The ability to accurately predict the mechanical properties of metals is essential for their correct use in the design of structures and components. This is even more important in the presence of materials, such as metal cast alloys, whose properties can vary significantly in relation to their constituent elements, microstructures, process parameters or treatments. This study shows how a machine learning approach, based on pattern recognition analysis on experimental data, is able to offer acceptable precision predictions with respect to the main mechanical properties of metals, as in the case of ductile cast iron and compact graphite cast iron. The metallographic properties, such as graphite, ferrite and perlite content, extrapolated through macro indicators from micrographs by image analysis, are used as inputs for the machine learning algorithms, while the mechanical properties, such as yield strength, ultimate strength, ultimate strain and Young’s modulus, are derived as output. In particular, 3 different machine learning algorithms are trained starting from a dataset of 20–30 data for each material and the results offer high accuracy, often better than other predictive techniques. Concerns regarding the applicability of these predictive techniques in material design and product/process quality control are also discussed.

This paper discusses an approach developed for exploiting the local elementary movements of evolution to study complex networks in terms of shared common embedding and, consequently, shared fractal properties. This approach can be useful for the analysis of lung cancer DNA sequences and their properties by using the concepts of graph theory and fractal geometry. The proposed method advances a renewed consideration of network complexity both on local and global scales. Several researchers have illustrated the advantages of fractal mathematics, as well as its applicability to lung cancer research. Nevertheless, many researchers and clinicians continue to be unaware of its potential. Therefore, this paper aims to examine the underlying assumptions of fractals and analyze the fractal dimension and related measurements for possible application to complex networks and, especially, to the lung cancer network. The strict relationship between the lung cancer network properties and the fractal dimension is proved. Results show that the fractal dimension decreases in the lung cancer network while the topological properties of the network increase in the lung cancer network. Finally, statistical and topological significance between the complexity of the network and lung cancer network is shown.

There is a large body of research devoted to identifying the complexity of structures in networks. In the context of network theory, a complex network is a graph with nontrivial topological features—features that do not occur in simple networks, such as lattices or random graphs, but often occur in graphs modeling real systems. The study of complex networks is a young and active area of scientific research inspired largely by the empirical study of real-world networks, such as computer networks and logistic transport networks. Transport is of great importance for the economic and cultural cooperation of any country with other countries, the strengthening and development of the economic management system, and in solving social and economic problems. Provision of the territory with a well-developed transport system is one of the factors for attracting population and production, serving as an important advantage for locating productive forces and providing an integration effect. In this paper, we introduce a new method for quantifying the complexity of a network based on presenting the nodes of the network in Cartesian coordinates, converting to polar coordinates, and calculating the fractal dimension using the ReScaled ranged (R/S) method. Our results suggest that this approach can be used to determine complexity for any type of network that has fixed nodes, and it presents an application of this method in the public transport system.

This paper presents a mathematical explanation of one of the Multi-Attribute Decision-Making (MADM) methods—the Ranking based on Distance and Range (RADAR) method—along with its modified variant, RADAR II. Through mathematical proofs, the influence of each step of the method on the final ranking of alternatives is analyzed. The methods are tested on three numerical examples with varying criterion weights. The robustness of the methods, as well as their fundamental characteristics, is demonstrated. A comparative analysis reveals that although both methods prioritize alternatives based on their stability across all criteria—particularly the most important ones—the RADAR II method is somewhat more rigorous and stringent, whereas the original RADAR method is more flexible and yields more objective results.

Nowadays, laser hardening is a consolidated process in many industrial sectors. One of the most interesting aspects to be considered when treating the surface-hardening process in steel materials by means of laser devices is undoubtedly the evaluation of the heat treatment quality and surface finish. In the present study, an innovative method based on fractal geometry was proposed to evaluate the quality of surface-steel-laser-hardened treatment. A suitable genetic programming study of SEM images (1280 × 950 pixels) was developed in order to predict the effect of the main laser process parameters on the microstructural geometry, assuming the microstructure of laser-hardened steel to be of a structurally complex geometrical nature. Specimens hardened by anthropomorphic laser robots were studied to determine an accurate measure of the process parameters investigated (surface temperature, laser beam velocity, laser beam impact angle). In the range of variation studied for these parameters, the genetic programming model obtained was in line with the complexity index calculated following the fractal theory. In particular, a percentage error less than 1% was calculated. Finally, a preliminary study of the surface roughness was carried out, resulting in its strong correlation with complex surface microstructures. Three-dimensional voxel maps that reproduce the surface roughness were developed by automating a routine in Python virtual environment.

The concept of “surface modeling” generally describes the process of representing a physical or artificial surface by a geometric model, namely a mathematical expression. Among the existing techniques applied for the characterization of a surface, terrain modeling relates to the representation of the natural surface of the Earth. Cartographic terrain or relief models as three-dimensional representations of a part of the Earth's surface convey an immediate and direct impression of a landscape and are much easier to understand than two-dimensional models. This paper addresses a major problem in complex surface modeling and evaluation consisting in the characterization of their topography and comparison among different textures, which can be relevant in different areas of research. A new algorithm is presented that allows calculating the fractal dimension of images of complex surfaces. The method is used to characterize different surfaces and compare their characteristics. The proposed new mathematical method computes the fractal dimension of the 3D space with the average space component of Hurst exponent H, while the estimated fractal dimension is used to evaluate, compare and characterize complex surfaces that are relevant in different areas of research. Various surfaces with both methods were analyzed and the results were compared. The study confirms that with known coordinates of a surface, it is possible to describe its complex structure. The estimated fractal dimension is proved to be an ideal tool for measuring the complexity of the various surfaces considered.