Users of geographic databases that integrate spatial data represented in vector and raster models, should not perceive the differences among the data models in which data are represented, nor should they be forced to apply different concepts depending on the model in which spatial data are represented. A crucial aspect of spatial query languages for such integrated systems is the need mechanism...

Test spaces (or manuals) provide a simple, elegant and very general mathematical framework for the study of probability theory – classical, quantum and otherwise. In many particular cases of interest, test spaces carry significant topological structure. This paper inaugurates a general study of topological test spaces. Among other results, we show that any topological test space with a compact ...

The purpose of this paper is to define the product related neutrosophic topological space and proved some theorems based on this. We introduce the concept of neutrosophic semiopen sets and neutrosophic semi-closed sets in neutrosophic topological spaces and derive some of their characterization. Finally, we analyze neutrosophic semi-interior and neutrosophic semi-closure operators also. Mathema...

Topological motion planning is a planning problem embedding topological concept of trajectories. In this work, we propose two asymptotically optimal sampling-based algorithms for topological motion planning: (a) a batch processingbased planner, termed Fast Marching Homology-embedded Tree star (FMHT*); and (b) an incremental anytime algorithm, termed Rapidly-exploring Random Homology-embedded Tr...

In this thesis we lay the foundations to develop multirelational learning systems which can cope better with the challenges posed by structural and topological domains. Even though many interesting application domains contain structural or topological data, current multirelational systems have difficulties dealing with the complexity of the search space of theses domains, their indeterminacy, a...

Over the past few years, point-based POMDP solvers scaled up to produce approximate solutions to mid-sized domains. However, to solve real world problems, solvers must exploit the structure of the domain. In this paper we focus on the topological structure of the problem, where the state space contains layers of states. We present here the Topological Order Planner (TOP) that utilizes the topol...