Achievable Angles Between two Compressed Sparse Vectors Under Norm/Distance Constraints Imposed by the Restricted Isometry Property: A Plane Geometry Approach

The angle between two compressed sparse vectors subject to the norm/distance constraints imposed by the restricted isometry property (RIP) of the sensing matrix plays a crucial role in the studies of many compressive sensing (CS) problems. Assuming that (i) u and v are two sparse vectors separated by an angle thetha, and (ii) the sensing matrix Phi satisfies RIP, this paper is aimed at analytically characterizing the achievable angles between Phi*u and Phi*v. Motivated by geometric interpretations of RIP and with the aid of the well-known law of cosines, we propose a plane geometry based formulation for the study of the considered problem. It is shown that all the RIP-induced norm/distance constraints on Phi*u and Phi*v can be jointly depicted via a simple geometric diagram in the two-dimensional plane. This allows for a joint analysis of all the considered algebraic constraints from a geometric perspective. By conducting plane geometry analyses based on the constructed diagram, closed-form formulae for the maximal and minimal achievable angles are derived. Computer simulations confirm that the proposed solution is tighter than an existing algebraic-based estimate derived using the polarization identity. The obtained results are used to derive a tighter restricted isometry constant of structured sensing matrices of a certain kind, to wit, those in the form of a product of an orthogonal projection matrix and a random sensing matrix. Follow-up applications to three CS problems, namely, compressed-domain interference cancellation, RIP-based analysis of the orthogonal matching pursuit algorithm, and the study of democratic nature of random sensing matrices are investigated.Comment: submitted to IEEE Trans. Information Theor

Research on the Foreign Direct Investment Factors of Japanese Hotel Industry in Taiwan-Taking Okura Hotel as an Example

Due to the impact of COVID-19 in 2019, the global hotel industry has been severely impacted by the disconnection of the tourism industry. However, even with the impact of the epidemic, the Japanese hotel industry’s investment in Taiwan has not stopped. What are the factors that drive the Japanese hotel industry to defy the threat of the epidemic and choose Taiwan as its destination for foreign direct investment? This is the research goal of this article. This article intends to adopt Push-Pull-Mooring (PPM)migration theory to construct the possible factors of why the Japanese hotel industry chooses Taiwan as its foreign direct investment destination. These factors consist of three effects to describe Japan Okura hotel’s migration. First, the push effect refers to factors that induce people to leave their place of origin. Second, the pull effect refers to factors that attract people to a destination. Third, the mooring effect refers to intervention variables for push and pull effects that facilitate or inhibit the determination of movement. The finding is that push and pull factors still play an active role in promoting Okura Hotel’s investment in Taiwan, even if the influence of some factors is slightly reduced due to the shift in international conditions. With the development of globalization and high technology, mooring factors are no longer the reason that hinders Japanese Okura’s investment in Taiwan. Combined with push and pull factors, PPM migration model can fully explain why the Japanese hotel industry chooses to conduct foreign direct investment in Taiwan, even if it is affected by COVID-19.It’s just that COVID-19 has not stopped so far, and the unstable situation on both sides of the strait may impact the original PPM model and affect the results of the analysis. It is worth further observation and research by subsequent researchers

Photon blockade with a trapped Λ\Lambda-type three-level atom in asymmetrical cavity

We propose a scheme to manipulate strong and nonreciprocal photon blockades in asymmetrical Fabry-Perot cavity with a $\Lambda$-type three-level atom. Utilizing the mechanisms of both conventional and unconventional blockade, the strong photon blockade is achieved by the anharmonic eigenenergy spectrum brought by $\Lambda$-type atom and the destructive quantum interference effect induced by a microwave field. By optimizing the system parameters, the manipulation of strong photon blockade over a wide range of cavity detuning can be realized. Using spatial symmetry breaking introduced by the asymmetry of cavity, the direction-dependent nonreciprocal photon blockade can be achieved, and the nonreciprocity can reach the maximum at optimal cavity detuning. In particular, manipulating the occurring position of nonreciprocal photon blockade can be implemented by simply adjusting the cavity detuning. Our scheme provides feasible access for generating high-quality nonreciprocal single-photon sources