We consider finite point-set approximations of a manifold or fractal with the goal of determining topological properties of the underlying set. We use the minimal spanning tree of the finite set of points to compute the number and size of its -connected components. By extrapolating the limiting behavior of these quantities as → 0 we can say whether the underlying set appears to be connected, to...

Several consumer demand choices are characterized by the choice of multiple alternatives simultaneously. An example of such a choice situation in activity-travel analysis is the type of discretionary (or leisure) activity to participate in and the duration of time investment of the participation. In this context, within a given temporal period (say a day or a week), an individual may decide to ...

A new approach to multiport switching in arrays of nonlinear waveguides is proposed. Whereas other schemes have relied on suppressing the inherent transverse discreteness of these arrays, this approach takes advantage of that feature. One of the effects of discreteness is to keep intense beams trapped in a single waveguide for the length of the array. Switching may be achieved by use of a contr...

An actuator array is a form of distributed manipulation where an object being transported and manipulated rests on a large number of stationary supporting actuators. The authors have developed a macroscopic actuator array consisting of many motorized wheels. The analysis of such an array as opposed to a MEMS array requires the explicit modeling of the discreteness in the system, including the s...

We establish a link between contextuality of quantum mechanics and quantum-mechanical computation. Specifically, we show that no deterministic measurement-based quantum computation evaluating a non-linear function can be described by a non-contextual hidden-variable model. We give examples for such computations derived from quantum codes with suitable transversality properties, and from a count...

The collision between a kink and a high amplitude breather in the Frenkel-Kontorova chain with a small degree of discreteness was studied numerically and the results were compared with an exact three-soliton solution to the sine-Gordon (SG) equation. It was found that there exists a narrow range of parameters of quasiparticles where the collision in the discrete system is strongly inelastic and...

High-frequency financial data are not only discretely sampled in time but the time separating successive observations is often random. We analyze the consequences of this dual feature of the data when estimating a continuous-time model. In particular, we measure the additional effects of the randomness of the sampling intervals over and beyond those due to the discreteness of the data. We also ...

We study the dynamics of magnetic domain walls in the Peierls potential due to the discreteness of the crystal lattice. The propagation of a narrow domain wall (comparable to the lattice parameter) under the effect of a magnetic field proceeds through the formation of kinks in its profile. We predict that, despite the discreteness of the system, such kinks can behave like sine-Gordon solitons i...