The specifics of the Galois field GF(257) and its use for digital signal processing.

An algorithm of digital logarithm calculation for the Galois field G F ( 257 ) is proposed. It is shown that this field is coupled with one of the most important existing standards that uses a digital representation of the signal through 256 levels. It is shown that for this case it is advisable to use the specifics of quasi-Mersenne prime numbers, representable in the form p = 2 n + 1 , which includes the number 257. For fields G F ( 2 n + 1 ) , an alternating encoding can be used, in which non-zero elements of the field are displayed through binary characters corresponding to the numbers + 1 and - 1. In such an encoding, multiplying a field element by 2 is reduced to a quasi-cyclic permutation of binary symbols (the permuted symbol changes sign). Proposed approach makes it possible to significantly simplify the design of computing devices for calculation of digital logarithm and multiplication of numbers modulo 257. A concrete scheme of a device for digital logarithm calculation in this field is presented. It is also shown that this circuit can be equipped with a universal adder modulo an arbitrary number, which makes it possible to implement any operations in the field under consideration. It is shown that proposed digital algorithm can also be used to reduce 256-valued logic operations to algebraic form. It is shown that the proposed approach is of significant interest for the development of UAV on-board computers operating as part of a group.

The Method of Direct and Reverse Phase Portraits as a Tool for Systematizing the Results of Studies of Phase Transitions in Solutions of Thermosensitive Polymers.

It is shown that a more than significant amount of experimental data obtained in the field of studying systems based on thermosensitive hydrophilic polymers and reflected in the literature over the past decades makes the issue of their systematization and classification relevant. This, in turn, makes relevant the question of choosing the appropriate classification criteria. It is shown that the basic classification feature can be the number of phase transition stages, which can vary from one to four or more depending on the nature of the temperature-sensitive system. In this work, the method of inverse phase portraits is proposed for the first time. It was intended, among other things, to identify the number of phase transition stages. Moreover, the accuracy of this method significantly exceeds the accuracy of the previously used method of direct phase portraits since, for the first time, the operation of numerical differentiation is replaced by the operation of numerical integration. A specific example of the application of the proposed method for the analysis of a previously studied temperature-sensitive system is presented. It is shown that this method also allows for a quantitative comparison between the results obtained by the differential calorimetry method and the turbidimetry method. Issues related to increasing the resolution of the method of direct phase portraits are discussed.

Effect of the Formation of Hydrophilic and Hydrophobic-Hydrophilic Associates on the Behavior of Copolymers of N-Vinylpyrrolidone with Methyl Acrylate in Aqueous Solutions.

It has been shown that there exist conditions under which thermosensitive copolymers of N-vinylpyrrolidone with methyl acrylate form hydrophobic-hydrophilic associations, which are unstable dynamic meshes, the bonds in which are continuously broken and created again, and the nature of the formation of such meshes depends significantly on the proportion of the hydrophobic component in the copolymer. It is shown that the interaction of the above copolymers with polyacrylic acid results in the formation of not only classical interpolymer complexes, but also hydrophilic interpolymer associates, which also represent unstable networks existing in a dynamic mode. In such meshes, the molecules of the above copolymers serve as a kind of cross-agent connecting the polyacid molecules. There are also conditions under which such meshes acquire a complex structure, since unstable bonds between macromolecular tangles of both the same and different types take part in their formation. It is shown that the transition from the formation of interpolymer complexes to the formation of hydrophilic interpolymer associates can occur, among other things, due to changes in the acidity or concentration of low-molecular salt in solution.

Improving the efficiency of using multivalued logic tools: application of algebraic rings.

It is shown that in order to increase the efficiency of using methods of abstract algebra in modern information technologies, it is important to establish an explicit connection between operations corresponding to various varieties of multivalued logics and algebraic operations. For multivalued logics, the number of variables in which is equal to a prime number, such a connection is naturally established through explicit algebraic expressions in Galois fields. It is possible to define an algebraic δ-function, which allows you to reduce any truth table to an algebraic expression, for the case when the number of values accepted by a multivalued logic variable is equal to an integer power of a prime number. In this paper, we show that the algebraic δ-function can also be defined for the case when the number of values taken by a multivalued logic variable is p - 1, where p is a prime number. This function also allows to reduce logical operations to algebraic expressions. Specific examples of the constructiveness of the proposed approach are presented, as well as electronic circuits that experimentally prove its adequacy.

Improving the efficiency of using multivalued logic tools.

Multivalued logics are becoming one of the most important tools of information technology. They are in great demand for creation of artificial intelligence systems that are close to human intelligence, since the functioning of the latter cannot be reduced to the operations of binary logic. At the same time, the problem of improving the efficiency of using the results of research in multivalued logics, as well as the problem of interpreting variables of multivalued logic, is acute. These problems create certain interdisciplinary barriers and make it difficult to implement the results of research in the field of multivalued logics in other fields of knowledge. It is shown that the problem of interpreting multivalued logic variables can be removed by establishing correspondence with fuzzy logic variables. Improving the efficiency of using of operations of multivalued logics and their variables can be provided by using their close connection to Galois fields. This connection, among other things, makes it possible to reduce any operations of multivalued logics, the number of variables in which is equal to a prime number, to algebraic functions whose arguments take values in Galois fields. This allows, among other things, to eliminate the very cumbersome constructions used in works on multivalued logic and make its apparatus convenient for use in related scientific disciplines in information technology. Direct verification of the adequacy of algorithms based on the use of Galois fields can be carried out by means of radio-electronic circuits, examples of which are presented in the present paper.

Analysis of the GSTP1 rs1695 polymorphism association with the development of asthma and phenotypic manifestations.

OBJECTIVE: The development of asthma and its related phenotypes is most likely due to the polymorphism of the so-called modifier genes. The goal of this study was to evaluate the polymorphic locus rs1695 of the GSTP1 gene association with risk factors for developing asthma and its phenotypic manifestations. METHODS: This case-control study involved 164 patients with confirmed asthma diagnosis and 147 age- and sex-matched controls. Patients were divided into two groups: with (n = 121) and without complications (n = 43). Among asthmatic patients, 34 manifested hypersensitivity to household allergens. The GSTP1 rs1695 polymorphism was genotyped using the technique of polymerase chain reaction-restriction fragment length polymorphism. RESULTS: There were no differences between patients and controls in allelic or genotype frequencies of polymorphic locus rs1695 of the GSTP1 gene. However, the frequency of the A/A genotype in the patient group with complications was significantly lower than that in complication-free patients (p = 0.040), while the frequency of the G allele was higher in patients with complications (p = 0.030). The frequency of the A/A genotype was decreased in the patient group with an allergic reaction to household allergens in comparison with controls (p = 0.037). CONCLUSION: These results suggest that the carriage of the A/A genotype of polymorphic locus rs1695 of the GSTP1 gene is a protective factor in the development of complications and an allergic reaction to house allergens among asthmatics, while the carriage of the G allele is associated with an increased risk for asthma complications.

Polymorphism of Glutathione S-transferase Genes and the Risk of Toxic Liver Damage in Petrochemical Workers.

BACKGROUND: Exposure to numerous chemicals, including industrial ones, may result in liver damage. The body susceptibility to the environmental hazards largely depends on the activity of the enzymes in the xenobiotic detoxification system. Function abnormalities of such enzymes due to genetic variations would increase the risk of developing various diseases. OBJECTIVE: To elucidate the relationship between polymorphism in glutathione S-transferase genes (GSTM1, GSTT1 and GSTP1) and the risk of toxic liver damage in a group of petrochemical workers. METHODS: This study was conducted on 72 workers with toxic liver injury, 156 healthy workers, and 322 healthy individuals without history of occupational exposure to chemicals. Genotyping of the GSTP1 rs1695 gene polymorphism was performed using polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) method. Polymerase chain reaction (PCR) was used to perform genotyping of the GSTM1 and GSTT1 genes polymorphism. RESULTS: There was a significant difference in genotype frequencies of the GSTP1 rs1695 gene polymorphism among the groups studied. The distribution of Val/Val genotype of the GSTP1 rs1695 gene polymorphism had a higher incidence in healthy workers compared with patients with toxic liver damage (p=0.036). No significant association was found between the GSTM1 and GSTT1 polymorphisms and toxic liver damage. CONCLUSION: The GSTP1 rs1695 gene polymorphism can play a protective role in the development of toxic liver damage in petrochemical workers.

The relationship of the immune response mediator genes' polymorphic variants with the methotrexate efficacy in juvenile idiopathic arthritis

Background/aim: The aim of the study was to analyze the relationship of the immune response mediator genes' polymorphic loci (TNFA rs1800629, LTA rs909253, IL1B rs16944, IL2-IL21 rs6822844, IL2RA rs2104286, IL6 rs1800795, IL10 rs1800872, MIF rs755622, CTLA4 rs3087243, NFKB1 rs28362491, PTPN22 rs2476601, PADI4 rs2240336) variants with the methotrexate efficacy in juvenile idiopathic arthritis (JIA). Materials and methods: The study included 274 JIA patients from the Republic of Bashkortostan, Russia. Achieving the American College of Rheumatology Pediatric 30 (ACR Pedi 30) response was regarded as the presence of the response to methotrexate (otherwise, as the absence), while achieving clinical remission on medication (Wallace et al., 2011) - as the sufficient response (otherwise, as the insufficient). Genotyping was conducted by the real-time polymerase chain reaction. Results: Associations with an altered risk of the nonresponse to methotrexate in JIA were observed for the alleles/genotypes of the lociIL10 rs1800872 (in girls) and NFKB1 rs28362491 (in girls); with an altered risk of the insufficient response to methotrexate in JIA ­ for the alleles/genotypes of the loci IL1B rs16944 (in boys), CTLA4 rs3087243 (in boys), NFKB1 rs28362491 (in girls) and the haplotype TNFA rs1800629*A - LTA rs909253*G (in girls). Conclusion: As a result of the study, the relationship of the alleles/genotypes of the IL1B rs16944, IL10 rs1800872, CTLA4 rs3087243, NFKB1 rs28362491 polymorphic lociand the TNFA rs1800629*A - LTA rs909253*G haplotype with the methotrexate efficacy in JIA was established (taking into account the differences by sex).

TP53 Gene Polymorphisms and Occupational Skin Cancer Risks for Workers of Glass Fiber Manufacture.

BACKGROUND: Determining the role of genetic markers in individual sensitivity to chemical exposures raises a possibility of risk assessment of occupational diseases and their prevention. This paper focuses on the results of the identification of molecular-genetic markers associated with occupational skin cancer susceptibility. This study aimed to explore an association between polymorphisms of the TP53 tumor suppressor gene and a risk of developing occupational skin neoplasms. METHODS: This case-control study was conducted on 71 workers with occupational skin neoplasms, 99 healthy workers, and 100 healthy population-based controls in Bashkortostan Republic, Russia in 2015. Genotyping of TP53 polymorphisms (rs1042522, rs1625895, and rs17878362) was performed by restriction fragment length polymorphism analysis of genomic DNA extracted from peripheral blood. Odds ratios and 95% confidence intervals were calculated to measure the strength of the association. RESULTS: Subjects carrying allele C of rs1042522 were associated with an increased risk of occupational skin neoplasms [P=0.027, odds ratio (OR)=1.97, 95% confidence intervals (CI) 1.08-3.63]. An increased risk was also associated with allele 16bp of rs17878362 (P=0.010, OR=3.32, 95 % CI=1.31-8.78) and allele A of rs1625895 (P=0.003, OR = 5.45, 95 % CI = 1.72-19.15). CONCLUSION: The polymorphic variants rs1042522, rs1625895 and rs17878362 of the TP53 gene are related to increased risks of occupational skin cancer. This study suggests the potential use of molecular-genetic data to assess increased individual risks of the development and prognosis of occupational skin neoplasms.