We extend the expressive power of the region connection calculus RCC-8 by allowing applications of the 8 binary relations of RCC-8 not only to atomic regions but also to Boolean combinations of them. It is shown that the statisfiability problem for the extended language in arbitrary topological spaces is still in NP; however, it becomes PSPACE-complete if only the Euclidean spaces R , n > 0, ar...

In many stochastic partial differential equations (SPDEs) involving random coefficients, modeling the randomness by spatial white noise may lead to ill-posed problems. Here we consider an elliptic problem with spatial Gaussian coefficients and present a methodology that resolves this issue. It is based on stochastic convolution implemented via generalized Malliavin operators in conjunction with...

Some individuals automatically and involuntarily “see” mental images of numbers in spatial arrays when they think of numbers (number forms). Makioka (2009) proposed a theoretical framework called self-organizing learning account of number forms (SOLA), which argues that number forms are generated by self-organizing learning between numerical and spatial representation. This framework explains t...

Multi-party local quantum operations with shared quantum entanglement or shared classical randomness are studied. The following facts are established: • There is a ball of local operations with shared randomness lying within the space spanned by the no-signalling operations and centred at the completely noisy channel. • The existence of the ball of local operations with shared randomness is emp...