For animals living in temperate latitudes, seasonal changes in day length are an important cue for adaptations of their physiology and behavior to the altered environmental conditions. The suprachiasmatic nucleus (SCN) is known as the central circadian clock in mammals, but may also play an important role in adaptations to different photoperiods. The SCN receives direct light input from the retina and is able to encode day-length by approximating the waveform of the electrical activity rhythm to the duration of daylight. Changing the overall waveform requires a reorganization of the neuronal network within the SCN with a change in the degree of synchrony between the neurons; however, the underlying mechanisms are yet unknown. In the present study we used PER2::LUC bioluminescence imaging in cultured SCN slices to characterize network dynamics on the single-cell level and we aimed to provide evidence for a role of modulations in coupling strength in the photoperiodic-induced phase dispersal. Exposure to long photoperiod (LP) induced a larger distribution of peak times of the single-cell PER2::LUC rhythms in the anterior SCN, compared to short photoperiod. Interestingly, the cycle-to-cycle variability in single-cell period of PER2::LUC rhythms is also higher in the anterior SCN in LP, and is positively correlated with peak time dispersal. Applying a new, impartial community detection method on the time series data of the PER2::LUC rhythm revealed two clusters of cells with a specific spatial distribution, which we define as dorsolateral and ventromedial SCN. Post hoc analysis of rhythm characteristics of these clusters showed larger cycle-to-cycle single-cell period variability in the dorsolateral compared to the ventromedial cluster in the anterior SCN. We conclude that a change in coupling strength within the SCN network is a plausible explanation to the observed changes in single-cell period variability, which can contribute to the photoperiod-induced phase distribution.

Reconstructing patterns of interconnections from partial information is one of the most important issues in the statistical physics of complex networks. A paramount example is provided by financial networks. In fact, the spreading and amplification of financial distress in capital markets are strongly affected by the interconnections among financial institutions. Yet, while the aggregate balance sheets of institutions are publicly disclosed, information on single positions is mostly confidential and, as such, unavailable. Standard approaches to reconstruct the network of financial interconnection produce unrealistically dense topologies, leading to a biased estimation of systemic risk. Moreover, reconstruction techniques are generally designed for monopartite networks of bilateral exposures between financial institutions, thus failing in reproducing bipartite networks of security holdings (e.g., investment portfolios). Here we propose a reconstruction method based on constrained entropy maximization, tailored for bipartite financial networks. Such a procedure enhances the traditional capital-asset pricing model (CAPM) and allows us to reproduce the correct topology of the network. We test this enhanced CAPM (ECAPM) method on a dataset, collected by the European Central Bank, of detailed security holdings of European institutional sectors over a period of six years (2009-2015). Our approach outperforms the traditional CAPM and the recently proposed maximum-entropy CAPM both in reproducing the network topology and in estimating systemic risk due to fire sales spillovers. In general, ECAPM can be applied to the whole class of weighted bipartite networks described by the fitness model.

The concept of “Structural Diversity” of a network refers to the level of dissimilarity between the various agents acting in the system, and it is typically interpreted as the number of connected components in the network. This key property of networks has been studied in multiple settings, including diffusion of ideas in social networks and functional diversity of regions in brain networks. Here, we propose a new measure, “Structural Entropy”, as a revised interpretation to “Structural Diversity”. The proposed measure relies on the finer-grained network communities (in contrast to the network’s connected components), and takes into consideration both the number of communities and their sizes, generating a single representative value. We then propose an approach for monitoring the structure of correlation-based networks over time, which relies on the newly suggested measure. Finally, we illustrate the usefulness of the new approach, by applying it to the particular case of emergent organization of financial markets. This provides us a way to explore their underlying structural changes, revealing a remarkably high linear correlation between the new measure and the volatility of the assets’ prices over time.