Motivated by the preponderance of so-called ‘heavy black holes’ in the binary black hole (BBH) gravitational wave (GW) detections to date, and the role that gravitational lensing continues to play in discovering new galaxy populations, we explore the possibility that the GWs are strongly lensed by massive galaxy clusters. For example, if one of the GW sources were actually located at z= 1, then...

Recent changes in computational sciences force reevaluation of the role of dense matrix multiplication. Among others, this resulted in a proposal to consider generalized matrix multiplication, based on the theory of algebraic semirings. The aim of this note is to outline an initial object oriented model of the generalized matrix-multiply-add operation.

A family of permutations in Sn is k-wise independent if a uniform permutation chosen from the family maps any sequence of k distinct elements to any sequence of k distinct elements with equal probability. Efficient constructions of k-wise independent permutations are known for k = 2 and k = 3 based on multiply transitive permutation groups but are unknown for k≥ 4. In fact, it is known that the...

The modified weighted checksum method is proposed, which can be used for deriving fault tolerant versions of most linear algebra algorithms. The purpose is the detection and correction of calculation errors occurred due to transient hardware faults during algorithm execution. Using the proposed method, the fault-tolerant versions of Jordan-Gauss and Faddeeva algorithms are designed. The computa...