For subsets in the standard symplectic space $(\mathbb{R}^{2n},\omega_0)$ whose closures are intersecting with coisotropic subspace $\mathbb{R}^{n,k}$ we construct relative versions of Ekeland-Hofer capacities respect to $\mathbb{R}^{n,k}$, establish representation formulas for such bounded convex domains $\mathbb{R}^{n,k}$. We also prove a product formula and fact that value this capacity on h...

Partisan gerrymandering poses a threat to democracy. Moreover, the complexity of the districting task may exceed human capacities. One potential solution is using computational models to automate the districting process by optimising objective and open criteria, such as how spatially compact districts are. We formulated one such model that minimised pairwise distance between voters within a dis...

The global Air Traffic Management (ATM) system represents one of the most complex human-machine systems known. As the system has evolved in step with traffic demands, automation has been increasingly called upon to augment the capacities of the human operator, namely the air traffic controller. Future generations of ATM automation seek to augment, or even replace, such human faculties as decisi...

Anumber of prominent artificial intelligence (AI) researchers and commentators (Moravec 1999a; Solomonoff 1985; Vinge 1993) have presented versions of the following argument: 1. Continued exponential improvement in computer hardware will deliver inexpensive processing power exceeding that of the human brain within the next several decades. 2. If human-level processing power were inexpensive, th...

In order to differentiate the semiotic capacities of animals and human beings we need to understand more exactly what these properties are. Instead of identifying all vehicles of meaning with signs, we certainly have to specify the notion of sign, but it will also be necessary to provide an inventory of other kinds of meaning, starting out from perception, and going through a number of intermed...