The general theme of my work concerns the application of mathematical theories to solve substantive psychological issues. Some more specific elaborations of this theme are:
Application of mathematical singularity theory (in particular catastrophe theory) to solve the longstanding debate about the reality of developmental stage transitions. This work (mathematical and stochastic modeling techniques, experimental designs and user-friendly software) has found wide acceptance and has been successfully applied in a series of ongoing research projects.
Application of nonlinear multivariate statistical signal analysis techniques to solve the problem of mapping theoretical models of cognitive information-processing onto dynamically interacting EEG/MEG neural sources embedded in spatio-temporally coherent backgrounds. These techniques have been adapted and extended to connectivity mapping based on fMRI BOLD time series obtained with heterogeneous subjects.
Application of mathematical-statistical ergodic theory to study the relationships between intra-individual (idiographic) analyses and inter-individual (nomothetic) analyses of psychological processes, triggering the development of innovative statistical multivariate time series techniques for the analysis of intra-individual processes (e.g., dynamic factor analysis) which now are applied in several research centers throughout the world. I have proven, based on the classical ergodic theorems, that for non-stationary processes such as learning and developmental processes it is necessary to focus on intra-individual variation (person-specific time series analysis). This proof necessitates a major re-orientation of psychometrics (e.g., test theory) and psychological methodology, which until now have been largely focused on analyses of inter-individual variation.
Application of advanced multivariate analysis techniques in quantitative genetics and developmental psychology.
Application of adaptive resonance theory (ART neural networks) to study the effects of nonlinear epigenetic processes, complemented by the use of mathematical biological models of self-organization.
Application of engineering control techniques to optimally guide psychological and disease processes of individual subjects in real time. In particular I focus on real-time optimal treatment of individual patients with type 1 diabetes and asthma under normal living conditions.