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Transient phenomena play a key role in coordinating brain activity at multiple scales, however,their underlying mechanisms remain largely unknown. A key challenge for neural data science is thus to characterize the network interactions at play during these events. Using the formalism of Structural Causal Models and their graphical representation, we investigate the theoretical and empirical properties of Information Theory based causal strength measures in the context of recurring spontaneous transient events. After showing the limitations of Transfer Entropy and Dynamic Causal Strength in such a setting, we introduce a novel measure, relative Dynamic Causal Strength, and provide theoretical and empirical support for its benefits. These methods are applied to simulated and experimentally recorded neural time series, and provide results in agreement with our current understanding of the underlying brain circuits.

Transient recurring phenomena are ubiquitous in many scientific fields like neuroscience and meteorology. Time inhomogenous Vector Autoregressive Models (VAR) may be used to characterize peri-event system dynamics associated with such phenomena, and can be learned by exploiting multi-dimensional data gathering samples of the evolution of the system in multiple time windows comprising, each associated with one occurrence of the transient phenomenon, that we will call "trial". However, optimal VAR model order selection methods, commonly relying on the Akaike or Bayesian Information Criteria (AIC/BIC), are typically not designed for multi-trial data. Here we derive the BIC methods for multi-trial ensemble data which are gathered after the detection of the events. We show using simulated bivariate AR models that the multi-trial BIC is able to recover the real model order. We also demonstrate with simulated transient events and real data that the multi-trial BIC is able to estimate a sufficiently small model order for dynamic system modeling., Comment: 12 pages, 4 figures

Time series datasets often contain heterogeneous signals, composed of both continuously changing quantities and discretely occurring events. The coupling between these measurements may provide insights into key underlying mechanisms of the systems under study. To better extract this information, we investigate the asymptotic statistical properties of coupling measures between continuous signals and point processes. We first introduce martingale stochastic integration theory as a mathematical model for a family of statistical quantities that include the Phase Locking Value, a classical coupling measure to characterize complex dynamics. Based on the martingale Central Limit Theorem, we can then derive the asymptotic Gaussian distribution of estimates of such coupling measure, that can be exploited for statistical testing. Second, based on multivariate extensions of this result and Random Matrix Theory, we establish a principled way to analyze the low rank coupling between a large number of point processes and continuous signals. For a null hypothesis of no coupling, we establish sufficient conditions for the empirical distribution of squared singular values of the matrix to converge, as the number of measured signals increases, to the well-known Marchenko-Pastur (MP) law, and the largest squared singular value converges to the upper end of the MPs support. This justifies a simple thresholding approach to assess the significance of multivariate coupling. Finally, we illustrate with simulations the relevance of our univariate and multivariate results in the context of neural time series, addressing how to reliably quantify the interplay between multi channel Local Field Potential signals and the spiking activity of a large population of neurons., Comment: 50 pages

The LFPs is a broadband signal that captures variations of neural population activity over a wide range of time scales. The range of time scales available in LFPs is particularly interesting from the neural coding point of view because it opens up the possibility to investigate whether there are privileged time scales for information processing, a question that has been hotly debated over the last one or two decades.It is possible that information is represented by only a small number of specific frequency ranges, each carrying a separate contribution to the information representation. To shed light on this issue, it is important to quantify the information content of each frequency range of neural activity, and understand which ranges carry complementary or similar information., Comment: To appear in Quian Quiroga and Panzeri (Eds) Principles of Neural Coding, CRC Press, 2012