•  2
    Kimesurface Representation and Tensor Linear Modeling of Longitudinal Data
    Neural Computing and Applications Journal 1 (34). 2022.
    Many modern techniques for analyzing time-varying longitudinal data rely on parametric models to interrogate the time-courses of univariate or multivariate processes. Typical analytic objectives include utilizing retrospective observations to model current trends, predict prospective trajectories, derive categorical traits, or characterize various relations. Among the many mathematical, statistical, and computational strategies for analyzing longitudinal data, tensor-based linear modeling offers…Read more
  •  4
    Determinism, Well-posedness, and Applications of the Ultrahyperbolic Wave Equation in Spacekime
    Journal of Partial Differential Equations in Applied Mathematics 100280 (5). 2022.
    Spatiotemporal dynamics of many natural processes, such as elasticity, heat propagation, sound waves, and fluid flows are often modeled using partial differential equations (PDEs). Certain types of PDEs have closed-form analytical solutions, some permit only numerical solutions, some require appropriate initial and boundary conditions, and others may not have stable, global, or even well-posed solutions. In this paper, we focus on one-specific type of second-order PDE — the ultrahyperbolic wave …Read more
  • The amount of new information is constantly increasing, faster than our ability to fully interpret and utilize it to improve human experiences. Addressing this asymmetry requires novel and revolutionary scientific methods and effective human and artificial intelligence interfaces. By lifting the concept of time from a positive real number to a 2D complex time (kime), this book uncovers a connection between artificial intelligence (AI), data science, and quantum mechanics. It proposes a new mathe…Read more