Directed Acyclic Graphs stand as one of the prevailing approaches for representing causal relationships within a set of variables. With observational or interventional data, certain undirected edges within a causal DAG can be oriented. Performing intervention can be done in two different settings, passive and active. Here, we prove that an optimal intervention set can be obtained based on the minimum vertex cover of a graph. We propose an algorithm that efficiently identifies such an optimal intervention set for chordal graphs within polynomial time. Performing intervention on this optimal set recovers all the undirected edges in graph G, regardless of the underlying ground truth DAG. Furthermore, we present an algorithm for evaluating the performance of passive algorithms. This evaluation provides insights into how many intervention steps of a specific algorithm are required to recover all edges in the causal graph for any possible underlying ground truth in the equivalence class. Experimental findings underscore that the number of nodes in the optimal intervention set increases with growing the number of nodes in a graph, where the edge density is fixed, and also increases with the rising edge density in a graph with a fixed number of nodes.

Directed Acyclic Graphs stand as one of the prevailing approaches for representing causal relationships within a set of variables. With observational or interventional data, certain undirected edges within a causal DAG can be oriented. Performing intervention can be done in two different settings, passive and active. Here, we prove that an optimal intervention set can be obtained based on the minimum vertex cover of a graph. We propose an algorithm that efficiently identifies such an optimal intervention set for chordal graphs within polynomial time. Performing intervention on this optimal set recovers all the undirected edges in graph G, regardless of the underlying ground truth DAG. Furthermore, we present an algorithm for evaluating the performance of passive algorithms. This evaluation provides insights into how many intervention steps of a specific algorithm are required to recover all edges in the causal graph for any possible underlying ground truth in the equivalence class. Experimental findings underscore that the number of nodes in the optimal intervention set increases with growing the number of nodes in a graph, where the edge density is fixed, and also increases with the rising edge density in a graph with a fixed number of nodes.

Heat exchangers are one of the most important devices of mechanical systems in modern society. Most industrial processes involve the transfer of heat and more often they require the heat transfer process to be controlled. A heat exchanger is the heat exchanged between two media, one being cold and the other being hot. There are different types of heat exchanger, but the type which is widely used in industrial application is the shell and tube. In this study, Experiments conducted based on fully replicable five-factor, five-level central composite design. Regression modelsare developed to analyse the effects of shell and tube heat exchange process parameter such as inlet temperature of hot fluid and flow rates of cold and hot fluid. The output parameters of a heat exchanger are used for analysing the direct and interactive effects of heat exchange process parameters.