Search Results (43)

High-gain linear polarized antennas are widely used in wireless communications. However, the insertion loss of the feed network increases, limiting the potential for enhancing antenna gain. In this paper, a high-gain linear polarized Fabry–Perot (FP) antenna based on a fractal structure, which consisted of a metasurface and 2 × 2 array antenna structure, was designed. The spacing between the metasurface structure and array antenna was a free space half-wavelength, forming an FP antenna with a high gain. The self-similarity of the fractal structure allowed miniaturization of the structure. The proposed antenna and metasurface structural units comprised a first-order Minkowski fractal structure. The antenna unit was further miniaturized by including a square gap structure in its unit structure, while its gain was improved by using an air dielectric layer as the dielectric substrate of the antenna unit. The antenna unit formed a 2 × 2 array antenna through a 1–4 feeding network. The reliability of the array antenna performance was verified by processing and measuring the antenna structure. Experimental results showed that the −10 dB working bandwidth of the antenna is 5.71–5.89 GHz, while at 5.8 GHz its gain is 16.5 dBi. The radiation efficiency is over 90%. The experimental results were consistent with the simulation results. The proposed antenna exhibits high gain and is suitable for short-distance wireless communication systems and other fields. Full article

Voronoi partitioning is a fundamental geometric concept with applications across computational geometry, robotics, optimization, and resource allocation. While Euclidean distance is the most commonly used metric, alternative distance functions can significantly influence the shape and properties of Voronoi cells. This paper presents a comprehensive mathematical analysis of various distance metrics used in Voronoi partitioning, including Euclidean, Manhattan, Minkowski, weighted, anisotropic, and geodesic metrics. We analyze their mathematical formulations, geometric properties, topological implications, and computational complexity. This work aims to provide a theoretical framework for selecting appropriate metrics for Voronoi-based modeling in diverse applications. Full article

This study evaluates hierarchical clustering methodologies to identify patterns associated with timeout requests for EuroLeague basketball games. Using play-by-play data from 3743 games spanning the 2008–2023 seasons (over 1.9 million instances), we applied Principal Component Analysis to reduce dimensionality and tested multiple agglomerative and divisive clustering techniques (e.g., Ward and DIANA) with different distance metrics (Euclidean, Manhattan, and Minkowski). Clustering quality was assessed using internal validation indices such as Silhouette, Dunn, Calinski–Harabasz, Davies–Bouldin, and Gap statistics. The results show that Ward.D and Ward.D2 methods using Euclidean distance generate well-balanced and clearly defined clusters. Two clusters offer the best overall quality, while four clusters allow for meaningful segmentation of game situations. The analysis revealed that teams that did not request timeouts often exhibited better scoring efficiency, particularly in the advanced game phases. These findings offer data-driven insights into timeout dynamics and contribute to strategic decision-making in professional basketball. Full article

Background: Traditional neonatal assessments rely on anthropometric measures such as weight, body size, and head circumference. However, recent studies suggest that objective movement quantification may serve as a complementary clinical indicator of development in preterm infants. Methods: This study evaluates non-invasive computer vision-based quantification of neonatal movement using contactless pose tracking based on computer vision. We analyzed approximately 800,000 postural data points from ten preterm infants to identify reliable algorithms, optimal recording duration, and whether whole-body or regional tracking is sufficient. Results: Our findings show that 30 s video segments are adequate for consistent motion quantification. Optical flow methods produced inconsistent results, while distance-based algorithms—particularly Chebyshev and Minkowski—offered greater stability, with coefficients of variation of 5.46% and 6.40% in whole-body analysis. Additionally, Minkowski and Mahalanobis metrics applied to the lower body yielded results similar to full-body tracking, with minimal differences of 0.89% and 1%. Conclusions: The results demonstrate that neonatal movement can be quantified objectively and without physical contact using computer vision techniques and reliable computational methods. This approach may serve as a complementary clinical indicator of neonatal progression, alongside conventional measures such as weight and size, with applications in continuous monitoring and early clinical decision-making for preterm infants. Full article

The cosmic time dilation observed in Type Ia supernova light curves suggests that the passage of cosmic time varies throughout the evolution of the Universe. This observation implies that the rate of proper time is not constant, as assumed in the standard FLRW metric, but instead is time-dependent. Consequently, the commonly used FLRW metric should be replaced by a more general framework, known as the Conformal Cosmology (CC) metric, to properly account for cosmic time dilation. The CC metric incorporates both spatial expansion and time dilation during cosmic evolution. As a result, it is necessary to distinguish between comoving and proper (physical) time, similar to the distinction made between comoving and proper distances. In addition to successfully explaining cosmic time dilation, the CC metric offers several further advantages: (1) it preserves Lorentz invariance, (2) it maintains the form of Maxwell’s equations as in Minkowski spacetime, (3) it eliminates the need for dark matter and dark energy in the Friedmann equations, and (4) it successfully predicts the expansion and morphology of spiral galaxies in agreement with observations. Full article

This work considers the Minkowski sum of an N-dimensional ellipsoid and hyperrectangle, a combination that is extremely relevant due to the usage of ellipsoid-adjacent primitives in computer graphics for work such as 3D Gaussian splatting. While parametric representations of this Minkowski sum are available, they are often difficult or too computationally intensive to work with when, for example, performing an inclusion test. For performance-critical applications, a lightweight approximation of this Minkowski sum is preferred over its exact form. To this end, we propose a fast, computationally lightweight, non-iterative algorithm that approximates the Minkowski sum through the intersection of two carefully constructed bounding boxes. Our approximation is a super-set that completely envelops the exact Minkowski sum. This approach yields an implicit representation that is defined by a logical conjunction of linear inequalities. For applications where a tight super-set of the Minkowski sum is acceptable, the proposed algorithm can substantially improve the performance of common operations such as intersection testing. Full article

The design of bridges must balance sustainability and construction simplicity. A game-theory-based optimization method was applied in this research to find a sustainable steel–concrete composite bridge design. The sustainability was evaluated through cost and environmental and social impact using the Life Cycle Assessment method. The optimization process considered four criteria simultaneously, using a discrete version of the SCA algorithm and a transfer function for discretization. The preferred solutions were selected using the Minkowski distances approach. Results showed a decrease in slab reinforcement and an increase in the amount of steel in the cross-section, leading to only an 8.2‰ increase in cost compared to similar studies. Regarding the cross-section, the geometry obtained considers cells in the upper and lower parts of the webs to improve the bending resistance. The proposed method allows for the simultaneous optimization of multiple criteria and provides a sustainable yet simple bridge design solution. Full article

While satellite-based remote sensing offers a promising avenue for large-scale LCC estimations, the accuracy of evaluations is often decreased by mixed pixels, attributable to distinct farming practices and diverse soil conditions. To overcome these challenges and to account for maize intercropping with soybeans at different growth stages combined with varying soil backgrounds, a hyperspectral database for maize was set up using a random linear mixed model applied to hyperspectral data recorded by an unmanned aerial vehicle (UAV). Four methods, namely, Euclidean distance, Minkowski distance, Manhattan distance, and Cosine similarity, were used to compare vegetation spectra from Sentinel-2A with the newly constructed database. In a next step, widely used vegetation indices such as NDVI, NAOC, and CAI were tested to find the optimum method for LCC retrieval, validated by field measurements. The results show that the NAOC had the strongest correlation with ground sampling information (R² = 0.83, RMSE = 0.94 μg/cm², and MAE = 0.67 μg/cm²). Additional field measurements sampled at other farming areas were applied to validate the method’s transferability and generalization. Here too, validation results showed a highly precise LCC estimation (R² = 0.93, RMSE = 1.10 μg/cm², and MAE = 1.09 μg/cm²), demonstrating that integrating UAV hyperspectral data with a random linear mixed model significantly improves satellite-based LCC retrievals. Full article

In this paper, we primarily investigate and establish several properties of spherical Steiner symmetrizations, along with the isoperimetric property of the spherical cap in ${\mathbb{S}}^n$. Specifically, we study the monotonically decreasing property of the measure of the symmetric difference of two spherical compact sets, the monotonically decreasing property of the spherical diameter of a spherical compact set, the convergence of iterative spherical Steiner symmetrizations, and so on. In particular, we prove that the sequence of iterative spherical Steiner symmetrizations of $K\subset {\mathbb{S}}^n$, which follow sequences selected from a finite set of directions, converges to a spherical cap with the same measure as K, extending the result from ${\mathbb{R}}^n$ to ${\mathbb{S}}^n$ on Steiner symmetrizations. It provides us with valuable insights for studying the relevant applications and conclusions of spherical Steiner symmetrizations. Full article

In this article, we study the properties of 4-by-4 metric matrices and characterize their dependence and independence by ${\mathcal{M}}^{4\times 4}=({\mathcal{M}}^{4\times 4}-D{\mathcal{M}}^{4\times 4})\cup D{\mathcal{M}}^{4\times 4}$, where $D{\mathcal{M}}^{4\times 4}$ is the set of all dependent metric matrices. $D{\mathcal{M}}^{4\times 4}$ is further characterized by $D{\mathcal{M}}^{4\times 4}=D{\mathcal{M}}_1^{4\times 4}\cup D{\mathcal{M}}_2^{4\times 4}$, where $D{\mathcal{M}}_2^{4\times 4}$ is characterized by $D{\mathcal{M}}_2^{4\times 4}=D{\mathcal{M}}_{21}^{4\times 4}\cup D{\mathcal{M}}_{22}^{4\times 4}$. These characterizations provide some insightful findings that go beyond the Euclidean distance or Euclidean distance matrix and link the distance functions to vector spaces, which offers some theoretical and application-related advantages. In the application parts, we show that the metric matrices associated with all Minkowski distance functions over four different points are linearly independent, and that the metric matrices associated with any four concyclic points are also linearly independent. Full article

The velocity obstacles (VO) method is widely employed in real-time obstacle avoidance research for UAVs due to its succinct mathematical foundation and rapid, dynamic planning abilities. Traditionally, VO assumes a circle protection domain with a fixed radius, leading to issues such as excessive conservatism of obstacle avoidance areas, longer detour paths, and unnecessary avoidance angles. To overcome these challenges, this paper firstly reviews the fundamentals and pre-existing defects of the VO methodology. Next, we explore a scenario involving UAVs in head-on conflicts and introduce an elliptic velocity obstacle method tailored to the UAV’s current flight state. This method connects the protection domain size directly to the UAV’s flight state, transitioning from the conventional circle domain to a more efficient elliptic domain. Additionally, to manage the computational demands of Minkowski sums and velocity obstacle cones, an approximation algorithm for discretizing elliptic boundary points is introduced. A strategy to mitigate unilateral velocity oscillation had is developed. Comparative validation simulations in MATLAB R2022a confirm that, based on the experimental results for the first 10 s, the apex angle of the velocity obstacle cone for the elliptical domain is, on average, reduced by 0.1733 radians compared to the circular domain per unit simulation time interval, saving an airspace area of 13,292 square meters and reducing the detour distance by 14.92 m throughout the obstacle avoidance process, facilitating navigation in crowded situations and improving airspace utilization. Full article

Motivated by two definitions of distance, “pre-symmetric w-distance” and “w-cone distance”, we define the concept of a pre-symmetric w-cone distance in a TVS-CMS and introduce its properties and examples. Also, we discuss the TVS-cone version of the recent results obtained by Romaguera and Tirado. Meanwhile, using Minkowski functionals, we show the equivalency between some consequences concerning a pre-symmetric w-distance in a usual metric space and a pre-symmetric w-cone distance in a TVS-CMS. Then, some types of various w-cone-contractions and the relations among them are investigated. Finally, as an application, a characterization of the completeness of TVS-cone metric regarding pre-symmetric concept is performed, which differentiates our results from former characterizations. Full article

The waterflooding effect evaluation of carbonate fractured–vuggy reservoirs constitutes a comprehensive multiple-information decision-making process involving quantitative unascertained measure theory. This paper establishes a novel comprehensive methodology to evaluate the waterflooding effects of carbonate fractured–vuggy reservoirs for the first time. A new evaluation grading criteria is proposed using the Mahalanobis distance method based on the multi-index comprehensive unascertained measure theory derived from a modified five-scale analytical hierarchy process–entropy weight method. The actual field data from the carbonate fractured–vuggy reservoirs and the nine evaluation indices are specifically applied to demonstrate the calculation process for the construction of the grading system model on the waterflooding effects and to verify the accuracy of the Mahalanobis distance method by comparing the calculation results with the Minkowski and Euclidean distance methods. The proposed methodology facilitates the effective evaluation of the waterflooding strategies implemented in carbonate fractured–vuggy reservoirs with three categories; the ones with outstanding performance usually demonstrated favorable index characteristics, with substantial contributions to the enhanced oil recovery, manifesting with complete well patterns, a balance in the injection–production dynamics, excellent waterflooding utilization, and control competence. In contrast, fractured–vuggy units with fair waterflooding performance revealed limitations in the enhanced oil recovery. It can also be inferred that the mediocre waterflooding performance of the fractured–vuggy units is associated with incomplete well patterns, an imbalance in the injection–production dynamics, low waterflooding utilization, and a negligible waterflooding effect. The results in this study show that this newly proposed integrated model can effectively assess the waterflooding effects quantitatively and provide a more precise scientific basis for evaluating the waterflooding effects in carbonate fractured–vuggy reservoirs, with potential applicability in other fields. Full article

Short-term power load forecasting refers to the use of load and weather information to forecast the Day-ahead load, which is very important for power dispatch and the establishment of the power spot market. In this manuscript, a comprehensive study on the frame of input data for electricity load forecasting is proposed based on the extreme gradient boosting algorithm. Periodicity was the first of the historical load data to be analyzed using discrete Fourier transform, autocorrelation function, and partial autocorrelation function to determine the key width of a sliding window for an optimization load feature. The mean absolute error (MAE) of the frame reached 52.04 using a boosting model with a 7-day width in the validation dataset. Second, the fusing of datetime variables and meteorological information factors was discussed in detail and determined how to best improve performance. The datetime variables were determined as a form of integer, sine–cosine pairs, and Boolean-type combinations, and the meteorological features were determined as a combination with 540 features from 15 sampled sites, which further decreased MAE to 44.32 in the validation dataset. Last, a training method for day-ahead forecasting was proposed to combine the Minkowski distance to determine the historical span. Under this framework, the performance has been significantly improved without any tuning for the boosting algorithm. The proposed method further decreased MAE to 37.84. Finally, the effectiveness of the proposed method is evaluated using a 200-day load dataset from the Estonian grid. The achieved MAE of 41.69 outperforms other baseline models, with MAE ranging from 65.03 to 104.05. This represents a significant improvement of 35.89% over the method currently employed by the European Network of Transmission System Operators for Electricity (ENTSO-E). The robustness of the proposal method can be also guaranteed with excellent performance in extreme weather and on special days. Full article

This paper presents a new method for separating the mixed audio signals of simultaneous speakers using Blind Source Separation (BSS). The separation of mixed signals is an important issue today. In order to obtain more efficient and superior source estimation performance, a new algorithm that solves the BSS problem with Multi-Objective Optimization (MOO) methods was developed in this study. In this direction, we tested the application of two methods. Firstly, the Discrete Wavelet Transform (DWT) was used to eliminate the limited aspects of the traditional methods used in BSS and the small coefficients in the signals. Afterwards, the BSS process was optimized with the multi-purpose Strength Pareto Evolutionary Algorithm 2 (SPEA2). Secondly, the Minkowski distance method was proposed for distance measurement by using density information in the discrimination of individuals with raw fitness values for the concept of Pareto dominance. With this proposed method, the originals (original source signals) were estimated by separating the randomly mixed male and two female speech signals. Simulation and experimental results proved that the efficiency and performance of the proposed method can effectively solve BSS problems. In addition, the Pareto front approximation performance of this method also confirmed that it is superior in the Inverted Generational Distance (IGD) indicator. Full article