Michael G. Sadovsky

Maximum Entropy Method in Analysis of Genetic Text and Measurement of its Information Content

The information capacity in frequency dictionaries of nucleotide sequences is estimated through the efficiency of reconstruction of a longer frequency dictionary from a short one. This reconstruction is performed by the maximum entropy method. Real nucleotide sequences are compared to random ones (with the same composition of nucleotides). Phages genes from NCBI bank were analyzed. The reliable difference of real genetic texts from random sequences is observed for the dictionary length q = 2, 5 and 6.

Comparison of Real Frequencies of Strings vs. the Expected Ones Reveals the Information Capacity of Macromoleculae

The information capacity of nucleotide sequences is defined through the calculation of specific entropy of their frequency dictionary. The specificentropy of the frequency dictionary is calculated against the reconstructeddictionary; this latter bears the most probable continuations of the shorterstrings. This developed measure allows to distinguish the sequences both from the randons ones, and from those with high level of (rather simple) order. Some implications of the developed methodology in the fields of genetics,bioinformatics, and molecular biology are discussed.

Entropy Approach in the Analysis of Anisotropy of Digital Images

Anisotropy is assumed to be the difference of a plane object observed in different dimensions. For digital images, anisotropy is determined in two ways. The first one is based on the comparison of mosaics bearing rectangular smalts developed in different (perpendicular, to be exact) directions. The comparison is provided through an intermediate mosaic called palette, that is the mosaic with the frequency of smalts equal to arithmetic mean of the frequency of smalts of compared mosaics. The latter is based on the calculation of the information capacity of the mosaics developed in different directions. The information capacity is the specific entropy of real mosaic calculated against the reconstructed one bearing the most probable expansions of smaller smalts. The problem of test object is discussed.

The Method to Compare Nucleotide Sequences Based on the Minimum Entropy Principle

A new method to compare two (or several) symbol sequences is developed. The method is based on the comparison of the frequencies of the small fragments of the compared sequences; it requires neither string editing, nor other transformations of the compared objects. The comparison is executed through a calculation of the specific entropy of a frequency dictionary against the special dictionary called the hybrid one; this latter is the statistical ancestor of the group of sequences under comparison. Some applications of the developed method in the fields of genetics and bioinformatics are discussed.

Comparison of Symbol Sequences: No Editing, No Alignment

The new method to compare two (or several) symbol sequences is developed. The method is based on the comparison of the frequencies of the small fragments of the compared sequences; it requires no string editing or other transformations of the compared objects. The comparison is provided through a calculation of the specific entropy of a frequency dictionary against the special dictionary called the hybrid one; the latter is the statistical ancestor of the group of sequences to be compared. Some applications of the method developed to genetics, bioinformatics, and linguistics are discussed.

Information Capacity of Symbol Sequences

The information capacity of sequences is considered through the calculation of specific entropy of their frequency dictionary. The specific entropy was calculated against the reconstructed dictionary which bears the most probable continuations of shorter strings. The measure developed allows to distinguish the sequences both from the random ones, and those with high level of (rather simple) order. Some applications of the developed methodology to genetics, bioinformatics, and linguistics are discussed.

Entropy Approach to Comparison of Images

Basically new pattern recognition method is implemented to compare two (or several) digital images. The method has neither feature alphabet, nor pattern dictionary recovery stages. It compares input images due to a special object called palette built from fragments of images. The measures to estimate the distances between images are based on a determination of the specific entropy of the frequency dictionary of an image with respect to the palette; that latter presents the statistical ancestor of the group of the images under comparison. The palette is defined as the frequency dictionary with frequencies of the fragments equal to arithmetic mean of the frequencies of the same fragments from the images to be compared. Such definition yields a minimum of the sum of specific entropies of the compared images with respect to the palette. Some preliminary results in the application of the method in pattern recognition and synergistics problems are presented. The limitations and basic properties of the method are discussed.

Entropy Based Approach to Data Loss Reparation Through the Indeterminate Fine-Grained Parallel Computation

The new method of a gap recovery in symbol sequences is presented. A covering is combined from the suitable reasonably short strings of the parts of a sequence available for observation. Two criteria are introduced to choose the best covering. It must yield the maximum of entropy of a frequency dictionary developed over the sequence obtained due to the recovery, if an overlapping combined from the copies of strings from the available parts of the sequence exists. The second criterion identifies the best covering in case when one has to use any string to cover the gap; here the best covering must yield the minimum of specific entropy of the frequency dictionary developed over the available parts of the sequence against the one developed over the entire sequence obtained due to the recovery. Kirdin kinetic machine which is the ideal fine-grained structureless computer has been used to resolve the problem of the reconstruction of a gap in symbol sequence.

Model of Prey–Predator Dynamics with Reflexive Spatial Behaviour of Species Based on Optimal Migration

We consider the model of spatially distributed community consisting of two species with “predator–prey” interaction; each of the species occupies two stations. Transfer of individuals between the stations (migration) is not random, and migration stipulates the maximization of net reproduction of each species. The spatial distribution pattern is provided by discrete stations, and the dynamics runs in discrete time. For each time moment, firstly a redistribution of individuals between the stations is carried out to maximize the net reproduction, and then the reproduction takes place, with the upgraded abundances. Besides, three versions of the basic model are implemented where each species implements reflexive behaviour strategy to determine the optimal migration flow. It was found that reflexivity gives an advantage to the species realizing such strategy, for some specific sets of parameters. Nevertheless, the regular scanning of the parameters area shows that non-reflexive behaviour yields an advantage in the great majority of parameters combinations.