Detecting dynamical causality by intersection cardinal concavity.

Area of Science:

• Complex Systems Science
• Neuroscience
• Time Series Analysis

Background:

• Discovering causality from time series data is crucial but challenging.
• Traditional methods like Granger causality and transfer entropy have limitations.
• Existing cross-mapping methods struggle with nonlinearity and noisy data.

Purpose of the Study:

• To develop a novel, robust, and nonlinear method for causality detection in time series data.
• To address limitations of existing cross-mapping techniques.
• To introduce the concept of "IC concavity" for reliable causal strength measurement.

Main Methods:

• Proposed cross-mapping cardinality (CMC) using intersectional cardinality (IC).
• Quantified IC from cause variable neighbors to effect variable cross-mapping neighbors in delay embedding space.
• Introduced and validated the "IC concavity" concept for dynamical causality.

Main Results:

• CMC demonstrates superior accuracy and robustness compared to existing methods on simulated and real-world data.
• Successfully identified causal relations between motor cortex neurons in a manual interception experiment.
• Validated the effectiveness of "IC concavity" in distinguishing causality from non-causality.

Conclusions:

• Cross-mapping cardinality (CMC) offers a powerful data-driven tool for detecting dynamical causality.
• The "IC concavity" concept provides a reliable measure of causal strength.
• CMC significantly advances causality detection in complex systems, particularly in neuroscience applications.