In the EDG methods, the numerical trace is taken to be continuous on a suitable collection of faces, thus resulting in an even smaller number of globally coupled degrees of freedom than in the HDG method.
Let T= s0, s1,…, s n ) be a finite numerical trace, π∈Π be an atomic proposition and ϕ, ψ be LTL formulae.
We simply require that the property describing the expected behavior can be expressed in temporal logic and that the behavior of the system can be represented by a numerical trace (possibly obtained by numerical simulation of deterministic or stochastic models).
It is worth noticing that when the numerical trace corresponds to a discrete representation of a continuous process, the discrete time semantics that we use may cause that particular events are 'missed' independently of the numerical errors that can be made by the numerical integration method.
Formally, a numerical trace is a finite sequence of tuples describing system's evolution with time: T= s0, s1,…, s n ), with being a strictly increasing sequence of time points, and being vectors of state variable values and of their derivatives at time t i.
Specifically, the input velocity model was calibrated to achieve a best match between experimental and numerical ultrasonic traces.
In this article, we consider that the behavior of a biological system is described by numerical timed traces.
This framework is general because it applies (i) to any biological function expressible in the temporal logic LTL, an expressive language for specifying dynamical behaviors widely used in computer science and engineering, and (ii) to any perturbation set, provided that the behaviors of the perturbed system can be obtained as numerical timed traces, for example by numerical integration of ODEs.
