,1,Computational Neuroscience, Time Complexity, and Spacekime Analytics
Ivo Dinov – Professor, HBBS/SoN, DCMB/SoM, MIDAS
The proliferation of digital information in all human experiences presents difficult challenges and offers unique opportunities of managing, modeling, analyzing, interpreting, and visualizing heterogeneous data. There is a substantial need to develop, validate, productize, and support novel mathematical techniques, advanced statistical computing algorithms, transdisciplinary tools, and effective artificial intelligence apps.
Spacekime analytics is a new technique for modeling high-dimensional longitudinal data, such as functional magnetic resonance imaging (fMRI). This approach relies on extending the notions of time, events, particles, and wavefunctions to complex-time (kime), complex-events (kevents), data and inference-functions, respectively. This talk will illustrate how the kime-magnitude (longitudinal time order) and kime-direction (phase) affect the subsequent predictive analytics and the induced scientific inference. The mathematical foundation of spacekime calculus reveals various statistical implications including inferential uncertainty and a Bayesian formulation of spacekime analytics. Complexifying time allows the lifting of all commonly observed processes from the classical 4D Minkowski spacetime to a 5D spacetime manifold, where a number of interesting mathematical problems arise.
Spacekime analytics transforms time-varying data, such as time-series observations, into higher-dimensional manifolds representing complex-valued and kime-indexed surfaces (kime-surfaces). This process uncovers some of the intricate structure in high-dimensional data that may be intractable in the classical space-time representation of the data. In addition, the spacekime representation facilitates the development of innovative data science analytical methods for model-based and model-free scientific inference, derived computed phenotyping, and statistical forecasting. Direct neuroscience science applications of spacekime analytics will be demonstrated using simulated data and clinical observations (e.g., UK Biobank).
