In this paper, several two-dimensional clustering scenarios are given. In those scenarios, soft partitioning clustering algorithms (Fuzzy C-means (FCM) and Possibilistic c-means (PCM)) are applied. Afterward, VAT is used to investigate the clustering tendency visually, and then in order of checking cluster validation, three types of indices (e.g., PC, DI, and DBI) were used. After observing the clustering algorithms, it was evident that each of them has its limitations; however, PCM is more robust to noise than FCM as in case of FCM a noise point has to be considered as a member of any of the cluster.

The integration of magnetic observatories of many countries into the Intermagnet network has provided researchers with new opportunities to investigate many geophysical processes. The joint processing of measurement evidence from magnetic observatories located in various geolocations makes it possible to better understand the dynamics of the interaction of solar plasma fluxes with the Earth's magnetosphere. For the correct interpretation of the dynamics of physical processes, the accuracy of the time reference of measurement results is of great importance. The measurement results of local observatories were transformed to a unified ecliptic coordinate system oriented towards the Sun in order to extract small variations in the magnetic field occurring before the magnetic storm commencement. Before transforming the coordinates, a constant component equal to the average daily value of the magnetic field components was removed from the results of minute-by-minute measurements. Owing to the averaging evidence from 84 magnetic observatories of the Intermagnet network, variations in the magnetic field of cosmic origin, preceding the magnetic storm commencement were detected. The correlation analysis of these variations recorded by different observatories revealed the presence of time shifts between the data series of different observatories. Only 62% of the observatories had a relative data shift within the range of ± 1 minute. Before the joint data processing in order to efficient use of data recorded with a time shift a method for correcting time shifts has proposed.

Pavement friction plays a crucial role in ensuring the safety of road networks. Accurately assessing friction levels is vital for effective pavement maintenance and management strategies employed by state highway agencies. Traditionally, friction evaluations have been conducted on a case-by-case basis, focusing on specific road sections. However, this approach fails to provide a comprehensive assessment of friction conditions across the entire road network. This paper introduces a hybrid clustering algorithm, namely the combination of density-based spatial clustering of applications with noise (DBSCAN) and Gaussian mixture model (GMM), to perform pavement friction performance rating across a statewide road network. A large, safety-oriented dataset is first generated by integrating network friction and vehicle crash data based on the attributes contributing possibly to friction related crashes. One-, two-, and multi-dimensional clustering analyses, respectively, are then performed to rate pavement friction. The Chi-square test is further employed to validate and identify the practical ratings. It is shown that by effectively capturing the hidden, intricate patterns within the integrated, complex dataset and prioritizing friction-related safety attributes, the hybrid clustering algorithm can produce pavement friction ratings that align effectively with the current practices of the Indiana Department of Transportation (INDOT) in friction management.

In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long–range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long–range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations and agent–based models. Reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first–passage time distributions. Research has lead us to question whether the observed long–range memory is a result of actual long–range memory process or just a consequence of non–linearity of Markov processes. As our most recent result we discuss the long–range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the ARFIMA sample series. Our newly obtained results seem indicate that new estimators of self–similarity and long–range memory for analyzing systems with non–Gaussian distributions have to be developed.