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Key research themes
1. How can non-linear time series analysis tools improve the understanding of complex dynamical systems across scientific fields?
This research theme focuses on the development and application of advanced non-linear time series analysis methodologies and toolboxes that enable the characterization of complex dynamical systems exhibiting non-linear behaviors. These methods integrate dynamical systems theory, recurrence quantification analysis, and information theory to provide accessible, robust, and comprehensive toolsets for scientists, including those with limited coding experience. Understanding non-linear temporal dynamics is vital in fields such as neuroscience, climatology, and physics, facilitating better modeling, prediction, and potentially improved diagnostics in complex systems where linear methods are insufficient.
Key finding: This work advances empirical dynamic modeling (EDM) by introducing a vector correlation metric for causal inference in non-linear systems, improving upon scalar correlation metrics by utilizing the full embedding dimension’s... Read more
Key finding: The paper elucidates that non-linear solutions to fundamental physics equations derive from the preserved symmetries and complex structure inherent to non-linear differential equations, producing stable and elegant solutions... Read more
2. What are effective methods for modeling and estimating non-linear relationships in longitudinal and mediation analyses to improve inference and prediction?
This theme investigates advanced statistical modeling techniques for capturing and estimating non-linear dynamics in longitudinal data and mediation frameworks. It addresses the limitations of traditional linear assumptions by incorporating flexible adaptive regression, mixed-effects, and latent curve modeling approaches that accommodate complex change patterns and monotonic or arbitrary non-linearities. Such methodological developments enhance the accuracy of parameter estimation, interpretation, and predictions in behavioral, medical, and social science research, especially where relationships evolve non-linearly over time or through indirect pathways.
Key finding: This study clarifies relationships and distinctions between nonlinear mixed-effects models and nonlinear latent curve models for longitudinal data, showing that partially nonlinear mixed-effects models are equivalent to some... Read more
Key finding: The paper extends adaptive regression methods based on fractional polynomials to model nonlinear monotonic mediation relationships, enabling researchers to assess and estimate mediation effects beyond linear assumptions. It... Read more
Key finding: Using generalized additive models (GAM), this study reveals significant non-linear effects of continuous predictors—including mother's age, mother's BMI, and child’s age—on child malnutrition (stunting) in Bangladesh, which... Read more
3. How do nonlinear effects manifest in physiological and engineering systems, and what modeling approaches capture these phenomena?
This research area centers on identifying, characterizing, and modeling nonlinear behaviors in physiological systems such as cochlear mechanics, as well as engineered components like RF amplifiers and composite materials. Nonlinearities include level-dependent responses, gain compression, modulus changes due to environmental factors, and their influence on system performance. The development of nonlinear regression, differential equation analyses, and empirical models enables capturing these complex effects critical for advancing biomedical understanding and optimizing technological designs.
Key finding: Rhode’s 50-year-old seminal physiological measurements established that basilar membrane (BM) motion in the cochlea exhibits level-dependent non-linearity—specifically, BM response gain decreases with increased stimulus level... Read more
Key finding: This study models RF amplifier nonlinearities, especially gain compression, and evaluates their detrimental impact on communication system performance through bit error ratio (BER) measurements under multilevel modulation... Read more
Key finding: Experimental data collected under controlled moisture and temperature conditions reveal that modulus of elasticity (MOE) and modulus of rupture (MOR) of wood composite particleboards exhibit nonlinear dependence on these... Read more