Adam Szustalewicz

Are amino acids counts in yeast ORFs negative binomial

The genetic code of living organisms is inscribed into so called Open Reading Frames (ORFs) positioned in chromosomes. The code uses 20 amino acids as building blocks for the inscribed information. We show that the number of appearances of a given amino acid in ORFs on a yeast chromosome may be described in a highly satisfactory manner by the Negative Binomial (NB) distribution. The fit is surprisingly good. We show the results for ORFs found in four yeast chromosomes, namely no. 4, 7, 11 and 13. The negative binomial fit is shown (1) graphically; (2) considering the Kolmogorov statistic; (3) performing a chi-square test and (4) using simulated samples. The applicability of the Kolmogorov test to the analysed data is discussed.

Intrinsic Dimensionality of Data and of their Representatives. A Case Study of Amino-Acid Distribution in ORFs

By intrinsic dimensionality of a data set we mean the smallest number of base vectors which permit to reconstruct the considered set. Nowadays we obtain very huge data sets, which are computationally demanding. Therefore we look for some representative data vectors (prototypes) which might yield an insight into the data and be used for a (preliminary) data analysis. Let D of size n times d denote the observed data set, and D1 of size M times d the set of representatives of the data. Denote by r, the number of base vectors spanning D, and by r1 the number of base vectors spanning the data set D1 appropriately. Our questions: (1) Are r and r1 equal? (2) Say, we want to choose base vectors k and k1 approximating the sets D and D1 with a given accuracy. Are k and k1 equal? We answer these questions by considering the data set amino 569 containing frequency distribution of twenty amino-acids composing the ORFs in the 7th yeast chromosome. The answer is: twice NO.

Calculating the Fractal Dimension of River Basins, Comparison of Several Methods

A new program was prepared for approximate calculation of the fractal dimension of natural objects. The program takes care to fulfill demand of the fractal theory about the minimal covering of the measured object. Three other programs are being presented for comparison and the results obtained by all of them on the same data sets are described

Visualisation of multivariate data using parallel coordinate plots and Kohonen’s SOM’s. Which is better?

Parallel coordinate plot is a convenient method for presenting a set of multivariate data points in simple two-dimensional form. Each data point is represented by a horizontal segment line connecting vertical axes corresponding to subsequent variables. Another very convenient method for representing multivariate data is their visualisation by use of self-organizing maps. Both methods were applied for visualisation of the differences between two sets of data representing randomly distorted letters printed in different fonts. Each letter was characterized by 16 statistical features.