title: 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. TheTheory of Connectivityproposes 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.
authors.affiliation: Brain and Behavior Discovery Institute and Department of Neurology, Medical College of Georgia, Augusta UniversityAugusta, GA, USA; The Brain Decoding Center, Banna Biomedical Research Institute, Yunnan Academy of Science and TechnologyYunnan, China.
authors.forename: Kun
authors.initials: K
authors.lastname: Xie
authors.affiliation: Brain and Behavior Discovery Institute and Department of Neurology, Medical College of Georgia, Augusta University Augusta, GA, USA.
authors.forename: Grace E
authors.initials: GE
authors.lastname: Fox
authors.affiliation: Brain and Behavior Discovery Institute and Department of Neurology, Medical College of Georgia, Augusta UniversityAugusta, GA, USA; The Brain Decoding Center, Banna Biomedical Research Institute, Yunnan Academy of Science and TechnologyYunnan, China.
authors.forename: Jun
authors.initials: J
authors.lastname: Liu
authors.affiliation: Department of Computer Science and Brain Imaging Center, University of GeorgiaAthens, GA, USA; School of Automation, Northwestern Polytechnical UniversityXi'an, China.
authors.forename: Cheng
authors.initials: C
authors.lastname: Lyu
authors.affiliation: Brain and Behavior Discovery Institute and Department of Neurology, Medical College of Georgia, Augusta University Augusta, GA, USA.
authors.forename: Jason C
authors.initials: JC
authors.lastname: Lee
authors.affiliation: Brain and Behavior Discovery Institute and Department of Neurology, Medical College of Georgia, Augusta University Augusta, GA, USA.
authors.forename: Hui
authors.initials: H
authors.lastname: Kuang
authors.affiliation: Brain and Behavior Discovery Institute and Department of Neurology, Medical College of Georgia, Augusta University Augusta, GA, USA.
authors.forename: Stephanie
authors.initials: S
authors.lastname: Jacobs
authors.affiliation: Brain and Behavior Discovery Institute and Department of Neurology, Medical College of Georgia, Augusta UniversityAugusta, GA, USA; The Brain Decoding Center, Banna Biomedical Research Institute, Yunnan Academy of Science and TechnologyYunnan, China.
authors.forename: Meng
authors.initials: M
authors.lastname: Li
authors.affiliation: Department of Computer Science and Brain Imaging Center, University of Georgia Athens, GA, USA.
authors.forename: Tianming
authors.initials: T
authors.lastname: Liu
authors.affiliation: McGovern Institute for Brain Research and Center for Brain-Inspired Computing Research, Tsinghua University Beijing, China.
authors.forename: Sen
authors.initials: S
authors.lastname: Song
authors.affiliation: Brain and Behavior Discovery Institute and Department of Neurology, Medical College of Georgia, Augusta UniversityAugusta, GA, USA; The Brain Decoding Center, Banna Biomedical Research Institute, Yunnan Academy of Science and TechnologyYunnan, China.
authors.forename: Joe Z
authors.initials: JZ
authors.lastname: Tsien
keywords: NMDA receptor; appetitive behavior; cell assembly; computational algorithms; computational logic; cortex; social behavior; wiring logic