Although the concept of d-separation was originally defined for directed acyclic graphs (see Pearl 1988), there is a natural extension of the concept to directed cyclic graphs. When exactly the same set of d-separation relations hold in two directed graphs, no matter whether respectively cyclic or acyclic, we say that they are Markov equivalent. In other words, when two directed cyclic graphs a...

The decoding algorithm for the correction of errors arbitrary Mannheim weight has discussed Lattice constellations and codes from quadratic number fields. Following these lines, algorithms length cyclic over quaternion integers Quaternion one up to two coordinates have considered. In continuation, case lengths studied improve error efficiency. this study, we present 2 (where is prime integer Eu...

Cyclic codes are among the most important families of in coding theory for both theoretical and practical reasons. Despite their prominence intensive research on cyclic over a half century, there still open problems related to codes. In this work, we use recent results equivalence create more efficient algorithm partition by based cyclotomic cosets. This is then implemented carry out computer s...

This paper presents a novel hybrid ant colony optimization approach called SS_ACO algorithm to solve the vehicle routing problem. The main feature of the hybrid algorithm is to hybridize the solution construction mechanism of the ant colony optimization (ACO) with scatter search (SS). In our hybrid algorithm, we use ACO algorithm and greedy heuristic to generate the initial solutions which are ...