On the efficient parallel computation of Legendre transforms

In this article, we discuss a parallel implementation of efficient algorithms for computation of Legendre polynomial transforms and other orthogonal polynomial transforms. We develop an approach to the Driscoll-Healy algorithm using polynomial arithmetic and present experimental results on the accuracy, efficiency, and scalability of our implementation. The algorithms were implemented in ANSI C using the BSPlib communications library. We also present a new algorithm for computing the cosine transform of two vectors at the same time

ER and PI3K pathway activity in primary ER positive breast cancer is associated with progression-free survival of metastatic patients under first-line tamoxifen

Estrogen receptor positive (ER+) breast cancer patients are eligible for hormonal treatment, but only around half respond. A test with higher specificity for prediction of endocrine therapy response is needed to avoid hormonal overtreatment and to enable selection of alternative treatments. A novel testing method was reported before that enables measurement of functional signal transduction pathway activity in individual cancer tissue samples, using mRNA levels of target genes of the respective pathway-specific transcription factor. Using this method, 130 primary breast cancer samples were analyzed from non-metastatic ER+ patients, treated with surgery without adjuvant hormonal therapy, who subsequently developed metastatic disease that was treated with first-line tamoxifen. Quantitative activity levels were measured of androgen and estrogen receptor (AR and ER), PI3K-FOXO, Hedgehog (HH), NFκB, TGFβ, and Wnt pathways. Based on samples with known pathway activity, thresholds were set to distinguish low from high activity. Subsequently, pathway activity levels were correlated with the tamoxifen treatment response and progression-free survival. High ER pathway activity was measured in 41% of the primary tumors and was associated with longer time to progression (PFS) of metastases during first-line tamoxifen treatment. In contrast, high PI3K, HH, and androgen receptor pathway activity was associated with shorter PFS, and high PI3K and TGFβ pathway activity with worse treatment response. Potential clinical utility of assessment of ER pathway activity lies in predicting response to hormonal therapy, while activity of PI3K, HH, TGFβ, and AR pathways may indicate failure to respond, but also opens new avenues for alternative or complementary targeted treatments