Plane Formation by Synchronous Mobile Robots in the Three Dimensional Euclidean Space

Creating a swarm of mobile computing entities frequently called robots, agents or sensor nodes, with self-organization ability is a contemporary challenge in distributed computing. Motivated by this, we investigate the plane formation problem that requires a swarm of robots moving in the three dimensional Euclidean space to land on a common plane. The robots are fully synchronous and endowed with visual perception. But they do not have identifiers, nor access to the global coordinate system, nor any means of explicit communication with each other. Though there are plenty of results on the agreement problem for robots in the two dimensional plane, for example, the point formation problem, the pattern formation problem, and so on, this is the first result for robots in the three dimensional space. This paper presents a necessary and sufficient condition for fully-synchronous robots to solve the plane formation problem that does not depend on obliviousness i.e., the availability of local memory at robots. An implication of the result is somewhat counter-intuitive: The robots cannot form a plane from most of the semi-regular polyhedra, while they can form a plane from every regular polyhedron (except a regular icosahedron), whose symmetry is usually considered to be higher than any semi-regular polyhedrdon

Radii in weakly-bound light halo nuclei

A systematic study of the root-mean-square distance between the constituents of weakly-bound nuclei consisting of two halo neutrons and a core is performed using a renormalized zero-range model. The radii are obtained from a universal scaling function that depends on the mass ratio of the neutron and the core, as well as on the nature of the subsystems, bound or virtual. Our calculations are qualitatively consistent with recent data for the neutron-neutron root-mean-square distance in the halo of $^{11}$Li and $^{14}$Be nuclei

Comment on "Efimov States and their Fano Resonances in a Neutron-Rich Nucleus"

By introducing a mass asymmetry in a non-Borromean three-body system, without changing the energy relations, the virtual state pole cannot move from the negative real axis of the complex energy plane (with nonzero width) and become a resonance, because the analytical structure of the unitarity cuts remains the same.Comment: To be published in PR

Supersymmetric Heavy Higgses at e^+e^- Linear Collider and Dark-Matter Physics

We consider the capability of the e^+e^- linear collider (which is recently called as the International Linear Collider, or ILC) for studying the properties of the heavy Higgs bosons in the supersymmetric standard model. We pay special attention to the large \tan\beta region which is motivated, in particular, by explaining the dark-matter density of the universe (i.e., so-called ``rapid-annihilation funnels''). We perform a systematic analysis to estimate expected uncertainties in the masses and widths of the heavy Higgs bosons assuming an energy and integrated luminosity of \sqrt{s}=1 TeV and L=1 ab^{-1}. We also discuss its implication to the reconstruction of the dark-matter density of the universe.Comment: 28 pages, 13 figures, version to appear in PR