Experiments on a Parallel Nonlinear Jacobi–Davidson Algorithm

AbstractThe Jacobi–Davidson (JD) algorithm is very well suited for the computation of a few eigen-pairs of large sparse complex symmetric nonlinear eigenvalue problems. The performance of JD crucially depends on the treatment of the so-called correction equation, in particular the preconditioner, and the initial vector. Depending on the choice of the spectral shift and the accuracy of the solution, the convergence of JD can vary from linear to cubic. We investigate parallel preconditioners for the Krylov space method used to solve the correction equation.We apply our nonlinear Jacobi–Davidson (NLJD) method to quadratic eigenvalue problems that originate from the time-harmonic Maxwell equation for the modeling and simulation of resonating electromagnetic structures

An efficient implementation of the block Gram--Schmidt method

The block Gram--Schmidt method computes the QR factorisation rapidly, but this is dependent on block size $m$. We endeavor to determine the optimal $m$ automatically during one execution. Our algorithm determines $m$ through observing the relationship between computation time and complexity. Numerical experiments show that our proposed algorithms compute approximately twice as fast as the block Gram--Schmidt method for some block sizes, and is a viable option for computing the QR factorisation in a more stable and rapid manner. References Bjorck, A., Numerical Methods for Least Squares Problems, SIAM, (1996). Elden, L., and Park, H., Block Downdating of Least Squares Solutions, SIAM J. Matrix Anal. Appl., 15:1018--1034 (1994). doi:10.1137/S089547989223691X Runger, G., and Schwind, M., Comparison of Different Parallel Modified Gram--Schmidt Algorithms, Euro-Par 2005, LNCS 3648:826--836 (2005). doi:10.1007/11549468_90 Katagiri, T., Performance Evaluation of Parallel Gram--Schmidt Re-orthogonalization Methods, VECPAR 2002, LNCS 2565:302--314 (2003). doi:10.1007/3-540-36569-9_19 Matrix Market, Mathematical and Computational Sciences Division, Information Technology Laboratory of the National Institute of Standards and Technology, USA. http://math.nist.gov/MatrixMarket/ Matsuo, Y. and Nodera, T., The Optimal Block-Size for the Block Gram--Schmidt Orthogonalization, J. Sci. Tech, 49:348--354 (2011). Moriya, K. and Nodera, T., The DEFLATED-GMRES(m, k) Method with Switching the Restart Frequency Dynamically, Numer. Linear Alg. Appl., 7:569--584 (2000). doi:10.1002/1099-1506(200010/12)7:7/8<569::AID-NLA213>3.0.CO;2-8 Moriya, K. and Nodera, T., Usage of the convergence test of the residual norm in the Tsuno--Nodera version of the GMRES algorithm, ANZIAM J., 49:293--308 (2007). doi:10.1017/S1446181100012852 Liu, Q., Modified Gram--Schmidt-based Methods for Block Downdating the Cholesky Factorization, J. Comput. Appl. Math., 235:1897--1905 (2011). doi:10.1016/j.cam.2010.09.003 Saad, Y. and Schultz, M. H., GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems, SIAM J. Sci. Stat. Comput., 7:856--869 (1986). doi:10.1137/0907058 Shiroishi, J. and Nodera, T., A GMRES($m$) Method with Two Stage Deflated Preconditioners, ANZIAM J., 52:C222--C236 (2011). http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/3984 Leon, S. J., Bjorck, A., and Gander, W., Gram--Schmidt Orthogonalization: 100 years and more, Numer. Linear Algebra Appl., 20:492--532 (2013). doi:10.1002/nla.1839 Stewart, G. W., Block Gram--Schmidt Orthogonalization, SIAM J. Sci. Comput., 31:761--775 (2008). doi:10.1137/070682563 Vanderstraeten, D., An Accurate Parallel Block Gram-Schmidt Algorithm without Reorthogonalization, Numer. Lin. Alg. Appl., 7:219--236 (2000). doi:10.1002/1099-1506(200005)7:4<219::AID-NLA196>3.0.CO;2-L Yokozawa, T., Takahashi, T., Boku, T. and Sato, M., Efficient Parallel Implementation of Classical Gram-Schmidt Orthogonalization Using Matrix Multiplication, (in Japanese) Information Processing Society of Japan (IPSJ), Computing System, 1:61--72 (2008)

Solid variant of serous cystadenoma of the pancreas

We describe a case of a solid variant of serous cystadenoma of the pancreas. The preoperative examination results led to a diagnosis of a nonfunctional pancreatic islet cell tumour, and the patient underwent a pylorus-preserving pancreaticoduodenectomy. The tumour was diagnosed as a solid variant of serous cystadenoma by histopathological examination. Solid variant of serous cystadenoma of the pancreas is difficult to diagnose preoperatively. More cases must be accumulated and investigated to obtain clues for accurate diagnosis

Interleukin-1α enhances the aggressive behavior of pancreatic cancer cells by regulating the α(6)β(1)-integrin and urokinase plasminogen activator receptor expression

BACKGROUND: In human pancreatic cancer progression, the α(6)β(1)-integrin is expressed on cancer cell surface during invasion and metastasis formation. In this study, we investigated whether interleukin (IL)-1α induces the alterations of integrin subunits and urokinase plasminogen activator/urokinase plasminogen activator receptor (uPA/uPAR) expression in pancreatic cancer cells. We hypothesize that the alterations of integrin subunits and uPA/uPAR expression make an important role in signaling pathways responsible for biological behavior of pancreatic cancer cells. RESULTS: IL-1α upregulated the expression of α(6 )and β(1 )integrins without any alterations of α(5 )and α(v )integrins expression. IL-1α also induced enhancement in the expression of uPA/uPAR in pancreatic cancer cells. IL-1α enhanced the proliferation, adhesion, and migration in pancreatic cancer cells, and IL-1α-induced alterations of uPA/uPAR expression correlated with the increased the migration of pancreatic cancer cells. Upregulation of α(6 )integrin subunit and uPA/uPAR correlated with the activation of Ras and downstream extracellular signal-regulated kinase (ERK) pathways. IL-1α-induced activation of Ras and downstream ERK can be inhibited by using inhibitory antibodies against α(6 )and β(1 )integrin and uPAR, consistent with the inhibition of proliferation, adhesion and migration of pancreatic cancer cells. Immunohistochemical analysis demonstrated a significant association between strong expressions of α(6 )integrin with uPAR in pancreatic cancer specimens. Furthermore, the strong expression of α(6 )integrin and uPAR was found to be independent prognosticator in pancreatic cancer patients. CONCLUSION: Based on these findings, we conclude that IL-1α can induce selective upregulation of α(6)β(1)-integrin and uPA/uPAR in pancreatic cancer cells and these changes may modulate the aggressive functions of pancreatic cancer

A time-delay suppression technique for DPWM control circuit

A proposed design of a low-cost digital pulse width modulation (DPWM) control circuit for non-isolated DC-DC converter without A/D converter is described. Also, propsed real-time PID control technique for DPWM is described. Some experimental results and simulation results are revealed the proposed circuit and scheme. The purpose of this research is striking a balance between minimizing cost increase by digitalizing of the control circuit of DC-DC converter and speeding up the control circuit.INTELEC 2009 - 2009 International Telecommunications Energy Conference : Incheon, South Korea, 2009.10.18-2009.10.2