Short Course: Complex-Time (Kime) Representation of Spatiotemporal Processes and Spacekime Analytics

Part one (8:00-8:55 AM): Course overview with a discussion of the basic mathematical-physics principles underlying the complex-time (kime) representation of repeated measurement longitudinal data.

Part two (9:00-9:55 AM): Translation of fundamental quantum mechanics principles into statistical inference models of time-varying processes. Specifically, we will demonstrate generalizing the classical 4D spatiotemporal sampling to a 5D spacekime manifold, where the phase of complex-time (an extra degree of freedom) encodes repeated random sampling at fixed spatiotemporal locations.

Part three (10:00-10:55 AM): Alternative strategies for transforming observed time-series into kime-surfaces, which are richer, computationally tractable, objects amenable to tensor-based statistical linear modeling and AI model-free inference.

Part four (11:00-11:55 AM): Simulated and real neuroimaging and macroeconomics data to demonstrate applications of spacekime analytics.

Core short course spacekime analytics themes:

•        Importing of repeated measurement longitudinal data,

•        Numeric (stitching) and analytic (Laplace) kimesurface reconstruction from time-series data,

•        Forward prediction modeling extrapolating the process behavior beyond the observed time-span

•        Group comparison discrimination between cohorts based on the structure and properties of their corresponding kimesurfaces. For instance, statistically quantify the differences between two or more groups,

•        Unsupervised clustering and classification of individuals, traits, and other latent characteristics of cases included in the study,

•        Constructing low-dimensional visual representations of large repeated measurement data across multiple individuals as pooled kimesurfaces (parameterized 2D manifolds),

•        Statistical comparison, topological quantification, and analytical inference using kimesurface representations of repeated-measurement longitudinal data.

Learning outcomes (performance objectives): 

•        Understand the rationale for, and the duality between, classical representation of repeated-measurement spacetime observations and it’s spacekime analytics counterpart – complex-time representation as higher-dimensional manifolds.