Manufacturing feature recognition is a basic component for systems that automatically generate manufacturing processes. When compared to the set of low level entities existing in a component's CAD model, features are a set of higher level entities that model the correspondence between design information and manufacturing activities. Graph-based methods, which use the part adjacency Graph to recognize features, are among the most common techniques in the existing feature recognition literature. In this paper, some techniques are proposed which significantly improve the performance of traditional Graph-based algorithms. The approach is more general and efficient than common Graph-based approaches dealing with the problem of feature interactions. The scope of the Graph-based approaches is also extended in this paper to include curved and 3D features in addition to polyhedral features, where most of the existing Graph-based algorithms have focused only on the polyhedral objects.

One of the standard criteria for expressing the relationship between two random variables is the correlation coefficient. Correlation between variables shows that changing the value of one variable leads to changing another variable in a certain direction. It is also possible to use the value of one variable to predict the value of another. In statistics, the correlation coefficient measures the direction and strength of the tendency to change. In machine learning, the correlation coefficient is known as a measure of classification quality. In fact, as a starting step for classification, the correlation between different samples should be estimated using a specific method. There are various methods to estimate the correlation of different data types, which have disadvantages such as low accuracy or high computational time. One of the methods that can overcome these problems, due to its high capability in modeling correlation between samples is Graphical modeling. In this research, a new covariance model based on Graph Theory and Graph neural network for estimating the correlation between samples is presented. The results show the improvement of the proposed model in accuracy, sensitivity, precision, F-Micro, F-Macro and statistical tests compared to Pearson and cosine methods.

The aim of the present work is two fold. In one hand it shows to mathematicians how the apparently pure mathematical concepts can be applied to the efficient solution of problems in structural mechanics. In the other hand it illustrates to engineers the important role of mathematical concepts for the solution of engineering problems. In this paper a number of applications of Graph Theory in structural mechanics are presented. These applications simplify the analysis of structures and make their optimal analysis feasible. For each case, the main problem is stated and then the formulation together with illustrative examples is presented.      

Much has been written about the golden ratio $\phi=\frac{1+\sqrt{5}}{2}$ and this strange number appears mysteriously in many mathematical calculations. In this article, we review the appearance of this number in the Graph Theory. More precisely, we review the relevance of this number in topics such as the number of spanning trees, topological indices, energy, chromatic roots, domination roots and the number of domatic partitions of Graphs.

For large-scale structures, the pattern of structural matrices are of great importance. Improving the patterns of sparse matrices not only reduces the cost of solution, but also makes the processing of large matrices feasible.In the present paper, concepts and definitions from Graphs and algebraic Graph Theory are briefly presented. Various methods are investigated for optimal ordering to reduce the profile of the structural matrices. Special attention is paid to Sloan s method as a powerful approach for profile reduction. In order to show the capability of this method, examples of Everstine are examined. Different values are adopted for the priority function of Sloan and the results are compared. Three parameters are used in place of two, and the resulting profiles are compared. The uniformaty and non-uniformaty of nodal degrees in various models are also studied.The spectral method using the Laplacian matrix of the models is programmed and applied to Everstine s examples. The difficulty of computational time is reduced employing improved hybrid spectral-Graph method. Combining the hybrid Ritz method and Sloan's approach, an improved hybrid Ritz method is developed.

Urban bus transportation is one of the common public transportation modes, which has a significant position among all other modes. Any attempt in order to increase the effectiveness and desirability of this mode has a positive influence on the urban trips. Bus network design due to its considerable influence on the performance of this mode is of great importance. And various approaches have been proposed in this context, which have different advantages and disadvantages. Reaching the optimal network in the shortest possible time, considering the parameters which are in conflict with each other most of the time, is the main reason of the complexity of bus network design problem, and makes constraints for the designers. The present paper proposes a heuristic approach for solving bus network design, which is based on Graph Theory. The proposed methodology designs bus network in two steps of route generating and route selection. For the evaluation purpose, this method compared to other heuristic methods. The results showed that the proposed method outperforms the other existing heuristic network design methods.

One of the factors that can be the link between our intentions and actions and their external consequences is human agency, which indicates the conscious design and intentional execution of actions by the individual in order to influence future events.Objective and Method: This research with a developmental approach of psychometric method and method 1, examines the psychometric indices of the Human Factor Characteristics Scale using the classical Theory of test score measurement and the graduated question-answer Theory. The purpose of this study, which included high school students in Tehran, was selected by cluster sampling of 500 people as a sample size and statistical analysis was performed on 481 data. To collect the data, the ion Human Agent Characteristics Scale (2011) was used and the research questions were evaluated using IRTPRO and SPSS software.Results:The assumption of local independence based on Pearson x2 index was established by applying Simjima's calibrated question-answer Theory and the assumption of being one-dimensional based on the analysis of multidimensional question-answer Theory. Diagnosis parameters with question-answer approach and classical approach Test score Both item 25 approach had the lowest and item 2 had the highest diagnosis parameter. The answer thresholds for all the questions were so far apart that no option was covered by the other option, and the options were independently selected by individuals at intervals of theta. The total scale was calculated with Cronbach's alpha of 0.945, intentionality of 0.894, foresight of 0.780, self-reactivity of 0.871 and rethinking of 0.762. Also, the role of each item in internal consistency was investigated by the loop method, which all questions had a favorable role in internal consistency of this scale. The value of the validity coefficient obtained from the question-answer Theory was obtained by marginal method for intentionality 0.92, forethought 0.85, self-reaction 0.91, rethinking 0.83..

Graphs are an effective tool for planetary gear trains (PGTs) synthesis and for the enumeration of all possible PGTs for transmission systems. In the past fifty years, considerable effort has been devoted to the synthesis of PGTs. To date, however, synthesis results are inconsistent, and accurate synthesis results are difficult to achieve. This paper proposes a systematic approach for synthesizing PGTs depending on spanning trees and parent Graphs. Trees suitable for constructing rooted Graphs are first identified. The parent Graphs are then listed. Finally, geared Graphs are discovered by inspecting their parent Graphs and spanning trees. To precisely detect spanning trees, a novel method based on two link assortment equations is presented. Transfer vertices and edge levels are detected without the use of any computations. This work develops the vertex matrix of the rooted Graph, and its distinctive equation is used to arrange the vertex degree arrays according to the vertex levels and eliminate the arrays that violate the distinctive equations. The precise results of the 5-link geared Graphs are confirmed to be 24. The disparity between the recent and previous synthesis results can be attributed to the fact that the findings of the current method, which employs rooted Graphs, are more comprehensive than those obtained with Graphs lacking multiple joints. A novel algorithm for detecting structural isomorphism is proposed. By comparing the vertex degree listings and gear strings, non-isomorphic geared Graphs are obtained. The algorithm is simple and computationally efficient. The Graph representation is one-to-one with the vertex degree listing and gear string representation. This allows for the storage of a large number of Graphs on a computer for later use.