We present a new combinatorial algorithm for Boolean matrix multiplication that runs in O(n(log log n)/ log n) time. This improves the previous combinatorial algorithm by Bansal and Williams [FOCS’09] that runs in O(n(log log n)/ log n) time. Whereas Bansal and Williams’ algorithm uses regularity lemmas for graphs, the new algorithm is simple and uses entirely elementary techniques: table looku...

Overgeneration is the main source of computational complexity in previous principle-based parsers. This paper presents a message passing algorithm for principle-based parsing that avoids the overgenera-tion problem. This algorithm has been implemented in C++ and successfully tested with example sentences from (van Riemsdijk and Williams, 1986).

Overgeneration is the main source of computational complexity in previous principle-based parsers. This paper presents a message passing algorithm for principle-based parsing that avoids the overgenera-tion problem. This algorithm has been implemented in C++ and successfully tested with example sentences from (van Riemsdijk and Williams, 1986).

We present an algorithm to find two non-linear polynomials for the Number Field Sieve integer factorization method. This algorithm extends Montgomery’s “two quadratics” method; for degree 3, it gives two skewed polynomials with resultant O(N5/4), which improves on Williams O(N4/3) result [12].

background: chronic non-specific low back pain is a common disorder that often has no clear mechanism. exercise therapy is an effective and safe method for treatment of chronic musculoskeletal disorders such as back pain. pilate’s and williams’ exercises are two types of distinct exercises used for the treatment of back pain, but there is no evidence for the advantage of these two exercises in ...