We introduce a generalization of intervals over compact matrix Lie groups. Interval group elements are defined using a midpoint-radius representation. Furthermore, we define the respective group operations and the action of interval group elements on vector spaces. We developed structures and operations are implemented for the special case of orthogonal matrices in the matrix library of the COC...

Methods We compare three methods: (1) the Stevens method, which uses the average range size of all species within each elevational band (100-m bands); (2) the midpoint method, which uses the average range size of species whose midpoints occur in each elevational band; and (3) a quartile method that examines the distribution of only the smallest ranges (less than one-quarter of the mountain heig...

Travel time estimation is a critical ingredient for transportation management and traveler information—both infrastructure-based and in-vehicle. Infrastructure managers and operators are interested in estimating optimal freeway sensor density for new construction and retrofits. Focusing on freeway travel time estimation for display on roadside variable message signs, this paper describes a conc...

A new recursive prediction error algorithm (RPEM) based on a nonlinear ordinary differential equation (ODE) model of black-box state space form is presented. The selected model is discretised by a midpoint integration algorithm and compared to an Euler forward algorithm. When the algorithm is applied, scaling of the sampling time is used to improve performance further. This affects the state ve...

We present a symplectic integrator, based on the implicit midpoint method, for classical spin systems where each spin is a unit vector in R{3}. Unlike splitting methods, it is defined for all Hamiltonians and is O(3)-equivariant, i.e., coordinate-independent. It is a rare example of a generating function for symplectic maps of a noncanonical phase space. It yields a new integrable discretizatio...

This paper introduces vector agents (VA), an approach to impose a systematic framework on the geometric element of Torrens and Benenson’s Geographic Automata System (GAS). Both schemes use vector geometry as an antidote to the geographically unrealistic regular tessellation cellular automata (CA). The work reported here explores the properties of irregular and dynamic VAs in particular, a subcl...