For decades,engineers have utilized Petri nets to develop automated systems with specific functional requirements or characteristics.Nonetheless,the ex-isting formalism prevents the use of classic traversal techniques...For decades,engineers have utilized Petri nets to develop automated systems with specific functional requirements or characteristics.Nonetheless,the ex-isting formalism prevents the use of classic traversal techniques to examine and analyze a system’s functional behavior.This paper provides a novel tech-nique to represent Petri nets as directed Euler graphs.It enables design engi-neers to examine and traverse the various states of a system utilizing the vari-ous methodologies and traversal processes applicable to Euler graphs.In this study,we present an iterative approach for determining an optimal path in terms of the least number of edges(vertices)required to cover and contain the system’s states,which are represented as Petri nets.The goal is to leave one vertex and return to the same vertex of the graph in a finite number of steps.This is a new method for determining the attribute of the system’s reset,which is represented by Petri nets and allows the system to return to its starting state,the resting state.The goal is to broaden the ontological basis of Petri nets by displaying linkages or relationships between Petri nets that are akin to directed Euler graphs.展开更多
Genome sequencing is the process of determining in which order the nitrogenous bases also known as nucleotides within a DNA molecule are arranged. Every organism’s genome consists of a unique sequence of nucleotides....Genome sequencing is the process of determining in which order the nitrogenous bases also known as nucleotides within a DNA molecule are arranged. Every organism’s genome consists of a unique sequence of nucleotides. These nucleotides bases provide the phenotypes and genotypes of a cell. In mathematics, Graph theory is the study of mathematical objects known as graphs which are made of vertices (or nodes) connected by either directed edges or indirect edges. Determining the sequence in which these nucleotides are bonded can help scientists and researchers to compare DNA between organisms, which can help show how the organisms are related. In this research, we study how graph theory plays a vital part in genome sequencing and different types of graphs used during DNA sequencing. We are going to propose several ways graph theory is used to sequence the genome. We are as well, going to explore how the graphs like Hamiltonian graph, Euler graph, and de Bruijn graphs are used to sequence the genome and advantages and disadvantages associated with each graph.展开更多
文摘For decades,engineers have utilized Petri nets to develop automated systems with specific functional requirements or characteristics.Nonetheless,the ex-isting formalism prevents the use of classic traversal techniques to examine and analyze a system’s functional behavior.This paper provides a novel tech-nique to represent Petri nets as directed Euler graphs.It enables design engi-neers to examine and traverse the various states of a system utilizing the vari-ous methodologies and traversal processes applicable to Euler graphs.In this study,we present an iterative approach for determining an optimal path in terms of the least number of edges(vertices)required to cover and contain the system’s states,which are represented as Petri nets.The goal is to leave one vertex and return to the same vertex of the graph in a finite number of steps.This is a new method for determining the attribute of the system’s reset,which is represented by Petri nets and allows the system to return to its starting state,the resting state.The goal is to broaden the ontological basis of Petri nets by displaying linkages or relationships between Petri nets that are akin to directed Euler graphs.
文摘Genome sequencing is the process of determining in which order the nitrogenous bases also known as nucleotides within a DNA molecule are arranged. Every organism’s genome consists of a unique sequence of nucleotides. These nucleotides bases provide the phenotypes and genotypes of a cell. In mathematics, Graph theory is the study of mathematical objects known as graphs which are made of vertices (or nodes) connected by either directed edges or indirect edges. Determining the sequence in which these nucleotides are bonded can help scientists and researchers to compare DNA between organisms, which can help show how the organisms are related. In this research, we study how graph theory plays a vital part in genome sequencing and different types of graphs used during DNA sequencing. We are going to propose several ways graph theory is used to sequence the genome. We are as well, going to explore how the graphs like Hamiltonian graph, Euler graph, and de Bruijn graphs are used to sequence the genome and advantages and disadvantages associated with each graph.
基金Supported by National Natural Science Foundation of China(60904051)the Innovative Team Program of the National Natural Science Foundation of China(61021002)the Royal Academy of Engineering-Research Exchanges with China and India Awards
