Search Results (51)

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

The leaf area index (LAI) is a crucial variable in climate, ecological, and land surface modeling. However, the estimation of the LAI from coarse-resolution remote sensing data can be affected by the spatial scaling bias, which arises from the nonlinearity of retrieval models and the heterogeneity of the land surface. This study provides an algorithm named Arithmetic Mean and Geometric Mean (AM–GM) to correct the spatial scaling bias. It is established based on negative logarithmic functions and avoids second-order stationarity. In this algorithm, relationships are derived between the scaling bias of LAI and the arithmetic and geometric means of directional gap probability for two commonly used remote sensing models, the Beer–Lambert law and a semi-empirical transfer function, respectively. According to the AM–GM algorithm, the expression representing the model nonlinearity is derived and utilized for the analysis of LAI scaling bias. Furthermore, the AM–GM algorithm is simplified by a linear relationship, which is constructed between two quantities related to the directional gap probability between two specific resolutions. Two scenes simulated by the LargE-Scale remote sensing data and image Simulation framework (LESS) model and three sites are used to evaluate the proposed algorithm and analyze the scaling bias of LAI. The validation results show that the AM–GM algorithm provides accurate correction of LAI scaling bias. The analyses based on the AM–GM algorithm demonstrate that the scaling bias of LAI increases with the increase in the LAI value, with stronger surface heterogeneity and coarser spatial resolution. The validation results of the simplified AM–GM algorithm demonstrate that at the Sud-Ouest site, the absolute value of the bias for the estimated LAI decreases from 0.10, 0.22, 0.29, and 0.31 to 0.04, 0.01, 0.04, and 0.05 at 200 m, 500 m, 1000 m, and 1500 m resolutions, respectively. In conclusion, the proposed algorithm is effective in the analysis and correction of the scaling bias for coarse-resolution LAI. Full article

Standard unit operations/equipment have not evolved for the traditional rice varieties of the Cauvery Deltaic region of Tamil Nadu. The fame of traditional rice is increasing nowadays owing to its health benefits. Non-standard unit operations may cause rice grains to crack during milling, accumulating more broken rice and yields in products of inferior quality. As a result, research into the physical properties of rice is crucial for the development of rice processing equipment that minimizes post-harvest losses during milling. Hence, an assessment was made to evaluate 30 traditional rice cultivars on their Physical (grain length, width, thickness, shape, and size), gravimetric (bulk, true, tapped density, porosity, Carr’s index, and Hausner ratio), and engineering characteristics (equivalent, arithmetic, square mean, and geometric mean diameter) using standard protocols, with the goal of reviving and preserving older varieties. The results from the analysis showed significant variations (p < 0.05) between all properties that were evaluated. According to length, a substantial amount of traditional rice varieties were long grain (76.7%), whereas (16.7%) belonged to the medium type and (3.3%) were short-grain types, respectively. There were variations among the three different categories of local rice grains when it comes to size, ranging from 3.26 to 4.69 mm for arithmetic mean diameter, 2.84 to 4.00 mm for geometric mean diameter, and 3.02 to 4.28 mm for square mean diameter, respectively. Sphericity, aspect ratio, and surface area measurements of the samples varied from 37.7% to 81.2%, 0.26 to 1.00, and 25.4 to 50.1 mm², respectively. Of the 30 varieties, 28 were under the high amylose category, and 2 belonged to the intermediate type. The Pearson correlation was established to study the interrelationships between the dimensions and engineering properties. Principal component analysis (PCA) reduced the dimensionality of 540 data into five principal components (PC), which explained 95.7% of the total variance. These findings suggest that it is possible to revive old landraces through careful selection and analysis of these properties. The superior characteristics of these traditional varieties can be further evaluated for breeding programs in order to improve the cultivation of these cherished rice landraces to enhance nutritional security. Full article

The spawning grounds are important areas for the survival and reproduction of aquatic organisms and play an important role in the replenishment of fishery resources. The density of fish larvae in the Pearl River Estuary (PRE) was analyzed to establish Habitat Suitability Index (HSI) based on marine environmental factors. Survey data and satellite remote sensing data, including sea surface temperature, sea surface salinity and chlorophyll a concentration, from 2014 to 2017 during April–September were analyzed. Results showed that the accuracy of the HSI model based on the larval density and environmental factors was more than 60%, and the distribution trend of HSI was consistent with the distribution trend of larval density. The HSI models constructed based on Arithmetic Mean Model (AMM), Geometric Mean Model (GMM) and Minimum Model (MINM) methods can better predict the spatial–temporal distribution of larvae in the PRE. Among them, the accuracy of the HSI model constructed by the AMM and GMM methods was the highest in April (71%) and September (93%); the accuracy of the HSI model constructed by the MINM method was the highest in June (70%), July (84%) and August (64%). In general, the areas with high HSI values are mainly distributed in the offshore waters of the PRE. The spatial–temporal distribution of larvae in the PRE was influenced by monsoon, Pearl River runoff, Guangdong coastal currents and the invasion of high-salinity seawater from the outer sea. Full article