Gaussian processes (GPs) are flexible distributions over functions that enable highlevel assumptions about unknown functions to be encoded in a parsimonious, flexible and general way. Although elegant, the application of GPs is limited by computational and analytical intractabilities that arise when data are sufficiently numerous or when employing non-Gaussian models. Consequently, a wealth of ...

SUMMARY We present a new nonlinear monotone finite volume method for diffusion and convection-diffusion equations and its application to two-phase black oil models. We consider full anisotropic discontinuous diffusion/permeability tensors and discontinuous velocity fields on conformal polyhedral meshes. The approximation of the diffusive flux uses the nonlinear two-point stencil which reduces t...

The notion of approximation coverage is developed. It is applicable to first-order declarative programs (e.g., logic programs, constructive algebraic specifications, and attribute grammars) in two dimensions in a natural way. For an attribute grammar, for example, there is a syntactic dimension corresponding to the underlying context-free grammar, and there is also a semantic dimension correspo...

To tackle the problem with inexact, uncertainty and vague knowl- edge, constructive method is utilized to formulate lower and upper approx- imation sets. Rough set model over dual-universes in fuzzy approximation space is constructed. In this paper, we introduce the concept of rough set over dual-universes in fuzzy approximation space by means of cut set. Then, we discuss properties of rough se...

Firstly, two kinds of natural distances between intuitionistic fuzzy sets are generated by the classical natural distance between fuzzy sets under a unified framework of residual intuitionistic implication operators. Secondly, the continuity and approximation property of a method for solving intuitionistic fuzzy reasoning are defined. It is proved that the triple implication method for intuitio...

We present several iterative methods for finding the critical points and/or the minima of a functional which is essentially the difference between two convex functions. The underlying idea relies upon partial and exact regularization of the functional, which allows us to preserve the local feature in a large number of applications, as well as to obtain some convergence results. These methods ar...

In 1973, Victor Klee posed the following question: How many guards are necessary, and how many are sufficient to patrol the paintings and works of art in an art gallery with n walls? This resulted in many subsequent researches so that the various versions of the art gallery problem were posed. Most of the versions posed are NP-hard, so designing approximation algorithms becomes important. The b...