Mathematics

ABSTRACT Breast cancer diagnosis requires specific expertise from the Medical Doctors. Furthermore, prognosis, monitoring and early detection of malignant findings can be successfully realized through synergies between physicians, researchers and general population in concert with the health policy program of each country. Information technology and computational intelligence play a crucial role in the production of digital repositories and cancer registries as well as in the development of systems to support diagnosis. In this paper we present the concept and the architecture of an approved grant under the National Strategic Reference Framework 2007-2013 (NSRF), called e-Prolipsis. Through this project, we will design and implement a web based risk estimation platform and a Central Breast Cancer Registry (CBCR) that will co-operate to provide medical doctors and patients with services such as multiplicity in diagnostic opinions, synergy, computational risk estimation, access to statistical/epidemiological data for trend estimation. Such a system, will serve as a reference tool and will help the clinician, the radiologist, the rural doctor or trainee doctor in the final assessment on the existence or likelihood of breast cancer. The system will assist in the successful diagnosis of breast cancer, giving each patient access to a large pool of doctors and at the same time, the data stored in the CBCR will be used for statistical analysis, providing useful results for improving both the cancer detection application and for making a national policy for combating breast cancer. This system will be accessible through a Web Portal, with different access levels for patients, doctors and general public and different web services available to each user group, eliminating the geographical distances that would be imposed otherwise.

As the discovery of information from text corpora becomes more and more important there is a necessity to develop clustering algorithms designed for such a task. One of the most, successful approach to clustering is the density based methods. However due to the very high dimensionality of the data, these algorithms are not directly applicable. In this paper we demonstrate the need to suitably exploit the already developed feature reduction techniques, in order to maximize the clustering performance of density based methods.

ABSTRACT Statistics denoting the numbers of success runs of length exactly equal and at least equal to a fixed length, as well as the sum of the lengths of success runs of length greater than or equal to a specific length, are considered. They are defined on both linearly and circularly ordered binary sequences, derived according to the Pólya-Eggenberger urn model. A waiting time associated with the sum of lengths statistic in linear sequences is also examined. Exact marginal and joint probability distribution functions are obtained in terms of binomial coefficients by a simple unified combinatorial approach. Mean values are also derived in closed form. Computationally tractable formulae for conditional distributions, given the number of successes in the sequence, useful in nonparametric tests of randomness, are provided. The distribution of the length of the longest success run and the reliability of certain consecutive systems are deduced using specific probabilities of the studied statistics. Numerical examples are given to illustrate the theoretical results.

ABSTRACT The Polya-Eggenberger sampling scheme is considered, i.e., a ball is drawn at random from an urn containing w white (success) balls and b black (failure) balls, its color is observed, and then it is returned to the urn along with s additional balls of the same color of the ball drawn. This scheme is repeated n times, and Nn, k, l, s denotes the number of l-overlapping success runs of length k. If the balls drawn are arranged on a circle, the number of l-overlapping success runs of length k is denoted by . Finally, Wr, k, l, s denotes the number of drawings according to the Polya-Eggenberger sampling scheme until the rth occurrence of the l-overlapping success run of length k. Polya, inverse Polya, and circular Polya distributions of order k for l-overlapping success runs of length k are introduced as the distributions, respectively, of Nn, k,l, s, Wr, k, l, s, and . These distributions include as special cases known and new distributions of order k. Exact formulae are derived for their probability distribution functions and means, which generalize several results on well-known distributions of order k. Asymptotic results of the new distributions are also given, relating them, respectively, to the binomial, negative binomial, and circular binomial distributions of order k for l-overlapping success runs of length k.