingber, 1993c; Ingber, Fujio, and Wehner, 1991; Ingber and Sworder, 1991), to political systems (=-=Weidlich and Haag, 1983-=-), to pricing bonds on financial markets (Ingber, 1984c; Ingber, 1990; Ingber, Wehner et al, 1991). In this context, it has been noted that the activity of neurons may resemble the activity of a thron... |

21 |
Theory of Self-Organizing Neural Nets
- Field
- 1983
(Show Context)
Citation Context ...are respectable candidates for mechanisms that might fundamentally be responsible for macroscopic activity, other than those proposed here which detail synaptic dynamics of mesocolumnar interactions (=-=Amari, 1983-=-; Anninos et al, 1983; Basar, 1980; Freeman, 1978; Klemm and Sherry, 1981; Steriade, 1981; Traub and Llinás, 1979). For example, given the present lack of experimental knowledge, it is possible to for... |

21 |
1974], The Existence of Persistent States
- Little
(Show Context)
Citation Context ...G contribution to the drifts, the driving terms, in the Lagrangian. The mesoscopic development discussed below retains this sensitivity. This is similar to the mathematical result obtained by others (=-=Little, 1974-=-; Little and Shaw, 1978; Shaw and Vasudevan, 1974) who have modeled the neocortex after magnetic systems (Cragg and Temperley, 1954). However, the following is derived more generally, and has the neur... |

21 |
Tensorial approach to the geometry of brain function: Cerebellar coordination via metric tensor
- Pellionisz, Llinàs
- 1980
(Show Context)
Citation Context ...cortical interactions, i.e., most specifically in the cerebellum, and they hav e gone further to postulate this geometry as the essential component of their theory (A. Pellionisz and Llinás, 1979; A. =-=Pellionisz and Llinás, 1980-=-; A.J. Pellionisz, 1984).sStatistical mechanics of multiple scales ... -28- Lester Ingber As developed most notably by Einstein (Einstein et al, 1923), Riemannian geometry has been firmly established ... |

20 |
Statistical mechanics of combat with human factors
- Ingber, Sworder
- 1991
(Show Context)
Citation Context ... presented here also has been useful to describe phenomena in social systems, ranging from military command, control and communications (Ingber, 1991a; Ingber, 1993c; Ingber, Fujio, and Wehner, 1991; =-=Ingber and Sworder, 1991-=-), to political systems (Weidlich and Haag, 1983), to pricing bonds on financial markets (Ingber, 1984c; Ingber, 1990; Ingber, Wehner et al, 1991). In this context, it has been noted that the activity... |

20 |
Event-related potentials in individuals at risk for alcoholism. Alcohol
- Porjesz, Begleiter
- 1990
(Show Context)
Citation Context ...ta from a multi-electrode array under a variety of conditions. We fit data collected under a project sponsored by the National Institute on Alcohol Abuse and Alcoholism (NIAAA) project (Holden, 1991; =-=Porjesz and Begleiter, 1990-=-). 5.1. Algebraic development We take Eq. (14.6) as the basic probability distribution to fit this data. We also take advantage of and extend the results gained for the STM analysis discussed previous... |

19 |
Modern Theory of Critical Phenomena, Benjamin/Cummings
- Ma
- 1976
(Show Context)
Citation Context ...logical mesoscopic models, those in agreement with molecular theories but not capable of being rigorously derived from them. Phase transitions in magnetic systems, and many systems similarly modeled (=-=Ma, 1976-=-; K.G. Wilson, 1979; K.G. Wilson and Kogurt, 1974), require careful treatment of a continuum of scales near critical points. In general, rather than having a general theory of nonequilibrium nonlinear... |

18 |
Analytic study of the memory storage capacity of a neural network
- Little, Shaw
- 1978
(Show Context)
Citation Context ... to the drifts, the driving terms, in the Lagrangian. The mesoscopic development discussed below retains this sensitivity. This is similar to the mathematical result obtained by others (Little, 1974; =-=Little and Shaw, 1978-=-; Shaw and Vasudevan, 1974) who have modeled the neocortex after magnetic systems (Cragg and Temperley, 1954). However, the following is derived more generally, and has the neural parameters more spec... |

17 |
Coiumnar distribution of cortico-cortical fibers in the frontal association, limbic and motor cortex of the developing rhesus monkey
- GOLDMAN-RAKIC, NAUTA
- 1977
(Show Context)
Citation Context ...output diverging from an anatomical minicolumn out to a macrocolumnar extent. Calculations support observations of periodically alternating firings of columnar structures (Fitzpatrick and Imig, 1980; =-=Goldman and Nauta, 1977-=-; Hubel and Wiesel, 1962; Hubel and Wiesel, 1977; Jones et al, 1978). As pictured in Fig. 14-1, this microscopic scale is orders of magnitude larger than the molecular scale of membrane biophysics. Al... |

17 |
Fluctuations and nonlinear irreversible processes
- Grabert, Green
(Show Context)
Citation Context ...k equation is the discretization problem in the path integral and in the Langevin rate equations, both of which are equivalent mathematical representations of the Fokker-Plank equation (Dekker, 1980; =-=Grabert and Green, 1979-=-; Graham, 1977a; Graham, 1977b; Langouche et al, 1982; Schulman, 1981). An overview of these equations is required to at least note where the Riemannian geometry enters. The appendix of an SMNI paper ... |

17 |
intracortical connectivity of architectonic fields in the somatic sensory, motor and parietal cortex of monkeys
- JONES, COULTER, et al.
- 1978
(Show Context)
Citation Context ...ent. Calculations support observations of periodically alternating firings of columnar structures (Fitzpatrick and Imig, 1980; Goldman and Nauta, 1977; Hubel and Wiesel, 1962; Hubel and Wiesel, 1977; =-=Jones et al, 1978-=-). As pictured in Fig. 14-1, this microscopic scale is orders of magnitude larger than the molecular scale of membrane biophysics. Also note that “macrocolumns” spanning roughly 7 × 10 5 µm 2 have bee... |