Until a few years ago, the fastest known matrix multiplication algorithm, due to Coppersmith and Winograd (1990), ran in time O(n). Recently, a surge of activity by Stothers, Vassilevska-Williams and Le Gall has led to an improved algorithm running in time O(n), due to Le Gall (2014). These algorithms are obtained by analyzing higher and higher tensor powers of a certain identity of Coppersmith...

BACKGROUND This paper proposes a semantic segmentation algorithm that provides the spatial distribution patterns of pulmonary ground-glass nodules with solid portions in computed tomography (CT) images. METHODS The proposed segmentation algorithm, anatomy packing with hierarchical segments (APHS), performs pulmonary nodule segmentation and quantification in CT images. In particular, the APHS ...

On primitive roots of 1 mod p k , divisors of p ± 1, Wieferich primes, and quadratic analysis mod p Abstract Primitive roots of 1 mod p k (k >2 and odd prime p) are sought, in cyclic units group G k ≡ A k B k mod p k , coprime to p, of order (p − 1)p k−1. 'Core' subgroup A k has order p − 1 independent of precision k, and 'extension' subgroup B k of all p k−1 residues 1 mod p is generated by p+...

Background & aim: One of the most common causes of back deformities is spinal curve change in the waist. Physical therapy is one of the most common methods for treatment of lordosise and back pain. In the field of corrective exercise, the comparison of Williams and McKenzie’s training findings are small and inconsistent. So, the purpose of this study was to compare the effects of 8 weeks of Wil...

Let K ⊆ R be the unique attractor of an iterated function system. We consider the case where K is an interval and study those elements of K with a unique coding. We prove under mild conditions that the set of points with a unique coding can be identified with a subshift of finite type. As a consequence of this, we can show that the set of points with a unique coding is a graph-directed selfsimi...

A binary string B of length n = kt is a k-ary Dyck word if it contains t copies of 1, and the number of 0s in every prefix of B is at most k−1 times the number of 1s. We provide two loopless algorithms for generating k-ary Dyck words in cool-lex order: (1) The first requires two index variables and assumes k is a constant; (2) The second requires t index variables and works for any k. We also e...

The concept of admissibility with respect to clustering algorithms was introduced by Fisher and Van Ness (1971). They defined types of admissibility of an algorithm and indicated the relationships between these admissibilities and popular clustering algorithms. In recent years, admissibility with respect to space distortion (See, Lance and Williams, 1967) has been proposed by Chen and Van Ness ...

Truth Maintenance Systems (TMSs) are important tools for caching beliefs and inferences that support search and explanation tasks of general problem solvers. For embedded real-time systems, fast response from the TMSs is especially required. To achieve this, Nayak and Williams [9] presented an Incremental Truth Maintenance System (ITMS) based on depth-first numbering to avoid spending a signifi...