neural complexity

The following is an example of neural complexity from the book Consciousness by G. Edelman and G. Tononi.

“As an illustration, it is useful to calculate complexity for three extreme examples of the organization of a cerebral cortical area corresponding to an old, diseased brain; a young, immature brain; and a normal adult brain (the simulated examples are actually based on the primary visual cortex of the cat). The simulated cortical area contained 512 neuronal groups, each of which responded preferentially to a given position in the visual field and to a given stimulus orientation.10 The simulated cortical area was based on a detailed model that was used to investigate how the brain can give rise to the so-called Gestalt properties of visual perception—the way stimuli are grouped to form objects and are segregated from the background.” For the present purposes, we required that the simulated cortical area was isolated; it did not receive any visual input, and its neurons were “spontaneously” active.12
The first example in figure 11.3 (top row) represents a cortical area in which the density of intra-areal connections among different groups of neurons had been deliberately reduced (for example, in an old and deteriorated brain). In such a cortical area, individual groups of neurons are still active, but, because of the loss of intra-areal connections, they fire more or less independently. Such a system behaves essentially like a “neural gas” or, if examined on a computer monitor, like a TV set that is not properly tuned. The electroencephalogram of such a cortical area shows the absence of synchronization among its constituent neuronal groups.13 The entropy of the system is high because of the large number of elements and their high individual variance: The system can take a large number of states. From the point of view of an external observer or homunculus who might assign a different meaning to each state of the system, this system would indeed appear to contain a large amount of information. But what about information from the point of view of the system itself—the number of states that make a difference to the system itself? Since there is little interaction between any subset of elements and the rest of the system, whatever the state of that subset might be, there is little or no effect on the rest of the system, or vice versa. The value of the mutual information is correspondingly low, and since this holds true for every possible subset, the complexity of the system is also low. In other words, although there are many differences within the system, they make no difference to it. Such a neural system is certainly noisy, but it is not differentiated. The second example is of an immature, young cortex, in which every neuronal group is connected to all other neuronal groups in a uniform way (see figure 11.3, bottom row). In the simulations, all groups of neurons soon started oscillating together coherently almost without exception. The calculated EEG is hypersynchronous, resembling the high-voltage waves of slow-wave sleep or of generalized epilepsy. The system is highly integrated, but functional specialization is completely lost. Since the system can take up only a limited number of states, its entropy is low. The average mutual information between individual elements and the rest of the system is higher than in the previous case, since there are strong interactions. However, when larger and larger subsets are taken into consideration, the mutual information does not increase significantly because the number of different states that can be discriminated does not increase with the size of the subsets. The complexity of the system is correspondingly low. In other words, because there are few differences within the system, the difference they make to the system is small. The system is integrated but not differentiated.
In the third example, corresponding to a normal, adult cortex (see figure 11.3, middle row), groups of neurons are connected to each other according to the following rules. First, groups of neurons having similar visual orientation preferences tend to be more connected to each other. Second, they are connected so that the strength of the connections decreases with topographic distance. These rules of connectivity closely correspond to those found experimentally in the primary visual cortex.14 In this example, the dynamic behaviour of the system is far more complex than in the previous two: Groups of neurons show both an overall coherent behaviour yet group and regroup themselves dynamically according to their specific functional interactions. For example, neighbouring groups of similar orientation preference tend to fire synchronously more often than functionally unrelated groups, but at times, almost the entire cortical area may show short periods of coherent oscillations, as reflected by a calculated EEG that resembles that of waking or REM sleep. The entropy of the system is high, but not as high as in the first example (although the system can have a large number of states, some are more likely than others). The mutual information between individual elements and the rest of the system is, on average, high, reflecting significant interactions, just as in the second example. In contrast to the second example, however, the average mutual information increases considerably when we take into account subsets composed of a larger number of elements. Thus, the overall complexity is high because, in such a system, the larger the subset, the larger the number of different states that the subset can bring about in the rest of the system, and vice versa. In other words, there are many differences, and they make a lot of difference to the system. The system is both integrated and highly differentiated.”

graph-on-complexity1

FIGURE 1 1.3 HOW COMPLEXITY VARIES, DEPENDING ON NEUROANATOMICAL ORGANIZATION. Complexity values were obtained from simulations of a primary visual cortical area. The figure shows three cases. In the first case (upper row), the simulated cortical area has sparse connectivity (first column: Anatomy). Neuronal groups fire almost independently (second column: Activity): the 30 small squares within the rectangle indicate the pattern of firing every 2 milliseconds (from left to right and from top to bottom) of 512 neuronal groups that are spontaneously active. The third column represents the EEG, which is essentially flat, indicating that the neuronal groups are not synchronized. Complexity (the area under the curve in the fourth column) is low. In the third case (lower row), the simulated cortical area has random connectivity. Neuronal groups are completely synchronized and oscillate together. The EEG shows hyper-synchronous activity reminiscent of slow-wave sleep, epileptic seizures, or anesthesia. Complexity is low. In the second case (middle row), the simulated cortical area has a patchy connectivity that corresponds to the one found in the cortex. Neuronal groups display continually changing integrated activity patterns. The EEG shows that synchronization waxes and wanes and that different groups of neurons synchronize at different times. Complexity is high.

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One Response to “neural complexity”

  1. more on complexity « Philosophy of Nature Says:

    […] systems the interaction of constituting parts integrates them into a unified whole. (see also neural complexity) Possibly related posts: (automatically generated)The unreality of […]

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