Brain Computation Is Organized via Power-of-Two-Based Permutation Logic

Abstract

There is considerable scientific interest in understanding how cell assemblies—the long-presumed computational motif—are organized so that the brain can generate intelligent cognition and flexible behavior. The Theory of Connectivity proposes that the origin of intelligence is rooted in a power-of-two-based permutation logic (N = 2i–1), producing specific-to-general cell-assembly architecture capable of generating specific perceptions and memories, as well as generalized knowledge and flexible actions. We show that this power-of-two-based permutation logic is widely used in cortical and subcortical circuits across animal species and is conserved for the processing of a variety of cognitive modalities including appetitive, emotional and social information. However, modulatory neurons, such as dopaminergic (DA) neurons, use a simpler logic despite their distinct subtypes. Interestingly, this specific-to-general permutation logic remained largely intact although NMDA receptors—the synaptic switch for learning and memory—were deleted throughout adulthood, suggesting that the logic is developmentally pre-configured. Moreover, this computational logic is implemented in the cortex via combining a random-connectivity strategy in superficial layers 2/3 with nonrandom organizations in deep layers 5/6. This randomness of layers 2/3 cliques—which preferentially encode specific and low-combinatorial features and project inter-cortically—is ideal for maximizing cross-modality novel pattern-extraction, pattern-discrimination and pattern-categorization using sparse code, consequently explaining why it requires hippocampal offline-consolidation. In contrast, the nonrandomness in layers 5/6—which consists of few specific cliques but a higher portion of more general cliques projecting mostly to subcortical systems—is ideal for feedback-control of motivation, emotion, consciousness and behaviors. These observations suggest that the brain’s basic computational algorithm is indeed organized by the power-of-two-based permutation logic. This simple mathematical logic can account for brain computation across the entire evolutionary spectrum, ranging from the simplest neural networks to the most complex.

Coding By Quantum Entanglement Entropy

“…Several observations suggest that the brain's basic computational algorithm is indeed organized by the power-of-two-based permutation coding logic. (Xie et al, 2016) David Chalmers, a philosopher at New York University regularly questions the reality that conscious minds perceive. The problem is that any evidence we could ever get would be also simulated…James Gates Jr. pointed out that such a simulation would mean reincarnation was possible-the simulation could always be run again bringing everybody back to life !…”

Spike-timing pattern operates as gamma-distribution across cell types, regions and animal species and is essential for naturally-occurring cognitive states

“…Given that internal brain states (such as attention) are known to reduce neuronal variability [59][60][61], it will be highly interesting to investigate whether such regional variations reflect the underlying molecular and cellular differences (e.g., different cholinergic inputs or receptor expression profiles). In coupling with different NMDA receptor compositions across different regions [62][63][64][65][66], such intrinsic statistical characteristics of spiking-time distribution will likely influence not only how spike-timing patterns drive synaptic plasticity [2,3], but also how cell assemblies in various circuits perform neural computation [51,67,68].…”

“…We asked whether the excitatory units in the prelimbic region (PrL) of Golden Syrian hamsters would follow the gamma-like spike patterns. As described in our previous study [51], we implanted 64-channel tetrode arrays bilaterally into the PrL region and , mean ± SEM). The goodness-of-fit analysis showed that all PrL excitatory principal cells can be better described by using the gamma distribution models ( Figure 9C, 0 D > for all PrL excitatory principal cells), and D was linearly correlated with the mean firing rates (correlation coefficient is 0.79).…”

Coding by Quantum Entanglement Entropy

“…Several observations suggest that the brain's basic computational algorithm is indeed organized by the power-of-two-based permutation coding logic (Xie et al, 2016).…”