Recent theory suggests that animals should switch facultatively among canonical movement modes as a complex function of internal state, landscape characteristics, motion capacity, and navigational capacity. We tested the generality of this paradigm for free-ranging elk (Cervus elaphus) over 5 orders of magnitude in time (minutes to years) and space (meters to 100 km). At the coarsest spatiotemp...

We present a new path integral method to analyze stochastically perturbed ordinary differential equations with multiple time scales. The objective of this method is to derive from the original system a new stochastic differential equation describing the system’s evolution on slow time scales. For this purpose, we start from the corresponding path integral representation of the stochastic system...

We present a new method, based on averaging, to simulate certain systems with multiple time scales efficiently and demonstrate its utility in the context of the shallow-water equations. We first develop the method in a simple linear setting and analytically prove its stability. This is followed by an extension to the full equations and a presentation of a computational model for it. In this pre...

A new algorithm, called boosted hybrid method, is proposed for the simulation of chemical reaction systems with scale-separation in time and disparity in species population. For such stiff systems, the algorithm can automatically identify scale-separation in time and slow down the fast reactions while maintaining a good approximation to the original effective dynamics. This technique is called ...

In literature of face recognition many methods have been proposed which extract features at multiple scales for robust classification. In this paper, we proposed a novel method which utilizes Local Polynomial Approximation (LPA) techniques to capture the directional information of the face image at different scales. LPA based filters are used to obtain directional faces from the normalized face...

Gene network dynamics often involves processes that take place on widely differing time scales – from the order of nanoseconds to the order of several days. Multiple time scales in mathematical models often lead to serious computational difficulties, such as numerical stiffness in the case of differential equations or excessively redundant Monte Carlo simulations in the case of stochastic proce...

A fully discrete analysis of the finite element heterogeneous multiscale method (FEHMM) for elliptic problems with N + 1 well separated scales is discussed. The FEHMM is a numerical homogenization method that relies on macroscopic scheme (macro FEM) for the approximation of the effective solution corresponding to the multiscale problem. The effective data are recovered from micro scale computat...

The method of variation of constants is an important tool used to solve systems of ordinary differential equations, and was invented by Euler and Lagrange to solve a problem in orbital mechanics. This methodology assumes that certain "constants" associated with a homogeneous problem will vary in time in response to an external force. It also introduces one or more constraint equations. We show ...