Project Info
Dynamical systems and intra-individual variability data
Scott Strong
sstrong@mines.edu
Project Goals and Description:
Intra-individual variability refers to the meaningful fluctuations in a person's state—such as mood, cognition, or behavior—within that individual over time. These variations are not just random noise but can reveal important underlying system dynamics. Here, it is possible to think of an individual as a dynamical system with a personal attractor—an equilibrium around which emotional and cognitive states tend to fluctuate. Showing that these momentary fluctuations, especially increases in autocorrelation and variance or critical slowing down, have been explored as early warning signals for impending psychological transitions. At the same time, the network approach to psychopathology posits that mental disorders are causal systems of interacting symptoms rather than the result of a latent common cause. Importantly, symptoms activate and reinforce each other dynamically over a possibly larger number of measurable attributes. Consequently, a bottom-up modeling approach is unlikely to find an associated system of ordinary differential equations. In this project, we attempt to apply sparse identification of nonlinear dynamics to discover dynamical systems from publicly available longitudinal data sets with the goal of uncovering generalizable systems of ordinary differential equations predicting individual mental states.
More Information:
Grand Challenge: Advance health informatics.
A Dynamical Systems View of Psychiatric Disorders—Practical Implications, A Review
The Network Approach to Psychopathology: A Review of the Literature 2008–2018 and an Agenda for Future Research.
Slow down and be critical before using early warning signals in psychopathology
Critical slowing down as early warning for the onset and termination of depression
Primary Contacts:
sstrong@mines.edu
Student Preparation
Qualifications
A solid foundation in multivariate calculus and differential equations is required; familiarity with regression techniques, time-series data, and linear algebra is helpful but not required.
TIME COMMITMENT (HRS/WK)
5
SKILLS/TECHNIQUES GAINED
The student will gain skills in time-series analysis, particularly in identifying features like autocorrelation, variance, and indicators of critical slowing down. They will also develop proficiency with data-driven modeling techniques, especially the Sparse Identification of Nonlinear Dynamics (SINDy) framework. Additionally, the student will strengthen thThe successful applicant will be expected to grow toward independent research by keeping organized records of code, results, and insights, and by learning to report progress, obstacles, and next steps efficiently. Beyond these process-oriented goals, the student will gain exposure to nonlinear dynamical systems, network models in psychopathology, and data-driven techniques for identifying governing equations from time series data. To support this work, the principal investigator will meet weekly with the student to guide model interpretation, structure the exploration of literature, and help plan technically and conceptually sound next steps. eir ability to work with real-world, noisy longitudinal data, interpreting model outputs in psychologically meaningful terms.
MENTORING PLAN
The successful applicant will be expected to grow toward independent research by keeping organized records of code, results, and insights, and by learning to report progress, obstacles, and next steps efficiently. Beyond these process-oriented goals, the student will gain exposure to nonlinear dynamical systems, network models in psychopathology, and data-driven techniques for identifying governing equations from time series data. To support this work, the principal investigator will meet weekly with the student to guide model interpretation, structure the exploration of literature, and help plan technically and conceptually sound next steps.
Preferred Student Status
Sophomore
Junior
Senior