On the support of measures in multiplicative free convolution semigroups

In this paper, we study the supports of measures in multiplicative free semigroups on the positive real line and on the unit circle. We provide formulas for the density of the absolutely continuous parts of measures in these semigroups. The descriptions rely on the characterizations of the images of the upper half-plane and the unit disc under certain subordination functions. These subordination functions are $\eta$-transforms of infinitely divisible measures with respect to multiplicative free convolution. The characterizations also help us study the regularity properties of these measures. One of the main results is that the number of components in the support of measures in the semigroups is a decreasing function of the semigroup parameter

The effects of KSEA interaction on the ground-state properties of spin chains in a transverse field

The effects of symmetric helical interaction which is called the Kaplan, Shekhtman, Entin-Wohlman, and Aharony (KSEA) interaction on the ground-state properties of three kinds of spin chains in a transverse field have been studied by means of correlation functions and chiral order parameter. We find that the anisotropic transition of $XY$ chain in a transverse field ($XY$TF) disappears because of the KSEA interaction. For the other two chains, we find that the regions of gapless chiral phases in the parameter space induced by the DM or $XZY-YZX$ type of three-site interaction are decreased gradually with increase of the strength of KSEA interaction. When it is larger than the coefficient of DM or $XZY-YZX$ type of three-site interaction, the gapless chiral phases also disappear.Comment: 7 pages, 3 figure

A cluster-head selection and update algorithm for ad hoc networks

A novel cluster-head selection and update algorithm “Type-based Cluster-forming Algorithm (TCA)” is proposed, which outperforms both the lowest node ID (LID) and the Weighted Clustering Algorithm (WCA) in the ad hoc network scenario considered. The system’s performance is investigated in a scenario, when the 50 communicating nodes belong to three different groups, for example, a group of rescue workers, fire-fighters and paramedics. It is demonstrated that the carefully designed protocol is capable of outperforming the above-mentioned benchmarkers both in terms of a reduced number of cluster-head updates and cluster-change events. Hence its quality-of-service may be deemed higher

Egomotion estimation using binocular spatiotemporal oriented energy

Camera egomotion estimation is concerned with the recovery of a camera's motion (e.g., instantaneous translation and rotation) as it moves through its environment. It has been demonstrated to be of both theoretical and practical interest. This thesis documents a novel algorithm for egomotion estimation based on binocularly matched spatiotemporal oriented energy distributions. Basing the estimation on oriented energy measurements makes it possible to recover egomotion without the need to establish temporal correspondences or convert disparity into 3D world coordinates. There sulting algorithm has been realized in software and evaluated quantitatively on a novel laboratory dataset with ground truth as well as qualitatively on both indoor and outdoor real-world datasets. Performance is evaluated relative to comparable alternative algorithms and shown to exhibit best overall performance