An efficient AIM for the scattering computation of the finite sparse array

Based on the traditional adaptive integral method(AIM), a fast method called array AIM is proposed to accelerate the scattering calculation of the finite periodic array and the sparse array. On one hand, this method could eliminate the idle grids through the utilization of 5-level block-Toeplitz matrix. Furthermore, the procedure of near correction is eliminated by applying the zeros shielding technique. On the other hand, the block Jacobi preconditioning technique is used to improve the iterative convergence, and the technique of wave path difference compensation is applied to accelerate the post-processing. The numerical results show that the proposed method not only possesses good accuracy, but also has much less cost both in time and memory, in comparison with the traditional AIM. Moreover, this method could be applied to solve the scattering problems for the finite periodic array, as well as the sparse array.

A general multi-step matrix splitting iteration method for computing PageRank

Based on the general inner-outer (GIO) iteration method [5,34] and the iteration framework [6], we present a general multi-step matrix splitting (GMMS) iteration method for computing PageRank, and analyze its overall convergence property. Moreover, the same idea can be used as a preconditioning technique for accelerating the Krylov subspace methods, such as GMRES method. Finally, several numerical examples are given to illustrate the effectiveness of the proposed algorithm.

A Modified Adaptive Integral Method for Analysis of Large-scale Finite Periodic Array

A fast algorithm based on AIM is proposed to analyze the scattering problem of the large-scale finite array. In this method, by filling zeros into the local transformation matrix, the near and far fields are isolated thoroughly to eliminate the near correction process. In the far part, a 5-level block-toeplitz matrix is employed to avoid saving the idle grids without adding artificial interfaces. In the near part, only one local cube is required to compute the local translation matrix and near impedance matrix, which can be shared by all elements. Furthermore, the block Jacobi preconditioning technique is applied to improve the convergence, and the principle of pattern multiplication is used to accelerate the calculation of the scattering pattern. Numerical results show that the proposed method can reduce not only the CPU time in filling and solving matrix but also the whole memory requirement dramatically for the large-scale finite array with large spacings.

Comparison of Ischemic Preconditioning and Systemic Piracetam for Prevention of Ischemia-Reperfusion Injury in Musculocutaneous Flaps

Background Ischemia-reperfusion injury plays an important role in flap failure. Ischemic preconditioning technique is the only proven method for preventing ischemia-reperfusion injury, but it is not used widely in daily practice because of difficulties such as prolonging the operation time, need for surgical experience, and increasing the risk of complications. This study has been performed with the assumption that piracetam may be a simple and inexpensive alternative to the preconditioning technique due to its antioxidant, antiaggregant, rheological, anti-inflammatory, antiapoptotic, cytoprotective, and immune modulating effects. Methods Thirty-two rats were divided into four groups and latissimus dorsi musculocutaneous flaps were raised. No extra procedure was applied, and no treatment was given to the control group. Four hours of ischemia was created by clamping the thoracodorsal pedicle in the second group. The animals in the third group were treated with 10 minutes of ischemia and reperfusion periods as a preconditioning procedure before the 4 hours of ischemia. Animals in the fourth group received systemic piracetam 30 minutes before and 6 days after reperfusion. Nitric oxide and myeloperoxidase levels in serum and tissue, acute inflammatory cell response, and vascular proliferation in tissue were examined at the postoperative 24th hour and 10th day. Results Myeloperoxidase activity in both preconditioning and piracetam groups, was significantly lower than the ischemia-reperfusion group. Acute inflammatory cell response was similarly decreased in both preconditioning and piracetam groups compared with ischemia-reperfusion group. Tissue measurements of nitric oxide were also significantly higher in both preconditioning and piracetam groups than in the ischemia-reperfusion group. However, vascular proliferation increased in the preconditioning group, while it did not show any significant change in the piracetam group. Conclusion This study shows that systemic piracetam treatment provides protection against ischemia-reperfusion injury in musculocutaneous flaps and can offer a simple and inexpensive alternative to the preconditioning technique.