The importance of an architectural semantic for service-oriented computing starts with the characteristics of software systems that has been recognized with sharing and the utilization of resources. However, an architectural characteristic for service-oriented based applications depends on interaction patterns that utilizes a data format in communication. These patterns also help in establishing communication between service components. The goal of service-oriented computing methodologies could be achieved by adopting a logical separation of services from the actual mechanism of resource assignment and allotment. This shows that how services are reliable as interaction patterns between service provider and requester. It generates the binding patterns between these two and establishes communication between them. This article discusses the mathematical-based semantic model that presents an architectural view for systems that follows a service-oriented computing methodology. It also briefs describes about different execution states and routes, which addresses the service specifications in service-oriented computing.

No abstract

No abstract

No abstract

In the literature of graph theory, networks are represented as directed graphs or undirected graphs and a mixed of both combinations. In today's era of computing, networks like brain and facebook that do not belong to any of the mentioned networks category and in fact, it belongs to the combination of both networks which have connections as directed as well as undirected. To represent such networks, semi-directed graphs have been studied in this paper that provides the detailed mathematical fundamentals related to better understand the conceptualization for social media networks. This paper also discusses the suitable matrices analyze for the representation of the graphs. Few new terminologies like incidence number, complete-incidence related to semi-directed graphs and counter isomorphism of semi-directed graphs have been inculcated. A centrality measure, namely incidence centrality, has also been proposed based on incidence number on neighbors in social media networks.

Graph colouring is the system of assigning a colour to each vertex of a graph. It is done in such a way that adjacent vertices do not have equal colour. It is fundamental in graph theory. It is often used to solve real-world problems like traffic light signalling, map colouring, scheduling, etc. Nowadays, social networks are prevalent systems in our life. Here, the users are considered as vertices, and their connections/interactions are taken as edges. Some users follow other popular users' profiles in these networks, and some don't, but those non-followers are connected directly to the popular profiles. That means, along with traditional relationship (information flowing), there is another relation among them. It depends on the domination of the relationship between the nodes. This type of situation can be modelled as a directed fuzzy graph. In the colouring of fuzzy graph theory, edge membership plays a vital role. Edge membership is a representation of flowing information between end nodes of the edge. Apart from the communication relationship, there may be some other factors like domination in relation. This influence of power is captured here. In this article, the colouring of directed fuzzy graphs is defined based on the influence of relationship. Along with this, the chromatic number and strong chromatic number are provided, and related properties are investigated. An application regarding COVID-19 infection is presented using the colouring of directed fuzzy graphs.

No abstract

Data is always a crucial issue of concern especially during its prediction and computation in digital revolution. This paper exactly helps in providing efficient learning mechanism for accurate predictability and reducing redundant data communication. It also discusses the Bayesian analysis that finds the conditional probability of at least two parametric based predictions for the data. The paper presents a method for improving the performance of Bayesian classification using the combination of Kalman Filter and K-means. The method is applied on a small dataset just for establishing the fact that the proposed algorithm can reduce the time for computing the clusters from data. The proposed Bayesian learning probabilistic model is used to check the statistical noise and other inaccuracies using unknown variables. This scenario is being implemented using efficient machine learning algorithm to perpetuate the Bayesian probabilistic approach. It also demonstrates the generative function for Kalman-filer based prediction model and its observations. This paper implements the algorithm using open source platform of Python and efficiently integrates all different modules to piece of code via Common Platform Enumeration (CPE) for Python.