Foundations, Volume 4, Issue 1 (March 2024) – 9 articles

Nowadays, hydropower plants are being used to compensate for the variable power produced by the new fluctuating renewable energy sources, such as wind and solar power, and to stabilise the grid. Consequently, hydraulic turbines are forced to work more often in off-design conditions, far from their best efficiency point. This new operation strategy increases the probability of erosive cavitation and of hydraulic instabilities and pressure fluctuations that increase the risk of fatigue damage and reduce the life expectancy of the units. To monitor erosive cavitation and fatigue damage, acoustic emissions induced by very-high-frequency elastic waves within the solid have been traditionally used. Therefore, acoustic emissions are becoming an important tool for hydraulic turbine failure detection and troubleshooting. In particular, artificial intelligence is a promising signal analysis research hotspot, and it has a great potential in the condition monitoring of hydraulic turbines using acoustic emissions as a key factor in the digitalisation process. In this paper, a brief introduction of acoustic emissions and a description of their main applications are presented. Then, the research works carried out for cavitation and fracture detection using acoustic emissions are summarised, and the different levels of development are compared and discussed. Finally, the role of artificial intelligence is reviewed, and expected directions for future works are suggested. Full article

In this study, we undertake a systematic study of historic market volatility spanning roughly five preceding decades. We focus specifically on the time series of the realized volatility (RV) of the S&P500 index and its distribution function. As expected, the largest values of RV coincide with the largest economic upheavals of the period: Savings and Loan Crisis, Tech Bubble, Financial Crisis and Covid Pandemic. We address the question of whether these values belong to one of the three categories: Black Swans (BS), that is, they lie on scale-free, power-law tails of the distribution; Dragon Kings (DK), defined as statistically significant upward deviations from BS; or Negative Dragons Kings (nDK), defined as statistically significant downward deviations from BS. In analyzing the tails of the distribution with $RV>40$, we observe the appearance of “potential” DK, which eventually terminate in an abrupt plunge to nDK. This phenomenon becomes more pronounced with the increase in the number of days over which the average RV is calculated—here from daily, $n=1$, to “monthly”, $n=21$. We fit the entire distribution with a modified Generalized Beta (mGB) distribution function, which terminates at a finite value of the variable but exhibits a long power-law stretch prior to that, as well as a Generalized Beta Prime (GB2) distribution function, which has a power-law tail. We also fit the tails directly with a straight line on a log-log scale. In order to ascertain BS, DK or nDK behavior, all fits include their confidence intervals and p-values are evaluated for the data points to check whether they can come from the respective distributions. Full article

Visualizing multivariate data can be challenging, especially for the general public. The difficulties extend beyond determining how to present the data; they also involve comprehension. Early literature has identified various methods, including Chernoff’s face, but these methods often have significant drawbacks, making them challenging to interpret. Subsequently, other techniques, such as scatterplots, parallel coordinate plots, and dynamic graphics, have been introduced. However, many of these methods can be intricate to create and interpret, particularly when visualizing high-dimensional data. Additionally, simultaneously representing discrete aspects (including “space”) and continuous aspects (including “time”) presents another challenge. This study proposes a novel approach named the “Δ table” (delta table), which transforms space–time multivariate data consisting of discrete and continuous variables into a tabular format. The Δ table is believed to be more user-friendly for the general public, which is its most significant advantage compared to previous methods. Finally, we used a case study of the decoupling of the world’s developed, newly industrialized, and developing economies in recent decades as an example of an attempt to apply the Δ table. Full article

Natural mathematical objects for representing spatially distributed physical attributes are 3D field functions, which are prevalent in applied sciences and engineering, including areas such as fluid dynamics and computational geometry. The representations of these objects are task-oriented, which are achieved using various techniques that are suitable for specific areas. A recent breakthrough involves using flexible parameterized representations, particularly through neural networks, to model a range of field functions. This technique aims to uncover fields for computational vision tasks, such as representing light-scattering fields. Its effectiveness has led to rapid advancements, enabling the modeling of time dependence in various applications. This survey provides an informative taxonomy of the recent literature in the field of learnable field representation, as well as a comprehensive summary in the application field of visual computing. Open problems in field representation and learning are also discussed, which help shed light on future research. Full article

We develop the local convergence of the six order Contraharmonic-mean Newton’s method (CHN) to solve Banach space valued equations. Our analysis approach is two fold: The first way uses Taylor’s series and derivatives of higher orders. The second one uses only the first derivatives. We examine the theoretical results by solving a boundary value problem also using the examples relating the proposed method with other’s methods such as Newton’s, Kou’s and Jarratt’s to show that the proposed method performs better. The conjugate maps for second-degree polynomial are verified. We also calculate the fixed points (extraneous). The article is completed with the study of basins of attraction, which support and further validate the theoretical and numerical results. Full article

Inrecent years, there has been a notable increase in utilising multiple criteria decision-making (MCDM) methods in practical problem solving. The advancement of enhanced decision models with greater capabilities, coupled with technologies like geographic information systems (GIS) and artificial intelligence (AI), has fueled the application of MCDM techniques across various domains. To address the scarcity of irrigation water resources in Bortala, Northwest China, the selection of a dam site has been approached using a hybrid model integrating a multipolar Fuzzy set and a plithogenic Fuzzy hypersoft set along with a GIS. This study considered criteria such as a geological layer, slope, soil type, and land cover. Four potential and reasonably suitable dam locations were identified using a dam construction suitability map developed for Bortala. Ultimately, we showcased the benefits of the innovative method, emphasizing an open, transparent, and science-based approach to selecting optimal dam sites through local studies and group discussions. The results highlight the effectiveness of the hybrid approach involving a fuzzy hypersoft set and plithogenic multipolar fuzzy hypersoft set in addressing the challenges of dam site selection. Full article

The latest cellular technology, known as 5G-NR, is intended to significantly speed up and improve the effectiveness of wireless systems. A revolution in the telecom industry has been sparked by the widespread use of and increased reliance on cellular communication technology. Moreover, 5G and B5G technologies are expected to utilize an even higher-frequency range to achieve faster data transmission and lower latency communication. Consequently, while transmitting signals across various types of equipment and infrastructure, the general public is exposed to much higher frequencies of electromagnetic radiation. The increasing need for 5G NR base stations (gNodeB) has heightened public anxiety over potential negative health impacts. This study reviews recent research on the effects of electromagnetic waves on humans, particularly focusing on how these effects influence cognitive functions. Most research to date has not found significant differences in cognitive performance due to ubiquitous mobile communications. However, current research has largely been limited to 4G technologies, and the health effects of exposure to 5G user equipment (UE) and base stations in higher-frequency bands remain unexplored. If subsequent research suggests that exposure to high-frequency wireless networks significantly impacts cognitive functions, the deployment and acceptance of these technologies may face challenges and constraints. Therefore, such investigations are crucial for determining whether next-generation technologies pose no risk to individuals. Full article

Mathematical analysis is conducted on cyclical systems with goodwill in capitalization. Proportional goodwill vanishes with vanishing tangible value. Correspondingly, periodic boundary condition does not enable commercial utilization of the goodwill. Abandoning the periodic boundary condition enables commercial utilization of the goodwill. Even if a physical system is periodic, an agent can abandon the corresponding boundary condition by divesting. Example cases are shown in terms of boreal forestry systems. Full article