Topological relations between spherical spatial regions with holes

There is growing interest in globally modelling the entire planet.Although topological relations between spherical simple regions and topological relations between regions with holes in the plane have been investigated,few studies have focused on the topological relations between spherical spatial regions with holes.The 16-intersection model(16IM)is proposed to describe the topological relations between spatial regions with holes.A total of 25 negative conditions are proposed to eliminate the impossible topological relations between spherical spatial regions with holes.The results show that(1)3 disjoint relations,3 meet relations,66 overlap relations,7 cover relations,3 contain relations,1 equal relation,7 coveredBy relations,3 inside relations,1 attach relation,52 entwined relations,and 28 embrace relations can be distinguished by the 16IM and that(2)the formalisms of attach,entwined,and embrace relations between the spherical spatial regions without holes based on the 9IM and that between the spherical spatial regions with holes based on the simplified 16IM are different,whereas the formalisms of other types of relations between spherical spatial regions without holes based on the 9IM and that between the spherical spatial regions with holes based on a simplified 16IM are the same.

Qualitative spatial reasoning on topological relations by combining the semantic web and constraint satisfaction

Qualitative spatial reasoning on topological relations can extract hidden spatial knowledge from qualitatively described topological information,which is of significant importance for decisionmaking and query optimization in spatial analysis.Qualitative reasoning on spatial topological information based on semantic knowledge and reasoning rules is an efficient means of reducing both the known relations and the corresponding rules,which can result in enhanced reasoning performance.This paper proposes a qualitative reasoning method for spatial topological relations based on the semantic description of reasoning rules and constraint set.Combined with knowledge from the Semantic Web,the proposed method can easily extract potential spatial results consistent with both unique and non-unique rules.The Constraint-Satisfactionbased approach,describing constraint set with semantic expressions,is then used together with an improved path consistency algorithm to verify the consistency of the unique-rules-based and non-unique-rules-based reasoning results.The verification can eliminate certain reasoning results to ensure the reliability of the final results.Thus,the task of qualitative spatial reasoning on topological relations is completed.

Topological Recursion Relations from Pixton Relations

We propose an algorithm to derive tautological relations from Pixton relations. We carry out this algorithm explicitly to derive some results in genus 0, 1, 2, 3 and analyze the possibility to generalize to higher genera. As an application, some results about reconstruction of Gromov–Witten invariants can be derived.

A genus-4 topological recursion relation for Gromov-Witten invariants

In this paper,we give a new genus-4 topological recursion relation for Gromov-Witten invariants of compact symplectic manifolds via Pixton’s relations on the moduli space of curves.As an application,we prove that Pixton’s relations imply a known topological recursion relation on Mg,1 for genus g≤4.

Two topological approaches to resonance energy and the relation between them

Two of the present authors recently put forward a novel approach to resonance energy which is based on a similar topological reasoning as a previously elaborated resonance energy concept. It is shown that these two approaches are not completely equivalent. Several other properties of the new resonance energy are pointed out.