Statistical Field Theory and Neural Structures Dynamics: I, II, III & IV
Pierre Gosselin, Aïleen Lotz
Statistical Field Theory and Neural Structures Dynamics I: Action Functionals, Background States and External Perturbations
Abstract: This series of papers models the dynamics of a large set of interacting neurons within the framework of statistical field theory. The system is described using a two-field model. The first field represents the neuronal activity, while the second field accounts for the interconnections between cells. This model is derived by translating a probabilistic model involving a large number of interacting cells into a field formalism. The current paper focuses on deriving the background fields of the system, which describe the potential equilibria in terms of interconnected groups. Dynamically, we explore the perturbation of these background fields, leading to processes such as activation, association, and reactivation of groups of cells.
Statistical Field Theory and Neural Structures Dynamics II: Signals Propagation, Interferences, Bound States
Abstract: We continue our study of a field formalism for large sets of interacting neurons, together with their connectivity functions. Expanding upon the foundation laid in ([9]), we formulate an effective formalism for the connectivity field in the presence of external sources. We proceed to deduce the propagation of external signals within the system. This enables us to investigate the activation and association of groups of bound cells.
Statistical Field Theory and Neural Structures Dynamics III: Effective Action for Connectivities, Interactions and Emerging Collective States
Abstract: This paper elaborates on the effective field theory for the connectivity field previously introduced in ([7]). We demonstrate that dynamic interactions among connectivities induce modi cations in the background state. These modifications can be understood as the emergence of interacting collective states above the background state. The emergence of such states is contingent on both interactions and the shape of the static or quasi-static background, which acts as a conditioning factor for potential emerging states.
Statistical Field Theory and Neural Structures Dynamics IV: Field-Theoretic Formalism for Interacting Collective States
Abstract: Building upon the findings presented in the first three papers of this series, we formulate an effective field theory for interacting collective states. These states consist of a large number of interconnected neurons and are distinguished by their intrinsic activity. The field theory encompasses an infinite set of fields, each of which characterizes the dynamics of a specific type of collective state. Interaction terms within the theory drive transitions between various collective states, allowing us to describe processes such as activation, association, and deactivation of these states.
I, II, III & IV Keywords: Neural activity, Field theoretic formulation, Transitions, Emerging states, Collective states, connectivity functions.