Neural complexity: A graph theoretic interpretation

Abstract

One of the central challenges facing modern neuroscience is to explain the ability of the nervous system to coherently integrate information across distinct functional modules in the absence of a central executive. To this end Tononi et al. [Proc. Nat. Acad. Sci. USA 91, 5033 (1994)] proposed a measure of neural complexity that purports to capture this property based on mutual information between complementary subsets of a system. Neural complexity, so defined, is one of a family of information theoretic metrics developed to measure the balance between the segregation and integration of a system's dynamics. One key question arising for such measures involves understanding how they are influenced by network topology. Sporns et al. [Cereb. Cortex 10, 127 (2000)] employed numerical models in order to determine the dependence of neural complexity on the topological features of a network. However, a complete picture has yet to be established. WhileDe Lucia et al. [Phys. Rev. E 71, 016114 (2005)] made the first attempts at an analytical account of this relationship, their work utilized a formulation of neural complexity that, we argue, did not reflect the intuitions of the original work.In this paper we start by describing weighted connection matrices formed by applying a random continuous weight distribution to binary adjacency matrices. This allows us to derive an approximation for neural complexity in terms of the moments of the weight distribution and elementary graph motifs. In particular we explicitly establish a dependency of neural complexity on cyclic graph motifs.

Framework to study dynamic dependencies in networks of interacting processes

“…Following Ref. [79], the multi-information measures explicitly considering the dynamics could be used to analyze the relevant motifs in the microscopic causal structure (Sec. II B), leading to dynamic complexity in a system.…”

Deriving pairwise transfer entropy from network structure and motifs

“…This work will instead focus on the analytical treatment of the directed functional connectivity obtained via the pairwise TE for the VAR process. Building on previous studies of other information-theoretic measures in this process (regarding the TSE complexity [26] in [19,27] and active information storage in [28]), we explicitly establish the dependence of the TE for a given link on the related structural motifs. Motifs are small subnetwork configurations, such as feedforward or feedback loops, which have been studied as building blocks of complex arXiv:1911.02931v1 [cs.IT] 7 Nov 2019 networks [29].…”

Information storage, loop motifs, and clustered structure in complex networks

“…Recognizing that network structure gives rise to dynamics, but dynamics represents the specific action of a network, much recent work has focused on studying the complexity of dynamics on various network structures, e.g. [1][2][3]. Such investigations can reveal the dynamic capabilities of well-known structures, e.g.…”

“…Such investigations can reveal the dynamic capabilities of well-known structures, e.g. small-world networks [2,4,5]. We take an information-theoretic approach to this issue, exploring computational properties (e.g.…”

“…Despite such intuition, there is no direct analytic evidence for the role of loop motifs in information storage when embedded in networks, nor for which if any other motifs are involved. Here, we will follow Barnett et al [1,2] in making analytic inference of informationtheoretical measures of dynamics on networks. This involves linear stationary Gaussian processes, which are a simplification as compared to real-world processes, however can be viewed as approximating the weakly-coupled near-linear regime, and are commonly used in neuroscience for large-scale modeling [1].…”