A remark on the Restricted Isometry Property in Orthogonal Matching Pursuit

This paper demonstrates that if the restricted isometry constant $\delta_{K+1}$ of the measurement matrix $A$ satisfies $$\delta_{K+1} < \frac{1}{\sqrt{K}+1},$$ then a greedy algorithm called Orthogonal Matching Pursuit (OMP) can recover every $K$--sparse signal $\mathbf{x}$ in $K$ iterations from A\x. By contrast, a matrix is also constructed with the restricted isometry constant $$\delta_{K+1} = \frac{1}{\sqrt{K}}$$ such that OMP can not recover some $K$-sparse signal $\mathbf{x}$ in $K$ iterations. This result positively verifies the conjecture given by Dai and Milenkovic in 2009

Production of the top-pions from the higgsless--top-Higgs model at the LHC

The top-pions($\pi_{t}^{0,\pm}$) predicted by extra dimensional descriptions of the topcolor scenario have similar feature with those in four dimensional topcolor scenario, which have large Yukawa couplings to the third generation quarks. In the context of the higgsless--top-Higgs(HTH) model, we discuss the production of these new particles at the CERN Large Hadron Collider(LHC) via various suitable mechanisms (gluon-gluon fusion, bottom-bottom fusion, gluon-bottom fusion, and the usual Drell-Yan processes) and estimate their production rates. We find that, as long as the top-pions are not too heavy, they can be abundantly produced at the LHC. The possible signatures of these new particles might be detected at the LHC experiments.Comment: 18pages, 6 figures, discussions and references added, typos correcte

Comparison of daily and sub-daily SWAT models for daily streamflow simulation in the Upper Huai River Basin of China

Despite the significant role of precipitation in the hydrological cycle, few studies have been conducted to evaluate the impacts of the temporal resolution of rainfall inputs on the performance of SWAT (soil and water assessment tool) models in large-sized river basins. In this study, both daily and hourly rainfall observations at 28 rainfall stations were used as inputs to SWAT for daily streamflow simulation in the Upper Huai River Basin. Study results have demonstrated that the SWAT model with hourly rainfall inputs performed better than the model with daily rainfall inputs in daily streamflow simulation, primarily due to its better capability of simulating peak flows during the flood season. The sub-daily SWAT model estimated that 58% of streamflow was contributed by baseflow compared to 34 % estimated by the daily model. Using the future daily and three-hour precipitation projections under the RCP (Representative Concentration Pathways) 4.5 scenario as inputs, the sub-daily SWAT model predicted a larger amount of monthly maximum daily flow during the wet years than the daily model. The differences between the daily and sub-daily SWAT model simulation results indicated that temporal rainfall resolution could have much impact on the simulation of hydrological process, streamflow, and consequently pollutant transport by SWAT models. There is an imperative need for more studies to examine the effects of temporal rainfall resolution on the simulation of hydrological and water pollutant transport processes by SWAT in river basins of different environmental conditions

Warped Brane worlds in Critical Gravity

We investigate the brane models in arbitrary dimensional critical gravity presented in [Phys. Rev. Lett. 106, 181302 (2011)]. For the model of the thin branes with codimension one, the Gibbons-Hawking surface term and the junction conditions are derived, with which the analytical solutions for the flat, AdS, and dS branes are obtained at the critical point of the critical gravity. It is found that all these branes are embedded in an AdS$_{n}$ spacetime, but, in general, the effective cosmological constant $\Lambda$ of the AdS$_{n}$ spacetime is not equal to the naked one $\Lambda_0$ in the critical gravity, which can be positive, zero, and negative. Another interesting result is that the brane tension can also be positive, zero, or negative, depending on the symmetry of the thin brane and the values of the parameters of the theory, which is very different from the case in general relativity. It is shown that the mass hierarchy problem can be solved in the braneworld model in the higher-derivative critical gravity. We also study the thick brane model and find analytical and numerical solutions of the flat, AdS, and dS branes. It is find that some branes will have inner structure when some parameters of the theory are larger than their critical values, which may result in resonant KK modes for some bulk matter fields. The flat branes with positive energy density and AdS branes with negative energy density are embedded in an $n$-dimensional AdS spacetime, while the dS branes with positive energy density are embedded in an $n$-dimensional Minkowski one.Comment: 14 pages, 7 figures, updated version, accepted by EPJ