Spectral Modes of Network Dynamics Reveal Increased Informational Complexity Near Criticality

What does the informational complexity of dynamical networked systems tell us about intrinsic mechanisms and functions of these complex systems? Recent complexity measures such as integrated information have sought to operationalize this problem taking a whole-versus-parts perspective, wherein one explicitly computes the amount of information generated by a network as a whole over and above that generated by the sum of its parts during state transitions. While several numerical schemes for estimating network integrated information exist, it is instructive to pursue an analytic approach that computes integrated information as a function of network weights. Our formulation of integrated information uses a Kullback-Leibler divergence between the multi-variate distribution on the set of network states versus the corresponding factorized distribution over its parts. Implementing stochastic Gaussian dynamics, we perform computations for several prototypical network topologies. Our findings show increased informational complexity near criticality, which remains consistent across network topologies. Spectral decomposition of the system's dynamics reveals how informational complexity is governed by eigenmodes of both, the network's covariance and adjacency matrices. We find that as the dynamics of the system approach criticality, high integrated information is exclusively driven by the eigenmode corresponding to the leading eigenvalue of the covariance matrix, while sub-leading modes get suppressed. The implication of this result is that it might be favorable for complex dynamical networked systems such as the human brain or communication systems to operate near criticality so that efficient information integration might be achieved

The Mediating Role of Sleep in the Associations of Adult Attachment and Self Disclosure in Romantic Relationships

Research has shown that adult attachment style predicts self disclosure in relationships (Chen, Hi, Shi, & Chen, 2019 as cited in Collins and Allard, 2007). Previous research has also pointed to a positive relationship between healthy attachment and well-being, as well as sleep quality (Escolas, Hildebrandt, Maiers, Baker, & Mason, 2013 via Verdecia, Jean-Louis, Zizi, Casimir, & Browne, 2009). The purpose of this study was to examine sleep as a possible mediator between attachment styles and self disclosure. The current sample consisted of 202 participants recruited from Amazon Mechanical Turk (MTurk). Results indicated that sleep quality (indicated by sleepiness and insomnia) mediated the relationship between attachment and self disclosure. Future research may explore the potential benefits of high sleep quality to those who demonstrate avoidant or anxious attachment styles, as it could increase self disclosure in relationships

The Mediating Role of Sleep in the Link between Attachment Styles and Conflict Styles in Romantic Relationships

The goal of this study was to examine if sleep quality (e.g., onset latency, efficiency, daytime sleepiness) mediates the links between insecure attachment styles and conflict communication styles (i.e., criticism, contempt, defensiveness, and stonewalling). About 244 undergraduate students answered questions about sleep, attachment style characteristics, and conflict characteristics in their current or previous romantic relationships. Sleep was found to explain the relationship between attachment styles and conflict communication styles when flooding was used as an indicator for stonewalling. However, further research is needed to better understand why people with insecure attachment styles tend to use negative styles of conflict communication

A Cosine Rule-Based Discrete Sectional Curvature for Graphs

How does one generalize differential geometric constructs such as curvature of a manifold to the discrete world of graphs and other combinatorial structures? This problem carries significant importance for analyzing models of discrete spacetime in quantum gravity; inferring network geometry in network science; and manifold learning in data science. The key contribution of this paper is to introduce and validate a new estimator of discrete sectional curvature for random graphs with low metric-distortion. The latter are constructed via a specific graph sprinkling method on different manifolds with constant sectional curvature. We define a notion of metric distortion, which quantifies how well the graph metric approximates the metric of the underlying manifold. We show how graph sprinkling algorithms can be refined to produce hard annulus random geometric graphs with minimal metric distortion. We construct random geometric graphs for spheres, hyperbolic and euclidean planes; upon which we validate our curvature estimator. Numerical analysis reveals that the error of the estimated curvature diminishes as the mean metric distortion goes to zero, thus demonstrating convergence of the estimate. We also perform comparisons to other existing discrete curvature measures. Finally, we demonstrate two practical applications: (i) estimation of the earth's radius using geographical data; and (ii) sectional curvature distributions of self-similar fractals