Preconditioned iterative methods for solving linear least squares problems

New preconditioning strategies for solving m × n overdetermined large and sparse linear least squares problems using the conjugate gradient for least squares (CGLS) method are described. First, direct preconditioning of the normal equations by the balanced incomplete factorization (BIF) for symmetric and positive definite matrices is studied, and a new breakdown-free strategy is proposed. Preconditioning based on the incomplete LU factors of an n × n submatrix of the system matrix is our second approach. A new way to find this submatrix based on a specific weighted transversal problem is proposed. Numerical experiments demonstrate different algebraic and implementational features of the new approaches and put them into the context of current progress in preconditioning of CGLS. It is shown, in particular, that the robustness demonstrated earlier by the BIF preconditioning strategy transfers into the linear least squares solvers and the use of the weighted transversal helps to improve the LU-based approach.This work was partially supported by Spanish grant MTM 2010-18674 and the project 13-06684S of the Grant agency of the Czech Republic.Bru García, R.; Marín Mateos-Aparicio, J.; Mas Marí, J.; Tuma, M. (2014). Preconditioned iterative methods for solving linear least squares problems. SIAM Journal on Scientific Computing. 36(4):2002-2022. https://doi.org/10.1137/130931588S2002202236

An Examination of the Possibility of Lowering the Glycemic Index of Oat and Barley Flakes by Minimal Processing

Differences in glycemic responses to various starchy foods are related to differences in the rate of starch digestion and absorption. In this study, the importance of the degree of gelatinization and the product thickness for postprandial glycemic and insulinemic responses to rolled oats and barley were studied in healthy subjects (5 men and 5 women). Thick (1.0 mm) rolled oats were made from raw or preheated (roasted or steamed) kernels. In addition, thin (0.5 mm) rolled oats were made from roasted or roasted and steamed (processed under conditions simulating commercial production) oat kernels. Finally, steamed rolled barley kernels (0.5 or 1.0 mm) were prepared. All thin flakes elicited high glucose and insulin responses [glycemic index (GI), 88–118; insulinemic index (II), 84–102], not significantly different from white wheat bread (P . 0.05). In contrast, all varieties of thick oat flakes gave significantly lower metabolic responses (GI, 70–78; II, 58–77) than the reference bread (P , 0.05). Thick barley flakes, however, gave high glucose and insulin responses (GI, 94; II, 84), probably because the botanical structure underwent more destruction than the corresponding oat flakes. We conclude that minimal processing of oat and barley flakes had a relatively minor effect on GI features compared with the more extensive commercial processing. One exception was thick oat flakes, which in contrast to the corresponding barley flakes, had a low GI

High expression of cyclin B1 predicts a favorable outcome in patients with follicular lymphoma

Substantial research has been dedicated to the study of the relationship between genetic mechanisms regulating cell functions in tumors and how those tumors respond to various treatment regimens. Because these mechanisms are still not well understood, we have chosen to study the genetic makeup of 57 tumor samples from patients with follicular lymphoma (FL). Our goal was to develop a prognostic tool, which can be used as an aid in determining FL patients with tumors genetically predisposed to a successful treatment with the CHOP (cyclophosphamide, vincristine, doxorubicin, prednisone) regimen. To select relevant genes, high-density oligonucleotide arrays were used. There were 14 genes highly expressed in FL patients that responded well to CHOP chemotherapy, and 11 of these were involved in G(2)/M transition of the cell cycle, in mitosis, or in DNA modulation. A high expression of CCNB1 (cyclin B1), CDC2, CDKN3A, CKS1B, ANP32E, and KIAA0101, but not of the proliferation-related antigen Ki-67, was associated with better survival rate in a univariate analysis. CCNB1 expression had an independent prognostic value when included in a multivariate analysis together with the 5 parameters of the follicular lymphoma international prognostic index

Barley bread containing lactic acid improves glucose tolerance at a subsequent meal in healthy men and women.

In the present study, we evaluated whether a low glycemic index (GI) breakfast with lactic acid bread had an effect on glucose tolerance and insulinemia at a subsequent high GI lunch meal. A barley bread containing lactic acid and a reference barley bread were consumed in the morning after an overnight fast in random order by 10 healthy men and women. Four hours after the breakfasts, the subjects ate a standardized high GI lunch, and the blood glucose and insulin responses were measured for the next 3 h. Significant lowerings of the incremental glycemic area (-23%, P = 0.033) and of the glucose response at 95 min were found after the lunch meal when the barley bread with lactic acid was given as a breakfast. At 45 min after the lunch meal, the insulin level was significantly lower (-21%, P = 0.045) after the lactic acid bread breakfast, compared with the barley bread breakfast without lactic acid. We concluded that barley bread containing lactic acid eaten at breakfast has the potential to improve second-meal glucose tolerance at a high GI lunch meal 4 h later