Algorithm 971: An Implementation of a Randomized Algorithm for Principal Component Analysis.

Recent years have witnessed intense development of randomized methods for low-rank approximation. These methods target principal component analysis and the calculation of truncated singular value decompositions. The present article presents an essentially black-box, foolproof implementation for Mathworks' MATLAB, a popular software platform for numerical computation. As illustrated via several tests, the randomized algorithms for low-rank approximation outperform or at least match the classical deterministic techniques (such as Lanczos iterations run to convergence) in basically all respects: accuracy, computational efficiency (both speed and memory usage), ease-of-use, parallelizability, and reliability. However, the classical procedures remain the methods of choice for estimating spectral norms and are far superior for calculating the least singular values and corresponding singular vectors (or singular subspaces).

Differential Contributions of Intrinsic and Extrinsic Pathways to Thrombin Generation in Adult, Maternal and Cord Plasma Samples.

BACKGROUND: Thrombin generation (TG) is a pivotal process in achieving hemostasis. Coagulation profiles during pregnancy and early neonatal period are different from that of normal (non-pregnant) adults. In this ex vivo study, the differences in TG in maternal and cord plasma relative to normal adult plasma were studied. METHODS: Twenty consented pregnant women and ten consented healthy adults were included in the study. Maternal and cord blood samples were collected at the time of delivery. Platelet-poor plasma was isolated for the measurement of TG. In some samples, anti-FIXa aptamer, RB006, or a TFPI inhibitor, BAX499 were added to elucidate the contribution of intrinsic and extrinsic pathway to TG. Additionally, procoagulant and inhibitor levels were measured in maternal and cord plasma, and these values were used to mathematically simulate TG. RESULTS: Peak TG was increased in maternal plasma (393.6±57.9 nM) compared to adult and cord samples (323.2±38.9 nM and 209.9±29.5 nM, respectively). Inhibitory effects of RB006 on TG were less robust in maternal or cord plasma (52% vs. 12% respectively) than in adult plasma (81%). Likewise the effectiveness of BAX499 as represented by the increase in peak TG was much greater in adult (21%) than in maternal (10%) or cord plasma (12%). Further, BAX499 was more effective in reversing RB006 in adult plasma than in maternal or cord plasma. Ex vivo data were reproducible with the results of the mathematical simulation of TG. CONCLUSION: Normal parturient plasma shows a large intrinsic pathway reserve for TG compared to adult and cord plasma, while TG in cord plasma is sustained by extrinsic pathway, and low levels of TFPI and AT.

A Mathematical Motivation for Complex-Valued Convolutional Networks.

A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with complex-valued vectors, followed by (2) taking the absolute value of every entry of the resulting vectors, followed by (3) local averaging. For processing real-valued random vectors, complex-valued convnets can be viewed as data-driven multiscale windowed power spectra, data-driven multiscale windowed absolute spectra, data-driven multiwavelet absolute values, or (in their most general configuration) data-driven nonlinear multiwavelet packets. Indeed, complex-valued convnets can calculate multiscale windowed spectra when the convnet filters are windowed complex-valued exponentials. Standard real-valued convnets, using rectified linear units (ReLUs), sigmoidal (e.g., logistic or tanh) nonlinearities, or max pooling, for example, do not obviously exhibit the same exact correspondence with data-driven wavelets (whereas for complex-valued convnets, the correspondence is much more than just a vague analogy). Courtesy of the exact correspondence, the remarkably rich and rigorous body of mathematical analysis for wavelets applies directly to (complex-valued) convnets.

Anti-factor IXa Aptamer reduces propagation of thrombin generation in plasma anticoagulated with warfarin.

BACKGROUND: Warfarin is routinely used in the prevention and treatment of prothrombotic events. During initiation of warfarin therapy levels of factor (F) VII and protein C decrease rapidly but prothrombin, FIX and FX decline much slower. Therefore, propagation of thrombin generation (TG) remains unaffected much longer, increasing the risk of inadequate anticoagulation. Recently, a novel agent, anti-IXa aptamer, RB006, has been developed. Therefore, we have evaluated the in vitro effects of this agent in warfarin plasma. METHODS: The investigation consisted of two parts. First, a computer simulated time course of TG with warfarin alone and in combination with FIXa inhibition was evaluated and, second, normal volunteer, protein C deficient, FVII deficient and commercial warfarin plasmas (INR 2.1 and 3.1) were spiked with increasing concentrations of aptamer (0-24 microg/ml) and its anticoagulant effects were evaluated using prothrombin time (PT), activated partial thromboplastin time (aPTT) and TG with tissue factor and Actin as activators. Direct effects of aptamer on protein C were also evaluated. RESULTS: Simulation of coagulation during warfarin induction showed that TG can be significantly delayed and decreased by inhibiting FIXa (i.e., with anti-FIXa aptamer). The anti-FIXa aptamer inhibited TG in all tested plasmas, but was most efficacious in warfarin and FVII deficient plasma. The aptamer itself did not inhibit protein C and had no effect on PT, but concentration-dependently increased aPTT. CONCLUSION: The anti-FIXa aptamer potentiates the inhibitory effects of warfarin on TG, and may fill the need as an adjuvant agent during initiation of warfarin therapy.