6,033 research outputs found
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 -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 -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 -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
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