This is a theoretical study of correlations in spiking activity between neuronal populations. We focus on the spike firing of entire local populations without regard to the identities of the neurons that fire the spikes, and show that such a population-level metric is more robust than correlations between pairs of neurons. Between any source and target populations, there is an intrinsic response time characterized by the phase-shift that maximizes the correlation between their spiking. We find that the alignment of gamma-band rhythms contributes significantly to the positive correlations between populations. Hence, the correlation metric sheds light on the transference of gamma rhythms between populations; the effectiveness of such transference has been hypothesized to be connected to communication between brain regions. We investigate the dependence of correlations on connectivity and degree of synchrony, and consider multi-component network motifs with configurations known to occur in real cortex, studying the correlations between components that are directly or indirectly connected, by single or multiple pathways, with or without feedback. Mechanistic explanations are offered for many of the phenomena observed.

This is a theoretical study of correlations in spiking activity between neuronal populations. We focus on the spike firing of entire local populations without regard to the identities of the neurons that fire the spikes, and show that such a population-level metric is more robust than correlations between pairs of neurons. Between any source and target populations, there is an intrinsic response time characterized by the phase-shift that maximizes the correlation between their spiking. We find that the alignment of gamma-band rhythms contributes significantly to the positive correlations between populations. Hence, the correlation metric sheds light on the transference of gamma rhythms between populations; the effectiveness of such transference has been hypothesized to be connected to communication between brain regions. We investigate the dependence of correlations on connectivity and degree of synchrony, and consider multi-component network motifs with configurations known to occur in real cortex, studying the correlations between components that are directly or indirectly connected, by single or multiple pathways, with or without feedback. Mechanistic explanations are offered for many of the phenomena observed.

Cultural trends and popularity cycles can be observed all around us, yet our theories of social influence and identity expression do not explain what perpetuates these complex, often unpredictable social dynamics. We propose a theory of social identity expression based on the opposing, but not mutually exclusive, motives to conform and to be unique among one’s neighbors in a social network. We find empirical evidence for both conformity and uniqueness motives in an analysis of the popularity of given names. Generalizing across forms of identity expression, we then model the social dynamics that arise from these motives. We find that the dynamics typically enter random walks or stochastic limit cycles rather than converging to a static equilibrium. The dynamics also exhibit momentum, preserve diversity, and usually produce more conformity between neighbors, in line with empirical stylized facts. We also prove that without social network structure or, alternatively, without the uniqueness motive, reasonable adaptive dynamics would necessarily converge to equilibrium. Thus, we show that nuanced psychological assumptions (recognizing preferences for uniqueness along with conformity) and realistic social network structure are both critical to our account of the emergence of complex, unpredictable cultural trends.

Cultural trends and popularity cycles can be observed all around us, yet our theories of social influence and identity expression do not explain what perpetuates these complex, often unpredictable social dynamics. We propose a theory of social identity expression based on the opposing, but not mutually exclusive, motives to conform and to be unique among ones neighbors in a social network. We then model the social dynamics that arise from these motives. We find that the dynamics typically enter random walks or stochastic limit cycles rather than converging to a static equilibrium. We also prove that without social network structure or, alternatively, without the uniqueness motive, reasonable adaptive dynamics would necessarily converge to equilibrium. Thus, we show that nuanced psychological assumptions (recognizing preferences for uniqueness along with conformity) and realistic social network structure are both necessary for explaining how complex, unpredictable cultural trends emerge.