Narrow Results

Researchers hope that establishing a notion of proximity using topology will help to clarify the biological processes underlying the evolution of living organisms. The simple model presented here, using RNA shapes, can carry over to more general and complex genotype–phenotype systems. Proximity is an important component of continuity, in both real-world and topological terms. Consequently, phenotype spaces provide an appropriate setting for modeling and investigating continuous and discontinuous evolutionary change.

The purpose of this work is to construct a new crossover operator using the properties of DNA and RNA by using topological concepts in constructing flexible mathematical models in the field of biomathematics. Also, we investigate and study topological properties of the constructed operators and the associated topological spaces of DNA and RNA. Finally we use the process of exchange for sequence of genotypes structures to construct new types of topological concepts to investigate and discuss several examples and some of their properties.

Mathematical equations are now found not only in the books, but also they help in finding solutions for the biological problems by explaining the technicality of the current biological models and providing predictions that can be validated and complemented to experimental and clinical studies. In this research paper, we use the mset theory to study DNA & RNA mutations to discover the mutation occurrence. Also, we use the link between the concept of the mset and topology to determine the compatibility or similarity between “types”, which may be the strings of bits, vectors, DNA or RNA sequences, etc.

The aim of this paper is to use topological concepts in the construction of flexible mathematical models in the field of biological mathematics. Also, we will build new topographic types to study recombination of deoxyribonucleic acid (DNA) and ribonucleic acid (RNA). Finally, we study the topographical properties of constructed operators and the associated topological spaces of DNA and RNA.

Approximation space can be said to play a critical role in the accuracy of the set’s approximations. The idea of “approximation space” was introduced by Pawlak in 1982 as a core to describe information or knowledge induced from the relationships between objects of the universe. The main objective of this paper is to create new types of rough set models through the use of different neighborhoods generated by a binary relation. New approximations are proposed representing an extension of Pawlak’s rough sets and some of their generalizations, where the precision of these approximations is substantially improved. To elucidate the effectiveness of our approaches, we provide some comparisons between the proposed methods and the previous ones. Finally, we give a medical application of lung cancer disease as well as provide an algorithm which is tested on the basis of hypothetical data in order to compare it with current methods.