Five specific reverse-engineering methodologies are developed, based on the following dynamics: Langevin, geometric Langevin, diffusion, growth-collapse, and decay-surge.
This relaxed-clock model imposes a correlation of rates between ancestral and descendant branches by modeling rate change on the tree as a geometric Brownian diffusion process [ 53, 54].
This level-set based variational approach yields a computational system of coupled geometric evolution and diffusion partial differential equations.
However, the topographic and geometric relationships between diffusion imaging derived streamline fiber connection patterns and cortical folding patterns remain largely unknown.
Fig. 6 Geometric interpretation of diffusion matrix.
Two different ways for calculating the global geometric metric are diffusion based metric and geodesic distance based metric (i.e. shortest path).
In this review, we focus on three different theoretical approaches - geometric modeling, reaction-diffusion modeling, and continuum mechanical modeling - and discuss how, taken together, these models have identified the geometric principles necessary to build an efficient bronchial network, as well as the patterning mechanisms that specify airway geometry in the developing embryo.
In this review, we focus on three different theoretical approaches – geometric modeling, reaction-diffusion modeling, and continuum mechanical modeling – and discuss how, taken together, these models have identified the geometric principles necessary to build an efficient bronchial network, as well as the patterning mechanisms that specify airway geometry in the developing embryo.
Deposition times of 15 to 60 s slightly increased the geometric and steady state diffusion electroactive areas while the linear diffusion electroactive area grew significantly, indicating an increase in electrode roughness.
In contrast to other dopant ions, the charge density determined from the geometric and steady state diffusion electroactive areas was nearly constant with increased deposition time while the linear diffusion charge density decreased.
