The report discusses when the non-linear dynamic equations of a non-linear system in a limit-cycle can be determined from measured data. The minimal order needed for this turns out to be the minimal dimension in which the stable orbit of the system does not intersect itself. This is illustrated with a fourth order spiking neuron model, which is identified using a non-linear second order differe...

First, I argue that scientific progress is possible in the absence of increasing verisimilitude in science's theories. Second, I argue that increasing theoretical verisimilitude is not the central, or primary, dimension of scientific progress. Third, I defend my previous argument that unjustified changes in scientific belief may be progressive. Fourth, I illustrate how false beliefs can promote...

--We consider the problem of adaptive modulation for wideband DS-CDMA Rayleigh fading channels with imperfect channel state information (CSI). We assume a multidimensional signal subspace spanned by a collection of random spreading codes (multicoding) and study the effects of both the subspace dimension and the probability distribution of the transmitted symbols on the mutual information betwee...

We consider a fully practical nite element approximation of the fourth order nonlinear degenerate parabolic equation u t + r:(b(u)ru)= 0; where generically b(u) := juj p for any given p 2 (0; 1). An iterative scheme for solving the resulting nonlinear discrete system is analysed. In addition to showing well-posedness of our approximation, we prove convergence in one space dimension. Finally som...

Asymptotic heat kernel expansion for nonminimal differential operators on curved manifolds in the presence of gauge fields is considered. The complete expressions for the fourth coefficient (E4) in the heat kernel expansion for such operators are presented for the first time. The expressions were computed for general case of manifolds of arbitrary dimension n and also for the most important cas...

A workstation was used to postprocess volume-rendered three-dimensional (3D) dynamic contrast material-enhanced magnetic resonance (MR) images of a breast carcinoma and a breast adenoma. Use of a 3D cursor allowed stereoscopic interactive probing of specific voxels to quantify contrast enhancement over time, which was mapped to a gray scale that effectively displayed enhancement as a fourth dim...

Purpose Aerospace is a demanding technological and industrial sector. Several regulations policies via innovative digital transformation have been integrated to impact production systems supply chains, including safety measures. Studies demonstrated that the Fourth Industrial Revolution (4IR) technologies could enhance productivity growth The 4IR role in influencing airlines’ yet receive in-dep...

For a Dirac particle in one dimension with random mass, the time evolution for the average wavefunction is considered. Using the supersymmetric representation of the average Green’s function, we derive a fourth order linear difference equation for the low-energy asymptotics of the average wavefunction. This equation is of Poincaré type, though highly critical and therefore not amenable to stand...