Neural Field Continuum Limits and the Structure–Function Partitioning of Cognitive–Emotional Brain Networks

Simple Summary Pessoa postulates that bran anatomy associated with the processing and expression of emotion-laden content, such as the amygdala and limbic cortices, is resource capacity-limited. Thus, brains require multichannel or parallel structure-function connectivity to effectively perceive, motivate, integrate, represent, recall, and execute cognitive-emotional relationships. Pessoa employs 2D graph network theory to support his views on distributed brain organization and operation, concluding that brains evolve through dual-process competition and cooperation to form highly embedded computational architectures with little structure–function compartmentalization. Low-dimensional graph theory has become a popular mathematical tool to model, simulate, and visualize evolving complex, sometimes intractable, brain networks. Graph theory offers advantages to study and understand various biological and technological network behaviors and, for Pessoa, it permits a framework that accounts for structure–function features thus far poorly explained by perhaps “traditional” perspectives, which advocate for the mapping of structure–function relationships onto well-localized brain areas. Pessoa nonetheless fails to fully appreciate the significance of weak-to-strong structure-function correlations for brain dynamics and why those correlations, caused by differential control parameters such as Hebbian and antiHebbian neuronal plasticity, are best assessed using neural field theories. Neural fields demonstrate that embedded brain networks optimally evolve between exotic computational phases and continuum limits with the accompaniment of some network partitioning, rather than unconstrained embeddedness, when rendering healthy cognitive-emotional functionality. Abstract In The cognitive-emotional brain, Pessoa overlooks continuum effects on nonlinear brain network connectivity by eschewing neural field theories and physiologically derived constructs representative of neuronal plasticity. The absence of this content, which is so very important for understanding the dynamic structure-function embedding and partitioning of brains, diminishes the rich competitive and cooperative nature of neural networks and trivializes Pessoa’s arguments, and similar arguments by other authors, on the phylogenetic and operational significance of an optimally integrated brain filled with variable-strength neural connections. Riemannian neuromanifolds, containing limit-imposing metaplastic Hebbian- and antiHebbian-type control variables, simulate scalable network behavior that is difficult to capture from the simpler graph-theoretic analysis preferred by Pessoa and other neuroscientists. Field theories suggest the partitioning and performance benefits of embedded cognitive-emotional networks that optimally evolve between exotic classical and quantum computational phases, where matrix singularities and condensations produce degenerate structure-function homogeneities unrealistic of healthy brains. Some network partitioning, as opposed to unconstrained embeddedness, is thus required for effective execution of cognitive-emotional network functions and, in our new era of neuroscience, should be considered a critical aspect of proper brain organization and operation.