This paper presents the HDG learning algorithm, which uses a hierarchical decomposition of the state space to make learning to achieve goals more efficient with a small penalty in path quality. Special care must be taken when performing hierarchical planning and learning in stochastic domains, because macro-operators cannot be executed ballistically. The HDG algorithm, which is a descendent of ...

Bimodal provability logic GLB, introduced by G. Japaridze, currently plays an important role in the applications of provability logic to proof-theoretic analysis. Its topological semantics interprets diamond modalities as derived set operators on a bi-scattered bitopological space. We study the question of completeness of this logic w.r.t. the most natural space of this kind, that is, w.r.t. an...

The purpose of this paper is to introduce the notions g̃-R0, g̃-R1, g̃-T0, g̃-T1 and g̃-T2 in bitopological spaces.

Using the molecular dynamics method, of hydrogen bond (HB) networks emerging on surface a graphene sheet during its functionalization with hydroxyl groups OH are simulated. It is demonstrated that two form an energetically more advantageous structure when they covalently attached one side to carbon atoms forming opposite vertices hexagon valence bonds sheet. Attaching located at hexagons leads ...

We present a Stone duality for bitopological spaces in analogy to the duality between topological spaces and frames, and discuss the resulting notions of sobriety and spatiality. Under the additional assumption of regularity, we prove a characterisation theorem for subsets of a bisober space that are compact in one and closed in the other topology. This is in analogy to the celebrated Hofmann-M...

We obtain the further properties of quasi Mcontinuous functions which were introduced and investigated in order to establish the unified theory for several variations of quasi-continuity between bitopological spaces.

in this paper, we discuss the equivalent conditions of pretopological and topological $l$-fuzzy q-convergence structures and define $t_{0},~t_{1},~t_{2}$-separation axioms in $l$-fuzzy q-convergence space. {furthermore, $l$-ordered q-convergence structure is introduced and its relation with $l$-fuzzy q-convergence structure is studied in a categorical sense}.

Given a compact metric space $X$, we associate to it an inverse sequence of finite $T_0$ topological spaces. The limit this contains homeomorphic copy $X$ that is strong deformation retract. We provide method approximate the homology groups and other algebraic invariants. Finally, study computational aspects implementation method.