The $-calculus is the extension of the π -calculus, built around the central notion of cost and allowing infinity in its operators. We propose the $-calculus as a more complete model for problem solving to provide a support to handle intractability and undecidability. It goes beyond the Turing Machine model. We define the semantics of the $-calculus using a novel optimization method (the kΩ -op...

We consider the problem of selecting an optimality criterion, when total costs diverge, in deterministic infinite horizon optimization over discrete time. Our formulation allows for both discrete and continuous state and action spaces, as well as time-varying, that is, nonstationary, data. The task is to choose a criterion that is neither too overselective, so that no policy is optimal, nor too...

We theoretically investigate microwave transmission through a zero-index metamaterial loaded with dielectric defects. The metamaterial is impedance matched to free space, with the permittivity and permeability tending towards zero over a given frequency range. By simply varying the radii and permittivities of the defects, total transmission or reflection of the impinging electromagnetic wave ca...

Sensitivity analysis aims at exploring which of a number of variables have an impact on a certain response. Not only are the individual variables of interest but also whether they interact or not. By analogy with the total sensitivity index, used to detect the most influential variables, a screening of interactions can be done efficiently with the so-called total interaction index (TII), define...

In past years, topological indices are introduced to measure the characters of chemical molecules. Thus, the study of these topological indices has raised large attention in the field of chemical science, biology science and pharmaceutical science. In this paper, by virtue of molecular structure analysis, we determine the total Szeged index, vertex-edge Wiener index and edge hyper-Wiener index ...

Let T be a terrain, and let P be a set of points (locations) on its surface. An important problem in Geographic Information Science (GIS) is computing the visibility index of a point p on P , that is, the number of points in P that are visible from p. The total visibility-index problem asks for computing the visibility index of every point in P . Most applications of this problem involve 2-dime...