Applications of Long Range Dependence Characterization in Thermal Imaging & Heart Rate Variability
Abstract
The world we live in is nonlinear. Fortunately, there are several mathematical methods to linearize a system. However, a multitude of nonlinear systems exists that cannot be fully linearized; such as economical, ecological, and biological systems. Linear or linearized systems are desired due to their predictable characteristics. On the other hand, nonlinear systems are unpredictable and considered stochastic. Is it possible to predict the unpredictable? Yes it is possible, to a degree. However, traditional or integer based mathematics do not suffice. Utilizing fractional calculus (FC) as a mathematical tool, one is able to describe nonlinearity in a system; with the assumption that there is memory or fractal properties embedded in the system. The Hurst exponent (H), also known as the Hurst parameter, is used to determine the intensity of memory in a system. The range of the Hurst is 0