In this paper, we mainly consider the Cauchy problem of a hyperbolic-parabolic model vasculogenesis in dimension three. We first obtain optimal $ L^2 $-decay rate solution and its highest order derivatives when initial perturbation is small H^3(\mathbb{R}^3) bounded L^1(\mathbb{R}^3) $. Here, optimality means there no decay loss for highest-order spatial derivatives. This refines that [21], whe...

A hyperbolic model for chemotaxis and chemosensitive movement in one space dimension is considered. In contrast to parabolic models for chemotaxis the hyperbolic model allows us to take the dependence of the particle speed on external stimuli explicitly into account. This qualitatively covers recent experiments on chemotaxis in which it has been shown that particles adapt their speed to the sur...

The mixture of factor analyzers model, which has been used successfully for the model-based clustering of high-dimensional data, is extended to generalized hyperbolic mixtures. The development of a mixture of generalized hyperbolic factor analyzers is outlined, drawing upon the relationship with the generalized inverse Gaussian distribution. An alternating expectation-conditional maximization a...

An integrable interpolative (Pivotal) model for the (1 + 1)-dimensional Hyperbolic Heisenberg and Hyperbolic sigma models is proposed and some solutions classifiable by an integer winding number examined.

Psychological models of temporal discounting have now successfully displaced classical economic theory due to the simple fact that many common behavior patterns, such as impulsivity, were unexplainable with classic models. However, the now dominant hyperbolic model of discounting is itself becoming increasingly strained. Numerous factors have arisen that alter discount rates with no means to in...