Let G be the Cartesian product of a regular tree T and finite connected transitive graph H. It is shown in [4] that Free Uniform Spanning Forest (FSF) this may not connected, but dependence connectedness on H remains somewhat mysterious. We study case when positive weight w put edges H-copies G, conjecture FSF exhibits phase transition. For large enough we show while for wide family T, disconne...

We use the Shokurov connectedness principle and the Corti inequality to prove the birational superrigidity of a nodal hypersurface in P 5 of degree 5. We assume that all varieties are projective, normal and defined over C.

Primed matching was used to examine the microgenesis of perceptual organization for line configurations that vary in the connectedness between their four line components, and for hierarchical patterns composed of four outline closed figures. The results for the line configurations showed that the configural organization of the disconnected line segments was available for priming very early, and...

It is proved that the phase shift of a polarized neutron interacting with a spatially uniform time-dependent magnetic field, demonstrates the same physical principles as the magnetic Aharonov-Bohm effect. The crucial role of inert objects is explained, thereby proving the quantum mechanical nature of the effect. It is also proved that the nonsimply connectedness of the fieldfree region is not a...

This paper expands the role of the new field of computational topology by surveying methods for incorporating connectedness in shape modeling. Two geometric representations in particular, recurrent models and implicit surfaces, can (often unpredictably) become connected or disconnected based on typical changes in modeling parameters. Two methodologies for controlling connectedness are identifie...

The tricorn is the connectedness locus in the space of antiholomorphic quadratic polynomials z 7! z2 + c. We prove that the tricorn is not locally connected and not even pathwise connected, confirming an observation of John Milnor from 1992. We extend this discussion more generally for antiholomorphic unicritical polynomials of degrees d 2 and their connectedness loci, known as multicorns.

Background: The exponential growth of smartphones has afforded many users with ubiquitous access to socialization as seen in the various mobile apps used to communicate and connect with others. The present study employed mixed-method approaches to analyse the impact of phubbing on social connectedness among adolescents in Malaysia. Methods:</stron...

In this paper we consider a natural extremal graph theoretic problem of topological sort, concerning the minimization of the (topological) connectedness of the independence complex of graphs in terms of its dimension. We observe that the lower bound dim(I(G)) 2 − 2 on the connectedness of the independence complex I(G) of line graphs of bipartite graphs G is tight. In our main theorem we charact...