Search Results (54)

The widespread use of location-based services (LBSs) has led to the continuous collection of user location and trajectory data, increasing the risk of privacy leakage and creating a persistent tradeoff between privacy protection and data utility. To address this problem in discrete location query scenarios, this paper proposes a single-point location privacy protection method based on Q-R tree retrieval and differential privacy, termed QRDPP. QRDPP combines the adaptive spatial partitioning capability of a Q-tree with the minimum bounding rectangle (MBR)-based indexing capability of an R-tree. It applies an improved geometric privacy budget allocation strategy to leaf nodes and an arithmetic allocation strategy to non-leaf nodes, followed by Laplace perturbation of the corresponding location data and node information. For continuous trajectory query scenarios, this paper proposes a spatiotemporal generalization and differential privacy method, termed STG-DPTP, to address inadequate temporal protection, inappropriate generalization, and trajectory distortion. STG-DPTP performs hierarchical spatiotemporal clustering, separately models temporal and spatial distributions using Gaussian kernel density estimation, dynamically optimizes bandwidth parameters through Bayesian optimization, selects representative candidate subsets using the exponential mechanism, and generates protected trajectories through constrained sampling. Experiments on the GeoLife dataset evaluate the proposed methods in terms of query accuracy, computational efficiency, spatial trajectory similarity, reconstruction error, adversarial uncertainty, and temporal preservation. The results show that QRDPP improves the utility and efficiency of privacy-preserving spatial queries, while STG-DPTP better preserves the spatial distribution, trajectory structure, and temporal characteristics of the original data under the adopted differential privacy framework. Full article

Recovery of critical materials from industrial byproducts is often presented as a near-term United States (U.S.) supply-security strategy, yet contained inventories, pilot output, announced capacity, and commercial production are not equivalent. This study evaluates eight U.S. pathways for gallium, germanium, tellurium, lithium, magnesium, and cobalt, classified as operational, demonstration/pilot, announced target-year, or technical upper-bound cases. Facility- and stream-specific quantities were converted to qualifying domestic output and incorporated into same-stage material balances under explicit assumptions for utilization, eligibility, demand, and import displacement. Supply risk was calculated from the net import dependence and governance-adjusted production and trade concentration using a geometric index, with arithmetic formulations as robustness checks. The operational U.S. copper-refining tellurium pathway yielded the largest central reduction (49.29%). Announced 2030 Clarksville capacity reduced modeled risk by 13.87% for gallium and 8.75% for germanium, conditional on project completion, feed attribution, product qualification, utilization, and demand. All other central cases produced reductions of 4.63% or less; the current lithium demonstration, Stillwater cobalt, and aluminum-residue magnesium cases had negligible national effects. Policy support should therefore be differentiated by qualifying output, market scale, project maturity, and evidence quality rather than by contained material or nameplate capacity alone. Full article

The operational dynamics of the steel industry constitute one of the work systems with the highest severity and accident rates. To address this, this research multidimensionally evaluates and stochastically predicts the preventive capability of the safety system in a steel plant. Using a quantitative, evaluative, and longitudinal three-phase design, the retrospective evaluation of nine preventive variables was employed using Six Sigma metrics (DPMO, $Z$, $Y$), along with the evaluation of overall performance through the Geometric Capability Indicator (GCI) and the Arithmetic Capability Indicator (ACI), and the stochastic modeling of the process using Markov chains. It was demonstrated that evaluating processes in isolation hides structural inefficiencies, as four variables showed an Excellent individual performance ($Z\approx 6.0$), but the comprehensive multivariate evaluation revealed a Deficient systemic state (GCI of 0.471 and ACI of 0.493). Furthermore, Markov modeling on the compliance of the process management index predicted a 100% probability of long-term stagnation in a deficient absorbing state ($x_1=1$). It is concluded that the proposed method functions as a rational anticipation system that provides potential managerial benefits by offering early warning indicators of operational degradation, supporting corrective decision-making on unstable preventive indicators. Full article

This paper investigates the finite-horizon survival probability for a system of correlated arithmetic Brownian motions with heterogeneous drifts and volatilities, focusing on the event in which one component remains strictly below all others. Using a whitening transformation of the covariance structure, we reduce the problem to the survival of a standard Brownian motion in a simplicial cone, characterized by its spherical cross-section. While explicit solutions are available in low dimensions, we address the computationally challenging tetrahedral angular case. We derive a semi-analytic formula for the survival probability via an eigenfunction expansion of the Dirichlet Laplace–Beltrami operator on this curved domain. For efficient implementation, we construct a diffeomorphism from the spherical tetrahedron to a fixed Euclidean tetrahedron, enabling the computation of angular eigenpairs through a stable finite-element scheme. For higher-dimensional regimes, we also introduce a covariance-based difficulty index and geometric bounds based on an inscribed spherical cap to assess spectral convergence and estimate long-time decay rates. Numerical experiments show that this offline–online approach achieves high accuracy and substantial speedups relative to Monte Carlo benchmarks. Full article

Efficient spatial indexing is critical for processing large-scale remote sensing datasets (e.g., LiDAR point clouds, orthophotos, hyperspectral imagery). We present a bidirectional, hierarchical index based on the Polish PL-2000 coordinate reference system for (1) direct computation of a map-sheet identifier from metric coordinates (forward encoder) and (2) reconstruction of the sheet extent from the identifier alone (inverse decoder). By replacing geometric point-in-polygon tests with closed-form arithmetic, the method achieves constant-time assignment O(1), eliminates boundary-geometry loading, and enables multi-scale aggregation via simple code truncation. Unlike global spatial indices (e.g., H3, S2), a CRS-native, aligned with cartographic map sheets in PL-2000 implementation, removes reprojection overhead and preserves the legal sheet semantics, enabling the direct use of deterministic O(1) numeric keys for remote-sensing data and Polish archives. We detail the algorithms, formalize their complexity and boundary rules across all PL-2000 zones, and analyze memory trade-offs, including a compact 26-bit packing of numeric keys for nationwide single-table indexing. We also discuss integration patterns with the OGC Tile Matrix Set (TMS), ETL pipelines, and GeoAI workflows, showing how bidirectional indexing accelerates ingest, training and inference, and national-scale visualization. Although demonstrated for PL-2000, the approach is transferable to other national coordinate reference systems, illustrating how statutory map-sheet identification schemes can be transformed into high-performance indices for modern remote sensing and AI data pipelines. Full article

This article introduces the Index of Distributive and Developmental Outlook (IDDO), a composite indicator designed to jointly assess economic performance and income inequality across EU-27 Member States. While GDP per capita is widely used to evaluate national prosperity, and the Gini coefficient captures income distribution, their separate use often obscures the interaction between growth and equity—an essential dimension of sustainable development. To address this gap, the IDDO integrates normalized values of both indicators using arithmetic and geometric means. The study applies the IDDO to a longitudinal dataset covering the years 2005, 2014, and 2024, allowing for comparative and temporal analysis. Based on IDDO scores, countries are classified into four development types: balanced development, growth with inequality, equity with stagnation, and dual vulnerability. Results show that while some Member States, such as Luxembourg, Czechia, and Slovenia, maintain consistently high IDDO levels, others—including Bulgaria, Romania, and Latvia—exhibit persistent challenges in aligning growth with equitable outcomes. The findings underscore the need for cohesion policies that prioritize not only economic convergence but also distributive fairness. The IDDO provides a practical and adaptable tool for diagnosing development patterns, benchmarking performance, and informing policy design within the EU framework. Full article

This study investigates regional and gender disparities in educational attainment across Italy in 2021, drawing on the Fair and Sustainable Well-being (BES) dataset from ISTAT. By applying cluster analysis and composite indicators—including the Mazziotta–Pareto Index (MPI), geometric and arithmetic means, min-max normalization, and principal component analysis (PCA)—we assess the robustness and consistency of educational performance across regions. A key methodological innovation is the use of the stacking method to ensure comparability between genders. Results show persistent North–South educational divides and a consistent female advantage across all indicators. The paper contributes to Sustainable Development Goals by providing empirical insights into SDG 4 (Quality Education) through measurement of educational inequality and access; SDG 5 (Gender Equality) by highlighting structural advantages of women in educational outcomes; and SDG 10 (Reduced Inequalities) through a territorial analysis of disparities and policy implications. The findings offer both a methodological contribution—by testing multiple aggregation techniques—and a practical tool for policy evaluation, emphasizing the importance of multidimensional and gender-sensitive approaches in achieving educational sustainability. Full article

Vulnerability impacts have increased in an unprecedented way with the effects of global warming, climate change, erosion, sea level rise, tsunami, flood, and drought—natural events that jointly cause geomorphological changes, especially in coastal zones. There are no analytical mathematical formulations under a set of assumptions due to the complexity of the interactive associations of these natural events, and the only way that seems open in the literature is through empirical formulations that depend on expert experiences. Among such empirical formulations are the Coastal Vulnerability Index (CVI), the Environmental Vulnerability Index (EVI), the Socioeconomic Vulnerability Index (SVI), and the Integrated Coastal Vulnerability Index (ICVI), which is composed of the previous indices. Although there is basic experience and experimental information for the establishment of these indices, unfortunately, logical aspects are missing. This paper proposes a Coastal Fuzzy Vulnerability Index (CFVI) based on fuzzy logic, aiming to improve the limitations of the traditional Coastal Vulnerability Index (CVI). Traditional CVI relies on binary logic and calculates vulnerability through discrete classification (such as “low”, “medium”, and “high”) and arithmetic or geometric means. It has problems such as mutation risk division, ignoring data continuity, and unreasonable parameter weights. To this end, the author introduced fuzzy logic, quantified the nonlinear effects of various parameters (such as landforms, coastal slope, sea level changes, etc.) through fuzzy sets and membership degrees, and calculated CFVI using a weighted average method. The study showed that CFVI allows continuous transition risk assessment by fuzzifying the parameter data range, avoiding the “mutation” defect of traditional methods. Taking data from the Gulf of Mexico in the United States as an example, the calculation result range of CFVI (0.38–3.04) is significantly smaller than that of traditional CVI (0.42–51), which is closer to the rationality of actual vulnerability changes. The paper also criticized the defects of traditional CVI, being that it relies on subjective experience and lacks a logical basis, and pointed out that CFVI can be expanded to integrate more variables or combined with other indices (such as the Environmental Vulnerability Index (EVI)) to provide a more scientific basis for coastal management decisions. This study optimized the coastal vulnerability assessment method through fuzzy logic, improved the ability to handle nonlinear relationships between parameters, and provided a new tool for complex and dynamic coastal risk management. Further research possibilities are also mentioned throughout the text and in the Conclusion section. Full article

Recently, the exponential arithmetic–geometric index ($EAG$) was introduced. The exponential arithmetic–geometric index ($EAG$) of a graph G is defined as $EAG\left(G\right)={\displaystyle \sum _{v_i{v}_j\in E\left(G\right)}}{e}^{{\displaystyle \frac{d_i+d_j}{2\sqrt{d_i{d}_j}}}}$, where $d_i$ represents the degree of the vertex $v_i$ in G. The characterization of extreme structures in relation to graph invariants from the class of unicyclic graphs is an important problem in discrete mathematics. Cruz et al., 2022 proposed a unified method for finding extremal unicyclic graphs for exponential degree-based graph invariants. However, in the case of $EAG$, this method is insufficient for generating the maximal unicyclic graph. Consequently, the same article presented an open problem for the investigation of the maximal unicyclic graph with respect to this invariant. This article completely characterizes the maximal unicyclic graph in relation to $EAG$. Full article

Consider a unicyclic graph G with edge set $E\left(G\right)$. Let $\mathfrak{f}$ be a real-valued symmetric function defined on the Cartesian square of the set of all distinct elements of G’s degree sequence. A graphical edge-weight-function index of G is defined as ${\mathcal{I}}_{\mathfrak{f}}\left(G\right)={\sum }_{xy\in E\left(G\right)}\mathfrak{f}(d_G\left(x\right),d_G\left(y\right))$, where $d_G\left(x\right)$ denotes the degree a vertex x in G. This paper determines optimal bounds for ${\mathcal{I}}_{\mathfrak{f}}\left(G\right)$ in terms of the order of G and a parameter $\mathfrak{z}$, where $\mathfrak{z}$ is either the number of pendent vertices of G or the matching number of G. The paper also fully characterizes all unicyclic graphs that achieve these bounds. The function $\mathfrak{f}$ must satisfy specific requirements, which are met by several popular indices, including the Sombor index (and its reduced version), arithmetic–geometric index, sigma index, and symmetric division degree index. Consequently, the general results obtained provide bounds for several well-known indices. Full article

This study focuses on efficient asset allocations that properly include T-bills, T-bonds, and the S&P 500 stock index. It checks that their annual real rates of linear return are both normal and almost lognormal. It reexamines how efficient portfolios based on the rates of linear return may turn into efficient portfolios based on the rates of logarithmic return. It finds that each efficient asset allocation has the lowest possible standard deviation as well as the highest possible arithmetic and geometric means. It eventually reconsiders the relationship between the confidence interval of a geometric mean and an expected long-run capital accumulation. As a consequence, it bridges a gap in the scientific literature by enabling financial advisors to trade off the mean rate of return on a portfolio more rigorously against the value at risk. Full article

Understanding the spatial distribution of fishing activity and suitable fishing areas is important for improving sustainable fisheries management and protecting vulnerable fish stocks. To identify climate-related habitat changes and variations in the distribution of fishing activity for squid-jigging vessels in the Northwest Pacific Ocean, two types (weighted arithmetic mean method, weighted-AMM; weighted geometric mean method, weighted-GMM) of habitat suitability index (HSI) models were developed in this study with marine environmental data at different depths. The boosted regression tree (BRT) model was adopted to access the monthly important environmental variables and the relative influence of the corresponding variables. The results showed that the weighted-AMM has better prediction performance than the weighted-GMM. The suitable fishing areas showed significant seasonal changes in both spatial location and coverage area. The hotspot map showed that the suitable fishing area for squid-jigging vessels was located in the scope of 42${}^{\circ }$ N∼44${}^{\circ }$ N, 155${}^{\circ }$ E∼170${}^{\circ }$ E throughout the year during 2012∼2019, which suggests that high squid-jigging fishing pressure should be given more attention in fishery management. The HSI model also had good prediction performance for the fishery data of Chinese companies, except for June and July. Additionally, fishing efforts could be used as alternative data for fishery research. The study has also suggested that fishery data are restricted by spatial and temporal distribution and fishing experience, which probably biases the results of the research. Full article

Graph theory serves as an engaging arena for the investigation of proof methods within the field of discrete mathematics, and its findings find practical utility in numerous scientific domains. Chemical graph theory is a specialized branch of mathematics that uses graphs to represent and analyze the structure and properties of chemical compounds. Topological indices are mathematical properties of graphs that play a crucial role in chemistry. They provide a unique way to connect the structural characteristics of chemical compounds to their corresponding molecular graphs. The flabellum graph $F_n^{(k,j)}$ is obtained with the help of $k\ge 2$ duplicates of the cycle graph $C_n$ with a common vertex (known as, central vertex). Then, in j of these duplicates, additional edges are added, joining the central vertex to all non-adjacent vertices. In this article, we compute different degree-based topological indices for flabellum graphs, including some well known indices, such as the Randić index, the atom bond connectivity index, the geometric–arithmetic index, and the Zagreb indices. This research provides an in-depth examination of these specific indices within the context of flabellum graphs. Moreover, the behavior of these indices is shown graphically, in terms of the parameters $j,k$, and n. Additionally, we have extended the concept of the first Zagreb index, to address the issue of cybercrime. This application enables us to identify criminals who exhibit higher levels of activity and engagement in multiple criminal activities when compared to their counterparts. Furthermore, we conducted a comprehensive comparative analysis of the first Zagreb index against the closeness centrality measure. This analysis sheds light on the effectiveness and relevance of the topological index in the context of cybercrime detection and network analysis. Full article

The present study utilised a geometric mean model in which sea surface temperature, oxygen, and sea surface salinity were used to predict the effects of climate change on the habitats of mature albacore tuna in the Indian Ocean under multiple representative concentration pathway (RCP) scenarios. Data pertaining to the albacore tuna fishing conducted by Taiwanese longline fisheries during the October–March period in 1998–2016 were analysed. The fishery data comprised fishing location (latitude and longitude), fishing effort (number of hooks used), number of catches, fishing time (month and year), and fish weight. Nominal catch per unit effort data were standardised to mitigate the potential effects of temporal and spatial factors in causing bias and overestimation. The Habitat Suitability Index (HSI) scores of potential habitats for mature albacore in the Indian Ocean are predicted to change considerably in response to varying levels of predicted climate change. Under projected warm climate conditions (RCP 8.5), the stratification of water is predicted to cause low HSI areas to expand and potential habitats for mature albacore to shift southward by 2100. The findings derived from these mature albacore habitat forecasts can contribute to the evaluation of potential hazards and feasible adaptation measures for albacore fishery resources in the context of climate change. The distribution trends pertaining to potential habitats for mature albacore should be used with caution and can provide resource stakeholders with guidance for decision-making. Full article

Boolean operations on geometric models are important in numerical simulation and serve as essential tools in the fields of computer-aided design and computer graphics. The accuracy of these operations is heavily influenced by finite precision arithmetic, a commonly employed technique in geometric calculations, which introduces numerical approximations. To ensure robustness in Boolean operations, numerical methods relying on rational numbers or geometric predicates have been developed. These methods circumvent the accumulation of rounding errors during computation, thus preserving accuracy. Nonetheless, it is worth noting that these approaches often entail more intricate operation rules and data structures, consequently leading to longer computation times. In this paper, we present a straightforward and robust method for performing Boolean operations on both closed and open triangulated surfaces. Our approach aims to eliminate errors caused by floating-point operations by relying solely on entity indexing operations, without the need for coordinate computation. By doing so, we ensure the robustness required for Boolean operations. Our method consists of two main stages: (1) Firstly, candidate triangle intersection pairs are identified using an octree data structure, and then parallel algorithms are employed to compute the intersection lines for all pairs of triangles. (2) Secondly, closed or open intersection rings, sub-surfaces, and sub-blocks are formed, which is achieved entirely by cleaning and updating the mesh topology without geometric solid coordinate computation. Furthermore, we propose a novel method based on entity indexing to differentiate between the union, subtraction, and intersection of Boolean operation results, rather than relying on inner and outer classification. We validate the effectiveness of our method through various types of Boolean operations on triangulated surfaces. Full article