Kaidi Shao

Kaidi Shao, Nikos K. Logothetis, Michel Besserve

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.

Salar Nouri, Kaidi Shao, Shervin Safavi

Quantifying transient causal interactions from non-stationary neural signals is a fundamental challenge in neuroscience. Traditional methods are often inadequate for brief neural events, and advanced, event-specific techniques have lacked accessible implementations within the Python ecosystem. Here, we introduce trancit (Transient Causal Interaction Toolbox), an open-source Python package designed to bridge this gap. TranCIT implements a comprehensive analysis pipeline, including Granger Causality, Transfer Entropy, and the more robust Structural Causal Model-based Dynamic Causal Strength (DCS) and relative Dynamic Causal Strength (rDCS) for accurately detecting event-driven causal effects. We demonstrate TranCIT's utility by successfully capturing causality in high-synchrony regimes where traditional methods fail and by identifying the known transient information flow from hippocampal CA3 to CA1 during sharp-wave ripple events in real-world data. The package offers a user-friendly, validated solution for investigating the transient causal dynamics that govern complex systems.

Yuanchao Xu, Kaidi Shao, Nikos Logothetis et al.

Analyzing the long-term behavior of high-dimensional nonlinear dynamical systems remains a significant challenge. While the Koopman operator framework provides a powerful global linearization tool, current methods for approximating its spectral components often face theoretical limitations and depend on predefined dictionaries. Residual Dynamic Mode Decomposition (ResDMD) advanced the field by introducing the \emph{spectral residual} to assess Koopman operator approximation accuracy; however, its approach of only filtering precomputed spectra prevents the discovery of the operator's complete spectral information, a limitation known as the `spectral inclusion' problem. We introduce ResKoopNet (Residual-based Koopman-learning Network), a novel method that directly addresses this by explicitly minimizing the \emph{spectral residual} to compute Koopman eigenpairs. This enables the identification of a more precise and complete Koopman operator spectrum. Using neural networks, our approach provides theoretical guarantees while maintaining computational adaptability. Experiments on a variety of physical and biological systems show that ResKoopNet achieves more accurate spectral approximations than existing methods, particularly for high-dimensional systems and those with continuous spectra, which demonstrates its effectiveness as a tool for analyzing complex dynamical systems.