Given a finite nonempty sequence S of integers, write it as XY k, where Y k is a power of greatest exponent that is a suffix of S: this k is the curling number of S. The curling number conjecture is that if one starts with any initial sequence S, and extends it by repeatedly appending the curling number of the current sequence, the sequence will eventually reach 1. The conjecture remains open. ...

Many thinning algorithms for 2D binary images, or modifications of existing ones, have been proposed in recent years. The one given herein is surprisingly simple compared to most of them, and still it has theoretically favorable properties. Actually, it provides a connected single-pixel in width whenever possible well-centered homototic skeleton that allows shapes to be nearly reconstructed. In...

After pre-processing and segmenting suspicious masses in mammographies based on the Top-Hat and Markov Random Fields methods, we developed a mass-detection algorithm that uses gray level cooccurrence matrices, gray level difference statistics, gray level run length statistics, shape descriptors and intensity parameters as the entry of a vector support machine classifier. During the classificati...

For an improved monitoring of process parameters, it is generally desirable to have ef?cient designs of control charting structures. The addition of Shewhart control limits to the cumulative sum (CUSUM) control chart is a simple monitoring scheme sensitive to wide range of mean shifts. To improve the detection ability of the combined Shewhart–CUSUM control chart to off-target processes, we deve...

The problem of quickest change detection (QCD) under transient dynamics is studied, where the change from the initial distribution to the final persistent distribution does not happen instantaneously, but after a series of transient phases. The observations within the different phases are generated by different distributions. The objective is to detect the change as quickly as possible, while c...

Shewhart, exponentially weighted moving average (EWMA), and cumulative sum (CUSUM) charts are famous statistical tools, to handle special causes and to bring the process back in statistical control. Shewhart charts are useful to detect large shifts, whereas EWMA and CUSUM are more sensitive for small to moderate shifts. In this study, we propose a new control chart, named mixed CUSUM-EWMA chart...

In this paper we give an infinite family of strings for which the length of the Lempel-Ziv’77 parse is a factor Ω(log n/ log log n) smaller than the smallest run-length grammar.

We propose a two-dimensional model for a complete description of the dynamics of molecular motors, including both the processive movement along track filaments and the dissociation from the filaments. The theoretical results on the distributions of the run length and dwell time at a given ATP concentration, the dependences of mean run length, mean dwell time and mean velocity on ATP concentrati...

Given a set of sequences, the distance between pairs of them helps us to find their similarity and derive structural relationship amongst them. For genomic sequences such measures make it possible to construct the evolution tree of organisms. In this paper we compare several distance measures and examine a method that involves circular shifting one sequence against the other for finding good al...