A note on the growth factor in Gaussian elimination for generalized Higham matrices

The Higham matrix is a complex symmetric matrix A=B+iC, where both B and C are real, symmetric and positive definite and $\mathrm{i}=\sqrt{-1}$ is the imaginary unit. For any Higham matrix A, Ikramov et al. showed that the growth factor in Gaussian elimination is less than 3. In this paper, based on the previous results, a new bound of the growth factor is obtained by using the maximum of the condition numbers of matrixes B and C for the generalized Higham matrix A, which strengthens this bound to 2 and proves the Higham's conjecture.Comment: 8 pages, 2 figures; Submitted to MOC on Dec. 22 201

Effective generation of Ising interaction and cluster states in coupled microcavities

We propose a scheme for realizing the Ising spin-spin interaction and atomic cluster states utilizing trapped atoms in coupled microcavities. It is shown that the atoms can interact with each other via the exchange of virtual photons of the cavities. Through suitably tuning the parameters, an effective Ising spin-spin interaction can be generated in this optical system, which is used to produce the cluster states. This scheme does not need the preparation of initial states of atoms and cavity modes, and is insensitive to cavity decay.Comment: 11pages, 2 figures, Revtex

Institutional Herding and Investor Sentiment

We investigate the role of investor sentiment in institutional herding behavior and its impact on stock prices. We find that institutional investors exhibit more herding behavior during periods of high sentiment, which has a significant impact on stock prices. Our results show that herding has a stabilizing effect on the stock market when investor sentiment is low, while it causes price distortions when sentiment is high. We also show that the impact of sentiment on price is particularly pronounced for small, non-profitable, low tangibility, high-growth firms

Generation of two-mode entanglement between separated cavities

We propose a scheme for the generation of two-mode entangled states between two spatially separated cavities. It utilizes a two-level atom sequentially coupling to two high-Q cavities with a strong classical driving field. It is shown that by suitably choosing the intensities and detunings of the fields and coherent control of the dynamics, several different entangled states such as entangled coherent states and Bell states can be produced between the modes of the two cavities.Comment: 4pages,1figur