The main strategy of algorithms in this class is to substitute “repeated strings”, i.e., exact replicas of a substring in a string, within the text with a convenient coding scheme. Those methods generally fall into the Macro Model for Data Compression introduced and studied by Storer and Szymanski (1982). The well known algorithms by Ziv and Lempel (1977, 1978), as well as many others, turn out...

Detection of ventricular tachycardia (VT) and ventricular fibrillation (VF) is crucial for the success of saving the patient’s life. The complexity of the heart signals has changed significantly when the heart state switches. In this study we proposed a novel method for detection of ventricular fibrillation (VF) and ventricular tachycardia (VT), based upon the Lempel-Ziv complexity and Wavelet ...

A theorem of Cohn and Lempel [J. Combin. Theory Ser. A 13 (1972), 83-89] gives an equality involving the number of directed circuits in a circuit partition of a 2-in, 2-out digraph and the GF (2)-nullity of an associated matrix. This equality is essentially equivalent to the relationship between directed circuit partitions of 2-in, 2-out digraphs and vertexnullity interlace polynomials of circl...

We describe a universal information compression scheme that compresses any pure quantum i.i.d. source asymptotically to its von Neumann entropy, with no prior knowledge of the structure of the source. We introduce a diagonalisation procedure that enables any classical compression algorithm to be utilised in a quantum context. Our scheme is then based on the corresponding quantum translation of ...

A real number x is absolutely normal if, for every base b≥2, two equally long strings of digits appear with equal asymptotic frequency in the base-b expansion x. This paper presents an explicit algorithm that generates binary x, nth bit appearing after npolylog(n) computation steps. speed achieved by simultaneously computing and diagonalizing against a martingale incorporates Lempel-Ziv parsing...